A Numerical Technique for the Calculation of Transonic Flows in Turbomachinery Cascades

Gopalakrishnan, S.; Bozzola, R.

doi:10.1115/71-gt-42

Cited by 17 publications

(6 citation statements)

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“…, 3Q +r, 8Q Sl.r ~T + n Sl,z dz dr (4) The normal vector n sl necessary for this conversion can be established by the geometry of the stream surface.…”

Section: Basic Equationsmentioning

confidence: 99%

Theoretical and Experimental Analysis of the Flow through Supersonic Compressor Rotors

Broichhausen

Gallus

1982

AIAA Journal

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In the present paper theoretical and experimental results referring to different supersonic rotors are discussed. The theoretical approach, based on the Euler equations of motion, is valid for transonic rotor flows. The shocks are treated separately on the basis of the Rankine-Hugoniot equations. The measurements were performed by time-averaging and time-dependent techniques. Comparing the theoretical approach with the experimental data, special attention is paid to the structure of detached front waves and strong channel shocks. These discontinuity surfaces proved to be remarkably spatially curved, so that the pressure rise in the shocks is lower than in the twodimensional case. With respect to the channel and the rotor outlet flow the presented theoretical results conform to the experimental data, if three-dimensional viscous effects are not dominant. Nomenclature a= velocity of sound c, u, w = absolute, circumferential, and relative velocity c v = specific heat d( )/ds = differential change in streamline direction d/ = increment in streamline direction (r, z plane) /blade = blade force h rot =rothalpy M rel ,M Z -relative, axial Mach number n (e} = normal (unity) vector n/n 0 = speed ratio P(t)*T (t ) = (total)pressure, (total) temperature p = time dependent pressure Q = arbitrary variable r = radius rd$ = increment in circumferential direction R = gas constant, =c p -c v s = entropy S = finite area x,y = profile coordinates (d)z = (increment in) axial direction a.== Mach angle F = circulation 7, tp, \ = flow angle in r-z; r-rdd plane, SI surface e = blade angle M k Q -central difference in /, k direction K -ratio of specific heats p (/) = (total) density a = three-dimensional shock angle co = angular velocity Q =vorticity Subscripts abs, rel u,r,z I S1,S2 sh = absolute, relative system = grid point = circumferential, radial, axial = streamline (r, z plane) = S1, S2 surface = shock

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“…, 3Q +r, 8Q Sl.r ~T + n Sl,z dz dr (4) The normal vector n sl necessary for this conversion can be established by the geometry of the stream surface.…”

Section: Basic Equationsmentioning

confidence: 99%

Theoretical and Experimental Analysis of the Flow through Supersonic Compressor Rotors

Broichhausen

Gallus

1982

AIAA Journal

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“…The initial conditions are arbitrari! assigned as in reference (1). They have no eff' on the final solution, to reach convergence.…”

Section: Application To Compressor Cascadesmentioning

confidence: 99%

“…If a 2u/ax2 is of order (1), and is of order (1/A), the error is of order (A 2 ). The error term can be shown to be dissipative (1) and, hence, may be considered as an "artificial viscosity" term. The "coefficient of viscosity" can be defined…”

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confidence: 99%

Computation of Shocked Flows in Compressor Cascades

Gopalakrishnan

Bozzola

1972

ASME 1972 International Gas Turbine and Fluids Engineering Conference and Products Show

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A numerical technique is presented for the calculation of shocked flows in compressor cascades. The problem is posed in the time-dependent form and the asymptotic solution at large times provides the solution of the steady physical problem. The solutions exhibit the formation and movement of shocks as the static pressure ratio across the cascade is varied. The resulting inlet and outlet angles and total pressure loss are also shown.

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“…In some methods for calculating transonic flow in a cascade, the Time-dependent Method is used to solve the Euler equations [ 1 ] and Relaxation Methods are used to solve the potential eauation [ 2 ], [ 3 ]or the stream function equation [ 4], [5], In general, the Time-dependent Method needs more computer time than the others. The method of solving the potential equation is only suitable for irrotational flow.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Transonic Stream Function Equation on S1 Stream Surface in Cascade

1986

Volume 1: Turbomachinery

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A method is presented in this paper for calculating transonic flow field in turbomachinery cascades. With respect to non-orthogoanl curvilinear coordinates, the stream function equation governing fluid flow was established. Using the Artificial Compressibility Method, the discretization of the partial differential equation was carried out by use of the standard central difference formula. The set of linear algebraic equations obtained is solved by means of the Direct Matrix Method. In order to overcome the non-uniqueness of density in transonic flow in the stream function method, the velocities at grid nodes are first obtained by integrating the momentum equation and then the densities are determined from the energy equation. Application of this method to some transonic cascade-flow with supersonic or subsonic inlet velocity shows that the solution obtained is in fair agreement with experimental data.

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A Numerical Technique for the Calculation of Transonic Flows in Turbomachinery Cascades

Cited by 17 publications

References 0 publications

Theoretical and Experimental Analysis of the Flow through Supersonic Compressor Rotors

Theoretical and Experimental Analysis of the Flow through Supersonic Compressor Rotors

Computation of Shocked Flows in Compressor Cascades

Numerical Solution of Transonic Stream Function Equation on S1 Stream Surface in Cascade

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