Handbook of Turbomachinery Second Edition Revised - Ventech!

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The density can now be determined: r 2 ¼ 44:1lbf =in 2 3 53:34 144 in2 ft 2 ft lbf lbm R ð564:2RÞ and the required flow area: A2 ¼ 1:798 lbm=sec ¼ 0:0703 lbm ft 3 ð0:0703 lbm=ft 3 Þð535:0ft=secÞ 144 in:2 ft 2 ¼ 6:882 in:2 The rotor exit hub and tip radii cannot be uniquely determined until either shaft speed, blade height, or hub-to-tip radius ratio is specified. Once one parameter is specified, the others are determined. For this example, we choose a hub-to-tip ratio of 0.7 as a compromise between performance and manufacturability. If the turbine shaft speed were restricted to a certain value or range of values, it would make more sense to specify the shaft speed. The turbine tip radius is determined from ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A2 rt2 ¼ p½1 ðrh=rtÞ 2 s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 6:882 in: ¼ Š 2 p½1 ð0:7Þ 2 s ¼ 2:073 in: Š This results in a hub radius of 1.451 in., a mean radius of 1.762 in. and a blade height of 0.622 in. The shaft speed is found from Eq. (8): o ¼ Um=rm ¼ 891:6ft=sec ¼ 6073 rad=sec ð1:762 inÞð1ft=12 inÞ or 57,600 rpm. The tip speed of the turbine is 1,049 ft/sec, well within our guidelines. The next step is to calculate the overall efficiency. From Smith’s chart, a stator inlet to rotor exit total-to-total efficiency at zero clearance is available. We must correct this for tip clearance effects, the inlet loss, and the exit kinetic energy loss. At l ¼ 1:3 and f ¼ 0:6, Smith’s chart predicts Z 0 0 2 0 ZC ¼ 0:94 Assuming a tip clearance of 0.015 in., the total-to-total efficiency including the tip clearance loss is calculated from Eq. (55) using a value of 2 for Kc: Z 0 0 2 0 ¼ðZ 0 0 2 0 ZCÞ 1 2 rt rm d h 2:073 0:015 ¼ 0:94 1 2 1:762 0:622 ¼ 0:8867 Equation (56) is used to determine the overall efficiency including inlet and exit losses. From the problem statement, we know that the overall pressure Copyright © 2003 Marcel Dekker, Inc.
atio ðp 0 in =pdisÞ is 3. The stator inlet to rotor exit total-to-total pressure ratio is calculated from p0 2 p0 0 ¼ pdis p 0 in p 0 2 pdis p 0 in p 0 0 Based on earlier discussions, we assume an inlet total pressure loss ratio of 0.99. With no diffuser, the discharge and rotor exit stations are the same, so the ratio of static to total pressure is found from the rotor exit Mach number: pdis p 0 2 ¼ p2 p0 ¼ 1 2 " # g g 1 g þ 1 V2 acr2 2 g 1 ¼ 1 " # 2 3:5 ¼ 0:8652 1 6 535 1085 We can now calculate the total-to-total pressure ratio from stator inlet to rotor exit and the overall efficiency: and p0 2 p0 0 ¼ 1 3 1 0:8652 1 0:99 1 3 ¼ 0:3891 1 ð0:3891Þ0:4=1:4 ZOA ¼ð0:8867Þ ¼ 0:7779 0:4=1:4 1 This completes the first iteration on the turbine size and performance for the case without a diffuser. To improve the accuracy of the result, the preceding calculations would be repeated using the new values of overall efficiency and tip clearance loss. Turbine with Diffuser For an auxiliary type of turbine such as this, a diffuser recovery of 0.4 is reasonable to expect with a well-designed diffuser. The rotor exit total pressure is calculated from the definition of diffuser recovery given in Eq. (35): p 0 2 ¼ pdis Rpð1 p2=p0 2Þþp2=p0 2 ¼ and the rotor exit static pressure is p2 ¼ð15:99 psiaÞð0:8652Þ ¼13:84 psia Copyright © 2003 Marcel Dekker, Inc. 44:1 psia=3 ¼ 15:99 psia 0:4ð1 0:8652Þþ0:8652
Page 1 and 2:
D E K K E R Handbook of Turbomachin
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MECHANICAL ENGINEERING A Series of
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61 Computer-Aided Simulation in Rai
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127 Designing for Product Sound Qua
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Preface to the Second Edition The o
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Preface to the Second Edition Prefa
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Contributors Nathan G. Adams The Bo
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1 Introduction Earl Logan, Jr.*, an
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HISTORICAL BACKGROUND Earl Logan, J
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MECHANICAL AND THERMAL DESIGN CONSI
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Figure 1 Cross-section showing the
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Figure 2 Turboprop engine, TPE 331-
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Figure 4 Auxiliary power unit, APU1
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Durability. The mechanical and ther
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with time during flight. Such a typ
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experience and existing similar des
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adverse pressure gradient against w
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and its attachments. A substantial
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Figure 9 Typical high-pressure turb
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and the measurement of local heat-t
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due to cyclic operation. In additio
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the steady and transient conditions
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Table 3(a) Steps in a Three-Dimensi
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Figure 16 Schematic Goodman diagram
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occur due to particles of unburned
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pressures at critical points. These
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1. Ceramics are subject to ‘‘in
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with Transient Tests and Surface Co
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Overall engine performance goals tr
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Much of the complexity of turbomach
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End-wall boundary layers can also h
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pressure at the wake centerline. Th
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the same vaneless diffuser and shro
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from internal cooling passages, thr
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Further downstream, the wake was ev
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to its original position. This unst
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cooling film was found to trip the
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shroud static pressure and the exit
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stage in the design process allows
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Flow Physics Modeling Modeling of t
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passage to the next, assuming that
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The next step in modeling accuracy
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tend to be large, due to the necess
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Navier-Stokes equations are time-ma
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To satisfy these requirements, it i
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are discussed by a number of author
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source code, and to assign each seg
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selected locations in the flow path
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of the component designers must be
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Trends in Flow Modeling Capabilitie
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optimize the flow behavior. The eff
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20. D. Eckardt, ‘‘Flow Field An
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49. K. R. Kirtley, ‘‘An Algebra
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INTRODUCTION 3 Turbine Gas-Path Hea
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Figure 1 Maximum turbine rotor inle
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Figure 2 Intersecting S1 and S2 sur
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determination. Nothing in the simpl
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e well matched with the engine. The
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case different forms of the popular
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volume will be equal to the accumul
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Figure 9 Nusselt number vs. vane su
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Furthermore, to keep computer time
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Figure 12 Comparison of three turbu
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and small and cooled and uncooled t
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Figure 15 Miniature heat flux gauge
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Figure 17 Time resolved heat transf
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Figure 19 Surface pressure changes
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NONUNIFORM INLET FLOW All gas turbi
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Figure 22 Typical distributions of
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4. Better instrumentation for heat-
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24. R. H. Ni, ‘‘A Multiple Grid
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4 Selection of a Gas Turbine Coolin
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Re L ¼ rVL=m—Reynolds number bas
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(1,300 8F). But modern gas turbines
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during engine operation are compati
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Figure 3 Airfoil cooling techniques
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expected to increase this limit to
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1. Reduce the effect of main-stream
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P? is total inlet pressure. Tc=T? i
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thereby increasing both the skin-fr
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After four decades of advancement i
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correspondingly high coolant-side t
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component. Use of a hot cascade for
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nozzle vanes is limited by their ox
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Figure 9 Typical turbine hot sectio
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important factor to consider for tr
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Figure 10 Evolution of nozzle geome
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the exit of the combustor section f
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Figure 12 Inlet turbulence effect o
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in heat transfer as the Reynolds nu
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easonably well using correlations e
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in the section on blade cooling tha
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mass flow rate (e.g., M ¼ 1 for a
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holes. Cooling hole pattern is an i
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coolant flow with the main stream,
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above equation assumes a constant f
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Figure 15 Definition of film-coolin
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edistribution of the external heat-
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Three-Dimensional Effects The three
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In order to achieve the bulk metal
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coefficient is given by Nud ¼ hd=k
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Where G ¼ 2:24ðw=tÞ 0:1 ðReeÞ
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pressure drop. The 608/458 V-shaped
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Some of the studies have found that
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of the cooling air and the turning
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Figure 20 Impingement geometry defi
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correlated by Nu a d ¼ 0:63ðGd=m
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tangentially to the inner wall, beh
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The effectiveness of a suction surf
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vortex structure. Their studies sho
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Figure 23 Effect of preswirler pres
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component to the cooling air that c
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axial gap. A static pressure variat
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Weight, cost, and complexity constr
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Figure 28 Effectiveness of liner co
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thickness. A problem this poses is
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portion of the hole has been shown
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unacceptable engine performance pen
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analysis, in order to provide accur
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Figure 30 Application of PSP for fi
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thermocouple positioned close to th
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spray-painted black (Hallcrest, BB-
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Figure 32 Schematics of a hot casca
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the turbine static temperature (rot
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Figure 33 Experimental rig for inve
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their color when exposed to higher
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margins defined within each discipl
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them. The larger gas-path divergenc
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Figure 36 Blade-cooling selection d
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8. B. Barry, Turbine Blade Cooling:
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40. A. K. Tolpadi and M. E. Crawfor
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73. R. S. Abhari, ‘‘Comparison
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106. J. M. Owen and R. H. Rogers, F
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138. I. Egorov, G. Kretinin, I. Les
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integrity (stress levels) will have
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Figure 1 Instant entropy contours o
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Aerodynamic Interaction (Unsteady L
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Figure 3 Pitchwise time-averaged en
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The above considerations are all fo
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lades, the wavelength of the distur
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forcing and damping, and hence the
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frequency and its higher harmonics
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The two-cell pattern with a relativ
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Figure 9 Typical blade flutter boun
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field is generated to satisfy the t
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Figure 11 Instant static pressure c
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Figure 12 Calculated instantaneous
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Figure 14 Time-space static pressur
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one period Tp (neglecting change of
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It should be noted that the effects
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There are some further points to no
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Figure 17 Flow around an NACA-65 ai
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(11) for a simple case]: Where WA
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Regardless whether loosely coupled
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Several methods have been developed
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significant difference is introduce
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losses, but it may affect to a mini
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when we refine a mesh in an unstead
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8. W. S. Barankiewicz and M. D. Hat
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6 Fundamentals of Compressor Design
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Figure 3 AlliedSignal 331 turboprop
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each of the selected radii. The pro
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components of gas velocity upstream
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Observe that each of the curves for
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The conservation of angular momentu
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allowable static pressure ratio of
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Figure 7 Boundary layers and wakes
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component that is perpendicular to
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Figure 10 (a) Deflection of flow of
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increase in the downstream pressure
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Mach number at a compressor outlet
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Figure 12 Sketch of flow surface an
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useful shapes and orientations of b
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where G and oa are constant along a
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There is a good reason for this sit
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Projected Shape in Meridional Plane
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inherent flow range of the impeller
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compressors. Multistage centrifugal
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turbines. In these designs the high
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Corrections for Streamline Curvatur
Page 361 and 362: Preparation of Maps Once the losses
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Page 367 and 368: tests. One should take pains to pro
Page 369 and 370: e predicted in advance. Total press
Page 371 and 372: Cv Coefficient of heat at constant
Page 373 and 374: 15. S. Lieblein, J. Basic Eng., Tra
Page 375 and 376: INTRODUCTION 7 Fundamentals of Turb
Page 377 and 378: Figure 1 Cross sections of generic
Page 379 and 380: espectively. Radial-inflow turbines
Page 381 and 382: Figure 4 Typical rotor blade shapes
Page 383 and 384: Figure 6 The expansion process acro
Page 385 and 386: the average for the gas flowing thr
Page 387 and 388: etween the velocity diagram and the
Page 389 and 390: gas dynamics relation p 00 p ¼ T 0
Page 391 and 392: Figure 9 Variations in turbine velo
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Page 397 and 398: different turbines easier, dimensio
Page 399 and 400: where and y ¼ T 0 in TSTD d ¼ p0
Page 401 and 402: sizing exercises where the details
Page 403 and 404: where Rth is the Reynolds number ba
Page 405 and 406: order to determine the overall turb
Page 407 and 408: The classical approach to satisfyin
Page 409 and 410: clearance. Since tip clearance repr
Page 411: turbine with an effective diffuser,
Page 415 and 416: Automation of Calculations and Trad
Page 417 and 418: and for the rotor Zrotor ¼ ð0:1Þ
Page 419 and 420: the energy extracted and the rotor
Page 421 and 422: RADIAL-INFLOW TURBINE SIZING Differ
Page 423 and 424: interpolations from existing design
Page 425 and 426: Glassman [1], the optimum ratio of
Page 427 and 428: design fault in the radial-inflow t
Page 429 and 430: [27]. In order to avoid manufacturi
Page 431 and 432: The rotor exit critical velocity is
Page 433 and 434: The hub-to-tip radius ratio at the
Page 435 and 436: REFERENCES 1. A. J. Glassman (ed.),
Page 437 and 438: 8 Steam Turbines Thomas H. McCloske
Page 439 and 440: Figure 3 Reciprocating steam engine
Page 441 and 442: This process began in the 1920s, al
Page 443 and 444: First Law of Thermodynamics The fir
Page 445 and 446: the amount of fuel burned and the p
Page 447 and 448: Figure 7 Rankine cycle temperature-
Page 449 and 450: The Mollier diagram is quite useful
Page 451 and 452: Figure 10 Theoretical Rankine cycle
Page 453 and 454: stages of the turbine is at a highe
Page 455 and 456: calculate the relevant thermodynami
Page 457 and 458: Figure 14 Steam leakage losses for
Page 459 and 460: can reveal nozzle and/or blade eros
Page 461 and 462: Figure 17 Enlarged portion of the M
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Traditionally, pressures have been
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Figure 21 Wetness thermodynamic los
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Figure 23 Radial steam turbine flow
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Figure 25 Percentage stage reaction
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The power output of the stage can b
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the LP turbines is split into paral
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Turbine Inlet Two stages in particu
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of 20%, which would cause excessive
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Figure 30 Typical low-pressure stea
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ductility and poor toughness, since
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‘‘tramp’’ elements to minim
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End Seals End seals or packing glan
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Drains Condensate can form during s
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Figure 32 Steam turbine blade roots
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Figure 34 Cross-section view of thr
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Figure 36 Interblade shroud and Tie
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Where The influence of notch sensit
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Similarly, LP turbine blades are su
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those made of steel. Note, however,
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esult, significant attention must b
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Figure 38 Centrifugal stresses on a
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Figure 39 Centrifugal bending stres
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onto the rotating blade. These can
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Vortex shedding from blade trailing
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Figure 42 Torsional coupled vibrati
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Figure 44 Stall flutter of low-pres
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Start-Stop Transients/Overspeeds La
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(4) ellipiticity, such as caused by
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Figure 47 Campbell diagram (frequen
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Furthermore, in practice each manuf
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Figure 49 Modal diameters of a low-
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Figure 51 Three-dimensional computa
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Figure 52 Converging wedge and resu
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value as the operating value of uv/
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Lubrication Supply System Design De
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Figure 56 Steam turbine oil system
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The main oil reservoir is located b
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Although a light oil does provide a
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temperatures are suspected as reaso
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There is no fixed or absolute value
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pivots incorporated in this bearing
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covers and doors. Pipe scale, rust,
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Figure 63 Mechanical hydraulic cont
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Figure 64 Steam turbine electro-hyd
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Figure 65 Steam turbine electro-hyd
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generator rotor moment of inertia h
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the turbine against overspeed. This
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an additional electronic overspeed
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Figure 68 Steam turbine protective
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3. Need for better understanding of
Page 563 and 564:
REFERENCES 1. J. C. Zink, ‘‘Ste
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No. TWDPS-1, The American Society o
Page 567 and 568:
58. A. V. Sarlashkar and T. C. T. L
Page 569 and 570:
81. IEEE Guide for Abnormal Frequen
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Atlanta, GA, Oct. 18-22, 1992, PWR-
Page 573 and 574:
Performance Enhancement Program, he
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of the design process toward achiev
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procedure capable of addressing mul
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to achieve a specific target pressu
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objective was to minimize the downs
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more closely represents the largest
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temperature by forming a thin film
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such as the one described here. For
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k is the thermal conductivity of th
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through finite differences. Mathema
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Figure 4 Comparison of blade cross-
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integration of multiple disciplines
Page 597 and 598:
17. S. S. Talya, ‘‘Multidiscipl
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INTRODUCTION 10 Rotordynamic Consid
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Figure 1 (c) AlliedSignal 331 turbo
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Figure 2 Rotor system displacements
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Figure 3 Elliptic lateral whirl. av
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vibration (either forward or backwa
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Figure 6 The Laval-Jeffcott rotor.
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are 1808 out of phase (i.e., the be
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this graph is quite simple; however
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included on these types of graphs b
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on the shaft is zero. Thus, the ste
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are uðtÞ ¼e zeott uo cos ott þ
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satisfies the inequality O < ot 1
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Figure 16 Laval-Jeffcott rotor tran
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Figure 18 Whirl speed map: Laval-Je
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Figure 20 Laval-Jeffcott rotor: ste
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Figure 22 Typical precessional mode
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Figure 24 Examples of flexible disk
Page 633 and 634:
ackward modes, however, involve con
Page 635 and 636:
Figure 29 Steady unbalance response
Page 637 and 638:
assist in attenuating high vibratio
Page 639 and 640:
properly sizing the damper, a highl
Page 641 and 642:
Figure 31 Gas turbine schematic and
Page 643 and 644:
Flexible Disk If the frequency of a
Page 645 and 646:
motion for each subsegment to form
Page 647 and 648:
Figure 35 Whirl speed map—straddl
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Figure 37 Rotor-bearing-support str
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DESIGN STRATEGIES AND PROCEDURES Ro
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Figure 38 Straddle mounted rotor. (
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Figure 39 Unbalance response: strad
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Figure 40 Double overhung rotor—d
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earing supports are reduced. The th
Page 661 and 662:
and also increases the critical spe
Page 663 and 664:
Examples of structure modes couplin
Page 665 and 666:
REFERENCES 1. D. Childs, Turbomachi
Page 667 and 668:
section is intended to place today
Page 669 and 670:
pressure-fed propellant systems. Hi
Page 671 and 672:
normally be considered a very small
Page 673 and 674:
increase of required suction perfor
Page 675 and 676:
displaced by the F-1 oxidizer pump
Page 677 and 678:
exposure may be subjected to imping
Page 679 and 680:
the exhaust duct. Sized to create s
Page 681 and 682:
excess of 6,000 psi for consumption
Page 683 and 684:
lifetime. With very few exceptions,
Page 685 and 686:
using hydrocarbon fuel combustion p
Page 687 and 688:
can yield noticeable savings in req
Page 689 and 690:
Figure 3 Rocket engine system schem
Page 691 and 692:
Figure 6 Staged combustion system,
Page 693 and 694:
each stage. The term C0 represents
Page 695 and 696:
Figure 10 Some representative turbo
Page 697 and 698:
emembered that the second (and any
Page 699 and 700:
the greatest demands on turbopump p
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momentum exchange between working f
Page 703 and 704:
Figure 13 Arrangement of various tu
Page 705 and 706:
pressure levels. As long as combust
Page 707 and 708:
Figure 14 Approxmate values of pump
Page 709 and 710:
liquid rocket engine systems, and e
Page 711 and 712:
above becomes a factor. This statem
Page 713 and 714:
We can then state (correctly) that,
Page 715 and 716:
Figure 15c Typical 2-D centrifugal
Page 717 and 718:
have seen that the flow rate throug
Page 719 and 720:
somewhat smaller magnitude of vecto
Page 721 and 722:
general indicator. Nss will give us
Page 723 and 724:
U ¼ rotor tangential velocity. By
Page 725 and 726:
and pump flow derived from the engi
Page 727 and 728:
In addition to shaft seals, shaft b
Page 729 and 730:
should be understood that the optim
Page 731 and 732:
stable operation is assured. In som
Page 733 and 734:
From Eq. (16) an impeller radial ou
Page 735 and 736:
Figure 18 Examples of centrifugal p
Page 737 and 738:
tional to clearance distance) with
Page 739 and 740:
I would like to conclude this secti
Page 741 and 742:
generally result in lower pump hydr
Page 743 and 744:
Figure 15h Cross-section of a typic
Page 745 and 746:
solutions of Eq. (7) for both stage
Page 747 and 748:
Figure 15k H-Q characteristics for
Page 749 and 750:
Figure 15l Typical inducer configur
Page 751 and 752:
camber) is proportionally lower. Th
Page 753 and 754:
Figure 22 Single-stage impulse turb
Page 755 and 756:
the velocity ratio K, but in somewh
Page 757 and 758:
~V and ~n ¼ fluid velocity and con
Page 759 and 760:
Fig. 25. The nature of the flow in
Page 761 and 762:
Although shrouded centrifugal impel
Page 763 and 764:
is a parasitic device, whose flow r
Page 765 and 766:
apidly than does the inducer thrust
Page 767 and 768:
Figure 30 LH2 turbopump rotor mecha
Page 769 and 770:
eplacement of a failed bearing with
Page 771 and 772:
shall see, contemporary rocket engi
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needs of the aircraft gas turbine a
Page 775 and 776:
was increased due to engine upratin
Page 777 and 778:
12 Turbomachinery Performance Testi
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istics. The more accurate the perfo
Page 781 and 782:
Inlet Distortion Most turbomachiner
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Gas Thermodynamic Properties Turbom
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ought to rest isentropically. Total
Page 787 and 788:
include not only the pressure chang
Page 789 and 790:
The circumferential placement of th
Page 791 and 792:
simply arithmetically averaging the
Page 793 and 794:
usually mounted in radial immersion
Page 795 and 796:
Figure 12(b) Radial flow angle prof
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Figure 15 Wake rake total pressure
Page 799 and 800:
Figure 16 Blade-tip pressure traces
Page 801 and 802:
Figure 18 Typical test rig schemati
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INSTRUMENTATION DESIGN CONSIDERATIO
Page 805 and 806:
Dynamic Pressure. Dynamic pressure
Page 807 and 808:
thermocouples. With care in constru
Page 809 and 810:
Figure 24 Typical two-dimensional f
Page 811 and 812:
Thermocouple lead wires should be i
Page 813 and 814:
Corrected Flow The flow rates used
Page 815 and 816:
pressure ratio [15]. It can be calc
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SYMBOLS A Cross-section area Cd Dis
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INTRODUCTION 13 Automotive Supercha
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Figure 2 A Roots-type supercharger
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The supercharger was in routine use
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Table 1 Superchargers Versus Turboc
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1960s, turbocharging was used by US
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Roots Blower The Roots-type blower
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speeds. The sound is caused by the
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Figure 8b How the Ro-charger operat
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The vanes in many designs are preve
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Figure 11a Key components of the G-
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Figure 11c G-Lader supercharger is
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Figure 12b Schematic of centrifugal
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Figure 14b Components of the typica
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Turbine Design The turbine housing
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inertia of the wheel assembly. Mini
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Figure 18 (a) Turbocharger compress
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Theoretically this efficiency is: o
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The overall turbine efficiency incl
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adjust the spring force to vary the
Page 857 and 858:
Figure 22b Two vanes are used to pr
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However, the temperature has to be
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air can reduce carbon monoxide and
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Figure 25 (a) Schematic of the COMP
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this plus the fact that the exhaust
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14 Tesla Turbomachinery Warren Rice
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press at the time of the invention
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can be made to simplify the equatio
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comparison of the results of variou
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y composing them of nested cones ra
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26. E. Bakke, ‘‘Theoretical and
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61. M. Piesche, ‘‘Investigation
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15 Hydraulic Turbines V. Dakshina M
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Table 1 Variables of Interest in Tu
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Figure 1 Variation of impeller shap
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Figure 2 Flow and velocity componen
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Figure 3 Schematic diagram of Pelto
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shown in Fig. 5(see KadambiandPrasa
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classified according to the directi
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The manufacturers of hydraulic turb
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The direction of the relative veloc
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Table 3 Variation of Some Quantitie
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denoted by hd. Thus the efficiency
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Figure 14 Draft tube setting. same
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REFERENCES 1. J. J. Fritz, Small an
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