THE DESIGN OF A LOW-NOISE ROTOR-ONLY AXIAL FLOW FAN SERIES Sybrand Johannes van der Spuy Thesis presented in partial fulfillment of the requirements for the degree of Master of Engineering (Mechanical) at the University of Stellenbosch Thesis Supervisor: ProfT. W. von Backstrom Department of Mechanical Engineering University of Stellenbosch December 1997 DECLARA TION I, Sybrand Johannes van der Spuy, the undersigned, hereby declare that this thesis is my own original work. It is being submitted for the Degree of Master of Engineering (Mechanical) at the University of Stellenbosch. It has not been submitted, in its entirety or in part, for any degree or examination at any other University. ~ Signature of candidate This .Ip ..t.b ..day of ..F~-;".~..~.\.:.:<~~.)....1998 Stellenbosch University http://scholar.sun.ac.za ABSTRACT A design routine was derived for designing a series of rotor-only axial flow fans. The routine was applied by designing two different series of axial flow fans. The first design was for a general application rotor-only axial flow fan. This fan series was designed, built and tested in co-operation with Howden Air Industries for both research and commercial purposes. The second design was for a low-noise fan series, which was designed, built and tested by the University of Stellenbosch for research purposes only. The design theory used the principle of blade cropping, meaning that one blade was designed to fit all the different fan sizes. The fan series was designed for diameters ranging from 315 mm to 1000 mm. The fan rotors were designed to conform to a velocity profile of minimum exit kinetic flux. The general application fan design was concentrated around the popular fan diameter sizes of 500 rnm, 560 mm and 630 mm and a rotor speed of 1440 rpm, using a commercially available fan series as reference. The low-noise fan design concentrated on one fan size only, namely 630 mm, while also making use of the principle of forward blade sweep. The remaining fan design principles stayed the same as for the general application fan design. The F-series airfoils were used as blade sections for both fan designs. Both fan series were tested for fan noise and performance in accordance with the BS 848 Standards part 1 (1980) and 2 (1985). A selection of fan diameter sizes was tested for the general application fan to verify its perfo!"mance over a range of fan sizes. This indicated a fan series with a wide range of efficient operation, including excellent noise characteristics. A 630 mm diameter fan was used to test the low-noise fan series. It showed both high efficiency and low noise characteristics. The reduction in fan noise achieved with the low-noise fan does not justi1)' the amount of work and costs involved in the designing process, compared to the general application fan. 11 Stellenbosch University http://scholar.sun.ac.za OPSOMMING 'n Ontwerpsroetine vir die ontwerp van 'n reeks enkelrotor aksiaalwaaiers is ontwikkel. Die roetine is toegepas deur twee verskillende reekse aksiaalwaaiers te ontwerp. Die eerste ontwerp was vir 'n algemene toepassings enkelrotor aksiaalwaaier. Die waaierreeks is ontwerp, gebou en getoets in samewerking met Howden Air Industries vir beide navorsings - en kommersieIe doeleindes. Die tweede ontwerp was vir 'n lae geraas waaierreeks. Die reeks is ontwerp, gebou en getoets deur die Universiteit van Stellenbosch vir navorsingsdoeleindes. Die onwerpsteorie het gebruik gemaak van die beginsel van lemverkorting, waardeur een lem ontwerp is om op al die groottes waaierdeursnee te pas. Die waaierreekse is ontwerp vir waaierdeursnee tussen 315 mm en 1000 mm. Die rotors is ontwerp om 'n uitlaatsneIheidsprofiel te gee wat 'n minimum verlies in kinetiese energie toelaat. Die algemene toepassings waaierontwerp het gekonsentreer rondom die gewilde waaierdeursnee van 500 mm, 560 en 630 mm. Dit is ontwerp vir 'n rotorspoed van 1440 met 'n kommersieel beskikbare waaierreeks wat as verwysing gebruik is. Die lae geraas waaierreeks het op slegs een waaiergrootte gekonsentreer, naamlik 630 mm. Die lae geraas waaierreeks is ook ontwerp met vorentoe gekurfde lemme. Die res van die ontwerpsbeginsels was dieseIfde as vir die algemene toepassings waaierreeks. Die F-reeks vleuelprofiele is gebruik vir die lemseksies van beide waaierreekse. Beide waaiereekse is getoets vir waaiergeraas en -effektiwiteit deur gebruik te maak van die BS 848 Standaarde deel 1 (] 980) en 2 (] 985). 'n Verskeidenheid van waaierdeursnee van die algemene toepassings waaierreeks is getoets om die waaier se vertoning oor 'n gebied van waaiergroottes te bepaal. Die resuItaat was 'n waaierreeks met 'n wye gebied van effektiewe werking, asook uitstekende geraaseienskappe. 'n 630 mm Deursnee waaier is gebruik om die lae geraas waaier te toets. Die toetse het 'n waaier getoon wat beide hoe effektiwiteit en lae geraaseienskappe het. Die afname in waaiergeraas wat verkry is met die lae geraas waaier, in vergelyking met die algemene toepassings waaier, regverdig egter rue die werk en kostes verbonde aan die ontwerp van die waaierreeks nie. 111 Stellenbosch University http://scholar.sun.ac.za ACKNOWLEDGEMENTS I would like to thank the following individuals and organisations for their assistance with the completion of this thesis: Professor 1. W. von Backstrom for his consistent guidance and expertise. The members of the Department of Mechanical Engineering for their theoretical and practical contributions. Howden Air Industries who contributed financially. My wife, Elana, and parents for their support and patience towards the completion of the thesis. My friends for their help and inspiration. IV Stellenbosch University http://scholar.sun.ac.za TABLE OF CONTENTS DECLARA TION ABSTRACT OPSOMMING ACKNOWLEDGEMENTS LIST OF TABLES LIST OF FIGURES NOMENCLATURE 1. INTRODUCTION 2. LITERATURE SURVEY 2.1 ADVANCES IN FAN DESIGN 2.2 GENERAL FAN DESIGN ASPECTS 2.2.1 OUTLET VELOCITY PROFILE SELECTION 2.2.2 DETERMINlNG THE OPTIMillvl HUB-TIP RATIO 2.2.3 FAN BLADE DESIGN 2.3 FAN NOISE 2.3. J SOURCES OF AXIAL FLOW FAN NOISE 2.3.2 FAN NOISE PREVENTION 2.3.3 LOW-NOISE FAN DESIGN 3. FAN LAY-OUT DESIGN 3.1 EXIT VELOCITY PROFILE 3.2 FAN HUB DESIGN FOR FAN SERIES 3.2.1 DETERMINING THE OPTIMUM HUB-TIP RATIO 3.2.2 DETERMINlNG THE DISTRIBUTION OF HUB DIAMETERS 4. FAN BLADE DESIGN 4.1 CALCULATION OF FAN EXIT VELOCITY PROFILE 4.1.1 CHOOSING THE VALUES FOR a. A AND B 4.1.2 ANALYSIS OF THE VELOCITY PROFILES 4.1.3 APPLYING ACTUATOR DISK THEORY TO THE VELOCITY PROFILES v I II ITl IV IX XI XV 1 4 4 5 5 7 9 12 I3 15 16 20 20 )'"_J 23 26 29 30 30 33 34 Stellenbosch University http://scholar.sun.ac.za 4.2 GENERAL APPLICATION FAN BLADE DESIGN 4.2. I BLADE SECTION PROFILE 4.2.2 CALCULATING THE CHORD LENGTHS AND LIFT COEFFICIENTS 4.2.3 CALCULATING THE CAMBER AND STAGGER ANGLES 4.2.4 BLADE ROOT DESIGN 4.3 LOW-NOISE FAN BLADE DESIGN 4.3.1 DESIGN VARIABLES .U.2 CALCULATING THE BLADE DESIGN VARIABLES 4.4 STRENGTH CALCULATIONS FOR FAN BLADES 4.4.1 AERODYNAMIC LOADS 4.4.2 CENTRIFUGAL LOADS .+.4.3 BLADE STRESSES 4.4.4 AEROELASTIC CALCULATIONS FOR FORWARD-SWEPT FAN BLADES 4.5 FAN BLADE MANUFACTURE 5. EXPERIMENTAL ANALYSIS OF FAN DESIGNS 5. I TEST FACILITY 5. I. I GENERAL LAY -OUT OF THE TEST FACILITY 5.1.2 LAY-OUT OF TEST APPARATUS 5.2 GENERAL TEST PROCEDURE FOR FAN TESTS 5.2.1 TEST PROCEDURE FOR MEASURING FAN PERFORMANCE 5.2.2 TEST PROCEDURE FOR MEASURING FAN NOISE 5.3 PROCESSING OF FAN TEST DATA 5.3.1 PROCESSING OF FAN PERFORMANCE DATA 5.3.2 PROCESSING OF FAN NOISE DATA 6. DISCUSSION 6.1 TEST PROCEDURE 6.2 GENERAL FAN DESIGN 6.2.1 FAN DIAIviETER 6.2.2 FAN SOLIDITY 6.2.3 BLADE SETTING ANGLE 6.2.4 FAN SPEED 6.3 LOW-NOISE FAN 7. CONCLUSIONS AND RECOMMENDATIONS 7.1 TEST PROCEDURE 7.2 DESIGN PROCEDURE 7.3 GENERAL APPLICATION FAN 7.4 LOW-NOISE FAN VI 36 36 37 41 42 42 43 45 48 50 54 55 57 59 61 62 6~.' 64 65 67 67 68 69 70 72 72 74 74 80 83 86 88 91 91 92 93 94 Stellenbosch University http://scholar.sun.ac.za 8. FIGURES 9. TABLES to. REFERENCES APPENDIX A: FAN LAY-OUT DESIGN Al EXIT VELOCITY PROFILE AU DESIGN LIMITATIONS AL2 MINIMISATION FORMULATION AU MINIMISATION SOLUTION A2 DETERMINING THE OPTIMUM HUB-TIP RATIO APPENDIX B: FAN BLADE DESIGN CALCULATIONS B.I CALCULATION OF FAN EXIT VELOCITY PROFILE B.l.l CHOOSING THE VALVES FOR a. A AND B B.l.2 APPLYING ACTUATOR DISK THEORY TO THE VELOCITY PROFILES B.2 GENERAL APPLICATION FAN BLADE DESIGN B.2.1 CALCULATING THE CHORD LENGTHS AND LIFT COEFFICIENTS B.2.2 CALCULATING THE CAMBER AND STAGGER ANGLES B.3 LOW-NOISE FAN BLADE DESIGN 8.3.1 CALCULATING THE LOW-NOISE DESIGN VARIABLES APPENDIX C: SAMPLE CALCULA TIONS FOR STRENGTH ANALYSIS C.I AERODYNAMIC LOADS C.2 CENTRIFUGAL LOADS C.3 BLADE STRESSES C.4 AEROELASTIC CALCULATIONS FOR FORWARD SWEPT FAN BLADES APPENDIX D: PHOTOS OF FAN BLADES AND TEST FACILITY COMPONENTS APPENDIX E: CALmRA TION OF TEST FACILITY E.I TORQUE TRANSDUCER E.2 PRESSURE TRANSDUCER E.3 PROXIMITY SWITCH E.4 SOUND LEVEL METERS E.5 EXTENSION CABLE VB 96 146 155 Al Al A2 A3 A5 A5 Bl BI BI B5 B12 B12 B16 B18 B19 Cl Cl C4 C7 CI1 Dl El EI E2 E3 E3 E5 Stellenbosch University http://scholar.sun.ac.za APPENDIX F: SAMPLE CALCULATIONS FOR PROCESSING OF FAN TEST DATA Fl F.I PROCESSING OF FAN PERFORMANCE DATA F~ F.2 PROCESSING OF FAN NOISE DATA FlO VlIl Stellenbosch University http://scholar.sun.ac.za LIST OF TABLES 1.] Design requirements set forth by HAl 3.1 Optimisation results 4.1 Summary of data for lay-out design 4.2 Different configurations for which velocity profiles were optimised 4.3 Calculated blade design variables for general application fan 4.4 Calculated blade properties for low-noise fan 4.5 Fan blade material properties 4.6 Force coefficients used in design 4.7 Resultant aerodynamic forces 4.8 Resultant centrifugal forces 4.9 Calculated stresses and safety factors 4. ]0 Blade properties at hub and tip 4. ] I Values for A.I) obtained using equation 4.61 5. 1 Summary of fan tests done in the type D test facility 6.1 Summary of fan performance for different fan diameters at 25 0 blade angle 6.2 Summary of fan noise for different fan diameters at 25 0 blade angle 6.3 Summary of fan performance for different blade solidities at 25 0 blade angl~ 6.4 Summary of fan noise for different blade solidities at 25 0 blade angle 6.5 Summary of fan performance for different blade angles 6.6 Summary of fan noise for different blade angles 6.7 Summary of fan performance for different fan speeds 6.8 Summary of fan noise for different fan speeds 6.9 Summary of fan performance for different fan speeds 6.10 Summary of fan noise for different fan speeds 6.1] Summary of fan performance for different fan types 6.12 Summary offan noise for different fan types 6.13 Sound data for 483/1501l Oil 440 fan 6.14 Sound data for 63 Oil 50/5/1440 fan 6.15 Sound data for 630/150/10/1440 fan 6.16 Sound data for 630/250/7/1440 fan 6.17 Sound data for 630/2501l 4/1440 fan 6.18 Sound data for 63 Oil 5Oil 0/960 fan IX 28 29 "')-'- 40 48 49 51 54 55 57 58 59 61 74 75 81 81 84 84 86 86 88 88 89 90 146 147 148 149 150 151 Stellenbosch University http://scholar.sun.ac.za 6.19 Sound data for three different fans at 720 rpm 6.20 Sound data for three different fans at 960 rpm 6.21 Sound data for three different fans at 1200 rpm B. 1 Optimised exit velocity profile E. 1 Calibration readings for torque transducer E.2 Calibration readings for pressure transducer E.3 Bruel and Kjaer sound level meter calibration readings E.4 Rion sound level meter calibration readings E.5 Deviation values for BrueI and Kjaer extension cable F.l C2 correction values for sound pressure levels x 152 153 154 B4 El E2 E4 E4 E6 F12 Stellenbosch University http://scholar.sun.ac.za LIST OF FIGURES 1.1 Classic axial flow fan (Van der Spek, 1994) 1.2 Super low-noise axial flow fan (Van der Spek, 1994) 2.1 Velocity diagrams 3.1 Example of optimised and free vortex velocity profiles for v = = \jJ = 0.5 (Von Backstrom et a!.) 4. 1a Approximate blade camber for different configurations 4.1b Approximate blade stagger for different configuration 4.2a Swirl velocity profiles for general application fan design 4.2b Axial velocity profiles for general application fan design 4.3a Swirl velocity profiles for low-noise fan design 4.3b Axial velocity profiles for low-noise fan design 4.4 F-series airfoil geometry (Wallis, 1983) 4.5 Graph for lift interference factors used in design process (Wallis, 1983) 4.6 Definition of camber and stagger angles (Wallis, 1983) 4.7 Graph for incidence angles used in design process (Wallis, 1983) 4.8 Graph of angles of attack used in design process (Wallis, 1983) 4.9 Stagger and camber angle distribution for general application fan 4.10 Blade profile distribution for general application fan design (Scale 1:1) 4.11 Blade root diagram 4.12 Estimated sweep angle required for a 10 dB reduction of a given mode (m) (Wright, 1989) 4.13 Geometric sweep angle definition (rotor viewed in plane of rotation) 4.14 Transformation triangle between geometric and aerodynamic sweep 4.15 Transformation of variables due to blade sweep 4.16 Stagger and camber angle distribution for low-noise fan 4.17 Blade profile distribution for low-noise fan (Scale 1:1) 4.18 Diagram of aerodynamic blade forces 4. 19 Drag coefficients used for F-series airfoil (Wallis, 1983) 4.20 Graph for area of 10% thick F-series profile vs. camber angle (Wallis, 1983) 4.21 Graph ofJ) for 10% thick F-series profile vs. camber angle (Wallis, 1983) 4.22 Graph of h for 10% thick F-series profile vs. camber angle (Wallis, 1983) 4.23 Comparison of wing critical speeds (Bisplinghoffet a!., 1955) Xl 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 104 105 105 106 106 107 107 108 109 110 110 III III 112 112 Stellenbosch University http://scholar.sun.ac.za 4.24 Sweptwing geometry (Dowell et al., 1995) 113 4.25 General application fan blade design in AutoCad 114 4.26 Low-noise fan blade design in AutoCad 115 4.27 Blade setting angle definition for general application fan design 116 5.1 Schematic lay-out of Type A test facility for 1000 mm diameter general application fan (Venter, 1990) 117 5.2 Schematic lay-out of Type D test facility for 630 mm diameter fan 118 5.3 Schematic lay-out of Type D test facility for 800 mm diameter fan 119 5.4 Fan static pressure vs. volume flow for different blade angles for 630/250/14/1440 fan 120 5.5 Fan total efficiency vs. volume flow for 630/250/14/1440 fan 120 5.6 Schematic lay-out of measuring equipment 121 6.1 Static pressure vs. volume flow for 483/150/5/1440 fan 122 6.2 Total efficiency vs. volume flow for 483/150/5/1440 fan 122 6.3 Static pressure vs. volume flow for 483/150/10/1440 fan 123 6.4 Total efficiency vs. volume flow for 483/150/1 0/1440 fan 123 6.5 Static pressure vs. volume flow for 483/250/7/1440 fan 124 6.6 Total efficiency vs. volume flow for 483/250/7/1440 fan 124 6.7 Static pressure vs. volume flow for 483/250/14/1440 fan 125 6.8 Total efficiency vs. volume flow for 483/250/14/1440 fan 125 6.9 Static pressure vs. volume flow for 630/150/5/1440 fan 126 6.10 Total efficiency vs. volume flow for 630/150/5/1440 fan 126 6.11 Static pressure vs. volume flow for 630/150/1 0/1440 fan 127 6.12 Total efficiency vs. volume flow for 630/150/10/1440 fan 127 6.13 Static pressure vs. volume flow for 630/250/7/1440 fan 128 6.14 Total efficiency vs. volume flow for 630/250/7/1440 fan 128 6.15 Static pressure vs. volume flow for 630/250/14/1440 fan 129 6.16 Total efficiency vs. volume flow for 630/250/14/1440 fan 129 6.17 Static pressure vs. volume flow for 630/150/1 0/960 fan 130 6.18 Total efficiency vs. volume flow for 630/150/1 0/960 fan 130 6.19 Static pressure vs. volume flow for 800/150/5/1440 fan 131 6.20 Total efficiency vs. volume flow for 800/150/5/1440 fan 131 6.21 Static pressure vs. volume flow for 800/150/10/1440 fan 132 6.22 Total efficiency vs. volume flow for 800/150/10/1440 fan 132 XlI Stellenbosch University http://scholar.sun.ac.za 6.23 Static pressure vs. volume flow for 800/250/7/1440 fan 133 6.24 Total efficiency vs. volume flow for 800/250/7/1440 fan 133 6.25 Static pressure vs. volume flow for 800/250/14/1440 fan 134 6.26 Total efficiency vs. volume flow for 800/250/14/1440 fan 134 6.27 Sound pressure levels for 483/150/1 0/1440 fan 135 6.28 Sound pressure levels for 630/150/5/1440 fan 135 6.29 Sound pressure levels for 630/150/1 0/1440 fan 136 6.30 Sound pressure levels for 630/250/7/1440 fan 136 6.31 Sound pressure levels for 630/250/14/1440 fan 137 6.32 Sound pressure levels for 630/150/10/960 fan 137 6.33 Comparison of sound pressure levels of three different fans at 720 rpm 138 6.34 Comparison of sound pressure levels of three different fans at 960 rpm 138 6.35 Comparison of sound pressure levels of three different fans at 1200 rpm 139 6.36 Static pressure vs. volume flow for low-noise fan 140 6.37 Total efficiency vs. volume flow for low-noise fan 140 6.38 Static pressure measured and scaled for diameter for 630/150/1 0/1440 fan 141 6.39 Total efficiency measured and scaled for diameter for 630/150/10/1440 fan 141 6.40 Static pressure measured and scaled for fan speed for 630/150/1 0/1440 fan 142 6.41 Total efficiency measured and scaled for fan speed for 630/150/10/1440 fan 142 6.42 Static pressure measured and scaled for low-noise fan 143 6.43 Total efficiency measured and scaled for low-noise fan 143 7.1 Static pressure for 1000/250/7/1440 fan and design point 144 7.2 Static pressure for general application fan and comparative fan for 630/150/1 0/1440 144 7.3 Total efficiency for general application fan and comparative fan for 630/150/10/1440 145 Dl Photo of Jeluton wood blocks with mould halves on top of them D2 02 Photo of blade section showing steel insert and full length swept blade 02 D3 Photo of 630 mm diameter general application fan with 150 mm hub diameter D3 04 Photo of 630 mm diameter general application fan with 250 mm hub diameter D3 D5 Photo of 630 mm diameter low-noise fan D4 D6 Photo of test facility for 630 mm diameter fan 04 D7 Photo of flow straightener used for 630 mm diameter fans D5 D8 Photo of conical inlet of test facility 05 XlII Stellenbosch University http://scholar.sun.ac.za D9 Photo of throttled outlet of test facility D 10 Photo of performance measuring apparatus used in fan tests Dll Photo of torque transducer installed in 630 mm diameter fan casing D] 2 Photo of noise measuring apparatus used in fan tests XIV D6 D6 D7 D7 Stellenbosch University http://scholar.sun.ac.za NOMENCLA TURE Symbol a a ao A A A A ~I Aroot b B c c c C C C C Cpi d d d delPT delta df di d( c'Bcor Description outer/inner radius ratio swirl coefficient air sonic velocity dimensionless work rate test ducting area blade section area blade segment area circumferential area between two streamlines blade root area outer wall radius dimensionless flow rate chord length constant for axial velocity blade chord lenbrth in direction perpendicular to blade axis of swept blade force coefficients absolute velocity sound measurement correction fan characteristic value ideal static pressure rise coefficient ducting diameter nose droop in % chord or fraction of chord blade root diameter total pressure change angle between F and L on blade wake width at blade trailing edge diameter of conical inlet blade thickness at blade trailing edge fan noise correction term xv Units variable m/s m2 ~m~ ~m~ ~m~ m2 m m m m/s dB dBA m m Pa (0) m m m dBA Stellenbosch University http://scholar.sun.ac.za ~dB sound pressure level decay dB D drag force on blade N Dw downwash perturbation mls Dr fan diameter m E Young's modulus Pa E fan sound power W f frequency Hz F resultant blade force N F dimensionless kinetic energy flux F value used to compare sound levels of different configurations m8/s6 g gravitational acceleration mls2 G constant for defining blade axis sweep -Im h pressure m H2O h perpendicular distance from fan hub m hd hub diameter m incidence angle (0) I second moment of area 4m J second polar moment of area m4 k constant for swirl velocity k profile adaption coefficient for camber (Orl K constant for defining blade axis sweep K kinetic energy J K] constant for flow coefficient profile adaption coeffcient for thickness la length of torque transducer calibration arm m lmom moment arm of aerodynamic forces m blade length in direction of blade axis of swept blade m L lift force on blade N L kinetic energy flux W Lp sound pressure level for fan dB LIF lift interference factor m mass kg m profile adaption coefficient for droop XVI IStellenbosch University http://scholar.sun.ac.za m deviation angle coefficient rna mass of torque transducer calibration arm kg rna number of cycles of circumferential pressure variation mV milliVolt reading mV mVdc1ta pressure transducer milli Volt offset mV mVcxt extension cable correction mV mVpvf milliVolt pressure over conical inlet mV. m mass flow kg/s M moment Nm Mcm critical circumferential Mach number of rotor tip Mm circumferential Mach number of rotor tip MR radial blade Mach number n number of blade segments n swirl exponent nb number of blades p fan pressure Pa p pressure drop Pa p pressure at a point Pa prcf reference sound pressure Pa pslm sound pressure Pa L1p pressure drop across conical inlet Pa Palm atmospheric pressure Pa P power W PWL sound power level dBW q dynamic pressure Pa qm mass flow rate kg/s Q volume flow m3/s Qrnax maximum volume flow for specific fan m3/s r radius m rstJ radial location of streamline m rpm rotational speed rpm R gas constant J/kg.K Re Reynolds number XVII Stellenbosch University http://scholar.sun.ac.za s blade pitch m sf safety factor SPL sound pressure level dB SPLr turbulent fan noise dB t radius as fraction of fan outer radius t blade thickness in % chord T temperature K T shaft torsion Nm Tatm atmospheric temperature K Troo( torsion in blade root Nm u dimensionless swirl velocity U circumferential blade speed m1s v dimensionless axial velocity V velocity m1s W relative velocity mls Wo fan power consumption W x axial distance from rotor m x distance along blade chord as fraction of chord ~x distance offset between segment centroid and quarter-chord point m ~Xd change in distance parallel to rotor m yc distance of blade camberline perpendicular on chord as fraction of chord y profile coordinates perpendicular on chord in % chord z distance along axis of rotation m Greek Symbols a absolute flow angle (0) a angle of attack (0) af: flow coefficient Uod angle of attack for zero nose droop (0) /3 relative flow angle (0) ~ axial velocity perturbation XVlll Stellenbosch University http://scholar.sun.ac.za ~ /),,0 8 E y r tan(y) 11 11 A Ao A J.l v e es p p () () "( n ill \j! ~ ~ axial velocity perturbation at actuator disk downwash deviation angle deviation angle whirl coefficient flow coefficient angle between F and rotor plane of rotation pitch angle (relative to plane of rotation) blade circulation dragllift ratio geometric blade sweep angle efficiency aerodynamic blade sweep angle eigenvalue for divergence condition sweep angle viscosity hub-tip ratio camber angle blade axis sweep angle fan blade material density density soliditv ratio axial stress shear stress rotational speed rotational speed pressure coefficient stagger angle (relative to axis of rotation) flow loss coefficient for fan test facility XIX (0) (0) (0) (0) m2/s (0) C) (0) Ns/m2 rad (0) kg/m3 kg/m3 Pa Pa rad/s rad/s rad I,Stellenbosch University http://scholar.sun.ac.za Subscripts a a add axial atm bend bo c cent c/4 df D e f f mner k L L Li m m mc/4 o outer p p r ro axial annulus additional moment due to lift force offset axial force ambient bending moment usable air power corrected sound pressure level moment due to centrifugal forces quarter-chord moment fan dynamic pressure drag coefficient effective power sound pressure level at point fan inner radius of blade root inner radius of hub radius milliVolt reading over conical inlet kinetic power loss lift coefficient lower profile of blade lift coefficient taking blade interference into account mean value mechanical quarter-chord moment coefficient outer radius or blade tip radius outer radius of blade root pressure height at pressure measuring point pressure transducer milliVolt reading rotor read-out xx Stellenbosch University http://scholar.sun.ac.za root s s s sf shear sigma slm swept t tau tf torsion total T U vf w water 2 ".) 4 x. blade root section "swept" blade variables static shaft power fan static pressure shear force axial stress sound level meter milliVolt reading moment due to forward blade sweep total shear stress fan total pressure torsion moment total stress torque transducer milliVolt reading upper profile of blade pressure height at conical inlet whirl water fan inlet side fan outlet side measuring point upstream of fan measuring point downstream of fan axial distance far up- or downstream from rotor XXI Stellenbosch University http://scholar.sun.ac.za 1. INTRODUCTION The trend in low cost fan manufacturing today is to design a series of fans consisting of different fan diameters using one rotor blade design and two or more hub sizes. The rotor blades are sized (cropped) to fit different combinations of fan and hub diameters inside the specified fan casing. Instead of designing one fan for a specific operating point, a series of fans must be designed to satisfy an operating range. The objectives of this thesis were as follows: 1. Formulate a simple, general fan design process for a fan series. 2. Apply this theory to general application fan design. 3. Apply this theory to low-noise fan design. 4. Manufacture and test the designed fans. This thesis was written in conjunction with a project by the University of Stellenbosch Department of Mechanical Engineering to design a general application rotor-only axial flow fan series for Howden Air Industries (HAl), which could compete successfully in the South African market. This provided the unique opportunity of a practical thesis, because the final product would not only be a once-off test model, but a marketable product. HAl provided a set of design requirements that the fan series had to adhere to. Regular discussions were held with HAl to ensure that the specified design requirements were met. It was decided to use these requirements as basis for the thesis as well. The design requirements as given by HAl are in Table 1.1. Table 1.1: Design requirements set forth by HAl Fan diameters [mm] 315,400,560,630, 710,800,900, 1000 Pressure duty [Pa] 100 to 1800 Flowrate [m3/s] 0.2 to 30 Maximum tip speed [mls] 115 Stellenbosch University http://scholar.sun.ac.za The fans that were designed, are used in an air handling capacity to provide ventilation for roorns, factories and laboratories, to transport various gaseous fluids, to provide cooling through air movement and in air conditioning units. In South Africa, with its wide variety of primary industries, combined with a harsh climate, the need for air handling is very large. A wide variety of axial flow fans is available on the local market. This includes a number of imported fan designs as well as some local manufactured designs. Unfortunately the local fan designs are often copies made of imported designs under the pretext of reverse engineering. The apparent simplicity of the rotor-only axial flow fan design has lead to numerous low-efficiency applications, where these fans or systems are not designed to meet the required pressure duty. This leads to the occurrence of fan stalling and consequently an increase in fan noise. Often the occurrence of fan noise is due to bad engineering principles used when designing fan installations (Wallis, 1983). These include obstructions in the airways in front of and behind the fan, mismatch between fan and system characteristics, fan stalling and unnecessary fan vibration due to incorrect mounting. The need for low-noise machinery was motivated by an increased awareness of hearing health. For instance, the maximum acceptable noise in a laboratory prescribed by the South African Bureau of Standards (SABS, 1983) is 40 dB. Axial fans must be installed correctly and designed with low-noise performance in mind. Reducing noise levels by means of sound insulation can be very costly. The technology for low-noise fans is available in South Africa in the form of imported products, for example air-conditioning units. Illustrations of a general application axial flow fan and a low noise axial flow fan are included in Figure 1.1 and Figure 1.2 on page 97. This thesis is a continuation and extension of the work done by Bruneau (1994). It must be emphasised that where Bruneau's thesis was a pure research project, this thesis was in principal a manufacturing thesis with research being a secondary objective. Bruneau designed a general application single rotor axial flow fan using the main fan design principles as explained by Wallis (1983). The purpose of Bruneau's thesis was to improve the efficiency of large diameter axial flow fans. He did this by designing fans of 1.2 m diameter and testing them on a BS 848 type A, free inlet and free outlet, testing facility. He designed two prototypes, each one with a different wing profile, and compared them with the scale models of axial flow fans used in air-cooled condensers in power plants. He verified his design procedure by obtaining good results from his fan designs. 2 Stellenbosch University http://scholar.sun.ac.za The fans designed in this thesis were noise and performance tested on a test facility which was designed using the BS 848 Standards (1980 and 1985) as a guide. This test facility, situated in one of the laboratories of the University of Stellenbosch, made provision for a type 0 fan, namely a fan with a ducted inlet and outlet. The test facility, as well as the instrumentation used, is described in a final year project by Van der Spuy (1994). This test facility was not suitable for large diameter fans because the length of the test facility increases as the fan diameter being tested increases, giving rise to a problem with laboratory space if the fan diameter is too large. The type 0 test facility is the facility type most often used by designers of fan series to test their fans. This type of test facility was used for most of the tests done during this project. The type A test facility previously mentioned is also owned by the University of Stellenbosch but is situated outdoors where the fan size is not of prime importance. Fan diameters up to 1.5 m can be tested in this facility. The thesis was divided into three main parts, namely: 1. Designing a series of general application axial flow fans 2. Designing a series of low-noise axial flow fans 3. Testing the designed fans The first part included the basic fan design procedure made applicable to a series of axial flow fans. The second part used the procedure described in the first part to design a series of low-noise axial flow fans, while the third part included the testing of both fan designs in such a way that a good estimate of the feasibility of the designs and design procedure could be obtained. It was attempted to keep all procedures as simple as possible. 3 Stellenbosch University http://scholar.sun.ac.za 2. LITERATURE SURVEY According to Wallis (1983), axial flow fans can be placed in three main categories, namely: 1. Air circulator, or free fan - a fan that rotates in an open air space 2. Diaphragm-mounted fan - transfers air between two relatively large air spaces 3. Duc:ed fan - the fan is enclosed by a duct entering and leaving the fan. As explained previously, the researcher concentrated on the third category because of the test facilities available. The basic fan design principles should not differ between the fans of the three different categories. 2.1. ADVANCES IN FAN DESIGN According to Bass (1987) the basis of fan design stemmed from the aircraft propeller theory developed by Betz, Prandtl and Glauert. According to Van Niekerk (1964) this theory, along with the book by Keller (1937) on ducted axial flow fans formed the early guidelines for fan design. Other early contributions, specifically on wind tunnel applications, were made by Patterson (1944) and Thwaites (1951). Van Niekerk provided a pioneering approach to fan design by minimising empirical methods and assumptions used in the design procedure. He also attempted to bring fan noise minimisation into the fan design procedure. The comprehensive book on axial flow fan design, analysis and testing by Wallis (1983), focused on optimised fan design techniques, while also referring to aspects sueh as fan noise and dueting. Bass (1987) distinguished between two different fan design routines, namely an isolated airfoil approach and a rotating cascade approach. He advocated the use of two- dimensional airfoil characteristics and referred to the generation of acoustic noise by improper fan installation. Smith (1987) promoted the use of a simple three dimensional approach to axial flow fan design, because it allowed for the estimation of deviation and losses. The involvement of computers in fan design depends on the complexity of the design theory used. Bard et al. (1987) discussed the use of computers to calculate flow patterns in rotating machinery. This tool is also useful for estimating system effects on fan performance. Wright et al. (1987) provided a simple analysis of axial flow fan design theory to be used for computer aided design of 4 Stellenbosch University http://scholar.sun.ac.za these fans. He managed to relate aerodynamic performance to the geometric features of a fan and provided a framework for estimating performance, efficiency and noise. This work was continued by Jackson et al. (1991) in developing an axial flow fan design system. Bruneau (1994) drew up a design routine for ducted rotor-only axial flow fans using the guidelines provided by Wallis (1983) and implemented it in the form of three computer programmes. He also designed and built two experimental fans and tested them in accordance with the BS 848 standards. These fans performed very well. 2.2. GENERAL FAN DESIGN ASPECTS Bruneau (1994) divided his design procedure into three categories: 1. Optimisation of the vortex distribution for the fan outlet velocity profile. This included the application of radial equilibrium to the optimised swirl velocity distribution to determine the accompanying axial velocity distribution. 2. Optimisation of the hub-tip ratio. 3. Designing the fan blades. This section included calculation of the blade parameters. Since the work in this thesis is based on the work done by Bruneau (1994), the design assessment is done in a similar order but the contents of the theory are not the same. 2.2.1. OUTLET VELOCITY PROFILE SELECTION The most popular fan whirl distribution used by fan designers is the free vortex velocity distribution. This constitutes a constant axial velocity distribution, zero radial velocity through the fan annulus, zero inlet circumferential velocity and an outlet circumferential velocity that is inversely proportional to the fan radius. Van Niekerk (1965) used the free vortex velocity distribution in his work, because of the simplifications due to the axial velocity that is constant with radius. As pointed out by Van Niekerk (1965) this velocity leads to an outlet whirl coefficient that is a linear function of the inverse of the fan radius, where the whirl coefficient was defined as: CW2 ?= C.2 5 (2.1) Stellenbosch University http://scholar.sun.ac.za where C =c.2 kCW2 =-r and c and k are constant values. Wallis (1983) also centred his design techniques on a free vortex velocity distribution. He pointed out that the constant total pressure rise and axial velocity along the fan blade span, associated with this design assumption, are never present in practice due to the annulus wall boundary layers and off- design conditions. Wallis (1983) also stated that a steady, swirl-free, axisymmetric, axial and unseparated fan entry flow is a requirement for this approach. Although these requirements can seldom be met in practice due to the nature of the duct system, he maintained that a free vortex design approach provides the most satisfactory results. According to Bass (1987) other advantages of the free vortex design are that no energy loss occurs due to a downstream redistribution of kinetic energy and that it occurs naturally in the absence of constraints. The disadvantage of the free vortex design is the high blade root loading it implies, which restricts it to low fan loading and high hub-tip ratios. Downie et al. (1993) pointed out that the pressure rise capabilities of an axial fan rotor is limited by the use of a free vortex flow design, while the local total pressure rise increases towards the blade tip when an arbitrary vortex flow design is used. Bruneau (1994) assumed a power law distribution for the design of axial flow turbomachines: Cw:=axrn (2.2) He distinguished between four different swirl distributions: 1. Free vortex (n = -1). As stated already, this distribution leads to considerable computational simplifications. Bruneau (1994) also claimed that it leads to a blade design with excessive blade twist and root swirl. 2. Constant flow angle design (n = 1). This results in broadly similar velocity triangles as the free vortex case, with the same resulting problem of high blade twist. 3. Super vortex (n = -2). This results in severe blade twist and large exit velocity variations. 4. Constant swirl (n = 0). This results in a large radial variation of axial velocity. 6 Stellenbosch University http://scholar.sun.ac.za Bruneau (1994) stated that the design of a fan with a non-free vortex velocity distribution is far more complex than a free vortex design: the axial velocity distribution and the work rate are not constant but has to be computed by integrating between the fan hub and tip. He optimised the vortex distribution for the minimum loss of exit kinetic energy, using n and a in equation (2.2). This indicated that an outlet swirl distribution nearly identical to a free vortex was the optimum distribution for his axial fan application. An article by Von Backstrom et al. (1996) described the minimisation of the exit kinetic energy loss of an axial fan by optimising the exit velocity distribution. This optimisation did not assume any form of vortex distribution as was the case with Bruneau (1994), but adhered to the constraints of constant volume flow and work input and simple radial equilibrium. Although the exit kinetic energy flux was reduced by a maximum of 1.8 percentage points, compared to the free vortex case for the constraints imposed, the exit velocity distribution can lead to a 50 % decrease in blade twist. 2.2.2. DETERMINING THE OPTIMUM HUB-TIP RATIO Van Niekerk (] 965) determined relationships between fan efficiency, volume flow through the fan, pressure rise across the fan and hub-tip ratio, working from basic fan design principles. His theory was restricted by the availability of the correct values for the annulus efficiency (11a) and the average values for the dragllift ratio (tan y) for the fan blades. To summarise this theory, the method used by Bruneau (] 994) is given. He specified the following input data: ]. The range of different hub-tip ratios to be used. 2. The desired fan static pressure. 3. The volume flow rate 4. The estimated value of average dragllift ratio for the blade. 5. Tip radius. 6. Rotational speed. 7. An estimated value for annulus efficiency. 7 Stellenbosch University http://scholar.sun.ac.za Bruneau then used the equations of Van Niekerk to calculate values of total and static efficiency The equations for the efficiencies are as follows: (1 _ ) = ~ x (tan y te x (1 - V3) + 2(tan y te x [~ - ?jV]11t Ive. 3 ~ (I _ v2) (1 + v) ~ ) X+(1-111 2?jv (2.3) l (I - l1sLe 2=-x3 (tan Y)O\< ~ X _(I_-_v_3)+ 2(tan yte x [~- ?jv] (I-v2) (l+v) ~ ~ [ )2 In v ]+(l-11.)x-+-x 1-2x(?jv x( 2)2? V 2? V I - VI I (2.4 ) The use of the equations resulted in a series of constant hub-tip ratio curves, where fan efficiencies were plotted against fan static pressure rise. The value for static pressure rise was given by: Pr=n xpx.oxrxC J.s ? IS I Yo _ 1 Since the desired static pressure value was known, the optimum hub-tip ratio was determined as the value which gave the highest efficiency for the specified pressure rise. This indicated an optimum hub-tip ratio of 0.4 for his application. Although Wallis (1983) did not describe a procedure for optimising the hub-tip ratio, he mentioned the fact that to increase the dynamic pressure rise through the fan, the relative velocity has to be increased by increasing the hub-tip ratio. He determined the hub-tip ratio by restricting the hub swirl coefficient, Ei, to be less than one, where: Cw2i ?. = 1 Ca 2i 8 (2.5) Stellenbosch University http://scholar.sun.ac.za 2.2.3. FAN BLADE DESIGN According to Wallis (1983) each fan blade section can be considered as a two-dimensional airfoil that is independent of conditions at other radii. Bruneau (1994) followed a similar approach in his design procedures, although he discussed the effects of radial equilibrium through the fan annulus. Bass (1987) stated that a two-dimensional design approach would be satisfactory partly due to the complexity of the computational techniques needed for a three-dimensional analysis, although he mentioned the fact that three-dimensional effects tend to occur at the interaction between the fan blade and fan hub and shroud. These effects tend to delay the onset of stalling due to the radial displacement of the boundary layer. Smith (1987) advocated the use of a simple three-dimensional approach to design an axial fan blade. He divided the fan annulus into five annular stream tubes, spaced in equal radial intervals, and then performed the calculations at the six boundaries, taking radial equilibrium between the stream tubes into account. A similar approach was advocated by Wright et aL (1987) who called it a "mild three- dimensional" modeL Keller (1937) advised loading factors and solidities to be below 1.0 and 1.1 respectively, while Van Niekerk (1965) restricted his design theory to the use of isolated airfoil data by constraining the blade loading factor to be smaller than 1.0. Wallis (1961) considered fan blades to be in cascade above solidities of 1.0. In his later work Wallis (1983) assumed a smooth transition from cascade to isolated airfoil data and derived a series of simple design curves. These curves represent the variation of C;CLi versus solidity and stagger angle. Hay et al. (1978) stated that the most significant cascade effect is the change in lift coefficient. He also proposed the use of a plot of CL/CLi against pitch/chord ratio. This change of lift coefficient depends on the value of stagger angle. The advantage of this plot above the one used by Wallis (1983), was that it also allowed for cases where the lift coefficient was increased by cascade effects. Wright (1987) advocated the use of NACA two-dimensional cascade rules for solidities higher than 0.6. He based the values for zero solidity on isolated airfoil data and then interpolated between 00 and 0.6 to obtain the required airfoil data. In an article by Meyers et aL (1993) a new inviscid design '.9 :- Stellenbosch University http://scholar.sun.ac.za technique, developed from low-solidity procedures, was used to obtain the airfoil data betweEn 0.0 and 0.6. In his book on fan design Wallis (1983) listed five different blade profiles suitable for fan blade design: 1. F-series profiles 2. NACA 65 series profiles 3. Flat undersurface (Clark Y, Gottingen and RAF 6) profiles 4. Elliptical airfoils 5. Cambered plate airfoils The use of elliptical fan blade profiles is restricted to reversible fan assemblies, since the airfoil characteristics are the same in both directions. In an article on the development of axial flow fan blade sections, Wallis (1972) compared the NACA 4-digit series, NACA 65 series, Clark Y, RAF 6, C4 and C7 blade profiles. He concluded that sections with a modified circular arc camber line, clothed with a C4 or C7 thickness profile, give the optimal design solution because of their high lift-drag ratios. In a further article Wallis (1978) investigated the F-series airfoils. These airfoil sections consist of circula.r arc camber lines, modified to incorporate leading edge droop. The camber lines are then clothed with C4 streamlined shapes. Wallis (1978) also documented the airfoil's shape and flow characteristics. Hay et a!. (1978) compared the NACA 65, Gottingen, circular arc cambered plates and C4 profiles They concluded that of these examples the cambered plate profile was the least efficient, while the C4 profile had the best lift-drag ratio and .was suitable for very high blade loading. For his thesis Bruneau (1994) selected two blade profiles, namely a Clark Y profile and a NASA LS series profile. He used the Clark Y profile blade as a control design with which he could compare the NASA LS profile. Although the NASA LS profile blades showed excellent lift-drag characteristics, they could not match the Clark Y profile blades in static pressure rise and static efficiency. This was mainly due to the Clark Y profile's larger hub chords, the fact that the NASA LS series blades could not be tailored for camber variation as well as the NASA LS series blades having a higher drag for the lift coefficient at which the blades were designed. 10 Stellenbosch University http://scholar.sun.ac.za A fan blade design procedure was described by Wallis (1983) in his book on fan design. The purpose of any fan blade design procedure is to determine the geometry of the blade that is described by the radial variation of chord, camber angle and stagger angle. These variables are defined in Figure 4.6 as part of the design process. Once the velocity profile through the fan annulus has been determined, the radial variation can be represented using velocity diagrams as illustrated in Figure 2.1. With the help of these diagrams the value for camber angle can be determined using: e = (f31 - f3J + (8 - i) The value for blade solidity, which is given by: C (J=- S is determined from the equation for blade loading factor: C I (J = 2 x (C W 2 J x cos f3- C m am where 1 tan f3m = 2 x (tan f31 + tan f3J 1Cam = 2 x(CaJ +C31) (2.6) (2.7) (2.8) (2.9) (2.10) Wallis (1983) recommended a value for CL of 1.0 at the hub and between 0.4 and 0.6 at the tip to be used in equation (2.8). A linear interpolation between the hub and tip lift coefficient gives the variation of CL along the blade span. Inserting these values for CL into equation (2.8) the variation of blade solidity along the blade span can be determined. From these values of (J the variation of chord along the blade span can be determined: c= 2xTI:xr (J x nb 11 (2.11 ) Stellenbosch University http://scholar.sun.ac.za Once the values for CL along the blade span has been determined, the variation of the angle of attack can be determined from suitable blade profile data. The blade stagger angle is then given by: ~=~I-a (2.12) McKenzie (1987) optimised the blade geometry by determining the optimum value for sic at the different radii: where (sic) = 9 x (0.567 - C .)opt pI C,;= I-(~J (2.13) (2.14) Hay et al. (1978) optimised the angle of attack for a specific camber angle to obtain the desired air exit angle. His choice of lift coefficients for the blade was governed by the stalling point of the blade profile. According to him the lift coefficient should be such that the corresponding angle of attack was at least 2? less than the stall angle of attack. A different design approach was followed by Downie et al. (1993) where the fan was designed without specifYing the velocity profile in the annulus. Instead the designer specified local total pressure rise coefficients according to which a trial swirl distribution was chosen. A number of iterations was needed before a practical rotor design was obtained. 2.3. FAN NOISE According to Gordon (1972) fan noise is aerodynamic in origin. When turbulent air flow interacts with a solid surface or when turbulence is generated by a solid surface, changes in the momentum field around the surface are generated. These momentum changes require fluctuating pressures which can be considered as the fan noise. Regarding fan noise, Gordon (1972) made a few important observations: 1. All fans create turbulent air flow, generating noise. 2. Since turbulence increases with flow speed, fan noise increases with air flow speed. 3. Flow separation or fan stall will increase fan noise. 4. Fixed surfaces close to the fan blades will increase the fan noise. 12 Stellenbosch University http://scholar.sun.ac.za 5. The vibration of the fan blades does not contribute to the fan noise. Graham (1975) stated that the noise characteristic is an integral part of the fan design. He pointed out that even well designed fans will generate noise, since the features that enable them to meet performance requirements also create noise. Fan noise can be kept to a minimum, but never completely eliminated. Since the primary purpose of a fan is to move a quantity of air against a given pressure difference, the relative importance of fan noise in the overall fan design problem must always be kept in perspective. Eck (1973) found that in many cases the sound level had its lowest value in the range of maximum efficiency. This statement was supported by Wallis (1983) who pointed out that excessive fan noise can be interpreted as indicative of some aerodynamic design flaw. 2.3.1. SOURCES OF AXIAL FLOW FAN NOISE The sources of axial flow fan noise have been described by many researchers of fan noise. This discussion concentrated on a few of the most extensive descriptions. Sharland (1964) stated that the nature of fan noise is indicated by its frequency spectrum. The general form of this frequency distribution is a broad spectrum extending over a wide range of frequencies with a number of discrete frequency peaks superimposed on it. These peaks occur at the fundamental blade passage frequency and its harmonics. The relative strength of the different noise components varies with the type of axial flow fan. Noise from low tip speed ventilating fans is almost entirely broad band, while the noise from high speed compressors is characterised by discrete frequency tones. The fact that fan noise levels are so dependent on blade speed suggests that the noise sources of a fan are dipole in nature. This means that the noise originates from fluctuating forces exerted by the fan blades on the air as it passes through the fan. As stated by Japikse (1986), broadband noise is generated on fan blade - and vane surfaces by the interaction of flow fluctuations that have random time histories. Sharland (1964) described three mechanisms by which broadband noise is created: 1. The surface pressure field arising from turbulent boundary layers inside a fan. 2. The vorticity shed from the fan blades into the air flow. 3. The cases where the fan blade is moving in a flow which is initially turbulent. 13 Stellenbosch University http://scholar.sun.ac.za All three of these mechanisms create fluctuating forces which result in fan noise. Wlight (1976) recognised another source of boundary layer noise, namely laminar boundary layer noise, which occurs at low rotor speeds. He described the two boundary layer noises, laminar and turbulent, as rotor self-noise. Although the laminar boundary layer noise is the most dominant noise source of the two, it is easy to prevent by inducing a turbulent boundary layer artificially. This means that the noise generated by the turbulent boundary layers is the primary source of broadband noise. Wright (1976) also discussed the discrete frequency peaks rising above the broadband noise. These peaks occur most frequently at multiples of the blade passing frequency. This means that a fan with many blades will have only one or two such peaks in its spectrum, while a fan with few blades will have a tightly packed spectrum. He identified three sources of these discrete frequencies: 1. The discrete frequencies produced by the steady thrust of the fan rotor are determined by the thrust, blade number and speed of the rotor. 2. On or near the axis of rotation, low order blade loading harmonics, produced by asymmetries in the flow, also contribute to the spectrum. This source of noise is negligible for low speed high blade number rotors where the blade loading is basically identical from blade to blade. 3. Excess rotor noise is generated by various degrees of impulsive blade loading. An example of this is the rotor-stator interaction in a fan. Tyler et al. (1962) considered the discrete frequencies, concentrating on the steady blade forces. They determined that these fluctuations will propagate along a circular duct when Mm, the circumferential Mach number of the rotor tips, is greater than a critical Mach number, MCm When M < Mem m the rate at which the fluctuations decay along the cylinder is given by: ~db ~ 2 2~-- = 8.69 x ffid x Me - M~Xd b m m (2.15) Wright (1976) concluded that the basic sources of rotor noise are the steady blade thrust noise and turbulent boundary layer noise. 14 Stellenbosch University http://scholar.sun.ac.za 2.3.2. FAN NOISE PREVENTION Wright (1976) defined excess rotor noise as the noise that is created by an axial flow fan and can be removed without redesigning the fan. This means that a certain amount of fan noise can be removed by proper installation and operation of the fan. Wright (1976) recognised rotor-stator interaction, flow separation, cross-winds, upstream flow obstructions and blade-tip vortex interaction as causes of this noise. Wallis (1983) stated that in order to achieve the minimum noise level for a normal axial flow fan, the fan must be designed, installed and operated in accordance with good aerodynamic principles. He listed these as follows: 1. The upstream duct system must be free of disturbed and swirling flow. 2. The flow into the fan annulus must be smooth. 3. The upstream vanes or support struts must be free of flow separation and have low drag Their trailing edges must be at least one half vane or strut chord upstream from the rotor leading edge. 4. The rotor blades must be properly matched in twist, chord and camber and have small tip clearances. 5. The straightener vanes or support struts must also be free of flow separation and have low drag. They must be located at least half a rotor blade chord downstream of the blade trailing edge 6. The number of rotor blades and stator vanes must be unequal and should not possess a common factor. The product of the number of stator vanes or support struts and the rotor rotational speed must also not equal the rotor blade llatural frequency 7. The flow downstream of the fan must be unseparated. Hayet al. (1987) proposed a different approach to fan noise prevention. Due to the large amount of fan noise caused by installation effects, they identified a requirement for a fan that is insensitive to flow maldistributions. This suggested that a fan must be designed well away from the stall line to allow a wide margin of flow variation before the fan reaches stall and its associated high noise levels. They followed the same design procedure as prescribed in a previous article by Hay et al. (1978) while taking the expected flow variations into account. The lower sensitivity of the fan to inflow distortion should lead to a lower installed noise level. This design philosophy is particularly suited for fans in industrial applications subject to various installation effects. 15 Stellenbosch University http://scholar.sun.ac.za 2.3.3. LOW-NOISE FAN DESIGN Graham (1975) stated that it is impossible to design a high pressure axial flow fan that generates only low sound power levels, since fan noise is an integral part of fan performance. He also pointed out that there is no quick way of lowering the noise of a good fan design. This means that there is no abrupt change in noise characteristics if the fan design is altered slightly. Wright (1976) concluded that the quietest rotor for a given thrust, from a broad band noise point of view, has a low tip speed, high solidity and maximum blade incidence angle of 40. The rotor diameter must also be as large as possible to enable a small throughflow velocity. Longhouse (1976) considered fan noise with design aspects such as tip clearance and pitch angles in mind. He concluded that no significant decrease in fan noise is achieved for reduced blade tip clearances, except for a zero blade tip clearance. Increasing the blade pitch angle will either increase or decrease the fan noise depending on the dominating noise source at a specific volume flow. Increasing the blade pitch angle requires a reduced fan speed to achieve the same pressure rise as before, but increases the blade loading. This means that while the loading noise increases, the noise due to the air speed decreases. Depending on which of these noise sources dominate at a certain volume flow, the fan noise will either decrease or increase. In an article on axial flow fan noise Fukano, Kodama and Senoo (1977) modelled an equation to describe the turbulent noise generation by a fan: SPL = 10 x 10g(3 x Palm X ao x E/8 X 1t X ZC X P~d) (2.16) where E = (1t X Patm X nb x Dr x U~/16800 x a~) x df (2.17) This was used as the basis of an article by Fukano, Kodama and Takamatsu (1977) who investigated the effect of number of blades, chord length and camber on the fan turbulent noise. The experimental values for noise level were compared with those obtained using the formula described in the first paper. The experiments agreed with the theory in predicting the trailing edge boundary layer thickness on the rotor blade, or wake width, as one of the important factors determining the sound 16 Stellenbosch University http://scholar.sun.ac.za pressure level of a fan, where the sum of the trailing edge thickness and the boundary layer is given by: df = d1 + (0.37 x cf4) x Re:O.2 (2.18) This means that the noise level increases with an increasing number of blades when the blade chord remains constant. If the number of blades is kept small, each blade can be seen as an independent noise source. The effect of a number of blades can therefore be seen as the product of the blade number and the sound power originating from one blade. Since the wake width increases with chord length, Fukano, Kodama and Takamatsu (1977) also concluded that the fan sound pressure level increases with chord length when comparing two sets of fan blades having the same number of blades and running at the same speed. They also found that the fan sound pressure level is independent of a change in camber angle for camber angles less than 20?. For camber angles larger than 20?, the wake width increases rapidly due to flow separation, leading to a subsequent increase in fan noise. Combining the effect of blade number and chord length for the same solidity, the sound pressure level is lower for the larger chord length and smaller blade number. This is due to the fact that the sound pressure level is directly proportional to the blade number and also proportional tll the 0.8 power of the chord length. In a further article by Fukano et al. (1978) a similar approach to that used in their previous articles was followed to determine the effect of rotational frequency, blade thickness and outer blade profile. As expected, they found that the fan noise increases with fan rotational speed and follows approximately a Uo58 law , where Uo is the fan tip speed. They also found that the fan sound pressure level is reduced by reducing the blade trailing edge thickness on the suction side of the blade. The fan sound pressure level is reduced further by sweeping the blade profile, either linearly or circularly, in the rotational direction to obtain a forward swept blade. This series of fan research was continued by Fukano et al. (1986) when they investigated the effect of blade tip clearance on fan noise and performance. They concluded that a smaller tip clearance reduce the sound pressure level significantly, although a too small tip clearance is impractical because of high manufacturing costs. A tip clearance of 0.6 mm is considered the optimum. Related to the tip clearance effect is the discrete frequency noise due to eccentricity between the duct axis and rotor shaft. These discrete frequency terms include a plane wave mode which travels down the duct without decaying. Although these 17 Stellenbosch University http://scholar.sun.ac.za discrete terms will not contribute much to the overall sound pressure level !ley can be very annoYing. According to Van der Spek (1994) the correct way to achieve fan noise reduction is by either decreasing the characteristic fan shape noise value (C) or the blade tip speed in the following equation for sound power level: p x QPWL = Cr + 30 x log U + 10 x log r - 5 x log Dr + dBo 1000 cor (2.19) without reducing the fan pressure rise, flow rate or fan efficiency. Obtaining the same pressure duty while reducing the fan blade tip speed is achieved by increasing the fan solidity using a larger number of blades. Reduction of the fan shape value (C) is achieved by enlarging the chord length, combined with a reduction of the number of blades and forward sweeping fan blades. The noise reduction due to the forward swept blades can be explained as follows: 1. The forward sweep causes a phase shifting cancellation offan noise generated at different radii. 2. Forward sweep limits the growth of boundary swirls at the blade edges by truncating the natural path of the trailing edge. 3. The velocity perpendicular to the trailing edge line, which generates noisy swirls, is smaller. 4. The big tip angle on the leading edge side reduces tip vortex shedding. Wright et al. (1989) investigated the effect of fan blade sweep and developed a design theory for designing swept blades. They compared previously designed swept blade axial flow fans and derived a graphical relation between a local sweep angle for a 10 dB noise reduction and the blade relative Mach number. Although Wright et al. (1989) listed other effects of blade sweep, no analytical data describing these effects is given. After designing and testing a forward-swept blade fan, they concluded that swept-blade fans show a significant reduction in fan noise levels. Kawaguchi et al (1993) examined the effect of the fineness of the fan blade nose on the fan noise and found that using a fan blade with a large radius leading edge brings about a decrease in fan turbulent noise without deterioration of fan performance. Akaike et el. (1994) did a rotational noise analysis on an axial flow fan and investigated the effect of unequal blade pitches on the blade passing 18 Stellenbosch University http://scholar.sun.ac.za frequency noise. By using unequally spaced blades these discrete noise components are dispersed into band frequency components. They found that the resulting band frequency components gave a decrease in fan rotational noise. 19 Stellenbosch University http://scholar.sun.ac.za 3. FAN LAY-OUT DESIGN A fan series normally consists of a single blade design that is adapted to the different fan diameters by blade cropping. The blades are used in conjunction with two or three different hub sizes with various blade numbers, to provide a variation of fan characteristics with one fan diameter size. When designing a fan series one has to optimise the whole range of fan configurations (combinations of fan diameter and hub diameter size) over the specified duty range to determine the best combination of fan diameter and hub size, the optimum hub diameters as well as the best whirl distribution from which to design the fan blade. The first step in designing the axial fan range was to determine a basic lay-out, combination of fan diameter and hub size, of all the fan sizes according to the specifications (see Table 1.1). This involved determining an optimum hub-tip ratio to be used in calculating the hub diameters. Since the popular tendency when designing an axial flow fan series is to constrict the design to the use of only two different hub diameters for the entire range, the design was simplified by following this trend. This meant that the distribution of the hub diameters along the range of fans had to be determined. This included determining the size of the two hub diameters. 3.1. EXIT VELOCITY PROFILE Von Backstrom et al. (1996) determined the optimum exit velocity profile by minimising the kinetic flux losses in varying the flow and pressure coefficient. These losses are considered to be the greatest source of losses in a rotor-only axial flow fan. The article by Von Backstrom et aL is described in more detail in Appendix A. The model incorporated the following assumptions 1. A uniform total pressure distribution across the fan inlet. 2. The Euler turbo-machinery equation is applicable. 3. Simple radial equilibrium applies in front of and behind the fan. 4. The flow is assumed to be incompressible and inviscid. The velocity profiles were obtained by minimising the integral for kinetic energy flux at the fan outlet. This is given by: TO L = 'IT x P x f r. Ca' ( C a2 + C w 2 ).dr ri 20 (3.1) Stellenbosch University http://scholar.sun.ac.za By non-dimensionalising as follows: t = r I ri a=r Iro I u( t) = Cw (r, x t) / (rj x 0) v( t) = Ca (rj x t) / (rj x 0) equation (3.1) was simplified to: F = L/(1! x P x r 5 x 03) ro = f V.(V2 + U2). t. dt n (3.2) (3.3) (3.4) (3.5) (3.6) This functional (equation (3.6)) was minimised according to the following constraints: 1) Radial Equilibrium: [ d(Cw.r)] C" [d(C".r)]Ox -- =-x -- +Cdr r dr a du u2 du dv:::::>L<-+u=-+ux-+vx- dt t dt dt 2) Dimensionless Work Rate: 1 ro? A = 2 5 fr-.Ca.C".dro x ri ri ?= f e. u. v. dt 1 = Wo / (2 x 1! x P x ris x 03) where ro W = 2 x 1! x P x 0 x f r 2 ? C .C . dro a w ri 21 dC.x- dr (3.7) (3.8) Stellenbosch University http://scholar.sun.ac.za 3) Dimensionless Flow Rate: B= 1 ron x r3 f r. C?. dr I ri ? = f 1. v. dt 1 where = ~/( 2 x TC x P x rj3 x n) ? ro m = 2 x TC X P x f r. C ?. dr rj (3.9) The minimisation problem was discretised into a numerical problem and solved for given values of a, A and B. Von Backstrom et al. found that discretising the blade radius into twenty equal intervals (n = 20) proved sufficient for this analysis. They also showed that if one keeps within the prescribed design limitations (see Appendix A), only a small percentage point decrease in exit kinetic energy is achieved when using the optimised velocity distribution instead of the free vortex velocity distribution for the same values of a, A and B. As illustrated in Figure 3.1 there is a distinct difference between the two velocity distributions. Since the variation in swirl velocity for the optimised velocity profile is less than for the free vortex velocity profile, the twist along the fan blade len.gth will be less than when a free vortex exit velocity distribution is used. This motivates the use of the optimised velocity in the blade design process by lowering the manufacturing costs of such a fan blade Von Backstrom at al. also found that when the design limitations are exceeded. larger improvements on the efficiency of a fan making use of the optimised profile are possible 22 Stellenbosch University http://scholar.sun.ac.za 3.2. FAN HUB DESIGN FOR FAN SERIES The fan hub design procedure included determining the optimum hub-tip ratio when using the minimum kinetic energy exit velocity profile, determining the hub diameter that would give the optimum performance when taking the whole fan diameter range into account and deciding how many different hub diameters to use. 3.2.1. DETERMINING THE OPTIMUM HUB-TIP RATIO The detailed derivation of the method used for this section is also given in Appendix A The hub-tip ratio was optimised for maximum static efficiency. This meant that the static efficiency of the fan had to be estimated without any knowledge of the form of the exit velocity profile or the blade design. The problem was solved by summarising the various power terms involved in a fan to give an account of the energy entering and leaving the fan. These included the effective power transferred to the air, the kinetic power loss, the power leaving the fan rotor and the shaft power transferred to the fan rotor. The following assumptions were made: 1. As mentioned previously in section 3. I the improvement obtained by using the optimised velocity profile instead of the free vortex velocity profile gave a decrease in exit kinetic energy flux of only 0 to 2 percentage points. This justified the use of the simplifications associated with the free vortex velocity profile at this stage where the form of the optimised velocity profile was not yet known. 2. No mechanical losses were assumed to occur in the fan. This meant that the shaft power entering the fan is equal to the Euler power 3. For the final calculations a rotor efficiency of 85 % was assumed. This enabled the calculation of the energy transfer from the power entering the fan rotor to that leaving the fan rotor. Taking these assumptions into account the power terms were given by: 1. Kinetic power loss ro 1 ? Pk = (f - C. - . pC. 2 rc r dr) .2n TO 1 ,+(f JCw-'pC. 2rcrdr) ri -- (3.10) 23 Stellenbosch University http://scholar.sun.ac.za 2. Shaft power ro Ps = f r .Q Cw. pC. 2 7! r dr ri 3. The uia_ble air power PDO = 11r x Ps 4. The effective fan power Pe = PDo - Pk The fan static efficiency is then: Pe 11s = P s = (P.o; P,) s = ( ~, - :,) s (3.11 ) (3.12) (3.13 ) (3.]4) The fan static efficiency calculated in equation (3.14) takes into account the swirl velocity behind the fan when calculating the kinetic power loss. This differs from the equations prescribed by the BS 848 Standards, where the dynamic pressure rise over the fan is calculated as the dynamic pressure due to the axial velocity behind the fan. The method of calculation used for the static efficiency and pressure is clearly stated when necessary. If the values for shaft power and kinetic power loss are inserted into the equation, taking free vortex flow into account, it follows that: Pk ] C. C. Cwo-=-X-X--+--x Ps 2 Uo Cwo Uo (I _I;::) x In(~;) 24 (3.15) Stellenbosch University http://scholar.sun.ac.za The terms of the equation were simplified by using the equations for hub-tip ratio, flow coefficient and total pressure rise coefficient. These equations are given in Appendix A, equations (A. 1) to (A.3). Equation (3.15) was simplified as follows: Pk f \V 1 ( 1) ~ = -;- +2 x (1 _ y2) X In y Inserting this equation into equation (3.14) gave: ( f \V 1 ~ 11, = ll1 r - -;- + 2 x (1 _ y 2) x In( y)) (3.16) (3.17) Using the maximum allowable value for the pressure coefficient according to equation (A.S), equation (3.17) was simplified to ( ~ YX~ (J11, = ll1 r - 2 x y + (1 _ y2) x In Y) (3.18) Since the hub-tip ratio can be used to calculate the flow area through the fan, there is a definite relation between the hub-tip ratio and the flow coefficient. This is given by: Q ~= "(")U 0 x TI:x fo- x 1 - y- K__ 1- (1 - y2) Inserting equation (3.19) into equation (3.18) the following was obtained: [ K yxK ]- _ 1 + 1 xiny11,- 11, 2xyx(l-y2) (l-y2f () 25 (3.19) (3.20) Stellenbosch University http://scholar.sun.ac.za In order to obtain the hub-tip ratio for maximum static efllciency, the derivative of equation (3.43) with respect to y was calculated: d1ls dy -K x(I-3y2) K 1 + ] 2 x (Y - y3f x [2 x (1- y2) +)83x y2J In(~)4 x (1 - y-) y K] (1 - y2 f (3.21) Setting equation (3.21) equal to zero and solving y, a hub-tip ratio was obtained that gave a maximum value for 115 in equation (3.20). Looking at equation (3.21) one will note that the constant K1 cancels out when setting equation (3.21) equal to zero. This means that the value for hub-tip ratio is independent of the volume flow. Although the optimum value for hub-tip ratio is not independent of the pressure coefficient, the variation of hub-tip ratio with variation in pressure coefficient was found to be very small. The optimum hub-tip ratio, corresponding to a maximum pressure coefficient, was calculated as: Yopt = 0.485 As mentioned earlier, this value applies to free vortex flow. Due to the small difference between the efficiencies of the two types of velocity profiles this fact could be ignored. 3.2.2. DETERMINING THE DISTRIBUTION OF HUB DIAMETERS A fan series usually consists of a range of different fan diameters, using the same blade and hub design. To increase the efficiency of the fan series as a whole, as well as to increase the number of possible configurations for the fan series, more than one hub size is used. A minimum of two hub diameters was used to optimise the different fan sizes. This means that a certain size hub diameter which suits the smallest diameter fan optimally will not necessarily suit the largest diameter fan to the same extent. To determine the different hub diameters, as well as for which diameter fan to use them, the fan series had to be optimised to a specific maximum, namely maximum efficiency as determined by equation (3.20) (assuming a maximum pressure coefficient). 26 Stellenbosch University http://scholar.sun.ac.za The two smaller hub diameters were calculated as: hd 1 = Vopt X 0 f1 hdz = Vopt x On (3.22) (3.23) The hub diameter size and distribution were optimised by integrating each fan's efficiency over its approximate flow range numerically and adding all these integrals together. The optimised solution was taken as the one providing the maximum sum of the above integrals. The fan diameters, Do and Do, were iteratively chosen from the series of commercial size fan diameters between 315 mm and 1000 mm (see Table 1.1) to be used in the optimisation. It was decided to equate Do in equation (3.22) equal to the smallest fan diameter in the series, to ensure a sufficient blade length (larger than 80 mm) when the small hub diameter, hd1, is used in conjunction with this fan diameter. The second hub diameter was calculated using any of the remaining fan diameters smaller than 1000 mm for Do in equation (3.23). In the optimisation, the fan sizes using the small hub diameter and the fan sizes using the larger hub diameter, were varied. This determined the optimum distribution of the hub diameters between the different fan diameters. While varying the hub diameters' distribution, the larger hub diameter's size was also varied from being optimised for the 400 mm fan to being optimised for the 1000 mm fan, depending on the distribution chosen for the hub diameters. The optimisation was also monitored to ensure proper blade lengths. When further uncertainties existed, the optimisation was performed using only the 500 mm to 630 mm diameter fans, since these are currently the most popular fan sizes in the industry. A summary of the results of this optimisation is given in Table 3. I. 27 Stellenbosch University http://scholar.sun.ac.za Table 3.1: Optimisation results Diameter Hub Diam. Blade Length Hub/tip Tip Speed [mm] [mm] [mm] [mls] 315 153 81 0.486 47.5 400 153 124 0.383 60.3 500 246 129 0.485 75.4 560 246 159 0.433 84.4 630 246 194 0.385 95.0 710 246 234 0.342 107.1 800 246 279 0.303 60.3 900 246 329 0.269 67.9 1000 246 379 0.243 75.4 The small hub diameter of ISO mm can also be used for the larger diameter fans, where the required pressure rise over the fan is low. Due to the blade length constraint, the second hub diameter can only be used for the 500 mm and larger diameter fans to ensure a higher pressure rise over the fan. The fan tip speeds are well within the constraint of lIS mis, where it is assumed that the fans with a diameter smaller than 710 mm would have a maximum speed of 2880 rpm and the larger fans a maximum speed of 1440 rpm. The average hub-tip ratio is 0.37. 28 Stellenbosch University http://scholar.sun.ac.za 4. FAN BLADE DESIGN This chapter describes the design of two fan blades to be used in a fan series: one for general application and one as a low-noise fan blade. It incorporated the data calculated in chapter 3 (see Table 4.1). Sample calculations of all the relevant calculations are given in Appendix B. Table 4.1 Summary of data for lay-out design Large hub diameter [mm] I 246 Small hub diameter [mm] I 153 Maximum blade length [mm] I 377 Minimum blade lenbrth [mm] I 81 Preferred fan speed [rpm] I 1440 It was decided to round the hub diameters off to 250 mm and 150 mm for the large and small hub diameter respectively, to correspond to existing hub designs. The preferred fan speed of 1440 rpm is the speed most commonly used for these fans. Speeds of 2880 rpm and 720 rpm occur at the small and large fan diameters respectively. The blade design procedure was very similar to that used by Bruneau (1994) with the biggest difference being the minimum exit kinetic energy velocity profile. Although Bruneau designed blades for a larger diameter fan, he followed the basic steps as specified by Wallis (1983). He used an exit velocity profile similar to a free vorte~ profile which assumes a constant axial velocity before and after the fan and a whirl velocity inversely proportional to the radius. This resulted in a certain number of simplifications, especially where the actuator disk theory was concerned. The same data and design procedures were used in designing both types of fan blades, although provision was made for blade sweep in the low-noise fan design. The blade profile was selected from standard profiles. 29 Stellenbosch University http://scholar.sun.ac.za 4.1. CALCULATION OF FAN EXIT VELOCIlY PROFILE The velocity profile was selected with the help of the paper by Von Backstrom et al. (1996). The actual calculations were done with the help of a computer programme written by Dr. 1. D. Buys of the Department of Mathematics. As explained in chapter 3 this method minimises the exit kinetic energy, which is the dominant source of energy loss in a rotor-only axial fan, while constraining the fan to do the same amount of work at the same volume flow as a fan with a free vortex velocity profile with the same hub-tip ratio. 4.1.1. CHOOSING THE VALUES FOR a, A AND B To obtain the flow - and work rate values according to which the blade design was done, values for v, ~ and \jf had to be selected (see equations (A. 1) to (A.3?. These values were selected with the help of the data sheets of a typical comparative fan series from HAl. Looking at a range of different fan sizes and taking the popular fan sizes (500 mm, 560 mm and 630 mm) into account, values of v, ~ and \jf were chosen for each possible fan configuration. These values made provision for the two hub diameters (150 mm and 250 mm) used on these fans, as well as half or full blade solidity for each hub diameter. The comparative fan series was designed in such a way that the 150 mm hub diameter can accommodate a maximum of ten blades and the 250 mm hub diameter a maximum of fourteen blades. This gives a 40% increase in solidity with each change in the blade number, from the minimum number of blades used, namely five, to the maximum number of blades used, namely fourteen. The values for ~ were obtained by taking each of the fan configurations' maximum obtainable volume flow rate and dividing it by two. This ensured that the design point for which the fan was designed, was in the centre of the fan configuration's area of operation. This gave: Ca~=-Uo with _ Q (1t x (r(~ - rn) n x ro Q = Qmax 2 n = 2 x 1t x rpm/60 30 (4.1) (4.2) (4.3) Stellenbosch University http://scholar.sun.ac.za The rpm value used was 1440 rpm as mentioned in the introduction of this chapter. The values for \jl were calculated by reading the values for fan shaft power from the comparative fan data sheets. The readings were made at the average blade setting angle of 25?. A rotor efficiency of 85% and mechanical efficiency of 90% were assumed to give a total efficiency of 76.5%. This value corresponded well to the optimum total efficiency for a 19J Woods fan (Van der Spuy, 1994). The fan shaft power was calculated as follows: Ps = Q x PI f /(11 m x 11J =QXP'f/TJ, This gives: (4.4 ) P, f If we assume: P X TJ,s Q (4.5) 2p, f \jJ= -U2P X 0 then 2P x TJ \jf = s I P X U~ x Q (4.6) The obtained values are shown in table 4.2. From these values it showed clearly that the values of \jl were exceeding the constraint mentioned in the optimised velocity profile calculations (equation (A.5)). Values of 115 calculated with the help of free vortex theory (see equation (3.17)) were approximately 40% for the selected flow - and work rate configurations for the different fans. The value for rotor efficiency in equation (3.17) was replaced by the value for total efficiency used in equation (4.4), taking mechanical efficiency into account. The value for total efficiency used in these calculations was 76.5%, as mentioned above. 31 Stellenbosch University http://scholar.sun.ac.za Table 4.2: Different configurations for which velocity profiles were optimised fan dia. Hub dia. Blades Q design Psdesign v ?> \jf 2?>v 1"), free vor. [mm] [mm] [m3/s] [W] 500 150 5 1.4 360 0.30 0.21 0.23 0.12 0.43 500 150 10 1.6 570 0.30 0.24 0.31 0.14 0.38 560 150 5 1.9 570 0.27 0.20 0.21 0.11 0.43 560 150 10 2.2 940 0.27 0.23 0.30 0.12 0.38 560 250 7 2 800 0.45 0.24 0.28 0.21 0.42 560 250 14 2.25 1150 0.45 0.27 0.36 0.24 0.38 630 150 5 2.7 850 0.24 0.19 0.17 0.09 0.42 630 150 10 3.1 1400 0.24 0.22 0.25 0.11 0.38 630 250 7 2.8 1200 0.40 0.22 0.24 0.18 0.42 630 250 14 3.1 1700 0.40 0.25 0.30 0.20 0.40 710 150 5 3.8 1350 0.21 0.19 0.15 0.08 0.41 710 250 7 4 1800 0.35 0.22 0.20 0.15 0.41 800 250 7 5.8 3000 0.31 0.21 0.18 0.13 0.40 900 250 7 7.8 4000 0.28 0.20 0.14 0.11 0.40 1000 250 7 10.4 5700 0.25 0.19 0.12 0.09 0.39 32 Stellenbosch University http://scholar.sun.ac.za 4.1.2. ANALYSIS OF THE VELOCITY PROFILES The velocity profiles were graphed for u(t) and vet) versus t, where t is the radius ratio (see equations (3.2) to (3.5?. From these profiles the relative inlet and exit velocity angles were calculated using standard fan velocity diagrams (see Figure 2.1). A uniform axial and zero whirl inlet velocity profile was assumed. This gave: a = 01 C 3 I = Q/(1t x (r02 - rn) C =0wI fl, = tan'(c~.J where U=Dxr On the exit side the calculated optimised velocity profiles were used to calculate: cr, = tan-{ ~.,) 32 fl, = tan'(U ~.~w,) From the relative inlet and outlet flow angles the approximate camber and stagger angles were calculated as follows: e = ~J - ~2 ~ = tan'[~ x (tan fl, + tan fl,)] (4.7) (4.8) Using the above equations, no deviation or incidence angles were assumed. Calculations of the above values were used to compare the approximate amount of blade camber and blade twist for the different configurations (see Figures 4. 1a and 4. 1b) . ..,..,-'-' Stellenbosch University http://scholar.sun.ac.za With the camber corresponding to the camber angle and the twist corresponding to the change in stagger angle over the blade length, the amount of camber and twist both seem to decrease with increasing hub-tip ratio, decreasing flow coefficient and pressure coefficient. To accommodate the different fan sizes, a profile with an 'average' camber and twist distribution was needed. This led to the use of the {O.25 / O.19 / O.12} configuration as the design velocity profile. In the above notation 0.25 is the hub-tip ratio, 0.19 the flow coefficient and 0.12 the pressure coefficient. This fan configuration represents the 1000 mm diameter fan with a 250 mm hub and half-solidity (see Table 4.2). Leading to a further advantage of using this configuration was the fact that it covered the whole range of blade lengths. This meant that it would not be necessary to extrapolate the profile to cover the full extent of all the different fan diameters. 4.1.3. APPLYING ACTUATOR DISK THEORY TO THE VELOCITY PROFILES The velocity profiles calculated in the previous section satisfy simple radial equilibrium, as given in equation (3.14) (Dixon, 1978), but this only applies far upstream and far downstream from the fan. Actuator disk theory was used to translate the velocity profiles to positions at the leading and trailing edge of the fan blade. Simple actuator disk theory assumes that halfway through the fan, at the actuator disk, the axial velocity is given by (Dixon, 1978): 1 ( )C =-x C +Ca III 'I a ..? I a .? :: (4.9) At the positions up- and downstream of the fan, a difference in axial velocity at a certain point and the far up- and downstream positions is seen as a velocity perturbation. The axial velocity perturbation at the actuator disk is given by L10 and that at a specific point by A According to the actuator disk theory the perturbations decay exponentially away from the actuator disk. This gives: -~ = 1 - exp(+ _7!_X_X J ~o fo - fj 34 (4.10) Stellenbosch University http://scholar.sun.ac.za The minus sign applies to the flow region in front of the fan and the plus sign to the flow region behind the fan. Since: C.l=C.m+~ C =C -~a 2 am 1~ = - X (C - C )o 2 a~l a~2 This gives: C'I = C''''I - ~ X (C."' - C.,.J x exp(+ 1C ~ x)_ r ro I c., = C", + ~ x (CO', - C."') x exp( - -;-~-:J o I (4.11) (4.12) (4.13) (4.14) (4.15) Equations (4.14) and (4.15) were used to determine the axial velocity distribution at the leading and trailing edges of the fan. The values for x were calculated as: x = 0.43 x c x cos(~) x = 0.57 x c x cos(~) (4.16) (4 17) where equation (4.16) applied to equation (4. 14) and equation (4.17) to equation (4.15) The values of 0.43 and 0.57 were obtained from the characteristics of the airfoil section used and corresponded to the position of the centroid This meant that an approximate blade chord length had to be obtained at the start of the calculations. A value of 80 mm was used since it corresponded to the blade chord length of the comparative fan series fan blade. The value for (ro - ri) was taken to be equal to the blade length, namely 375 mm. Using the fact that the mass flow between two streamlines is constant, the streamline shape and position through the fan rotor could be determined. Since tangential momentum is conserved along a streamline, the value for (r x C,,) is a constant along a streamline. The values for Cw at the far upstream and downstream positions were known, enabling tht~ calculation of Cw at the leading and trailing edge of the fan blade. The resulting velocity distributions for the two different blade designs are given in Figures 4.2 and 4.3. These velocity distributions had to be adjusted slightly as the blade chord length became more apparent, leading to an iterative process. 35 Stellenbosch University http://scholar.sun.ac.za 4.2. GENERAL APPLICATION FAN BLADE DESIGN This section describes the use of the velocity profiles obtained previously to design the general application fan blades. The design corresponded to the configuration of the fan for which the velocity profile was optimised. This meant that the design procedure was done for a seven bladed fan on the 250 mm hub diameter for the 1000 mm diameter fan. Since the hub diameters corresponded exactly to those of the comparative fan series it was decided to use the same number of fan blades, namely seven and fourteen blades, on the large hub diameter and ten and five blades on the small hub diameter. This meant that the hub and tip chord lengths of the designed fan blade had to be in the same region as those of the comparative fan series fan blades to keep the blade solidities in the same region. 4.2.1. BLADE SECTION PROFILE Because of its high lift-drag ratios it was decided to base the fan blade design on the F-series airfoil (see Figure 4.4). The F-series airfoils is a modification of the C4 profile. According to Wallis (1972), airfoils based on a modified circular arc camber line constitutes a near-optimum aerodynamic design solution. Wallis (1977) considered the F-series airfoil a preferred design solution. The F-series profile consists of the C4 airfoil, modified to incorporate nose droop. This is achieved by adjusting the leading edge of the C4 camber line to a NACA 230 camber line. The thickness of these profiles is adjusted independent of the camber angle. The equations for the camber lines are given as: I) for x < 0.2025 y = [( 0.5 J 2 ]12 c sin92 -(x-0.5r 0.5tan92 (4.18) + [120.5 x d x (x3 - 0.607 X x2 + 0.1147 x x)] 2) for x > 0.2025 y, = [(Si~~J-(x - 05)']" +(dx(l-x)J 0.5 tan 9 2 (4.19) where Yc, x and d are all in fractions of the chord length. 36 Stellenbosch University http://scholar.sun.ac.za (4.20) The co-ordinates for a 10% thick, 100 camber angle and 1% nose droop airfoil were calculated by Wallis (1983). These consist of the upper and lower profile values for given X values. These equations are accurate for values of e = 100 to 360, t = 7% to 13% chord length and d = 0% to 3% chord length. The characteristics of the lift coefficient versus angle of attack curve stay the same, regardless of the value for thickness or nose droop, except in the vicinity of stall. The co- ordinates for the profile given in Wallis (1983) can be adjusted for any chosen profile by means of the following equations: 1) upper profile Yu = Yu'+ku x(8-10)+lu x(t-IO) +mux(d-l) 2) lower profile YL =YL'+kL x(8-1O)+IL x(t-IO) +mL x(d-1) (4.21) The values for Y, t and d are in percentage chord, where Y is measured perpendicular to the chord line. The values for Y', k, I and m differ along the length of the chord. A table containing these values along with their corresponding X values is given by Wallis (1983). This table was used in generating the blade co-ordinates after the parameters were calculated. 4.2.2. CALCULATING THE CHORD LENGTHS AND LIFT COEFFICIENTS These calculations were based on the procedures described by Wallis (1983). According to Wallis ( 1983), the solidity ratio of the fan has to be taken into account during blade design. For a solidity higher than one, cascade effects had to be taken into account. For solidities less than one, the blades could be treated as isolated airfoils. Since the velocity profile used in the design was based on a seven bladed fan with a large hub diameter and chord lengths similar to that of the comparative series of fans, the solidity of the fan was never higher than 0.8. This simplified the calculations considerably, since no allowance had to be made for cascade effects. 37 Stellenbosch University http://scholar.sun.ac.za The first step in the design was to calculate the flow angles for the velocity profiles that were adjusted by means of the actuator disk theory: a = 01 p, = tan'(c~J u, = tan-{~"J a2 p, = tan'(U ~ C"'J a2 1 ~ m = tan -I "2 (tan ~1 + tan ~2 ) The average axial velocity over the blade chord was calculated as follows: 1Cam = "2 X (Cal + caJ These values were used to calculate the blade loading factor:-) (~JCL cr - - X Cam X cos ~111 with the solidity ratio: ccr = s We can also calculate s: 2 x TI: x rs = nh (The number of blades used in the design was seven, as explained earlier.) 38 (4.22) (4.23) (4.24) Stellenbosch University http://scholar.sun.ac.za The chord lengths at the hub and tip could now be calculated by choosing an c.ppropriate value for C,,: c 2 x 'IT x r x CLCJ Dh X CL (4.25) (4.26) In order to obtain solidities similar to those of the comparative fan series, the values for the hub and tip chord lengths had to be in the same size range as the comparative fan series'. This was achieved by selecting a CL value of 1.85 at the hub and a value of 0.8 at the blade tip. This gave a chord length of 86 mm at the hub and 71 mm at the tip. Although these values for C" are very high, the use of nose droop and blade thickness distribution improved the blade stall characteristics. The chord length distribution along the blade length was calculated by linearly interpolating between the hub and tip blade chord lenbrths. These results were used to calculate the lift coefficient distribution: C = 2 x ~ x (C W 2 J x cos n.l C I-'m C am Due to the effect of solidity the lift coefficient is altered by a lift interference factor. With the help of Wallis (1983) the lift interference factor was estimated (see Figure 4.5). This gave the final lift coefficient values as follows: Cli = Cl/LIF (4.27) The lift coefficients and chord lengths along with the flow angles are given in Table 4.3. 39 Stellenbosch University http://scholar.sun.ac.za Table 4.3: Calculated blade design variables for general application fan blade length chord CL 01 02 [m] [m] [0] [0] 0 0.0867 1.85 56.29 30.46 0.0197 0.0859 1.872 59.48 37.86 0.0395 0.0850 1.763 61.66 46.23 0.0592 0.0842 1.662 63.86 52.12 0.0789 0.0834 1.559 65.73 56.59 0.0987 0.0826 1.452 67.51 60.50 0.1184 0.0817 1.368 68.97 63.31 0.1382 0.0809 1.286 70.34 65.79 0.1579 0.0801 1.218 71.5 67.72 0.1776 0.0794 1.156 72.57 69.42 0.1974 0.0784 1.102 73.51 70.83 0.2171 0.0776 1.053 74.37 72.08 0.2369 0.0767 1.01 75.14 73.15 0.2566 0.0759 0.97 75.85 74.11 0.2763 0.0751 0.935 76.49 74.95 0.2960 0.0743 0.903 77.08 75.71 0.3158 0.0734 0.874 77.62 76.37 0.3355 0.0726 0.846 78.12 77.02 03553 0.0718 0.824 78.57 77.56 0.375 0.0709 0.8 79.01 78.1 40 Stellenbosch University http://scholar.sun.ac.za 4.2.3. CALCULATING THE CAMBER AND STAGGER ANGLES The stagger and camber angles are defined according to Figure 4.6. The variation in stagger angle reflects the amount of twist along the blade length, while the camber angle corresponds to the amount of curvature in the blade profile. The values for camber angle were obtained using: , 8 = ~1 - ~2 + 8 - i (4.28) The values for incidence angle were taken from a graph in Wallis (1983) (see Figure 4.7). The values for 8 were calculated using equation (4.29) (Carter, 1950): o = ( m x (fl, - fl,) xmj( 1 - m xm (4.29) This function gave deviation angle values that decreased with decreasing solidity, reaching a certain value from where it started increasing and eventually diverged. The values for deviation at these radii were kept constant with the lowest deviation angle value calculated. According to Bruneau (1994) the value for m could be approximated by equation (4.30): 02092-'" 0.2322389 ~ 0.3736909 ~2 0.8668135 ,.3ill =. ).) + J X S - 4 X S + " x C;10- 10 10 (4.30) As can be seen equation (4.30) uses the value for stagger angle. In order to calculate the value for camber angle, the stagger angle had to be obtained first, using equation (4.31): where ~ = ~1 - a a = angle of attack (4.31) The angles of attack for the blade profiles were obtained from the graph in Wallis (1983), reproduced in Figure 4.8. This angle had to be adjusted for the change in angle of attack because of the blade nose droop (Wallis, 1983): a = aOd - 0.57 x d where d is in percentage chord. 41 (4.32) Stellenbosch University http://scholar.sun.ac.za The blade was designed for a maxinum nose droop of 3% along the blade length to accommodate the high lift coefficients used in the design, while the blade thickness was varied linearly from 11% at the blade tip to 7% at the hub. According to Figure 4.8 the angle of attack is dependent on the camber angle of the blade profile. This meant that the angle of attack was obtained using the camber angle, which in turn affected the value for stagger angle, thereby changing the value for camber angle. In this way the value for both camber and stagger were obtained by iteration. To start the iteration the value for stagger angle was assumed to be equal to: ~ = ~rn The resulting camber and stagger distributions are illustrated in Figure 4.9, along with the blade profile distribution at the different radii (see Figure 4.10). 4.2.4. BLADE ROOT DESIGN The size of the new fan blade corresponded very well to that of the comparative fan series' fan blades. Therefore it was expected that the form and size of the blade root would not differ much from these blades' blade root. Since HAl already had a concept design for the blade root, it was decided to use this design and adapt it for the new blade design. The design has several improved features, such as a larger contact area as well as a well defined collar on the root shaft, which improves the ease of assembly by wedging into the cavity in the fan hub. Although the design was tested for static strength, it was expected to be able to withstand dynamic stresses also, because of the size similarities with the comparative fan series. A diagram of the blade root is illustrated in Figure 4.] ]. 4.3. LOW-NOISE FAN BLADE DESIGN Although the design of the low-noise fan was not part of the HAl project, the low-noise blade design was done on the same principles as the general application fan. The low-noise fan was designed to deliver the same pressure duty as the fourteen bladed, 1000 mm diameter general application fan of the comparative fan series. Since it was designed for low-noise applications, the pressure duty of the fourteen bladed general application fan was achieved by using seven blades with a larger chord length. Calculating the values for v, and \jf with the help of equations (AI) to (A3) 42 Stellenbosch University http://scholar.sun.ac.za (4.34) and (4.1) to (4.6), the {0.25/0.2/0.21}configuration values were obtained The velocity profile was calculated in the same way as for the general application fan and is illustrated in Figure 4.3. The F- series airfoil described in section 4.2.1 was also used for the low-noise fan, as well as the blade root design of section 4.2.4. This enabled the use of the same hub design for both blade designs. 4.3.1. DESIGN VARIABLES Due to the similar design techniques the design variables were the same as the general application fan design, although provision had to be made for blade sweep. Wright et. al. (1989) provided a set of sweep-angle curves (see Figure 4. 12) for various wave number modes which should result in a fan noise reduction of up to 10 dB for a specific mode number, when used to design a forward swept blade. According to him the curve for wave number mode equal to two will ensure a significant noise reduction in an axial flow fan. A mode number represents the frequency at which the noise occurs - a low mode number represents a low frequency noise. The curve was represented as follows: 11 = 37.9261 + 79.1634 x MR - 0.3152/MR - 23.0131 x M~ (4.33) where 11 represents the blade sweep angle viewed from the front of the axial flow fan, in the plane perpendicular to the fan shaft (see Figure 4.13) and MR is given by equation (4.34). M =Dxr R .JRT where R = 287 J/kgK T = 293.16 K (20?C) Integrating equation (4.33) gave the equation for es (see Figure 4.13). This equation was important in defining the form of the blade axis for design purposes: 8 s = 37.9261 x In(r) + 79.1634 x G x r + 0.3152 _ 23.0131 x G3 Gxr .) (4.35) 43 x r3 +K Stellenbosch University http://scholar.sun.ac.za where G = MR r Assuming a fan speed of 1440 rpm and using the fact that Ss equals zero at the fan hub (r = 0.125 m), it was found that: G = 0.4395 K = 68.778 Referring to Smith et. al. (1963) another angle was defined, namely the aerodynamic sweep angle, A, which represented the amount of blade sweep along the blade surface itself, taking the blade stagger angle into account. Using Figure 4. 14 to transform 11 into A: where tan A = tan 11 x cos ~ ~ = 90 - ~ (4.36) Following the reasoning of Smith et. al (1963) when calculating the blade variables, the flow was assumed to be on an 2xisymmetric stream surface, while the view parallel to the blade axis was used for the calculations. This meant that all the blade variables had to be transformed by the angle A at the different radii (see Figure 4.15). These variables were identical to those used for the general application design. According to Smith et. al (1963) there is a tendency for the fluid crossing the pressure side of a swept cascade blade to move a greater distance in the spanwise distance than on the suction side. This means that the flow pattern in the vicinity of a ''wall'', for instance the fan hub, would be disturbed. To account for this, a variable called downwash was calculated and added to the camber angle value. 44 Stellenbosch University http://scholar.sun.ac.za 4.3.2. CALCULATING THE BLADE DESIGN VARIABLES Using equation (4.33) the value for geometric sweep was calculated at the different radial stations. The flow angles were calculated with the help of the velocity triangles (see Figure 2. I). The velocities were obtained from the velocity profile mentioned in Section 4.1.3 (see Figure 4.3). The preliminary stagger angle was assumed to be equal to Pm: 13m = tan -I ~ (tan 131 + tan (32) This value was used in equation (4.36) to calculate the preliminary value for aerodynamic sweep, A. Once the aerodynamic sweep was calculated, the "swept" values for the flow angles were calculated (see Figure 4.15): 13sl = tan-I (tan 131 x cos Ie) 13s2 = tan -1 (tan 132 x cos Ie) I13sm = tan -I 2 (tan 13s1 + tan 13sJ These were used to calculate the blade loading factor: Cc" = 2 x (~.,) x cos~= am where the velocities were calculated as in Section 4.2.2. (4.37) The values for solidity ratio, G, at the fan hub and tip were calculated by selecting lift coefficient values at the hub and tip. A value for lift coefficient at the hub of 1.4 and at the tip of 0.7 was chosen, as proposed by Wallis (1983). Once the values for solidity ratio at the blade hub and tip were calculated, the values for "swept" blade spacing were calculated (Smith et. al. (1963)): Ss = s/ ~I + (tan TJr 45 (4.38) Stellenbosch University http://scholar.sun.ac.za The value for s was determined using equation (4.24). The number of blades used in equation (4.24) was seven as explained in Section 4.3. Using the values for "swept" spacing, the "swept" chord at the blade hub and tip were determined using equation (4.39): l c =crxss s (4.39) Interpolating linearly between the "swept" chord values at the hub and tip gave the "swept" chord distribution over the blade length. From these the solidity distribution over the blade were calculated usmg: cr = c)ss The values for the solidity distribution were used to calculate the lift coefficient distribution along the blade length by using equation (4.37): C 2 (C,,'JL = cr X C x cos 13sm am (4.40) The "swept" camber angle distribution was calculated using equation (4.41): e s = 13 sl - 13 sc + () - i + /10 (4.41) where 8 is obtained using equation (4.28) and i is obtained from the graph in Wallis (1983) (see Figure 4.7). The value ofi is dependent on the value ofe and therefore the calculation of the camber angle is an iterative process The value for downwash deviation angle, /1(),. was calculated at the fan hub using the method proposed by Smith et. al. (1963). The method starts off by calculating the value for downwash at the wall, Dww. This is followed by calculating the locations, a perpendicular distance h from the wall, for 50% and 10% of Dww, as a fraction of the chord length, c. A curve was fitted through these values to obtain the downwash distribution. The downwash deviation angles at the different radii were calculated as follows: /10 = 180-x n r cx W m x Ow 46 (4.42) Stellenbosch University http://scholar.sun.ac.za where Dw is the downwash at the appropriate radius C = C)COSA Wm = Cam/cos 13m with Cam and 13m calculated as in Section 4.2.2. r=27l:xlrxCW21 nb Due to the fact that the equations and graphs for deviation, incidence and downwash were more applicable to higher solidity blading, the camber angle would decrease with decreasing solidity until less than zero. This necessitated restricting the camber angle to be constant once it decreased to a value of 15?. This corresponded to the minimum value for camber angle used in the general application fan design which was equal to 160. The minimum values for camber angle were chosen from the preliminary calculated camber angles as those values that were close to ISO. The "swept" stagger angle distribution was calculated using equation (4.43): ): -n -ass - fJsl (4.43) The values for angle of attack, a, were obtained from the graph in Wallis (1983) (see Figure 4.8) Since the stagger angles were approximated at the start of the calculations, the calculations were repeated with the new stagger angle values. After each set of calculations the stagger angles were checked until it converged satisfactorily. Finally, the '\mswept" values for stagger and camber angle at the different radii were calculated: ~ = tan -I ( tan ~) cos A) e = tan-I (tan e)cos A) (4.44) (4.45) The calculated properties of the low noise blade design are given in Table 4.4. The resulting camber and stagger angle distribution for the low-noise fan is given in Figure 4.16 and the blade profile distribution in Figure 4.17. 47 Stellenbosch University http://scholar.sun.ac.za Table 4.4: Calculated blade properties for low-noise fan blade length chord CL PI Pz J.l A [m] [m] [0] [0] [0] [0] 0 0.17 1.3 55.14 14.41 36.55 29.16 0.0197 0.172 1.513 57.92 17.59 37.99 31.16 0.0395 0.174 1.525 60.32 27.47 39.3 32.72 0.0592 0.175 1.45 62.32 37.15 40.45 34.03 0.0789 0.176 1.36 64.18 45.1 41.48 35.29 0.0987 0.178 1.272 65.86 51.22 42.46 36.55 0.1184 0.179 1.192 67.32 55.8 43.43 37.82 0.1382 0.181 1.123 68.65 59.41 44.35 39.02 0.1579 0.183 1.063 69.83 62.25 45.21 40.22 0.1776 0.184 1.011 70.9 64.6 46 41.42 0.1974 0.186 0.964 71.87 66.53 46.87 42.57 0.2171 0.188 0.922 72.76 68.19 47.67 43.66 0.2369 0.19 0.884 73.56 69.61 48.41 44.69 0.2566 0.192 0.85 74.3 70.85 49.22 45.72 0.2763 0.194 0.819 74.98 71.93 49.96 46.7 0.2960 0.196 0.792 75.6 72.89 50.71 47.67 0.3158 0.197 0.766 76.18 73.74 51.45 48.59 0.3355 0.199 0.742 76.73 74.54 52.2 49.45 0.3553 0.201 0.72 77.2 75.2 52.94 50.31 0.375 0.203 0.7 77.68 75.87 53.63 51.17 4.4. STRENGTH CALCULATIONS FOR FAN BLADES The purpose of the strength calculations was to determine whether the manufactured fan blades could withstand the forces exerted on them during the tests performed. These calculations can also serve as guidelines for the production manufactured fan blades. With reference to Section 4.5, the 48 Stellenbosch University http://scholar.sun.ac.za general application fan blades were to be manufactured entirely from aluminium, while the low-noise blades were to be manufactured from polyurethane resin with a steel blade root inserted into them. This blade root consisted of a 10 mm threaded steel shaft covered with an aluminium bush that fitted into the same hub as the general application fan blade. A static strength analysis was performed on both the blades. The critical part of the blade static strength was expected to be the blade root section because of the fact that it had a comparatively small cross-sectional area in relation to the forces acting on it. This part was analysed by means of a few basic strength calculations. Referring to the comparative fan data sheets, two critical fan blade length and fan speed combinations were identified, namely 280 mm at 2880 rpm and 375 mm at 1440 rpm. Due to the difference between the forces acting on the blades, different critical combinations apply to different calculations. For the general fan design the calculations for centrifugal forces acting on the blade assumed a speed of 2880 rpm at the design blade angle of 13.8? and blade length of 280 mm. The aerodynamic force calculations assumed a speed of 1440 rpm at 13.8? blade angle and 375 mm blade length. The calculations were done for nylon 6.6 as well as for sand cast aluminium (LM 24) to facilitate both types of production possibilities. For the low-noise fan design both the aerodynamic and centrifugal force calculations assumed a speed of 1440 rpm at the design blade angle of 15.4? and blade length of375 mm. These calculations were done for a mild steel blade root. The material properties are given in Table 4.5. Since the swept blades were evaluated for the mild steel blade root and the blade root was identified as the critical part of the blade, only the density of the polyurethane material was needed to determine the centrifugal forces on the blade root. Table 4.5: Fan blade material properties Nylon 6.6 Aluminium [LM 24J Polyurethane Steel E [MPa] 2800 71000 not needed 207.103 Yield Strength [MPa] 75 180 not needed 370 Shear Strength [MPa] 37.5 90 not needed 185 Density [ kg/m3] 1140 2710 1577 7810 49 Stellenbosch University http://scholar.sun.ac.za According to Wallis (1983} the calculations could be divided into the calculations for stresses due to centrifugal forces and the calculations for stresses due to aerodynamic forces. The fOIWard-swept blades were also investigated for flutter and divergence with the help of Dowell et al. (1995). Sample calculations for the strength calculations are shown in Appendix C. 4.4.1. AERODYNAMIC LOADS These loads can be listed as follows (see figure 4.18): 1) Twisting moment This moment is introduced by the aerodynamic forces on the blade and deforms it into the high-pitch angle position. 2) Bending loads Due to the lift and drag forces on the wing, a bending moment is created around the blade root. This moment determines the blade deflection. 3) Shear loads The aerodynamic forces create a shearing load normal to the blade axis. To estimate the aerodynamic forces, the same values for lift coefficient were used as in the blade design stage. The values for drag coefficient were obtained from Wallis (1983) (see Figure 4.19). Since no data on quarter-chord moments for the F-series profiles were available, the corresponding values for a NACA 65-410 wing profile with approximately the same shape were used (Abott et aI., 1959). A list of these coefficients for both blade designs is included in Table 4.6 . 50 Stellenbosch University http://scholar.sun.ac.za Table 4.6: Force coefficients used in design general application fan low-noise fan Blade Length CL CD Ci\1c4 CL CD CMc'4 [mJ 0 1.85 0.0142 -0.075 1.3 0.013 -0.075 0.0197 1.877 0.0128 -0.075 1.513 0.014 -0.075 0.0395 1.763 0.013 -0.075 1.525 0.014 -0.075 0.0592 1.662 0.014 -0.075 1.45 0.013 -0.075 0.079 1.559 0.0145 -0.075 1.36 0.015 -0.075 0.0987 1.452 0.014 -0.075 1.272 0.016 -0.075 0.1184 1.367 0.0132 -0.075 1.192 0.017 -0.075 o 1382 1.286 0.012 -0.075 1.123 0.015 -0.075 0.1579 1.218 0.011 -0.075 1.063 0.0125 -0.075 0.1776 1.156 0.0105 -0.075 1.011 0.012 -0.075 0.1974 1.102 0.0105 -0.075 0.964 0.0115 -0.075 0.2171 1.053 0.0105 -0.075 0.922 0.01 -0.075 0.2368 1.01 0.0105 -0.075 0.884 0.01 -0.075 0.2566 0.97 0.0105 -0.075 0.85 0.01 -0.075 0.2763 0.935 0.0105 -0.075 0.819 0.01 -0.075 0.2961 0.903 0.0106 -0.075 0.792 0.0105 -0.075 0.3158 0.874 0.0106 -0.075 0.766 0.0105 -0.075 0.3355 0.846 0.0107 -0.075 0.742 0.0105 -0.075 0.3553 0.824 0.0107 -0.075 0.72 0.0105 -0.075 0.375 0.8 0.0108 -0.075 0.7 0.0105 -0.075 51 Stellenbosch University http://scholar.sun.ac.za Firstly, the lift and drag forces over each of the twenty segments were calculated. These segments were formed by the areas around each of the twenty radial divisions along which the blade was designed. 1 C L.L = CL X - X P X x A2 am 1 2D = Co x - x p x C x A2 am with p = 1.2 kglm3 A=cx& The value for resultant force was calculated: F = .Je + n2 and the angle between F and L: Ddelta = tan-I L (4.46) (4.47) Since the value for stagger angle varies over the blade length, the resultant force acts in a changing direction as the stagger angle changes along the length. It was simplified by assuming that the blade parameters stay constant over each of the blade segments. In order to calculate the values for maximum bending stress and shear force, the direction in which the components of the resultant forces over the different segments gave the maximum bending moment was needed, as well as the direction which gave the maximum shear force. These reference directions were iteratively calculated by alternately choosing one of the directions of the resultant forces as the direction of maximum bending moment or shear force. The values for maximum bending moment and shear force were calculated as follows: where M bend = i Fj X (co~$ j - $ ref)) X 1mom J=l Fsheu = i Fj X (Co~$ j - $ ref )) j=l Imom= the moment arm 52 (4.48) (4.49) Stellenbosch University http://scholar.sun.ac.za (4.50) ~j = deltaj ~ (90?- ~J n = 20 The aerodynamic twisting moment for each segment was calculated as follows: 1 ?M . = C'I ' X - X P X C - x A x cC "1' ;'\i C '"t 2 a rn Numerically, this gave: n M ='M.c 4 total L.... c 4 I i= I Since the quarter chord differed from the location of the segment centroid along which the blade segments were staggered, an additional moment is formed by this distance offset. According to Wallis (1983) the distance the centroid is located from the leading edge, parallel to the blade chord line, is almost constant at 43.45% of the chord length. This gave: L1x = (0.4345 - 0.25) x c = 0.1845 x c Taking the stagger angle into account this gave: Madd = 0.1845 x c x cos(~) x L Adding these values for the different blade sections gave: n M ='Madd lotal L.... add i i=l (4.51) (4.52) The forward swept blade also experienced a moment due to the distance that the blade axis is offset from the blade root axis. This changed equation (4.51) as follows: Madd = [0.1845 x c x cos(~) + r x sin 8s] x L 53 Stellenbosch University http://scholar.sun.ac.za The results from this section were as follows: Table 4.7: Resultant aerodynamic forces g~eral appl. fan low-floise fan Fshear [N] 4.19585 10.0468 Mbend [Nm] 0.68723 1.83897 Mc4 tolal [Nm] 0.00592 0.14216 Madd [Nm] 0.06257 2.09524 4.4.2. CENTRIFUGAL LOADS The centrifugal loads can be divided into: 1) Twisting moment This is a moment introduced by the fact that the blade is rotated around an axis other than the main axis of inertia and tends to deform the blade into the low-pitch position. 2) Centrifugal load Due to the weight of the blade a radial force is created in the direction of the blades' main axis. These forces are due to the revolution of the fan blades around a fixed axis. The biggest factor influencing these forces is the rotational speed of the fan blades. The axial force due to the centrifugal loads is given by: TO F.xi?1 = P X 0.2 X f (A x r). dr ri Where p = material density [kg/m3] n = fan revolution speed 303.687 rad/s A = cross-section area [m2] 54 (4.53) Stellenbosch University http://scholar.sun.ac.za The value for the cross-sectional area was obtained from a graph given by Wallis (1983) (see Figure 4.20). The centrifugal twisting moment is given by (Wallis, 1983): where Mccnr 02 ro = p x 2 x J (sin( 2 x y) x (J 2 - J J). dr n (4.54) y = 90? - ~ hand J I were also obtained from graphs in Wallis (1983) (see Figures 4.21 and 4.22). The results from this section were: Table 4.8: Resultant centrifugal forces (densities given in Table 4.5) general appl. fan low-noise fan Faxial [N] p X 1.5033 P X 6.1402 MCenl [Nm] p X 0.00146 P X 0.01436 4.4.3. BLADE STRESSES The critical part of the blade was identified as the blade root. For the general application fan these dimensions were as follows: router 0.0105 m rinner 0.004 m The inner radius was included because of the fact that the blade root was hollow to minimise the material used during manufacture. For the low-noise fan the corresponding dimensions were: rOUler = 0.008 m [inner 0 m The characteristic values for the cross-section were calculated as follows: A rool = 'IT x (router 2 - rinner 2) (4.55) Iroot 'IT X (douter 4 - dinner 4)= (4.56)64 55 Stellenbosch University http://scholar.sun.ac.za J root 1C x (doffier 4 - dinner 4) 32 (4.57) These values, along with the forces calculated earlier, were used to calculate the stresses: I) The shear stress perpendicular to the blade axis: 1 shear - Fshear A root (4.58) 2) The axial stress due to the centrifugal forces O"axial - Faxial A root (4.59) 3) The bending stress due to the aerodynamic forces where O"h~-nd - Mbend X Y max Iroot (4.60) Ymax = router [m] 4) The shear stress due to the torsion in the blade root Trool = -(Me ~total + M add tOlal ) + M cent + M "I=- 0.8 .~ ~ :J 0.7 0.6 0.5 0.5 0.6 I ~ 1 1Inu = psi = phi = 0.51 -u - optimized ----?- u - free vortex -e- v - optimized --9- I v - free vortex' i Figure 3. 1: Example of optimised and free vortex velocity profiles for v = = \jJ = 0.5 (Von Backstrom et al. 1996) 97 Stellenbosch University http://scholar.sun.ac.za .!! 20Clc:ct .! 15 E IIIo -+- .251.19/.12 ___ .241.191.17 -.- .4/.221.24 ~.211.19/.15' : II 5 I ~ Ij I~" I., II 1. tre Io . I I .~. *)( t< .1 , I ? ? ? ~ 10 25 35 r------.--1~.-~.-------.-30 "'- . ,---- --------r--- ---'I-~-~-- I I . II ! E o 0.2 0.4 0.6 0.8 llmensionless Blade Length Figure 4.1a: Approximate blade camber for different configurations ~ .21/.191.15 ,-'- .41.22/.24 -+- .251.191.12 ___ .241.191.17 60 70 80 C 50 I t 4OV/ I[ I I~ r I I ~~ 30] I I I I 20 I I I ! I I : iii I 10 I ': I I I Io J I . o 0.2 0.4 06 0.8 llmensionless Blade Length Figure 4.1b: Approximate blade stagger for different configurations 98 Stellenbosch University http://scholar.sun.ac.za -+- ON 1inf ~---'---~____ ON 112~ 1J .!!!oS ~ 8 U.52 ~ 6.. j fI) 41 I I I ! ' 21 I : I, I, I 1 __ 1_ I ' ! I I l :I i I . Oil .' ??????????????????? 0.125 0.175 0.225 0.275 0.325 0375 0.425 0.475 0.525 Radius [m] Figure 4.2a: Swirl velocity profiles for general application fan design 16 r-- .r- _...: 14 , i 12 'iii'E 10 ~g 8 Qj :: 6 III )( 8?.. j 6 (J) ---'-~--'--T-'~'I----~i- ii I-+- Cw 1 inf. II ?: Cw 1 -I --- -.-Cw2 I I---*- Cw 2 info 4 I21 i I I I I. I I o ??? I ?? L . i. I : J I???? '. ? I? ? ?? I iL 0.125 0.175 0.225 0.275 0.325 0375 0.425 0.475 0.525 Radius em] Figure 4.3a: Swirl velocity profiles for low-noise fan design I Ii I--~-'1 -+-~---Ca1inf.-+-=--_____ Ca1 - ---.-Ca2 I---*- Ca2 inf. -~--- I i 0.175 0.225 0.275 0325 0.375 0.425 0.475 0.525 Radius em] 18 I I 16 14 'iii' 12 ~ ~ 10 U0 8Gi> iii 6~ 4 2 0 0.125 Figure 4.3b: Axial velocity profiles for low-noise fan design 100 Stellenbosch University http://scholar.sun.ac.za Circlliar-arc camber line C4 Thickness form Figure 4.4: F-series airfoil geometry (Wallis, 1983) 1.01 s/c=1.6 1.5 1.4 J 0.9 ' 131 -.:; \.J ~ 0.8 u '2 0.7u~ '"uc: 0.6~~ '".s 0.5 ~ 0.4 20 30 40 50 60 70 Stagger Angle, ~ (degrees) Figure 4.5: Graph for lift interference factors used in design process (Wallis, 1983) 101 Stellenbosch University http://scholar.sun.ac.za Figure 4.6: Definition of camber and stagger angles (Wallis, 1983) Biade camber (%c) 8 3T 4 T 5 T 6 3020-410 ~.,.,e;, I ~ j/..-" 42., u;3 g"0.u "-."-;;; E 0 a.0 Camber angle (degrees! Figure 4.7: Graph for incidence angles used in design process (Wallis, 1983) 102 Stellenbosch University http://scholar.sun.ac.za -- - -- See Section 6.8.6 b C = 2% 4% Re ---- NACAairfoils-3x 106 ---- C4 airfoils-3 to 6x 105 12 10 8 ~ <1>~ 6Ol <1>:s 8~ 4u OJ::: OJ 0 <1>OJ 2c ::l,-., C/J 0e:... (l)-'--' Stellenbosch University http://scholar.sun.ac.za DLj/I1/' // ' Mc/4 I, Figure 4.18: Diagram of aerodynamic blade forces I 0.020 0.016 c'"~ 0.012 '"o ~ CDp'"-0 ~ 0.008ac: 0.004 ---,--- Re 3x 105 10%C4} [6.5J ---- 6x 105 10% C4 - - - 3x 106 NACA 4412 [NACA TN 1945J o 0.2 0.4 0.6 0.8 CL 1.0 1.2 1.4 Figure 4.19: Drag coefficients used for F-series airfoil (Wallis, 1983) 110 Stellenbosch University http://scholar.sun.ac.za 0.074 - 0.073-"~ '"OJ.'i 0.072 10 15 20 25 30 35 40 Camber angle. e (degrees) Figure 4.20: Graph for area of 10% thick F-series profile VS. camber angle (Wallis, 1983) 4 ;:: "~ S 2 x ...:;- o 10 Camber angle, e (degreesl Figure 4.21: Graph 001 for 10% thick F-series profile vs. camber angle (Wallis, 1983) 11 1 Stellenbosch University http://scholar.sun.ac.za 46 ;::, 44~ b x ..::; 42 '10 15 20 25 30 35 40 Camber angle. e (degrees) Figure 4.22: Graph of h for 10% thick F-series profile VS. camber angle (Wallis, 1983) Speed? Divergence speed Figure 4.23: Comparison of wing critical speeds (Bisplinghoffet aI., 1955) 112 Stellenbosch University http://scholar.sun.ac.za r CONSIDER BOTHTWIST. a e . ABOUTAND BENDING,h,OF Y (ELASTIC) AXIS- y -y Figure 4.24: Sweptwing geometry (Dowell et aI., 1995) 113 Stellenbosch University http://scholar.sun.ac.za zA x y Figure 4.25: General application fan blade design in AutoCad 114 Stellenbosch University http://scholar.sun.ac.za Stellenbosch University http://scholar.sun.ac.za I\~/ ~ /""'~.,~.."~.,. 52.50 Figure 4.27: Blade setting angle definition for general application fan 116 Stellenbosch University http://scholar.sun.ac.za 1. Inlet Bell-mouth 2. Flow straightener 3. 1l1rot11ing dcvice 4, Flow straightener 5. Auxiliary fan 6. Flow straightcnCf 7. Low guidc vanes 8. Plenum chamber 10. Fan rotor 11. Hydraulic POWcfpack 9. Stcel mesh SCfCCllS :;)':%: :%: ----,/,, t;:: T-t'/'.'I ~'I ,/ \, ; / rX\ ~---1 v/' 'I ~~ &;;/// e C-" --------j=cj."--,,, I I I+--"- : I TTT i ~,I ~ I ~I gi ! I",. I I I ~i 8',--",--------..,: -.L I ~ i~ I I ?>1V~.. -----l.~I .~ I I I '\J"" I !------l.I ! I ! ; i ! I \,~ ;j I ~ ~ 1 ~i:~ G-~ : ~ ~ 1 ~ ~I~ 8 ~,L!-J~ 1. Conical inl~ 2. Anechoic chambcr 3. Noise measuring point 4. Flow straightener 5. Pressure measuring point 6. Fan rotor 7. Fan motor and torque transducer 8. Alternative flow straightener (sec Se<:Xion5.1) 9. Pressure measuring point 10. Noise measuring point 11. Ancd10ie dlambcr 12. Throttle plate Figure 5.2: Schematic lay-out of Type 0 test facility for 630 mm diameter fan 118 Stellenbosch University http://scholar.sun.ac.za I. Conical inla (630 mm) 2. Conical section from 630 nml test facility 3. Pressure mcasuring point 4, Fan rotor 5. Fan motor and torque transduccr 6. Pressure measuring point 7. Throttle plate from 630 rnm test facility ~,\J'-- I Iii ~ :' ~ ~ : ~ ~ : ~~r+r' ,~ I: I10~--~ I I~ I ~ : I I I 1 01 I : I ~I I I I I I I I I _I _' .-L ,~\ ! ~ I ~I I II I I I I I , : II ~I ~, I\J~ '---.l I i 1 1 I~Jr---17l'--../ iii G m --'. Figure 5.3: Schematic lay-out of Type D test facility for 800 mm diameter fan 119 Stellenbosch University http://scholar.sun.ac.za 1--------------- I 350 i 300 'i' 250 ,--+-- 25? (fs)e:. ,____ 35? (fs) GI.. 1;::200 ---.-45? (fs) III GI ____ 25? (nfs)0: ~ 150 --+-- 35? (nfs)-.; U5 -+-- 45? (nfs) c 100 ----*"-pdfIII... 50 ! 0 0 1 2 3 4 5 6 Volume now (m3/s) Figure 5.4: Fan static pressure vs. volume flow for different blade angles for 630/250/14/1440 fan (fs - flow straightener, nfs - no flow straightener). 100I--------r-~-------- --~---.----------.....- 90 I . --+-- 25? (fs) , 80 t 35? (fs) ---.-45? (fs) , 1'. 70 __ 25?(",,) ~. ,'-'.g 60 - 35? (nfs) I : _ :_~ ~ 50 --+--45? (nfs) ~ ,E ~ . --' ~ 40 I i I I I ~ 30 I i I I I 20 10 o o 2 3 Volume Row (m3/s) 4 5 6 Figure 5.5: Fan total efficiency vs. volume flow for 630/250/14/1440 fan. 120 Stellenbosch University http://scholar.sun.ac.za (~ E}--{~ I. Pressure tappiug<; for determining volume flow 2. Noise measuring tube and microphone 3. Pressure measuring point in front offan 4. Fan rotor 5. Fan motor and HEM torque transduce:- 6. Pressure measuring point behind fan 7. Noise measuring tube and microphone 8. Betz manometer for calibrating pressure reading<; 9. Frequency rcad-Qut coupled to proximity switch 10. HEM pressure transduce:- II. Fe seleaion box 12. HEM bridge amplifier 13. B + K sOWld level metcr 14. FIT analyzer 15. Rion sOWldIcvclmetcr 16. Frequency inverter ~ ~ : ~ ~ : ~ ~i~-LJ'\ ' I .r--, I'-!"""'"~ ' I II FIiJMI~I I : II,~.,D", ! , 'c=JIIII~? ,~ ---'----l- I I --~- I 0 V ,:-~~ 1 ," ~ " ' 1'1' 'III' : I 0 ' ,,":;'.~ II~ i ,?i "-.J LU I! i ii I "-.J I I !,iF l 0 ----I I ';1 ,..._' II: I c) 'I I' III~ I .~I,~ II,~ i ~ II V~illl n~~' I I'I! v~ -"-"--, (;;, II~I i ~ ~,J "-1-" '~S I I 'r------\J: ?,t} I -;. .~ I % (7;' ' ~ ~ I ~ ~ ~ ~I~ 'P.~I ~ I~>_F, ~~ Figure 5.6: Schematic lay-out of measuring equipment. 121 Stellenbosch University http://scholar.sun.ac.za 43.5 ----T I -+-50____ 15 0 ~25? ~35?_____ 45 0 - I ~-pdf 32521.50.5 o o --_.-200 r.... \ 160 'iie:. ~ 120;:, III III~tl. U 80~en c: ftI U. 40 Volume Row [m3/s] Figure 6.1: Static pressure vs. volume flow for 483/150/5/1440 fan ---~-~----------_._----~ 20 , I t-~--~--~-~---+-5? 30 + ! I : 150 I ~25? I ~350 10 I I o ] I! ----- 450 o 0.5 1 1.5 2 2.5 3 3.5 4 50 40 ~~e.:. >.uc: .!!u Ew jij (5~ Volume Row [m3/s] Figure 6.2: Total efficiency vs. volume flow for 483/150/5/1440 fan 122 Stellenbosch University http://scholar.sun.ac.za 43.532.521.50.5 o o 40 80 280 ~I--"--I--'-'-----~----- -'-"'---'--""~---'--""7~'- -- -.--~-- '"'I . ---- 240 , . -+-5 0 Ii I I i I I ---- 15 0 2:. 200 I i ----.- 250~ I I I~ 160 I I ~35?? I I ><.. I -.-450_ . .2 120 I" I ~-pdf nien I: C'llu.. Volume Row (m3/s] Figure 6.3: Static pressure vs. volume flow for 483/150/1 0/1440 fan ~~e... >.t.lI: GIUIi:w C'll'0 I- Volume Flow (m3/s] Figure 6.4: Total efficiency vs. volume flow for 483/150/10/1440 fan 123 Stellenbosch University http://scholar.sun.ac.za 1 I IL -+-50-___ 15 0 ---6- 250 ~35? ~45? ~ --pdf 240 200 Ii Q.~160~:l III III GI 1200: .!:!"iiien 80 l::o:su.. 40 0 0 0.5 1,5 2 2,5 3 3.5 4 I Volume Row [m3/s] Figure 6,5: Static pressure vs. volume flow for 483/25017/1440 fan 1:: IL-__ .._,._"'_' "._"'_'_"_., "_.,,_-_'''_-'_-_--'_._--_-,---_--_-_._-_._-_---_-._-_-_1,-.-- 80~~---- 701" .~I. ,,:!~ I : Ie..... : I ~ 60 ---+-- --1- ---~ -:- I ----I 50 ---;---I----.~ -+-50 ~ 40 ~'--i I I i 150 ~ 30 ,-- I I ---6- 250, l i 1 20 1 : I ! ~35? -- . I 45010 r-~ -- o I. i ! o 0.5 1 1.5 2 2.5 3 3,5 4 Volume Row [m3/s] Figure 6.6: Total efficiency vs. volume flow for 483/25017/1440 fan 124 Stellenbosch University http://scholar.sun.ac.za --+-5?___ 15? --.-25? ---4E- 35?____ 45' f-- --pdf I 15 2 2.5 3 3.5 4 Volume Row [m3/s] Figure 6.7: Static pressure vs. volume flow for 483/250/14/1440 fan 100 r---------:--- , I 90 180 ~,-----------' ~ 701 I I~ iii ' ICJ 60 I t I~-----, -------j 50 II i ~~ :~ ~.~ ----~- w 40. ' ~_ I --+-5 - I I~ 30 ~: I I i 15? 1 L1. \ I I I I --.- 25?20 1"\ . ---4E- 35? 10 l' i I ---- 45? - o 'o 0.5 1 1.5 2 2.5 3 3.5 4 Volume Row [m3/s] Figure 6.8: Total efficiency vs. volume flow for 483/250/14/1440 fan 125 Stellenbosch University http://scholar.sun.ac.za 401---- ..------,-----.-:- ---,,---. -- --+- 5' 30 f 1 15'_ I 20 I I -.-- 25' ] ~F10 ~---------------------- 450 o ~I-------- _ o 0.5 1 1.5 2 2.5 3 3.5 4 4.5 250 T _._- .. - . --I _._-."- I --+-5' I I I 200 'iVe:. ~::l 150Ul Ul 41?..c.. .!:.! 100~U5 C IIIu.. 50 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Volume Flow (m3/s) Figure 6.9: Static pressure vs. volume flow for 630/150/5/1440 fan 100I . : 1-------------- '~ ~ 70 i--i- ?:s~.-==~--=-""---~~~--)-(--:'.l-:---x ~ 60 j __ ~ . I -~Tl- i~ I I I I I I -----.;-- ---- U 50 + : I I . ~E ----- w iii'0?... Volume Row (m3/s) Figure 6.10: Total efficiency vs. volume flow for 630/150/5/1440 fan 126 Stellenbosch University http://scholar.sun.ac.za 350 300 I ~ 250 I GI.. :I :::200 GI~ .2 150-;en c 100 . III~ 50 I 0 0 0.5 1 I 1 --+-50___ 15 0 -.-250 -w-35? __._450 --pdf 1.5 2 2.5 3 35 4 4~ 5 5.5 6 6.5 7 7.5 8 Volume Flow [m3/s) Figure 6.11: Static pressure vs. volume flow for 630/150/1 0/1440 fan I I I . --+-50___ 15 0 -- .,--.___ -.- 250 _.- -w-35? __._450n 1:r-T 80 i I ~ 70L >- 60g ! I oS! 50+-- ICJ I IIE . I ~ 4011-1~ ,o 30~ f- I I 20 10 I o r', ... r o 0.5 1 1.5 2 2~ 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Volume Row [m3/s) Figure 6.12: Total efficiency vs. volume flow for 630/150/1 0/1440 fan 127 Stellenbosch University http://scholar.sun.ac.za [ I 300 T .- ..- . ---r . I I 250 I i200 Ul Ul ~ 150 ll. .2;; I Ci5 100 I ~u. i 50 o o 0.5 1.5 2 2.5 .---.~-._~~---'--~-I-~---- ..- -i .:: 1'- ..-.- iii LL ---+----- 50 -___ 15 0 ----.- 250 ~35? ---.- 45 0 --pdfI I 3 3.5 4 4.5 5 5.5 6 6.5 Volume Flow (m3/s] Figure 6.13: Static pressure vs. volume flow for 630/250/7/1440 fan I I---T---.- I ----.- 250 ~35? -I---+--;----L-..:--. ---.-450 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Volume Row (m3/s] o o 0.5 10 30 20 1 1 __ . __ l_~5?l~;--1~ 40 . .rl e: (:;'60c - 60 i ~ - I ,~ -;--1- 1.~1~4 ~ 501- .!-- I n T~-w I 1 ~~._ 1 ,- "iii 40 I .1 I ~ I _! -_ I I - I i ~ 30 i I ~~ :--I----r-- _ I ,~ -+-15" 20 .: --.J ! 1 -----.- 25? I Ii ' ' -----*- 35? 1 I ---lIf- 45? Volume Row (m3/s] Figure 6.18: Total efficiency vs. volume flow for 630/150/1 0/960 fan 130 Stellenbosch University http://scholar.sun.ac.za 300 250 'ii ~200 QI?..::l III III~ 150 Q. .21Q U) 100 c IIIu.. 50 0 0 1 2 3 4 5 6 7 8 9 10 Volume Row (m3/s) Figure 6. 19: Static pressure vs. volume flow for 800/150/5/1440 fan 1098765 ---T - --Co.----1- ----,---T--- I i I --- I I 43o 100 r" .--~-----"- I 90~ 801 ~ 70. i : ,..--~f60: Z~. i~~._ 50 I : I i I T---- _-;-'--...!--- ~ I J -' I I : Iw 40 , ~ ~ I ? .......c I i ~ ~ i I ~ 30~. J'. I I : I .~~- I \ " I 20 !! ! I I I Volume Row (m3/s) Figure 6.20: Total efficiency vs. volume flow for 800/150/5/1440 fan 131 Stellenbosch University http://scholar.sun.ac.za 9 10 11 12 138 ,---+--5' l 11 __ 150 ' ---.-250 1 1~35?I 11---.-450I i I II-Pdf 765432 450 400 350'i' ~300~::l CII 250CII CII..c.. 200u;; 150a; c: t'll 100u. 50 0 0 Volume Row [m3/s] Figure 6.21: Static pressure vs. volume flow for 800/150/1 0/1440 fan 100 90 80 70~L>. 60uc: CII"0 50!Ew 40"iij 0?.... 30 20 10 o -- 0 2 3 4 5 6 7 8 ---+-- 5'__ 15 0 1- ---.- 250 - _I~~35? ! ---..- 450 9 10 11 12 13 Volume Row [m3/s] Figure 6.22: Total efficiency vs. volume flow for 800/150/1 0/1440 fan 132 Stellenbosch University http://scholar.sun.ac.za -+-50____ 15 0 - --.-250 ~35? -_____ 45 0 --pdf 350 300 'iii' 250e:. ~ ~200??GI..C. ~ 150:! C/) r:: 100 IIIu.. I 501 0 0 2 4 6 8 10 12 Volume Row [m3/s] Figure 6.23: Static pressure vs. volume flow for 800/250/7/1440 fan 12 _____ 45 0 108642 o o 10 20 --- - --- - ------- -- ----------- -._-- - ---': r-- 80 . ~ ?? ~ ~---' i o 70 1""'- : _)., . C , I - , _ G 60 ! I -+-5 0 r:: ! '1l 50 I I __ 15' iii .1 . -- I! 35 0 o ~ I. ~!- I IIi Volume Row [m3/s] Figure 6.24: Total efficiency vs. volume flow for 800/250/7/1440 fan 133 Stellenbosch University http://scholar.sun.ac.za ---+-50 I ____ 15 0 - --.-250 - ~35? - ---.-450 - -~pdf 'iii' 450c..-;400..= 350til til GI 3000:: .2250ftien 200c 150IIIu. 100 50 Io J 0 2 4 6 8 10 12 14 Volume Row [m3/s) Figure 6.25: Static pressure vs. volume flow for 800/250/14/1440 fan 50 : 1 -\._-:-__ ---' ...l--.._~ :=~:o-~ 20 i --.-250 j ~35?- 10 I I ---.- 450 -~o I ------- o 2 4 6 8 10 12 14 ----------------------~-------1: [I =-=--_-- ~----~-~-====_sol ~ 70~ ~ 60c GIc:; Ew iij'0?.... Volume Row [m3/s) Figure 6.26: Total efficiency vs. volume flow for 800/250/14/1440 fan 134 Stellenbosch University http://scholar.sun.ac.za 100 -+--5?___15?- -.-25. ~35?-' 95 75 70 ~------------------------- 63 125 250 500 1000 2000 4000 8000 Gi 90>CIl ..J ~ 85::l III III CIl ~ 80 'C C::loen iii' ~ Frequency [Hz] Figure 6.27: Sound pressure levels for 483/150/1 0/1440 fan 100 j I -+--5? 95 .. 150 ~ I!! I -.- 25? ~ 90 +1 : I I I ~35? ~85.~1 III ~80bJ ~I~ ! IE I l~ I 'Y"en 75 I, i I I I ,I ! i I70 -"-----------------------< 63 125 250 500 1000 2000 4000 8000 Frequency [Hz] Figure 6.28: Sound pressure levels for 630/150/5/1440 fan 135 Stellenbosch University http://scholar.sun.ac.za 100 f :1 J i -+-50 I I I I ___ 15 0 i -.-250 I I :; 85 ~ & ~35? CII...J ~ 85;;, '"'"~ [l. 80 'C C;;,o rn 75 70 63 125 250 500 1000 2000 4000 8000 Frequency [Hz] Figure 6.30: Sound pressure levels for 630/250/7/1440 fan 136 Stellenbosch University http://scholar.sun.ac.za 80 100 I---~------------~----~-----'~'-----i ---------------,-- - ... ~ 95 I : --+-----"---50- I iooLJI II I-~=:~:~]-=- ~ 85 :---;I-----'~ A , 450 I '"QICi. "C C::;,oen 75 8000400020001000500250125 70 :-=i ---~----------:...------___L---_1_-----' 63 Frequency [Hz] Figure 6.31: Sound pressure levels for 630/250/14/1440 fan 8000400020001000500250125 I 70 _I ~ __ _'___~ 63 ': 1-- ~-_..~-~---.----_._~~.--_.----~----.--..__._-, 1-.-.- --.--- or ] I Ii 00 ! I I=:~~.! CII : I I' .::; 85 ---..- 250 I - ,- '" ' '" I ~ I~F ~ .-g 80 1---- 4~ ::;, Io ' en 75 1 "I Frequency [Hz] Figure 6.32: Sound pressure levels for 630/150/1 0/960 fan 137 Stellenbosch University http://scholar.sun.ac.za 8000400020001000 -+- General Application Fan __ Low -noise Fan --.- Co~arative Fan 500250125 90 85 moo~ Gi 75>GI ...I ! 70='III III GI?.. 65Q. "Cc:=' 600 (I) 55 50 63 Frequency [Hz] Figure 6.33: Comparison of sound pressure levels of three different fans at 720 rpm ------------ ------90 ----------- .85f ------ moo~ ~ 751 ell I ; 70 r-- I cr 651 [ j - I ~ 60 I---~----+--Ge-ne-r-a~1 A-p-p-lic-a-t-io-n~F-an-----i---- ~- _ (I) I I __ Low -noise Fan 55 -I --6- Co~arative Fan 5O~' -------------------------- 63 125 250 500 1000 2000 4000 8000 Frequency [Hz] Figure 6.34: Comparison of sound pressure levels of three different fans at 960 rpm. 138 Stellenbosch University http://scholar.sun.ac.za 90 85 iii' 80~ Qj 75>41...I 41?.. 70:J III III 41 65ti. 'Cr:::J 600en 55 I I ..---- II I I I I i I I I I I I I I I I I I I-+- General Application Fan .I I 1 Low -noise Fan -~I--- ---.- CorTl'arative Fan -~-- --- - 50 63 125 250 500 1000 2000 4000 8000 Frequency [Hz] Figure 6.35: Comparison of sound pressure levels of three different fans at 1200 rpm 139 Stellenbosch University http://scholar.sun.ac.za --~-'----i-'-- -~-~-_...------I----------~-.--I-.- ---------~--._-- I' I ????? i i --+- 720 rpm ___ 960 rpm :----A-12OO rpm 300 250 'i'c..~ 200!;:, III III GI 150Q: .2or;u; 100 c: IVu.. 50 o o 0.5 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Volume Row (m3/s) Figure 6.36: Static pressure vs. volume flow for low-noise fan 100 r.-.------.... . .-.-----.-.------.- ..------. ...--.---..-..- ---- ..-.---------~----l. I I I I 90 .1 I__ ~--------I I 1 I I I 801 ~I ' -.t- 70~, I, ~! I ~ i I i~ I ' I I>. 60 I! '_~I __ ~ _g 1 --,--- I ! I ~ 50rT',-I i1---i-J ~ 40 I L :- J _-c-_! _ _ [ 1 L__---.l __ III lJ I ' I I I I ~ ' , I-0 30 ~- I 'i--+- 720 rpm ..1__ I- I l 1 I I, 1 I, 960 rpm ! 20 '_ I I _' __ , I 1 ----A- 1200 rpm ! 1:1=====================================:::::::::::=====~o 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Volume Row (m3/s) Figure 6.37: Total efficiency vs. volume flow for low-noise fan 140 Stellenbosch University http://scholar.sun.ac.za 400 r~----~---- - --"-'-----.-.. .._ .. 350 -+-5? (rreas.) _ -11-5? (scale) ~ 3(X) -.-15? (rreas.) -ftl Q.~ --*-150 (scale)!! 250:J -JE-25? (rreas) ,-uc CIlUEw "iij ~ 30 Volume Row [m3/s) Figure 6.39: Total efficiency measured and scaled for diameter for 630/150/10/1440 fan 141 Stellenbosch University http://scholar.sun.ac.za 350 300 'iii' 250'l.~ ~:J . 60ut: ClI U 50::w 40 C'll"0 30I- 20 10 0 0 0.5 1 -+-- 5? (meas.) I 1 - 5? (scale) ~. I~ .. 1 i :,x-.I ~'. --.1 -.-15?(meas)~ , I I :.. I. 15?,---~ ---+------,~~: _ ~ (scale) ~ ~ ' , "I ---"'-- 250 ('_~ . ' , I ---...- meas.)_1_1 ~+-LJ li-.-+--25?(SCale) ~ I I I I I I I I --+-35? (meas.) ~: ! I I ! I i _35? (scale) ! I -- 45?(meas.) - -+-- 45?(scale) ~ I I 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 Volume Flow [m3/s) Figure 6.41: Total efficiency measured and scaled for fan speed for 630/150/1 0/1440 fan 142 Stellenbosch University http://scholar.sun.ac.za 5.5 64.5 52.5 3 3.5 41.5 20.5 o o 400 350 'iij'300!:. ~250::r til? 200 !___-+-1200 I~") ?! -.-1200 (scale) 7;j 150en ---..- 1440 (scaIe) ; 100 __ '--pdfu.. Volume Flow [m3/s] Figure 6.42: Static pressure measured and scaled for fan speed for low-noise fan 65.554.543.532.521.50.5 ': f--i-~ ..... BOr ~~ 70 ~ _,' II;:60 I 11!~i' Io I I I . I ' ~ i I I I I U 50 I 1 I,lE I I~'-'~----', ~ 40 I I I i I IV I I ' ~ 30 I 1--+-11200 (~as) II ,~~ 20 1200 (scale) I I . ~10f-, :~1440(scale) o I I I i o Volume Row [m3/s] Figure 6.43: Total efficiency measured and scaled for fan speed for low-noise fan 143 Stellenbosch University http://scholar.sun.ac.za 450 400 350 'iii' ~300~::J Cll 250III GI..D.. 200.2 "iQu; 150 c IIIu.. 100 50 0 0 5 10 15 20 25 Volume Flow [m3/s] Figure 7.1: Test data for 1000/250/7/720 fan, scaled to 1440 rpm and compared with design point 350 f .- ...----.-- .- j . -r--'--~-I -------.300 t ? I ~ i I .------.- .? - .. - -------- 'iU 250!:.. ~::J 200III III GIn. .2 150 "iQu; c 100IIIu.. 50 0 0 1 2 3 4 5 6 Volume Row [m3/s] -+--5? g.aJ .-.15? ga.f --;*-15? comp ~25?g.a.f _____25? compo -...- 350 g.aJ. -+-35?comp __ 45? g.aJ. -pdf Figure 7.2: Comparison of fan static pressure vs. volume flow for general application fan and comparative fan for 630/150/1 0/1440 configuration 144 Stellenbosch University http://scholar.sun.ac.za -+-5? g.a.f. __ 15?g.a.f. ---"-15? cOrllJ. ----*- 25? g.a.f. i -JE- 25? cOrllJ. :---.- 35? g.a.f. i -+-- 35? cOrllJ. -45?g.a.f. 654 -----, .- I !!~ 32 90 80 70 ~60e.... >.u 50c:GlUE 4Dw iii'0 30 t- 20 10 0 0 Volume Row [m3/s] Figure 7.3: Comparison of fan total efficiency vs. volume flow for general application fan and comparative fan for 630/150/1 0/1440 configuration 145 Stellenbosch University http://scholar.sun.ac.za 9. TABLES Table 6.13: Sound data for 4831150/1011440 fan Volume Flow Sound Pressure Level per Octave Band [dB] - [m3ls] 63HZ 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz 5? Blade Angle 1.131 80.1 80.5 81.2 75.7 86.4 87.8 83.5 75.3 1.094 80.7 80.4 80.6 76.1 86.2 88.0 83.3 75.2 1.065 80.7 80.0 80.9 76.4 86.9 87.9 83.5 75.2 1.049 82.4 80.6 80.6 75.5 86.5 87.9 83.9 76.0 1.022 82.8 80.3 79.9 75.6 87.7 87.5 83.8 76.2 0.732 83.6 82.0 80.0 83.0 89.4 86.4 83.0 75.2 15? Blade Angle 1.743 83.8 82.4 80.8 79.2 87.2 87.2 83.6 76.7 1.729 84.2 83.0 81.3 78.4 86.7 87.1 83.4 76.3 1.703 84.8 83.0 81.3 78.5 87.2 87.0 83.2 76.1 1.691 84.6 82.7 80.8 78.7 87.2 86.5 82.9 75.5 1.658 85.0 83.5 81.1 78.4 86.5 85.7 82.7 75.1 1.399 84.6 85.5 82.9 79.2 86.8 85.2 81.8 74.2 25? Blade Angle 2.428 85.1 84.7 82.5 80.8 87.9 86.1 83.9 79.0 2.390 84.5 84.9 82.6 80.6 87.3 85.5 83.4 78.3 2.367 84.7 84.6 82.6 80.1 87.0 85.4 83.0 77.8 2.307 85.0 84.7 82.8 80.8 86.3 84.9 82.6 77.3 2.223 85.9 85.9 83.2 79.5 84.7 83.5 81.5 75.7 1.930 84.9 86.0 83.8 80.8 84.8 83.7 81.6 75.1 35? Blade Angle 2.927 84.3 85.7 84.7 82.1 87.0 86.1 84.7 81.7 2.894 85.7 86.5 84.9 82.1 87.4 85.4 84.1 81.0 2.824 85.4 86.6 84.4 81.7 87.2 85.7 84.1 80.9 2.754 85.4 86.9 85.0 81.6 85.7 84.9 83.5 80.0 2.623 86.2 85.6 84.4 81.2 85.9 84.4 83.1 79.5 2.178 86.3 87.5 86.2 82.6 85.0 84.4 83.0 79.1 45? Blade Angle 3.239 86.4 87.5 85.5 84.3 87.8 86.0 85.2 83.6 3.170 86.1 86.1 85.2 83.9 87.5 86.1 85.4 83.6 3.068 85.5 86.1 85.4 84.6 88.1 86.4 85.6 83.7 2.955 85.2 86.1 85.7 84.7 87.6 86.1 85.3 83.3 2.547 85.7 86.7 85.8 82.9 86.6 85.3 84.7 81.8 1.810 84.9 87.6 86.2 82.2 90.7 87.4 84.3 80.1 146 Stellenbosch University http://scholar.sun.ac.za Table 6.14: Sound data for 630/150/5/1440 fan Volume Flow Sound Pressure Level per Octave Band [dB] [m3/s] 63HZ 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz 5? Blade Angle 1.777 79.3 81.6 83.0 76.9 85.1 79.3 83.7 83.8 1.771 80.1 81.2 82.4 75.7 85.3 78.5 83.1 82.8 1.764 80.8 80.5 81.9 75.6 86.0 78.0 82.2 81.9 1.666 81.0 79.6 81.3 77.3 86.7 77.4 81.2 80.7 1.339 81.6 79.0 81.9 79.7 84.2 75.4 78.9 78.9 15? Blade Angle 2.786 80.2 78.9 79.6 76.3 82.1 75.9 79.5 81.6 2.754 82.1 79.7 79.5 75.0 82.5 74.6 78.6 79.9 2.654 79.9 80.6 81.1 78.3 83.6 77.8 80.9 82.3 2.369 82.6 82.5 82.9 79.6 85.9 79.9 82.5 83.8 25? Blade Angle 3.681 83.0 82.4 81.7 79.7 83.1 76.6 79.9 83.3 3.654 82.5 81.6 80.9 78.2 82.6 76.2 79.3 83.0 3.450 84.8 83.2 82.3 79.5 83.5 77.1 80.4 83.4 3.048 84.5 83.9 82.8 79.8 84.0 78.1 82.0 84.6 35? Blade Angle 4.260 84.3 85.0 84.0 80.2 83.7 78.5 83.1 87.2 4.221 84.2 84.2 83.2 79.5 83.4 78.0 82.6 86.8 4.054 84.2 84.4 83.7 79.4 83.2 78.1 82.8 86.3 3.797 85.0 85.5 84.4 79.9 83.5 78.3 83.2 86.5 45? Blade Angle 5.154 85.0 88.6 87.1 83.7 86.8 81.1 85.3 89.7 5.137 84.6 88.4 87.0 83.5 86.0 81.1 . 85.4 89.5 5.110 84.8 88.8 87.1 82.6 86.6 81.4 85.4 89.7 5.077 85.0 88.5 87.1 83.8 86.2 81.1 85.3 89.3 147 Stellenbosch University http://scholar.sun.ac.za Table 6.15: Sound data for 630/150/1 0/1440 fan Volume Flow Sound Pressure Level per Octave Band [dB] [m3/s] 63 HZ 125 Hz 250 Hz 500 Hz 1000 Hz 2000Hz 4000 Hz 8000 Hz 5? Blade Angle 1.586 79.9 82.6 83.5 78.6 88.3 79.6 84.7 83.4 1.586 81.0 83.6 84.8 81.2 89.3 81.2 85.9 86.3 1.564 80.7 83.3 84.2 81.5 89.3 80.8 85.3 85.5 1.543 80.3 82.9 83.8 82.0 90.1 80.1 84.7 84.8 1.365 79.8 82.1 83.5 85.6 88.6 79.9 83.5 83.9 15? Blade Angle 3.036 81.8 82.7 83.6 79.3 85.5 79.7 84.5 85.9 3.036 81.8 82.7 83.4 78.8 85.7 79.7 84.6 85.6 2.860 83.3 82.9 83.3 78.3 85.9 79.5 83.8 84.8 2.698 83.3 84.2 84.6 77.5 87.6 80.6 84.6 84.8 2.047 84.5 84.2 84.6 87.2 89.4 80.0 82.9 84.3 25? Blade Angle 4.200 85.3 85.2 83.8 80.8 84.9 78.7 82.2 87.1 4.149 84.6 84.9 83.8 80.9 84.6 78.4 82.0 86.4 3.956 84.6 84.3 83.8 79.2 85.2 78.2 82.3 86.1 3.476 85.1 86.0 86.0 83.7 88.9 81.0 84.0 86.5 2.206 84.4 90.2 87.5 83.6 88.2 79.1 83.4 84.6 35? Blade Angle 4.878 85.1 85.8 85.5 81.7 83.6 78.9 83.4 89.2 4.860 84.9 85.7 85.3 81.1 83.5 78.9 83.3 88.9 4.739 85.1 86.1 85.7 81.4 83.6 79.0 83.5 89.1 4.553 85.5 86.2 85.5 81.8 83.8 78.8 83.3 87.9 4.203 85.5 86.6 85.8 82.0 84.3 78.6 83.8 88.0 45? Blade Angle 6.294 85.5 86.3 86.9 82.5 84.3 80.4 85.4 91.8 6.242 85.4 87.1 86.7 83.0 84.5 80.5 85.3 91.4 6.225 85.2 86.8 86.7 82.2 84.2 80.3 85.3 90.7 6.178 85.3 86.9 86.8 82.4 84.3 80.2 84.9 90.5 148 Stellenbosch University http://scholar.sun.ac.za Table 6.16: Sound data for 630/250/7/1440 fan Volume Flow Sound Pressure Level per Octave Band [dB] I~~lm3ls] cc'63.HZ 125 Hz 250 Hz 500 Hz . 1000Hz ~2000 Hz 4000 Hz 8000 Hz 5? Blade Angle 2.073 87.0 84.0 83.6 76.3 85.0 79.1 84.3 81.5 2.060 87.6 84.2 83.5 75.8 84.6 79.2 84.0 80.9 2.021 87.7 84.4 83.2 75.7 85.4 79.2 83.7 80.7 1.971 87.8 84.1 83.0 75.6 85.3 79.5 83.2 80.3 1.859 86.9 83.3 82.8 76.7 87.3 80.4 82.6 79.7 15? Blade Angle 2.868 85.5 82.9 83.3 79.0 84.5 78.4 82.0 81.2 2.800 85.3 83.4 84.4 80.0 84.8 78.9 82.1 80.6 2.677 86.4 84.1 83.9 80.4 84.9 78.8 81.9 80.0 2.436 87.0 85.8 86.2 81.3 86.9 81.8 84.0 83.0 1.914 87.1 85.9 86.1 91.3 90.6 82.9 84.6 84.2 25? Blade Angle 3.921 88.6 87.2 85.9 83.6 88.1 79.9 82.1 83.2 3.798 89.9 89.1 86.8 84.1 87.1 79.9 82.2 83.3 3.567 89.6 88.8 87.2 84.0 86.9 79.8 82.1 82.6 3.247 90.8 90.6 87.9 83.8 85.2 79.9 82.8 83.0 2.962 90.5 90.6 88.6 86.0 87.0 81.8 84.6 84.7 35? Blade Angle 4.522 84.2 85.4 84.2 80.8 82.3 77.8 82.3 86.8 4.459 84.9 85.5 84.5 80.9 82.6 77.8 82.5 86.9 4.309 84.6 85.7 84.8 80.9 82.6 77.6 82.7 86.8 3.988 84.7 85.8 84.9 80.7 83.0 77.1 82.6 85.9 3.446 85.9 86.7 85.6 81.4 84.1 77.5 83.9 86.7 45? Blade Angle 5.655 85.3 86.8 86.1 81.5 83.6 79.1 84.8 90.5 5.540 85.4 87.0 86.0 81.6 84.2 79.1 85.3 89.9 5.269 85.3 86.7 86.5 82.1 84.5 79.0 84.6 88.8 5.030 85.5 88.8 87.4 83.5 86.8 80.7 85.4 88.5 149 Stellenbosch University http://scholar.sun.ac.za Table 6.17: Sound data for 630/250/14/1440 fan Volume Flow Sound Pressure Level per Octave Band [dB] [m3/s] 63HZ 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz 5? Blade Angle 1.886 82.8 85.2 86.4 78.4 86.5 81.2 86.8 87.3 1.874 82.3 84.7 85.8 77.9 86.1 80.6 86.6 86.6 1.868 83.3 85.5 86.5 79.0 86.6 81.8 87.2 87.8 1.849 83.3 85.3 86.2 78.8 86.9 82.0 86.8 87.6 1.819 83.1 85.4 85.5 77.7 87.5 82.4 85.8 87.1 1.642 83.0 85.9 84.1 81.5 89.8 81.6 83.9 85.7 15? Blade Angle 3.288 84.4 84.8 84.9 79.8 84.6 80.1 85.1 86.8 3.288 84.3 84.3 84.4 79.6 84.5 79.6 84.8 86.1 3.275 83.9 84.1 84.5 79.1 83.5 79.5 84.4 85.9 25? Blade Angle 4.372 84.5 85.1 84.4 80.4 83.8 78.3 82.1 86.3 4.328 84.7 85.1 84.6 80.8 83.7 78.1 82.0 86.1 4.198 84.8 85.4 85.0 81.6 83.7 78.2 82.1 86.1 3.683 85.3 86.5 85.9 81.6 84.4 79.1 82.5 85.4 35? Blade Angle 5.111 84.8 86.5 86.2 82.2 83.0 78.6 83.0 89.0 5.024 84.7 86.3 86.3 82.0 83.0 78.7 83.0 89.0 4.714 85.7 86.9 86.3 81.7 87.2 77.9 82.6 87.9 4.328 85.3 86.9 86.8 82.4 82.8 77.7 83.0 87.3 45? Blade Angle 6.642 85.4 87.0 87.9 84.0 83.4 80.1 84.9 91.4 6.586 85.4 87.1 87.6 84.4 83.7 80.1. 85.4 91.9 6.451 85.5 87.1 87.6 83.8 83.1 79.7 84.9 91.1 6.252 85.6 87.0 87.5 83.9 83.5 79.7 84.9 90.5 5.759 85.4 86.8 87.8 84.1 83.3 79.3 85.1 90.3 150 Stellenbosch University http://scholar.sun.ac.za Table 6.18: Sound data for 630/150/1 0/960 fan Volume Flow Sound Pressure Level per Octave Band [dB] [m3/s] 63 HZ 125 Hz 250 Hz SOD Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz 5? Blade Angle 1 _~19 74.2 77.6 79.5 79.2 83.3 78.0 75.3 77.9 1.019 78.0 78.9 79.6 87.1 81.9 70.6 70.3 77.6 1.019 74.9 77.7 79.5 79.9 82.9 77.8 75.4 77.7 0.997 71.6 74.4 76.7 77.2 81.3 74.7 72.8 75.8 0.928 75.5 80.1 79.6 80.6 82.2 75.7 74.4 78.4 15? Blade Angle 1.921 79.7 79.2 79.6 76.5 81.7 77.7 76.7 80.9 1.909 79.5 79.1 79.3 76.8 82.0 77.7 74.7 80.7 1.903 80.4 79.1 79.1 76.5 82.1 77.1 77.0 79.5 1.783 81.3 79.7 78.9 75.7 82.1 76.7 77.0 77.1 1.333 82.7 80.3 80.7 81.2 80.9 74.1 74.4 76.7 25? Blade Angle 2.761 84.9 82.0 80.0 79.2 81.1 73.6 75.1 79.8 2.725 84.2 81.5 79.7 79.9 81.3 73.2 74.9 79.7 2.589 84.1 81.5 79.5 77.7 81.4 73.2 75.0 80.0 2.292 84.5 82.4 81.3 78.5 81.8 74.2 75.9 79.0 1.457 83.6 87.0 81.9 79.0 81.1 73.9 74.9 77.7 35? Blade Angle 3.221 84.4 83.8 81.4 79.5 81.5 73.5 76.0 79.8 3.176 84.4 83.9 81.3 79.1 82.1 73.0 76.3 79.9 3.117 84.4 84.2 81.6 79.2 81.5 73.3 76.4 79.7 2.794 85.0 84.4 81.8 78.0 81.9 73.2 76.6 79.0 45? Blade Angle 4.141 85.0 85.0 82.8 79.6 82.8 74.8 78.5 82.0 4.115 85.1 85.1 82.9 80.6 81.9 75.0 78.3 81.2 4.000 85.1 84.9 82.9 79.5 82.7 74.9 78.4 81.6 4.049 84.2 84.4 82.5 79.3 82.3 74.6 78.1 81.1 151 Stellenbosch University http://scholar.sun.ac.za Table 6.19: Sound data for three different fans at 720 rpm Volume Flow Sound Pressure Level per Octave Band [dB] . [m3/s] 63HZ 125 Hz 250 Hz SODHz 1000 Hz 2000 Hz 4000 Hz 8000 Hz General Application Fan 2.154 67.3 65.2 62.5 62.1 69.7 61.7 68.0 72.6 2.138 66.9 64.8 62.3 60.9 70.0 60.4 68.0 71.7 2.102 67.3 64.6 62.0 62.1 69.0 61.1 68.3 72.3 2.012 67.0 64.9 61.6 61.2 68.7 61.1 68.4 72.7 1.847 68.5 65.8 63.1 61.5 69.0 60.7 68.3 72.2 Low-noise Fan 2.100 67.8 64.0 61.2 60.9 67.3 57.5 68.5 76.2 2.100 67.5 64.1 61.2 60.2 66.9 57.4 68.9 74.2 2.049 67.5 63.8 61.0 60.7 66.8 57.3 68.1 73.8 1.996 67.6 63.7 61.0 60.3 66.7 57.2 68.5 74.0 Comparative Fan 2.110 71.6 70.7 66.3 65.9 73.1 65.6 72.3 77.9 2.100 71.4 70.5 66.1 64.8 72.8 65.3 72.4 78.3 2.020 71.1 71.1 66.6 65.3 72.6 65.0 72.5 77.8 1.950 71.4 71.2 67.2 65.3 72.0 64.6 71.8 78.1 152 Stellenbosch University http://scholar.sun.ac.za Table 6.20: Sound data for three different fans at 960 rpm Volume Flow Sound Pressure Level per Octave Band [dB] [m3Js] 63HZ 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz General Application Fan 2.879 76.4 73.5 71.4 70.0 75.4 70.4 73.4 76.3 2.864 76.1 73.0 71.0 69.7 75.7 69.5 73.2 75.7 2.807 76.8 73.3 71.0 69.6 75.2 69.3 73.1 75.3 2.689 77.0 73.8 71.7 68.9 75.7 68.5 73.1 75.6 2.462 78.4 75.2 72.7 70.0 75.7 68.3 72.8 75.4 Low-noise Fan 2.923 77.1 74.4 71.3 69.3 76.3 67.5 71.5 79.2 2.919 76.4 74.3 71.2 68.8 75.5 67.0 71.8 78.6 2.867 76.1 73.8 70.6 68.6 75.6 66.8 71.7 78.3 2.782 76.2 72.9 70.0 68.4 75.2 66.9 71.7 77.5 2.609 77.6 74.3 71.6 68.0 74.0 65.1 71.4 75.0 Comparative Fan 2.900 77.0 77.1 73.7 70.8 77.9 71.2 76.4 80.6 2.800 76.3 76.7 73.4 71.2 78.5 70.7 76.5 80.1 2.750 76.0 77.2 73.9 71.4 78.5 70.6 76.2 80.4 2.610 77.2 77.6 75.1 72.8 78.5 70.6 76.3 80.6 153 Stellenbosch University http://scholar.sun.ac.za Table 6.21: Sound data for three different fans at 1200 rpm Volume Flow Sound Pressure Level per Octave Band [dB] :':::'''[m3/s] 63HZ 125 Hz = .250 Hz 500 Hz 1000 Hz 2000 Hz 4000 Hz 8000 Hz General Application Fan 4.347 84.3 81.3 79.0 77.4 79.1 76.9 79.1 81.9 4.315 83.9 81.1 78.7 76.6 78.7 76.5 78.7 81.3 4.213 85.2 81.4 78.7 76.0 78.9 75.5 78.4 80.7 4.067 85.6 81.7 78.9 76.1 78.2 75.0 78.6 79.1 3.742 86.4 84.0 80.5 77.4 79.5 74.7 78.8 81.2 Low-noise Fan 3.713 82.2 83.0 79.1 76.1 76.7 73.6 74.1 81.0 3.660 84.2 82.1 78.7 76.2 76.2 73.5 74.3 80.8 3.563 84.7 82.1 78.6 75.7 77.2 73.4 73.9 82.2 3.409 85.1 82.3 79.1 75.8 76.8 72.7 73.2 80.7 3.146 86.1 83.9 80.5 77.6 76.7 72.4 73.7 80.2 Comparative Fan 2.923 84.7 85.1 82.6 78.5 81.7 77.4 81.8 84.6 2.919 84.2 84.7 82.1 79.0 80.5 77.5 81.6 84.1 154 Stellenbosch University http://scholar.sun.ac.za 10. 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G., Wright, T., "An Invlscid Low-solidity Cascade Design Routine", American Society of Mechanical Engineers (Paper), GT-162, 1993. Patterson, G. N., "Ducted Fans: Design for High Efficiency", Report ACA-7, Australian Council for Aeronautics, July 1944. Powell, M. 1. D., "A Fast Algorithm for Non-linearly Constrained Optimisation Calculations", Lecture Notes in Mathematics 630, Springer Verlag, Berlin, 1978. Sharland, 1. 1., "Sources of Noise in Axial Flow Fans", Journal of Sound and Vibration, Vol. I, Part 3, 1964. Shigley, J. E., "Mechanical Engineering Design", First Metric Edition, McGraw-Hili, Inc., 1986. Smith, L. H., Hsuan, Y., "Sweep and Dihedral Effects in Axial Flow Turbomachinery", Transactions of the ASME, Journal of Basic Engineering, Vol. 85, 1963. Smith, T. W., "A Practical Approach to the Design of Axial and Mixed Flow Fans", Industrial Fans - Aerodynamic Design, Instn. ofMech. Engrs., April 1987. Thwaites, B., "A Note on the Design of Ducted fans", The Aeronautical Quarterly, Vol. 3, November 1951. Tyler, 1. M., Sofrin, T. G., "Axial Flow Compressor Noise Studies", Society of Automotive Engineers Transactions, Vol. 70, 1962. Van der Spek, H. F., "Advanced Low Noise Cooling Fans", 9th Cooling Tower and Spraying Pond Symposium IAHR, Von Karmen Institute for Fluid Dynamics, Brussels, September 1994. Van der Spuy, S. 1., "Die antwerp van 'n Waaiertoetstonnel vir Klank- en Werkverrigtingmeting", Final Year Project, University of Stellenbosch, 1994. 158 Stellenbosch University http://scholar.sun.ac.za Van Niekerk, C. G., "antwerp van Waaiers met Hoe Rendement en Lae Lawaai-intensiteit", D. Sc. thesis, University of Pretoria, 1964. Venter, S. 1., "The Effectiveness of Axial Flow Fans in A-Frame Plenums", Ph.D. thesis, University of Stellenbosch, 1990. Von Backstrom, 1. W., Buys, J. D. and Stinnes, W. H., "Minimisation of the Exit Loss of a Rotor- Only Axial Fan", Eng. Opt., Vol. 26, 1996. Wallis, R. A., "Axial Flow Fans and Ducts", John Wiley & Sons, Inc., (1983 & 1961). Wallis, R. A., "The Development of Blade Sections for Axial Flow Fans", Instn. Engrs. Aus., Mechanical and Chemical Engineering Transactions, Nov. 1972. Wallis, R. A., "The F-series Airfoils for Fan Blade Sections", Instn. Engrs. Aus., Mechanical Engineering Transactions, 1977. Wright, S. E., "The Acoustic Spectrum of Axial Flow Machines", Journal of Sound and Vibration, Vol. 45, Part 2, 1976. Wright, 1., Ralston, S. A., "Computer-Aided Design of Axial Fans Using Small Computers", ASHRAE Transactions, Vol. 93, Part 2, 1987. Wright, 1., Simmons, W. E., "Blade Sweep for Low-Speed Axial Fans", American Society of Mechanical Engineers (Paper), GT -53, 1989. 159 1 Stellenbosch University http://scholar.sun.ac.za APPENDIX A: FAN LAY-OUT DESIGN A.I EXIT VELOCITY PROFILE The theory comprising the article of Von Backstrom et al. (1996) is described in this section. The method determines the optimum exit velocity profile by minimising the kinetic flux losses in varying the flow and pressure coefficient. As mentioned in Chapter 3, the model incorporated the following assumptions: 1. A uniform total pressure distribution across the fan inlet. 2. The Euler turbo-machinery equation is applicable. 3. Simple radial equilibrium applies in front of and behind the fan. 4. The flow is assumed to be incompressible and inviscid. The simplifications associated with the free vortex velocity distribution as well as its applications in practise was used as reference case in the article. The following dimensionless coefficients were used in the analysis: 1. Hub - tip ratio rv = --'-- ro 2. Pressure Coefficient PI r\jJ = 1-pU2 0 3. Flow Coefficient C.~=-Uo pU Co \\0 1_ pU 22 0 2C \\" U" AI (A 1) (A.2) (A3) Stellenbosch University http://scholar.sun.ac.za A.I.1 DESIGN LIMITATIONS The traditional fan design limitations were summarized as follows: 1. Backflow will occur at the hub if the swirl velocity at the hub is too high in relation to the throughflow velocity. Backflow is prevented by limiting the hub absolute exit flow angle to about 50?, which gives the limitation: \If < 2.2 x v x Ij> (A4) 2. The maximum flow deflection in cascades limits the stagnation pressure rise obtainable from a certain number of fan blades, resulting in a maximum hub absolute exit flow angle of 45?. The maximum exit flow angle gives a more stringent limitation than in equation (A4): \IJ<2.0xvxlj> (AS) 3. The last limitation reflects the basic operation of a fan where the rotor should not turn the flow beyond the axial direction. If this happens, that section of the fan will create a static pressure drop instead of a static pressure rise. The rotor hub is limited to a relative exit flow angle of 0? The limitation is given as: \If < 2.0 x VC (A6) The hub-tip ratio cannot exceed unity and therefore equation (A6) puts an absolute limit of 2 on the value of the pressure coefficient. Combining this limitation, the fact that the hub-tip ratio must be less than unity and equation (AS), another constraint is formed namely: Ij> < 1 (A 7) A2 Stellenbosch University http://scholar.sun.ac.za A.1.2 MINIMISATION FORMULATION The velocity profiles were obtained by minimising the integral for kinetic energy flux at the fan outlet. The kinetic energy flux is given by: ro L = 7t x P x f r. C?. (C. 2 + C" 2 ).dr n By non-dimensionalising as follows: t=r/r , a = r / r. () , u( t) = C w (r, x t) / (r, x n) v( t) = C a (r, x t) / (r, X n) equation (A8) is simplified to: F = L/ (7t x P x r5 x n3 ) ro = f Y. (Y: + u:). t. dt n The following constraints applied to this functional (equation (A 13?: I) Radial Equilibrium (A8) (A9) (AlO) (All) (AI2) (A.13) n x [_d(_C,,_o._r)]= _C" x [_d(_C,_,._r)]+ C dr r dr ? du u2 du dv=>tx-+u=-+ux-+vx-dt t dt dt A3 dC.x-dr (A.14 ) Stellenbosch University http://scholar.sun.ac.za 2) Dimensionless Work Rate A= I ro, 02 x r.~ f C. C?. C w ? dr I n ? = f e. U. V. dt I = Wo/(2 x 7l: x P x ri~x 03) where ro W 0 = 2 x 7l: x P x 0 x f r 2 . C ?. C w ? dr ri 3) Dimensionless Flow Rate: B = I TOo x r3 f r. Ca' dr I ri ?= f t. v. dt I = ~/( 2 x 7l: X P X ri3 X 0) where ? '0 m = 2 x 7l: X P x f r. Ca' dr n (A.15) (A.16) The values for A, B and a were obtained from the free vortex theory as follows: a = 1/Y A = \(f x

, \jJ and v (equations (AI) to (A3)) equation (A.37) simplifies to: PK I cae a U 0 Cwo I ( 1)-=-x-x-x-+-x 2 xln-Ps 2 U 0 U 0 Cwo U 0 (I - v ) V f \jJ I (I)= - + - X ( ) X In - \jJ 2 I - v2 V Equation (A35) was simplified in a similar way: ( f \jJ I JTls= Tlr--;-+2x(I_v2)xln(v) (A39) Using the maximum allowable value for the pressure coefficient according to equation (A5), equation (A39) was simplified to: ( Q> v X Q> JTls = Tlr - - + ( 2) X In( v)2xv I-v The relation between flow coefficient and hub-tip ratio is as follows: Q Q> = ? ( ')U 0 X 7T: x fo- x I - v- _ K1-Fv2) where K = Q 1 U 'x 7T: x f-o 0 Inserting equation (A41) into equation (A40): ( K] v X K1 In()JTls = Tlr - 2 x v x (I _ v2) + (1 _ v2r x v A9 (A40) (A.41) (A42) (A43) Stellenbosch University http://scholar.sun.ac.za In order to obtain the hub-tip ratio for maximum static efficiency, the derivative of equation (A.43) with respect to v must be calculated: d -K x (1 - 3v2) ~ =] , + K] dv 2x(v-v3)- x [2 x (1 - v2) + ,8 3X v2 J In(~) 4x(I-v-) v K] (1 - v2f (A.44) Setting equation (A.44) equal to zero and solving v, a hub-tip ratio was obtained that maximises the static efficiency. The value for K] cancels out when one sets equation (A.44) equal to zero. AIO Stellenbosch University http://scholar.sun.ac.za APPENDIX B: FAN BLADE DESJGN CALCULATIONS With the advantage of hindsight, the data used in the calculations will be for the 1000/250/7/1440 fan configuration. This corresponds to the design configuration used to design the general application fan. The 1000/250/14/1440 fan configuration data will be used for the swept blade design calculations. B.I CALCULATION OF FAN EXIT VELOCITY PROFILE The equations from the article described in Appendix A, Section A 1 were used for the calculations in this section. 8.1.1 CHOOSING THE VALUES FOR a, A AND B The values for v, and \jJ were calculated (see equations (AI) to (A3)) using the values obtained from the data sheets of a comparative fan series from HAl (see Section 4.1.1). The value for was calculated from the data for the 1000/250/7/1440 fan as follows: Q = Qrna, 2 20.8= 2 = I 0.4 m~/s Q = 2 x 1! x rpm / 60 = 2 x 1! x 1440/60 = 150.796 m/s 81 ( 8.1) (8.2) Stellenbosch University http://scholar.sun.ac.za This gave: c.~=- u" Q (n x (r,,2 - rn) n x r" _ 10.4 (n x (0.52 - 0.1252)) 150.796 x 0.5 = 0.19 where Qmax = 20.8 m3/s ro = 0.5 m rj=0.125m rpm = 1440 rpm (8.3) (8.4 ) The value for \jl was calculated ITom the value for fan shaft power ITom the data sheets. A rotor efficiency of 85 % and a mechanical efficiency of 90 % were assumed. This gave a total efficiency of 76.5 %. The fan shaft power was calculated as follows: P x 11P = s 11 f 5700 x 0.765 10.4 = 419.28 Pa This gave: 2Pl f \jf = -U2P X 0 2 x 419.28 - 1.2 x 75.3982 = 0.12 where p = 1.2 kg/m3 Ps=5700W 82 (8.5) Stellenbosch University http://scholar.sun.ac.za The value for hub-tip ratio was calculated as: r.v=-'- ro 0.125-- 0.5 = 0.25 (B.6) The values for