Handbook of Turbomachinery Second Edition Revised - Ventech!

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(random and periodic) flows. A purely steady flow will satisfy the equations with the time derivatives being zero. To answer the question raised earlier, we apply the standard time-averaging technique. An instantaneous flow variable can be expressed in terms of a time-averaged part and a fluctuation: where f ðx; tÞ ¼f ðxÞþf 0 ðx; tÞ ð13Þ f ðxÞ ¼ 1 T Z f ðx; tÞdt and f 0 ðx; tÞ ¼0 If the flow is randomly unsteady (turbulent), the time scale T over which the averaging is carried out should be much larger than the scales of turbulence fluctuations. For a periodic flow, T is the time length of the period. We substitute the time-averaged and fluctuation parts into the unsteady flow equations [Eq. (12)]. Then the time-averaged equations would be as follows: qru ¼ 0 qx ð14aÞ qruu qx þ qðruÞ0u0 ¼ qx qP qx ð14bÞ qruh0 qx þ qðruÞ0h0 0 ¼ 0 ð14cÞ qx The above time-averaged equations can be compared to their counterparts for purely steady flows: qru ¼ 0 qx ð15aÞ qruu ¼ qx qP qx ð15bÞ qruh0 ¼ 0 qx ð15cÞ Comparing the time-averaged equations [Eq. (14)] with the steady equations [Eq. (15)], we have the following observations: 1. The mass continuity equation remains unchanged, i.e., the timeaveraged mass flow at the inlet and outlet of a flow domain must be conserved. 2. For the momentum and energy equations, the time-averaging generates extra terms, due to nonlinearity of the equations. These terms need extra relationships or equations to close. Copyright © 2003 Marcel Dekker, Inc.
It should be noted that the effects of the extra terms depend on the spatial gradients of the unsteady disturbances (not just their absolute magnitudes). Also note that the pressure term remains unchanged since it is linear. Thus, an unsteady flow with large velocity fluctuations (e.g., unsteady vortices) is likely to be have more significant effect on the time-averaged flow than one with mainly pressure fluctuation (e.g., pressure waves). Clearly, the timeaveraged results of an unsteady flow cannot be obtained by simply solving the steady flow equations. The most common and probably most complicated type of unsteady flows is ‘‘steady’’ turbulent flows. It is somehow ironic that we hear much more about how turbulence affects our ‘‘steady’’ flow results than we do about a periodic unsteadiness. In a case of a turbulent flow, the extra terms (e.g., ru 0 v 0 in a 2D case) are the turbulence (Reynolds) stress terms, which need to be closed by turbulence modeling in one form or another. The basic mechanism to generate turbulence stress terms is exactly the same as what is illustrated above using the 1D flow equations, i.e., by the nonlinearity of the inviscid part of the equations. The only difference is that the Reynolds stresses are generated by essentially random unsteadiness, while for the cases we consider here, the stresses terms are generated by unsteadiness with distinctive frequencies, and for this reason they are called deterministic stresses as cast in the framework for blade-row interactions by Adamczyk [20]. Likewise, an appreciation of the effects of turbulence is helpful in identifying those of a periodic unsteadiness on time-averaged flows. For instance, we know that magnitudes of turbulence fluctuations are generally much smaller than an averaged flow velocity. It is therefore not surprising that a periodic unsteadiness with a small magnitude could have a significant effect on a time-averaged flow. In general, as far as a time-averaged flow is concerned, periodic unsteadiness might be regarded as ‘‘regular turbulence.’’ The main difference is that the extra terms due to periodic disturbances can be directly evaluated by unsteady flow calculations or modeling with less uncertainties than conventional turbulence modeling for the Reynolds stress terms. Here are some simple examples concerning the loss associated with a periodic unsteady flow. Firstly, consider a shock wave in a quasi 1D duct flow (Fig. 15). In asteady flow situation with fixed upstream conditions, the solution of the shock wave (position, strength, and entropy rise, etc.) is determined by the downstream static pressure P2. Now the shock wave is made to oscillate by the downstream static pressure changing in the following form: P ¼ P2 þ Am sinðot þ fÞ ð16Þ Copyright © 2003 Marcel Dekker, Inc.
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
Page 247 and 248: the turbine static temperature (rot
Page 249 and 250: Figure 33 Experimental rig for inve
Page 251 and 252: their color when exposed to higher
Page 253 and 254: margins defined within each discipl
Page 255 and 256: them. The larger gas-path divergenc
Page 257 and 258: Figure 36 Blade-cooling selection d
Page 259 and 260: 8. B. Barry, Turbine Blade Cooling:
Page 261 and 262: 40. A. K. Tolpadi and M. E. Crawfor
Page 263 and 264: 73. R. S. Abhari, ‘‘Comparison
Page 265 and 266: 106. J. M. Owen and R. H. Rogers, F
Page 267 and 268: 138. I. Egorov, G. Kretinin, I. Les
Page 269 and 270: integrity (stress levels) will have
Page 271 and 272: Figure 1 Instant entropy contours o
Page 273 and 274: Aerodynamic Interaction (Unsteady L
Page 275 and 276: Figure 3 Pitchwise time-averaged en
Page 277 and 278: The above considerations are all fo
Page 279 and 280: lades, the wavelength of the distur
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Page 283 and 284: frequency and its higher harmonics
Page 285 and 286: The two-cell pattern with a relativ
Page 287 and 288: Figure 9 Typical blade flutter boun
Page 289 and 290: field is generated to satisfy the t
Page 291 and 292: Figure 11 Instant static pressure c
Page 293 and 294: Figure 12 Calculated instantaneous
Page 295 and 296: Figure 14 Time-space static pressur
Page 297: one period Tp (neglecting change of
Page 301 and 302: There are some further points to no
Page 303 and 304: Figure 17 Flow around an NACA-65 ai
Page 305 and 306: (11) for a simple case]: Where WA
Page 307 and 308: Regardless whether loosely coupled
Page 309 and 310: Several methods have been developed
Page 311 and 312: significant difference is introduce
Page 313 and 314: losses, but it may affect to a mini
Page 315 and 316: when we refine a mesh in an unstead
Page 317 and 318: 8. W. S. Barankiewicz and M. D. Hat
Page 319 and 320: 6 Fundamentals of Compressor Design
Page 321 and 322: Figure 3 AlliedSignal 331 turboprop
Page 323 and 324: each of the selected radii. The pro
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Page 327 and 328: Observe that each of the curves for
Page 329 and 330: The conservation of angular momentu
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Page 333 and 334: Figure 7 Boundary layers and wakes
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Page 337 and 338: Figure 10 (a) Deflection of flow of
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Page 343 and 344: Figure 12 Sketch of flow surface an
Page 345 and 346: useful shapes and orientations of b
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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
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Preparation of Maps Once the losses
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that circumferential gradients meas
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Nastran, which was developed by NAS
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tests. One should take pains to pro
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e predicted in advance. Total press
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Cv Coefficient of heat at constant
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15. S. Lieblein, J. Basic Eng., Tra
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INTRODUCTION 7 Fundamentals of Turb
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Figure 1 Cross sections of generic
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espectively. Radial-inflow turbines
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Figure 4 Typical rotor blade shapes
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Figure 6 The expansion process acro
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the average for the gas flowing thr
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etween the velocity diagram and the
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gas dynamics relation p 00 p ¼ T 0
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Figure 9 Variations in turbine velo
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pressure, inlet losses are usually
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diffuser recovery, defined as Rp ¼
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different turbines easier, dimensio
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where and y ¼ T 0 in TSTD d ¼ p0
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sizing exercises where the details
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where Rth is the Reynolds number ba
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order to determine the overall turb
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The classical approach to satisfyin
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clearance. Since tip clearance repr
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turbine with an effective diffuser,
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atio ðp 0 in =pdisÞ is 3. The sta
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Automation of Calculations and Trad
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and for the rotor Zrotor ¼ ð0:1Þ
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the energy extracted and the rotor
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RADIAL-INFLOW TURBINE SIZING Differ
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interpolations from existing design
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Glassman [1], the optimum ratio of
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design fault in the radial-inflow t
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[27]. In order to avoid manufacturi
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The rotor exit critical velocity is
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The hub-to-tip radius ratio at the
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REFERENCES 1. A. J. Glassman (ed.),
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8 Steam Turbines Thomas H. McCloske
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Figure 3 Reciprocating steam engine
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This process began in the 1920s, al
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First Law of Thermodynamics The fir
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the amount of fuel burned and the p
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Figure 7 Rankine cycle temperature-
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The Mollier diagram is quite useful
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Figure 10 Theoretical Rankine cycle
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stages of the turbine is at a highe
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calculate the relevant thermodynami
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Figure 14 Steam leakage losses for
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can reveal nozzle and/or blade eros
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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
Page 519 and 520:
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
Page 561 and 562:
3. Need for better understanding of
Page 563 and 564:
REFERENCES 1. J. C. Zink, ‘‘Ste
Page 565 and 566:
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-
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Performance Enhancement Program, he
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of the design process toward achiev
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procedure capable of addressing mul
Page 579 and 580:
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
Page 591 and 592:
through finite differences. Mathema
Page 593 and 594:
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
Page 603 and 604:
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
Page 631 and 632:
Figure 24 Examples of flexible disk
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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
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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
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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
Page 657 and 658:
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
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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
Page 701 and 702:
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
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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
Page 773 and 774:
needs of the aircraft gas turbine a
Page 775 and 776:
was increased due to engine upratin
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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
Page 797 and 798:
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
Page 803 and 804:
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
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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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Handbook of Turbomachinery Second Edition Revised - Ventech!

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