Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

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xii Preface to the Fifth Edition The opportunity has been taken to add some new information about the fluid mechanics <strong>of</strong> turbomachinery where appropriate as well as including various corrections to the fourth edition, in particular to the section on backswept vanes <strong>of</strong> centrifugal compressors. S.L.D.
Page 2: Fluid Mechanics, Thermodynamics of
Page 6: Preface to the Fifth Edition In the
Page 12: xiv Preface to the Fourth Edition i
Page 16: Acknowledgements The author is inde
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 52: Introduction: Dimensional Analysis:
Page 56: (1.7a) (1.7b) (1.7c) It is a simple
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Introduction: Dimensional Analysis:
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for pumps, and (1.12b) for turbines
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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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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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