Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

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List of Symbols A area A2 area of actuator disc a sonic velocity, position of maximum camber a – axial-flow induction factor a¢ tangential flow coefficient b passage width, maximum camber Cc chordwise force coefficient Cf tangential force coefficient CL, CD lift and drag coefficients CP power coefficient Cp specific heat at constant pressure, pressure coefficient, pressure rise coefficient Cpi ideal pressure rise coefficient Cv specific heat at constant volume CX, CY axial and tangential force coefficients c absolute velocity co spouting velocity D drag force, diameter Deq equivalent diffusion ratio Dh hydraulic mean diameter E, e energy, specific energy F Prandtl correction factor Fc centrifugal force in blade f acceleration, friction factor g gravitational acceleration H head, blade height HE effective head Hf head loss fue to friction HG gross head HS net positive suction head (NPSH) h specific enthalpy I rothalpy i incidence angle J tip–speed ratio j local blade–speed ratio K, k constants KN nozzle velocity coefficient L lift force, length of diffuser wall l blade chord length, pipe length xix
Page 2: Fluid Mechanics, Thermodynamics of
Page 6: Preface to the Fifth Edition In the
Page 10: Preface to the Fourth Edition It is
Page 14: Preface to Third Edition Several mo
Page 20: xx List of Symbols M Mach number m
Page 24: xxii List of Symbols x, y, z cartes
Page 28: vi Contents 3. Two-dimensional Casc
Page 32: viii Contents Inlet velocity limita
Page 36: CHAPTER 1 Introduction: Dimensional
Page 40: this context refers to the directio
Page 44: Introduction: Dimensional Analysis:
Page 48: which is frequently used is the vel
Page 56: (1.7a) (1.7b) (1.7c) It is a simple
Page 64: for pumps, and (1.12b) for turbines
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Introduction: Dimensional Analysis:
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p 02 p 01 1.0 Figures 1.10 and 1.11
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Direction of blade motion (a) outle
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Introduction: Dimensional Analysis:
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Basic Thermodynamics, Fluid Mechani
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Considering a system of mass m, the
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Euler’s pump and turbine equation
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If the process is adiabatic, dQ . =
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quite high and the corresponding ki
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C p (dT/ds) = T for a constant pres
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eheat factor RH as a measure of the
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(a) (b) Basic Thermodynamics, Fluid
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Flow R1 r t1 1 Basic Thermodynamics
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A 2/A 1-1 total pressure balance th
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Problems Basic Thermodynamics, Flui
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cascade is then a reasonable model
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following analysis the fluid is ass
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Experimental data are often present
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Efficiency of a compressor cascade
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Two-dimensional Cascades 65 applied
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1 ( 8 in) Two-dimensional Cascades
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There is a fundamental difference b
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midpoint of the working range or, l
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Two-dimensional Cascades 73 FIG. 3.
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atios are a possibility. The space-
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EXAMPLE 3.3. At the midspan of a pr
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where B = 0.5 for a plain tip clear
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Two-dimensional Cascades 89 The ear
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Two-dimensional Cascades 91 Dowden,
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along the chord to the point of max
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The continuity equation for uniform
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Stage losses and efficiency In Chap
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Axial-flow Turbines: Two-dimensiona
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With DW, U and cx fixed the only re
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or (4.22b) after using eqn. (4.21).
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have a dramatic increase in blade p
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Correcting for aspect ratio with eq
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maximum value of h tt decreases as
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Stage loading coefficient, y =DW/U
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Maximum total-to-static efficiency
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Calculations of turbine stage perfo
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For blades with a constant cross-se
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life” and also the “percentage
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(i) the rotational speed, (ii) the
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decrease with the addition of furth
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Combined with p/r = RT the above ex
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Oscillating air flow Oscillating ai
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concentric elementary rings, each r
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and also blade thickness ratio, tur
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hub-tip ratio, u 1.0 0.8 0.6 0.4 0.
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C t (a) C P (b) 2.5 2.0 1.5 1.0 0.5
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U R c x U R a w Axial-flow Turbines
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arrangements. Also, a full-scale 1.
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CHAPTER 5 Axial-flow Compressors an
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Axial-flow Compressors and Fans 147
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of diffusion of kinetic energy in t
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Reaction ratio For the case of inco
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where tanbm = 1 - 2 (tan b1 + tan b
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Stage pressure rise Consider first
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It is reasonable to take the stage
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Axial-flow Compressors and Fans 159
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(ii) At the operating point i = 0.4
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Flow Axial-flow Compressors and Fan
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Rotating stall and surge Axial-flow
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Tests on low pressure ratio compres
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used. This method can be of use in
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The torque exerted by one blade ele
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Lift coefficient of a fan aerofoil
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(i) a relative Mach number of 0.7 o
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CHAPTER 6 Three-dimensional Flows i
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therefore, The thermodynamic relati
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In Chapter 5, reaction in an axial
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vantage is the large amount of roto
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Assuming constant stagnation enthal
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where In the above example, 1 - a/W
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therefore (6.24) For this free-vort
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After differentiating the last term
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(6.38) after combining with eqn. (6
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Three-dimensional Flows in Axial Tu
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velocity undergoes an abrupt change
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adding these to the related radial
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References Adamczyk, J. J. (2000).
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and the axial velocity is constant
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engine turbochargers, chemical plan
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Centrifugal Pumps, Fans and Compres
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or since Since I1 = I2 across the i
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For the inlet geometry shown in Fig
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The required diameter of the eye is
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(Mr1) = mW 2 /(p k p 01 a01 3 ) ·
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(iii) Use of prewhirl at entry to i
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(7.13a) where cq2 is the tangential
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(number of blades). He also found t
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Determining the velocities and head
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efficiencies seldom exceeded 80% gi
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efficiently converting this energy
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Therefore Hence, The diffuser syste
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Dq (deg) 240 160 80 Centrifugal Pum
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(7.41) If choking occurs in the rot
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Van den Braembussche, R. (1985). De
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Assuming that the hydraulic efficie
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Radial Flow Gas Turbines 247 FIG. 8
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Basic design of the rotor Radial Fl
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Radial Flow Gas Turbines 253 (8.9)
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Thus, the total-to-static efficienc
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Now, Loss coefficients in 90deg IFR
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P S P S c 2 Direction of rotation (
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and, combining this with eqns. (8.2
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(ii) Rewriting eqn. (8.26), (iii) U
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Thus, combining eqns. (8.39) and (8
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U 2/c o 0.8 0.7 0.6 88 Radial Flow
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(a) the static pressure at rotor ex
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(a) (2) (1) w 2 b2 ¢ w 2 ¢ b2, op
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Radial Flow Gas Turbines 273 This e
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Radial Flow Gas Turbines 279 occurs
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(a) f = 0.83 a 0 = q 0 U 0 = -7.18
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Measured performance Radial Flow Ga
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Radial Flow Gas Turbines 287 Whitfi
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Radial Flow Gas Turbines 289 Absolu
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Hydraulic Turbines 291 TABLE 9.1. D
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TABLE 9.3. Operating ranges of hydr
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Hydraulic Turbines 295 ridge splits
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Hydraulic Turbines 297 (9.3) (9.4)
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Hydraulic Turbines 299 FIG. 9.8. Me
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Hydraulic Turbines 301 (9.10) The e
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Neglecting bearing and windage loss
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Hydraulic Turbines 305 Figure 9.12
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Hydraulic Turbines 307 It is of int
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Hydraulic Turbines 309 constant. Th
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(a) (b) Hydraulic Turbines 311 FIG.
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TABLE 9.4. Calculated values of flo
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Hydraulic Turbines 315 gave measure
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Hydraulic Turbines 317 using Thoma
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Avoiding cavitation Hydraulic Turbi
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Hydraulic Turbines 321 nozzles. The
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CHAPTER 10 Wind Turbines Take care
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FIG. 10.2. Tower Windmill, Bidston,
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Brake discs Flexible coupling Build
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Small HAWTs Small wind turbines wit
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(iii) no flow rotation produced by
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It is convenient to define an axial
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Example 10.2. Determine the radii o
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where a - T = 0.3262. Sharpe (1990)
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each element must have an associate
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In the actuator disc analysis the v
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operate in post-stall conditions wh
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Solving the equations The foregoing
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Pitch angle, b (deg) 30 20 10 0 0.2
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TABLE 10.4. Data used for summing t
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F 1.0 0.8 0.6 0.4 0.2 0 0.4 dX = 4
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TABLE 10.5. Summary of results for
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Power coefficient, C P 0.6 0.4 0.2
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C X/(JC L) 0.14 0.12 0.10 0.08 0.06
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The flow angle j at optimum power c
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R 1 2 3 8 3 CP = P ( prR cx )= ( -a
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caused by this increased roughness
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Airfoil S820 S819 r/R 0.95 0.75 pro
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Airfoil S817 S816 r/R 0.95 0.75 NRE
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C C 0.4 0.2 -0 -0.2 -0.4 -0.6 twist
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According to Tangler (2002), some l
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understanding of the complex phenom
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References Wind Turbines 375 Abbott
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Bibliography Cumpsty, N. A. (1989).
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APPENDIX 2 Answers to Problems Chap
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Chapter 8 1. 586 m/s, 73.75 deg. 2.
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Index Terms Links Axial flow compre
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Index Terms Links Cascades, two-dim
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Index Terms Links Coefficient of, c
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Index Terms Links Diffusers (Cont.)
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Index Terms Links Francis turbine 2
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Index Terms Links Illustrative exam
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Index Terms Links Mollier diagram,
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Index Terms Links Pressure head 4 P
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Index Terms Links Rotor configurati
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Index Terms Links Thoma’s coeffic
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Index Terms Links U Units Imperial
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Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

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