A Comparison between Measured and Computed Flow Fields in a Transonic Compressor Rotor

McDonald, P. W.; Bolt, C. R.; Dunker, R. J.; Weyer, H.

doi:10.1115/1.3230354

Cited by 17 publications

(16 citation statements)

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“…= angle between span of swept wing and incident flow 0 12 = angle between x l and x 2 line K = ratio of specific heats X = slope of characteristic line p = density of gas T = circumferential thickness of #2 stream filament i// = stream function defined on stream surface S 2 w = angular velocity of rotor…”

Section: Ftmentioning

confidence: 99%

“…The increases of V e r and s from inlet to exit are determined from measured data. 12 However, due to the limited data available, the variation of the thickness of stream sheet r is approximately taken to be proportional to the channel width.…”

Section: Numerical Calculationsmentioning

confidence: 99%

“…Measured data of this rotor have been published. 12 From the available Mach number contour plots on the S-^ surfaces located at a number of spanwise positions for peak efficiency operating condition at 100% design speed, 12 the projection on the meridional plane of the Mach number contours on the S 2^m surface is constructed and given in Fig. 5.…”

Section: Numerical Calculationsmentioning

confidence: 99%

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Solution of inverse problem of transonic flow on S2 surface using anelliptic algorithm

Chen

1987

AIAA Journal

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The flow on an 5* 2 surface with given V §r variation has been widely used in practice for direct and inverse problems of three-dimensional flows in turbomachines. The fact that the differential equations governing the flow remain elliptic as long as the meridional component of the absolute velocity is lower than the speed of sound, even in cases where the flow relative to the rotating blade is supersonic, is rigorously proved on the basis of the original system of first-order differential equations, as well as of the single second-order principal equation expressed in terms of the stream function. This provides a sound mathematical basis for solving the difficult transonic S 2 surface flow, especially for the design problem, by a well-developed method for solving an elliptic equation. It is pointed out, however, that in so doing, it is important that the prescribed variation of V 9 r should have an appropriate abrupt change at the shock so that an accurate detailed flow variation throughout the rotor passage can be obtained. The preceding argument is illustrated by an example in which the transonic S 2 m flow in a research axial-flow transonic compressor rotor is obtained by the use of a conventional method for solving the elliptic second-order partial differential equation for the stream function. C P D/Dt F H h I M P R r,

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Section: Ftmentioning

confidence: 99%

Section: Numerical Calculationsmentioning

confidence: 99%

Section: Numerical Calculationsmentioning

confidence: 99%

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Solution of inverse problem of transonic flow on S2 surface using anelliptic algorithm

Chen

1987

AIAA Journal

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“…The coupling terms thus modify the upwash on the reference blade by an amount At; 0 that can be calculated; thus, for the second-order problem, (22) where the second-order terms in Eq. (16) are to be taken for 4> y and <££. It should be noted that in the second-order problem, two upwash integral equations are obtained, one for the upper and one for the lower surface of the reference blade.…”

Section: Perturbation Approachmentioning

confidence: 99%

“…Because of the complex threedimensional shock structure existing in actual rotors (see, for example, Refs. [15][16][17][18], a complete solution of the problem must ultimately be based on the methods of computational fluid dynamics.…”

Section: General Modeling Aspectsmentioning

confidence: 99%

Role of shocks in transonic/supersonic compressor rotor flutter

Bendiksen

1986

AIAA Journal

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An investigation of the influence of shock motion on flutter of rotors and cascades is presented. The present paper illustrates how a perturbation scheme can be used to calculate the nonlinear effects due to thickness, camber, and incidence to second order in a perturbation parameter. An approximate theory is also given, that accounts for the first-order quasisteady effects of shock motion and also allows experimentally determined shock structures and parameters to be used. The unsteady aerodynamic forces resulting from shock movements are shown to have a pronounced effect on the flutter boundaries of cascades representative of large fan rotors. Both stabilizing and destabilizing effects are observed, depending on interblade phase angle and shock structure. At low reduced frequencies, the shock-induced loads can destabilize bending oscillations sufficiently to cause single-degree-of-freedom bending flutter. It is also possible to explain the stabilizing effect of the back pressure on supersonic rotor flutter, as observed experimentally. a c CLV> CMV h k k L m M M 2 N P u,v t/oo S x,y;x',y' Xr 7 6 6 2 P a v Nomenclature = speed of sound; also location of pitching axis, Eq. (8) = 2b = blade chord = force and moment coefficients, Eqs. (26), (27) = bending deflection, positive down = ub/U= reduced frequency --kM//3 2 -lift per unit span, positive up = mass per unit span of blade = moment per unit span, about midchord, positive clockwise; also Mach number = cascade exit Mach number = (7+ l)M 2 /(2]8 2 ); also number of blades in rotor = static pressure =/? 3 -/?! = pressure jump at shock reflection, Fig. 3 = V$ = velocity vector = perturbation velocities in x y y directions = freestream velocity at upstream infinity = blade spacing (Fig. 1) = total potential = phase angle of shock motion = circular frequency = SCOS0 = time = cascade coordinate systems (Fig. 1) = mean location of shock reflection point = instantaneous shock reflection point and oscillation amplitude, respectively = angle of attack; also torsional deflection its = ratio of specific heats of air = stagger angle = flow deflection at trailing edge = m/irpb 2 = mass ratio of blade = air density = interblade phase angle = steady (mean) perturbation potential = unsteady perturbation potential about mean flow Superscripts and Subscripts( " ) = nondimensional quantity: lengths with respect to semichord b, velocities with respect to £/",, pressure with respect to p^ U0 = amplitude of harmonic quantity oo = conditions at upstream infinity (freestream) s = quantity associated with shock wave

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References

2010

Aerothermodynamics of Turbomachinery

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A Comparison between Measured and Computed Flow Fields in a Transonic Compressor Rotor

Cited by 17 publications

References 0 publications

Solution of inverse problem of transonic flow on S2 surface using anelliptic algorithm

Solution of inverse problem of transonic flow on S2 surface using anelliptic algorithm

Role of shocks in transonic/supersonic compressor rotor flutter

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