Lewis R.I. Turbomachinery Performance Analysis

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Index

Actuator disc theory, 124--6,

158--62

analysis of single rotor axial

fan, 126-33

analytical solutions, 158-62

compressible flow, 162-78

density discontinuity, 170

meridional perturbation

growth, 126

mixed-flow fan, 157-8

mixed vortex rotor, 129-33

model of blade row, 125

multiple blade rows, 133-42

power law loading, 140-2

solid body swirl stator, 128

source actuator disc, 167-9

AD-ANAL.PAS (PC source code

on disc), 128

AD-DES.PAS (PC source code

on disc), 128

Advance coefficient (ducted

propeller), 227, 240-3

Aerodynamic forces, 25, 193

Aerofoil theory, Martensen's

method, 255

AEROFOIL.PAS (PC source

code on disc), 259, 260, 261

Annular aerofoil (or cowl),

268-70

Annulus geometry, 187-91, 280,

281

Aspect ratio, 66

Axial fan radial equilibrium

single rotor direct analysis,

121-4

Axial flow pumps, fans and

compressors, 16-20, 82-106,

108

Axial velocity profile

actuator disc, 125-7, 135,

139-41

compressible actuator disc,

169-78

radial equilibrium, 108, 114-24

smeared actuator discs, 178

Axisymmetric flow

Martensen's equation, 267

past annular aerofoil or engine

cowl, 268-70

past body of revolution, 266-8

past ducted propeller, 270-3

AXISYM.PAS (PC source code

on disc), 268

Back-diagonal correction (in

Martensen's method), 256

Base profiles, 33-4, 301-3

Blade pitch angle (propellers),

244

Blade row interference, 133,

138-9

BLADEROW.PAS (PC source

code on disc), 260-1, 265,

266

Blade-speed ratio, 80

Blade stacking, 23, 291,311-15

Blade-to-blade flow, 21-2

Bound circulation, 125, 219,

256-9

Boundary layer

momentum thickness, 41-3

surface vorticity equivalent,

246

Buckingham's 7r-theorem, 9, 11,

Camber line, 33, 291

position of maximum camber,

35,293

Carry-over kinetic energy, 76

CASCADE (PC executable code

on disc), 22, 30, 33-4, 37,

99-100, 104, 125, 133,

245-6, 259--60, 265-6

user instructions, Appendix II,

288-308

Cascade

fan and compressor, 25

flow, 21, 22

geometry, 25

Cascade dynamics, 24-9

lift and drag coefficients, 25

loss coefficient, 28, 39

Centrifugal pump or compressor,

9-15, 18-19, 184, 202-10

Characteristic curves

axial fan, 105--6

centrifugal impeller, 204-10

Kort nozzle ducted propeller,

237-43

pump, 11-13

Circular cylinder flow, 253-4

Circulation, 247, 255

Compressible actuator disc,

162-78

Compressor cascade

diffusion factor, 40-3

optimum incidence, 37, 40,

99-100

role as a diffuser, 30-2

CONSTWK.PAS (PC source

code on disc), 137

Continuity equation, 5, 145

Control volume

cascade, 24-5

mixed-flow fan, 5

Convection of

angular momentum, 153

smoke-ring vorticity, 155--6

stagnation pressure, 152

streamwise vorticity, 154-5

vortex sheet, 247, 249-50

Cordier diagram, 16-18

Coriolis acceleration and force,

182-4, 193

Coupling coefficients

(Martensen's)

axisymmetric flow, 267-8

cascade, 262

plane flow, 250-3

Craig and Cox axial turbine

correlation, 78

Curvilinear meridional

coordinates, 163

CYLINDER.PAS (PC source

code on disc), 254

Deflection, influence on losses,

66, 67

Deviation angle, 45, 46

326 Index

Diffuser efficiency, 29

Diffusion factors (Lieblein), 32,

40-3

axial compressors, 93, 98-9

axial fans, 103

Dimensional analysis

axial compressors, 86--8

centrifugal pump, 8-20

ducted propellers, 220-37

mixed-flow fans and pumps,

187-93

single turbine stage, 48-54

Dimensionless velocity triangles

axial compressors, 84-5, 87,

axial fans, 103

axial turbine, 58-9, 69

mixed-flow fans, 191-2

zero inter-stage swirl turbine,

77-9

Direct (analysis) method, 33-5

Drag force and coefficient, 25,

27, 92-3

Duct (annular aerofoil) frictional

loss, 226, 233--4

Ducted propellers, 270-3

DUCT.PAS (PC source code on

disc), 269

DUCTPROP.PAS (PC source

code on disc), 270, 272-3

Duty coefficients

axial compressor, 85, 87

axial fan (free-vortex type),

109

centrifugal impeller, 204

open propeller, 216

Duty point (4', $)

compressor, 83

turbine, 61, 65, 275

Dynamic similarity, 10-13

Efficiency contours (prediction),

72, 75, 79

Elementary turbines, 194

Engine cowl, 268-70

Euler pump equation, 7, 85, 96,

182

Euler turbine equation, 8

FIPSl (PC executable code on

disc), 47-8, 245

user instructions, Appendix I,

275-87

First law of thermodynamics, 6

Flow coefficient

axial compressor, 83

axial turbine, 52, 275

centrifugal impeller, 203

mixed-flow fan, 188

pump, 19

Francis turbine, 186, 194

Free-vortex

axial fan, 108-12, 131-2

axial turbine, 73-4, 275

ducted propeller, 228-30, 233

FVFAN.PAS (PC source code on

disc), 112

Global performance variables, 8,

Governing equations for

compressible actuator discs,

164-5, 169-77

meridional flow, 144, 150-4

source actuator discs, 166--9

Head coefficient (for a pump),

Impulse turbine stages, 72

Incidence angle, 38

Inducer section, 184

Inlet guide vanes, 84, 114

constant swirl, 117-18, 120

free-vortex, 117

Inverse (design) method, 35-7

Jet kinetic energy (downstream

of a propulsor), 214, 221

Jet wake velocity

ducted propeller, 221

open propeller, 212-14

Kelvin's theorem, 156

Kinetic energy coefficients (S. F.

Smith), 63

Kort nozzle ducted propeller,

218-19

Kutta-Joukowski trailing edge

condition, 255, 258, 269

Lift/drag ratio, 29

Lift force, coefficient

axial compressor, 91, 92

cascade, 25, 27-8

Lifting aerofoil theory, 255-60

Loading coefficient, 227

Local performance variables

pumps, 9

turbines, 47

Logarithmic-spiralled blades,

205-6

Loss coefficients

axial fan or compressor, 87-8

axial turbine, 52, 65

mixed-flow fan, 188-9

Loss weighting coefficients

axial compressor, 89

axial turbine, 64-5

ducted propeller, 234

mixed-flow fan, 189-91

Mach number, 60, 87

MAGNUS.PAS (PC source code

on disc), 257

Martensen's equation

axisymmetric flow, 267

ducted propellers, 270

plane flows, 251

Martensen's method for

potential flow analysis,

247-55

Meridional disturbances, 150

Meridional flow, 7, 21, 107-42,

143-78, 180

Meridional section

axial compressor, 83

Francis turbine, 195

mixed-flow fan, 186

Meridional streamline or stream

surface, 7-8, 21

axial fan, 108

mixed-flow fan, 143, 187

radial shift, 183-4

Mixed-flow cascades, 194-200

Mixed-flow pumps and fans, 7,

17-20, 157, 179-210, 186

Mixed-vortex fan, 129-33

Model compressor stage, 84

arbitrary reaction, 95-9

50% reaction, 85, 88, 89

Model turbine stage

experimental correlation (S. F.

Smith), 48, 60-3, 279

theoretical correlations, 62-8

Momentum equations,

axisymmetric flow

Eulerian form, 145-7

vorticity form, 147-8

MULTI.PAS (PC source code on

disc), 136, 138, 140-1

Newton's laws

applied to cascade, 27

applied to propulsor, 212

applied to pump rotor, 6

Nominal conditions for

compressor cascades

(Howell), 44--6

One-dimensional analysis for

propulsors

ducted propellers, 212-17,

220-2

open propellers, 212-17

Optimum axial turbine and

compressor stages, 91

Optimum blade profile

geometry, 99-101,299

Optimum ($, $) duty

axial turbines, 63-6, 71, 79-80

mixed-flow pumps and fans,

180-1

Optimum incidence, 37, 40

Optimum pitch/chord ratio

compressor cascade, 43-5

Index

327

Optimum reaction, axial

turbines, 70-1

Pitch/chord ratio selection

axial compressor, 93, 99

axial fan, 103

mixed-flow fan, 198

open propeller, 218

Power-law vortex

axial fan, 140

ducted propeller, 229-33

Profile (blade)

construction, 33, 291,311-15

base profiles, 33-4, 291,301-3

Propeller (ducted)

detailed losses, 226-36

downstream jet velocity, 221

propeller plane velocity, 220,

222, 224

propulsive power and

efficiency, 221-2

thrust coefficient, 221

thrust ratio, 220

wake kinetic energy losses Ew,

221

Propeller frictional loss, 226,

231-3

Propeller (open)

actuator disc model, 213

downstream jet velocity, 212,

215

duty coefficients ~b, ~k, 216

pitch/chord ratio, 218

propulsive thrust, power and

efficiency, 213-14

thrust coefficient, 214, 216-17

velocity triangles, 215-16

wake kinetic energy losses Ew,

214

Propulsive efficiency

ducted propeller, 221-2, 226,

242

open propeller, 214-15

Propulsive power

ducted propeller, 221

open propeller, 214

Pump jet, 218-19

PVD method, 35-7

Radial cascades, 199-200

Radial equilibrium

analysis, 112-24

direct problem, 114, 118-24

downstream of a rotor, 121-4

downstream of a stator,

119-20

inverse problem, 114-18

radial equilibrium equation,

113-14, 149

Radial momentum equation, 149

Radial turbomachines, 179-210

Reaction

arbitrary reaction axial

compressor, 95-9

arbitrary reaction axial

turbine, 68--72

axial fans, 102

axial turbine, 51

50% reaction axial

compressor, 85-95

50% reaction axial turbine,

55-60

variation with radius, axial

fans, 109-10

variation with radius, axial

turbine, 72-5

RE-ANAL.PAS (PC source code

on disc), 124

RE-DES.PAS (PC source code

on disc), 117-19, 124

Relative eddy, 184, 200-3

Reynolds number

axial compressors, 87-8

axial turbine stator and rotor,

machine Reynolds number,

14-15, 52, 87, 188

mixed-flow fan, 188

Rothalpy, 185-7

Selection of pumps and fans,

15-20, 180-1

Shock-free inflow, 37-8, 264-5

axial compressor blade rows,

99-101,299-301

Shut-off head, centrifugal

impellers, 205-8

SI units, 12

Slip factors

Busemann analysis 202, 205-6

definition, 201, 203

Lewis & Fisher analysis, 202,

206, 209

shut-off head slip factor, 204-5

Stanitz analysis, 202

Stodola analysis, 208-9

Slip flow, 184, 201,203, 208

Slipstream contraction,

propulsor, 212-18

Smeared actuator discs, 178

Smith charts

axial compressors, 90, 102

axial turbines, 62, 279

Smoke-ring vorticity, 154-8

Soderberg's loss correlation,

66-8, 72, 75, 79

Solid body swirl, 114

Specific speed and diameter, 15,

18-20, 180-1

Specific work, origins of, 182-4

Speed of sound, 51

STACK (PC executable code on

disc), 245, 265

user instructions, Appendix

III, 309-19

Stage losses

axial compressor, 88-9, 98

axial turbine, 55, 65, 70-71,

79-80

Stagger

axial cascade, 25, 38, 46

mixed-flow cascade, 198

Stagnation enthalpy, 6

Stagnation point, 31, 38

Stagnation pressure, 6, 26

losses, 55

rise in fans and compressors,

89, 109

Stall and stall margin, 40

Steady flow energy equation, 6,

7, 29

Stokes

equation, 152

stream function, 150

Streamline efficiency, 75-6

mass weighted, 76

Streamwise vorticity, 154-8

Sub-layer, 247

Surface pressure coefficient, 30

Surface vorticity model, 246-53

aerofoils, 255-60

axisymmetric flow, 265-9

cascades, 260-5

ducted propellers, 270-4

plane two-dimensional flow

246-55

Swept back impellers, 203-8

Swirl kinetic energy loss, ducted

propulsor, 226-31

S1, $2 Wu surfaces, 22, 24

Tangential vorticity in

axisymmetric flow, 149, 151,

153-6

Thrust, thrust coefficient

ducted propeller, 220-1

open propeller, 213-14, 217

Thrust ratio, ducted propellers,

220

Tip leakage losses, 226, 234-6

Torque coefficient, ducted

propellers, 227

Total-to-total efficiency

axial compressor, 86, 88-9, 98

axial fans, 103

axial turbines, 50, 52, 54--5

mixed-flow fans, 188-9

prediction for axial turbines,

64, 68, 70, 72, 75

zero interstage swirl turbines,

Transformation of mixed-flow

cascade to straight cascade,

196-200

328

Index

Turbine stages

arbitrary reaction, 68-72

50% reaction, 55--60

Vector mean angle and velocity,

25, 263-4

Velocity coefficient, ducted

propellers, 227

Velocity ratio or blade/speed

ratio, 80

Velocity transformation for

axial fan, 102

axial turbine, 50, 56, 58, 69,

279

cascade, 25

mixed-flow fans and pumps,

187, 191

open or ducted propeller, 216

zero interstage swirl turbine,

Vortex, potential, 109-10

Vortex array, 262-3

mixed-flow cascades, 199-200 Vortex shedding

Velocity triangles propeller blade, 235

axial compressor, arbitrary stator, 125,. 156

reaction, 96-9 Vorticity components in

axial compressor, 50% axisymmetric flow, 148

reaction, 84 Vorticity production in

axisymmetric flow, 143-58,

154

streamwise and smoke-ring

vorticity, 155-8

Wake kinetic energy loss

ducted propeller, 221, 226-31

open propeller, 214

Work coefficient

axial compressor, 83

axial turbine, 53, 275

centrifugal impeller, 204

mixed-flow fan, 188

pump, 19

Zero interstage swirl axial

turbines, 76-81

Authors' index

Abbott, I.H., 28, 33

Ackeret, J., 34

Anderson, A., 3

Balabaskaran, V., 244, 273, 274

Batchelor, G.K., 197, 199, 237,

253

Bragg, S.L., 158

Broderick, R.L., 40

Busemann, A., 200, 202, 205,

207

Casey, M.V., 90

Cheng, K.Y., 35

Cordier, O., 16, 180

Cox, H.J.A., 79

Craig, H.R.M., 79

Csanady, G.T., 16, 17

Cumpsty, N., 2, 39

Denton, J.D., 23

Dixon, S.L., 2, 29, 30

Dwight, H.B., 171

Ellis, G.O., 209

ESDU, 17, 20, 179

Fisher, E.H., 205, 206, 209

Frost, T.H., xiv

Gibson, I.S., 270, 271

Glover, E.J., 218, 270, 271

Gostelow, J.P., 2, 39

Hawthorne, W.R., 47, 66, 158,

162, 171

Hess, J.L., 270

Hesselgreaves, J.E., 235

Hildebrand, F.B., 160

Hill, V.P., 269

Horlock, J.H., 2, 30, 39, 44, 47,

66, 125, 133, 158, 162, 166,

168, 178

Howell, A.R., 29, 44, 45

Jacob, K., 256

Kearton, W.J., 76, 80

Kerwin, J.E., 218

Lamb, H., 148, 268

Lee, Chang-Sup., 218

Lewis, R.I., 2, 35, 63, 162,

178, 196, 200, 205, 209,

223, 237, 246, 252, 270, 273

Lieblein, S., 32, 40, 41, 42, 43,

102

Maass, D., 218, 269

Marsh, H., 23

Martensen, E., 248, 249, 251,

267, 270

Massey, B.S., 5, 9

Mayhew, Y.R., 6, 55

Oosterveld, M.W.C., 223, 236,

271,273

Pien, P.C., 218

Potts, I., 3, 23

Railly, J.W., 35

Riegels, F.W., 28, 33, 256

Ringrose, J., 162, 171

Rogers, G.F.C., 6, 55

Roudebush, W.H., 40

Ryan, P.G., 268, 270, 271

Saviolakis, A., 206

Schwenk, F.C., 40

Shepherd, D.G., 9

Smith, A.M.O., 270

Smith, S.F., 2, 3, 47, 48, 60, 61,

62, 63, 79

Soderberg, C.R., 66, 72, 75

Stanitz, J.D., 202, 209, 210

Stodola, A., 208, 209

Stratford, B.S., 36

Traupel, W., 260

Van Manen, J.D., 223, 236,

241,244, 271,273

Von Doenhoff, A.E., 28, 33

Weissinger, J., 218, 269

Wilkinson, D.H., 35

Wu, Chung-Hua, 21, 23, 24

Young, L., 197