Handbook of Turbomachinery Second Edition Revised - Ventech!

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phase lag relative to the input) of the ith displacement coordinate of the structure due to a unit amplitude harmonic force associated with the jth coordinate. The complete set of dynamic flexibility FRFs forms the dynamic flexibility matrix, ½FssðoÞŠ, for the structure, and the inverse of this matrix is the dynamic stiffness matrix, ½SssðoÞŠ, for the structure. A typical dynamic stiffness FRF, SijðoÞ, may be interpreted as the ith harmonic force associated with a unit amplitude harmonic displacement of the jth coordinate with all other coordinates constrained to zero. The dynamic flexibility matrix for a support structure may be established experimentally using modal testing techniques, e.g., Ewins [7], or analytically from a finite-element model of the support structure. Typically, only the support structure coordinates that dynamic flexibility modeling of the support structure. The dynamic stiffness matrices for the rotating assembly(s), ½SraðoÞŠ, and interconnecting components, ½SicðoÞŠ, may be determined analytically from their respective governing equations. The dynamic stiffness matrix for the system is then assembled and appears typically in the form shown in Eq. (25). It is mathematically convenient to express this type of equation in complex form. The coordinates linked with the interconnecting components constitute a subset of both the rotating assembly and support structure components, i.e., fqraðoÞg and fqssðoÞg, respectively. Thus, the interconnection components are not separately identified in Eq. (25). For additional information on rotor-foundation effects and analysis, see Gasch [9, 10]. 2 3 SraðoÞ 4 SicðoÞ 5 fqraðoÞg fqraðoÞg SssðoÞ ¼ fFraðoÞg ð25Þ f0g The harmonic force vector, fFraðoÞg, is typically the steady rotating assembly unbalance force vector, which is synchronous with the rotor spinspeed. The solution of Eq. (25) for a range of spin-speeds provides coordinate response information as well as the location of the critical speeds for the rotor-bearing-support structure system. When the rotor spins near a support structure natural frequency, the dynamic stiffness of the support structure tends to diminish significantly and the rotating assembly behaves as if it were decoupled from the support structure. A model such as suggested in Eq. (25) provides an analyst with a valuable tool to investigate the effect of the support structure design on the overall system dynamic characteristics. Based on this information, it may be possible to make support structure design changes to improve the overall system performance. Copyright © 2003 Marcel Dekker, Inc.
DESIGN STRATEGIES AND PROCEDURES Rotordynamic system response presents the following concerns: generated noise, rotor deflection at close clearance components (e.g., seals, rotor-tostructure rubs and rotor-to-rotor rubs), lateral bearing loads, and support structure loads. All of these are concerns associated with the overall goal of minimizing the response of a rotor-bearing system for both synchronous and nonsynchronous whirl. The largest responses usually occur when a forcing function acting on the system, e.g., mass unbalance, excites a natural frequency with its inherent dynamic magnification. Strategies for designing rotor-bearing systems with acceptable rotordynamic response characteristics thus focus on the critical speeds and associated mode shapes. For most rotor systems the preferred design sequence to minimize dynamic response is 1. Size the system, whenever possible, so the natural frequencies are outside the machine’s operating range. 2. Introduce damping if design constraints place natural frequencies within the operating range. 3. Reduce the excitation levels acting on the system. Designing the system so the natural frequencies are outside the operating range is an obvious benefit to improving rotor dynamic response characteristics. This strategy, however, can place severe constraints on the key design parameters perhaps requiring unrealistically stiff bearings and/or support structure, large shaft diameters, short bearing spans, etc. Larger shaft diameters naturally lead to larger diameter bearings, seals, compressors, and turbines. These larger components then limit the maximum allowable speed for overall system durability. The introduction of damping to minimize response near a system natural frequency is typically accomplished using an oil film between a bearing outer ring and the support structure. These ‘‘squeeze film dampers’’ can be quite effective in adding the beneficial external damping to the rotor provided that the excitation does not drive the oil film beyond its useful linear range. The excitations acting on the system should obviously be minimized (e.g., balancing the individual components) whenever possible even if the natural frequencies are outside the operating range. This method of controlling response, however, typically adds significantly to the manufacturing cost. Straddle-Mounted Rotor: Disks Inside the Bearings Consider, as an illustrative example, a straddle-mounted rotor-bearing system: 20.0-in. (50.8-cm) steel shaft with a 0.70-in. (1.78-cm) inner radius 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
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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
Page 599 and 600: INTRODUCTION 10 Rotordynamic Consid
Page 601 and 602: Figure 1 (c) AlliedSignal 331 turbo
Page 603 and 604: Figure 2 Rotor system displacements
Page 605 and 606: Figure 3 Elliptic lateral whirl. av
Page 607 and 608: vibration (either forward or backwa
Page 609 and 610: Figure 6 The Laval-Jeffcott rotor.
Page 611 and 612: are 1808 out of phase (i.e., the be
Page 613 and 614: this graph is quite simple; however
Page 615 and 616: included on these types of graphs b
Page 617 and 618: on the shaft is zero. Thus, the ste
Page 619 and 620: are uðtÞ ¼e zeott uo cos ott þ
Page 621 and 622: satisfies the inequality O < ot 1
Page 623 and 624: Figure 16 Laval-Jeffcott rotor tran
Page 625 and 626: Figure 18 Whirl speed map: Laval-Je
Page 627 and 628: Figure 20 Laval-Jeffcott rotor: ste
Page 629 and 630: Figure 22 Typical precessional mode
Page 631 and 632: 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
Page 649: Figure 37 Rotor-bearing-support str
Page 653 and 654: Figure 38 Straddle mounted rotor. (
Page 655 and 656: Figure 39 Unbalance response: strad
Page 657 and 658: Figure 40 Double overhung rotor—d
Page 659 and 660: 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
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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
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
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generally result in lower pump hydr
Page 743 and 744:
Figure 15h Cross-section of a typic
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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
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camber) is proportionally lower. Th
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Figure 22 Single-stage impulse turb
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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
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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
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
Page 783 and 784:
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
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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
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pressure ratio [15]. It can be calc
Page 817 and 818:
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
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
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speeds. The sound is caused by the
Page 833 and 834:
Figure 8b How the Ro-charger operat
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The vanes in many designs are preve
Page 837 and 838:
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
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
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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
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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
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press at the time of the invention
Page 871 and 872:
can be made to simplify the equatio
Page 873 and 874:
comparison of the results of variou
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
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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
Page 893 and 894:
classified according to the directi
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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
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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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