Handbook of Turbomachinery Second Edition Revised - Ventech!

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small, causing laminar-flow rotors to tend to be large and heavy for a prescribed throughflow rate. Extensive investigations have been made of Tesla-type liquid pumps using laminar-flow rotors [64]. It was found that overall pump efficiency was low even when rotor efficiency was high because of the losses occurring at the rotor entrance and exit mentioned earlier. CRITERIA FOR THE OCCURRENCE OF LAMINAR AND OF TURBULENT FLOW IN MULTIPLE-DISK ROTORS It is established that a wide range of types (or regimes) of flow can occur between corotating disks including wholly laminar flow, laminar flow with regions of recirculation, wholly turbulent flow, laminar flow proceeding through transition to turbulent flow, and turbulent flow proceeding through ‘‘reverse transition’’ or ‘‘relaminarization’’ to laminar flow. There is experimental evidence concerning these flows [26, 27, 31, 35, 42, 44], and the hydrodynamic stability of laminar flows between corotating disks has been investigated [31, 66]. Wu [78], considering all available experimental and analytical evidence, concluded that the viscogeometric number a proposed by Nendl [42, 55] most adequately characterizes the flow regime, where a ¼ uh 2 =vr. While the data of the various investigators are somewhat contradictory, a reliable guide appears to be that flow is laminar for a < 10, in transition for 104a < 20, and turbulent for a520. The various investigators introduce rather pragmatic and differing definitions of ‘‘laminar’’ and ‘‘turbulent,’’ which further complicates the matter. It is desirable that it be explored further both experimentally and by additional hydrodynamic stability analysis. MULTIPLE-DISK ROTORS HAVING TURBULENT FLOW The bulk-parameter (friction factor) type of analysis of flow in a multiple-disk type of rotor was referenced in the foregoing discussion of laminar flows. It has been used extensively to calculate turbulent flows but with mostly unknown degrees of adequacy. The transition criteria presented are not applicable for bulk-parameter use, the hydraulic diameter concept is required, and the assumption must be made that pipe-flow frictional correlations are valid for flows between corotating disks. Nevertheless, such analyses have been the only analytical prediction method available until relatively recently, and methods now becoming available are not yet well established. Wu [78] gives an extended Copyright © 2003 Marcel Dekker, Inc.
comparison of the results of various bulk-parameter methods of analysis with several sources of experimental data for turbulent flows between corotating disks. Momentum integral equation methods have been and continue to be used to calculate the subject turbulent flows [26, 34, 36]. In these methods, ordinary differential equations describing the flow are written based on assumed distribution forms for the velocity and on empirical expressions for the stresses in the flow. Some of these rely on experience and/or specialized experimental results and are found not to be universal. Within carefully noted bounds, however, these methods can be very successfully used by an experienced investigator and have yielded strong insights into and design information for the turbulent flows of interest. In principle, the set of partial differential equations applicable for turbulent flow can be written, provided with appropriate boundary and entrance conditions, and then solved in some manner using computer implemented calculations. In practice, there are several aspects of the process that cannot be executed with confidence that the calculated results will agree with reality. Principal among these is that a model or mechanism describing the turbulent transport of linear momentum must be prescribed. Furthermore, the partial differential equations are much more complicated for turbulent than for laminar flow. In the entrance region, the equations must be solved in elliptical form before changing over to simplified pseudoparabolic equations to continue the calculations. Truman [73] carried out calculations for turbulent flow between corotating disks using eddy-viscosity/mixing-length turbulence (stress) modeling, and using a finite-difference method for solving the partial differential equations. Wu [78] used a slightly modified version of the computer-implemented calculations provided by Truman, to compare calculated results with experimental data for turbulent flow due to Bakke [26] and Ko¨hler [34]. In general, agreement was good but with some qualifications and reservations discussed in detail by Wu [78]. It was noted that at high rotor angular speeds the calculations indicated recirculation in the turbulent flow that could not be detailed since the pseudo-parabolic equations are not applicable for recirculating flows. Truman et al. [76] have also calculated similar flows using an anisotropic two-equation turbulence model. More analytical study and much more experimental investigation of the turbulent flow between corotating disks are needed to establish the most applicable methods for calculating the flows with confidence and for the results to be useful in the design of turbomachines. Wu [78] has outlined an experimental apparatus and procedure that might provide the next needed insights for progress in this area. Copyright © 2003 Marcel Dekker, Inc.
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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
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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
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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
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REFERENCES 1. J. C. Zink, ‘‘Ste
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No. TWDPS-1, The American Society o
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58. A. V. Sarlashkar and T. C. T. L
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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
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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
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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
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ackward modes, however, involve con
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Figure 29 Steady unbalance response
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assist in attenuating high vibratio
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properly sizing the damper, a highl
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Figure 31 Gas turbine schematic and
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Flexible Disk If the frequency of a
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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
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Figure 40 Double overhung rotor—d
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earing supports are reduced. The th
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and also increases the critical spe
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Examples of structure modes couplin
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REFERENCES 1. D. Childs, Turbomachi
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section is intended to place today
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pressure-fed propellant systems. Hi
Page 671 and 672:
normally be considered a very small
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increase of required suction perfor
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displaced by the F-1 oxidizer pump
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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,
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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
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Figure 6 Staged combustion system,
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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
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Figure 13 Arrangement of various tu
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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
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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
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somewhat smaller magnitude of vecto
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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
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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
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Figure 18 Examples of centrifugal p
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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
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the velocity ratio K, but in somewh
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~V and ~n ¼ fluid velocity and con
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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
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Figure 30 LH2 turbopump rotor mecha
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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
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12 Turbomachinery Performance Testi
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istics. The more accurate the perfo
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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
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Figure 16 Blade-tip pressure traces
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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
Page 817 and 818:
SYMBOLS A Cross-section area Cd Dis
Page 819 and 820:
INTRODUCTION 13 Automotive Supercha
Page 821 and 822: Figure 2 A Roots-type supercharger
Page 823 and 824: The supercharger was in routine use
Page 825 and 826: Table 1 Superchargers Versus Turboc
Page 827 and 828: 1960s, turbocharging was used by US
Page 829 and 830: Roots Blower The Roots-type blower
Page 831 and 832: speeds. The sound is caused by the
Page 833 and 834: Figure 8b How the Ro-charger operat
Page 835 and 836: The vanes in many designs are preve
Page 837 and 838: Figure 11a Key components of the G-
Page 839 and 840: Figure 11c G-Lader supercharger is
Page 841 and 842: Figure 12b Schematic of centrifugal
Page 843 and 844: Figure 14b Components of the typica
Page 845 and 846: Turbine Design The turbine housing
Page 847 and 848: inertia of the wheel assembly. Mini
Page 849 and 850: Figure 18 (a) Turbocharger compress
Page 851 and 852: Theoretically this efficiency is: o
Page 853 and 854: The overall turbine efficiency incl
Page 855 and 856: adjust the spring force to vary the
Page 857 and 858: Figure 22b Two vanes are used to pr
Page 859 and 860: However, the temperature has to be
Page 861 and 862: air can reduce carbon monoxide and
Page 863 and 864: Figure 25 (a) Schematic of the COMP
Page 865 and 866: this plus the fact that the exhaust
Page 867 and 868: 14 Tesla Turbomachinery Warren Rice
Page 869 and 870: press at the time of the invention
Page 871: can be made to simplify the equatio
Page 875 and 876: y composing them of nested cones ra
Page 877 and 878: 26. E. Bakke, ‘‘Theoretical and
Page 879 and 880: 61. M. Piesche, ‘‘Investigation
Page 881 and 882: 15 Hydraulic Turbines V. Dakshina M
Page 883 and 884: Table 1 Variables of Interest in Tu
Page 885 and 886: Figure 1 Variation of impeller shap
Page 887 and 888: Figure 2 Flow and velocity componen
Page 889 and 890: Figure 3 Schematic diagram of Pelto
Page 891 and 892: shown in Fig. 5(see KadambiandPrasa
Page 893 and 894: classified according to the directi
Page 895 and 896: The manufacturers of hydraulic turb
Page 897 and 898: The direction of the relative veloc
Page 899 and 900: Table 3 Variation of Some Quantitie
Page 901 and 902: denoted by hd. Thus the efficiency
Page 903 and 904: Figure 14 Draft tube setting. same
Page 905: REFERENCES 1. J. J. Fritz, Small an
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Handbook of Turbomachinery Second Edition Revised - Ventech!

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