Numerical solution of transonic stream function equation

Hafez, M.; Lovell, Donald R.

doi:10.2514/6.1981-1017

Cited by 19 publications

(9 citation statements)

References 6 publications

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“…For the transonic flow the artificial density technique (Hafez et al, 1983) is used instead of density in the dynamic equation. It can be found by…”

Section: Artificial Compressibility Techniquementioning

confidence: 99%

A Generalized Numerical Method for Solving Direct, Inverse and Hybrid Problems of Blade Cascade Flow by Using Streamline-Co-Ordinate Equation

Chen

Zhang

1987

Volume 1: Turbomachinery

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“…For the transonic flow the artificial density technique (Hafez et al, 1983) is used instead of density in the dynamic equation. It can be found by…”

Section: Artificial Compressibility Techniquementioning

confidence: 99%

A Generalized Numerical Method for Solving Direct, Inverse and Hybrid Problems of Blade Cascade Flow by Using Streamline-Co-Ordinate Equation

Chen

Zhang

1987

Volume 1: Turbomachinery

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“…The main advantage of this approach is to reduce the unknown variables to one or two variables. The difficulty of the stream function method, which is the non uniqueness of density, has been overcome recently either by integrating the velocity gradient equation to determine the velocity distribution [2][3] or .by splitting the velocity vector into a potential (compressible) and a rotational (incompressible) part [4.…”

Section: Introductionmentioning

confidence: 99%

Implicit Time-Dependent Method for the Calculation of Transonic Blade-to-Blade Flows With Strong Shock Waves

Abdelrahman

1986

The International Conference on Applied Mechanics and Mechanica

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Based on Euler equations, an implicit time-dependent method is applied for the calculation of the transonic blade-to-blade flows with strong shock waves. The ntmerical method is based ' on a fully implicit time difference scheme. The stabilizing correction method is utilised as an ADI sequence to break down the two dimensional operator into two operators. These operators are selected so that at each time step the variables are determined independently of each other. The work presented here is an adaptation, to turbomachinery flows, of the basic method previously publicized and well applied in the internal nozzle flow.The purpose of this paper is to examine the ability of this method to predict the blade-to-blade transonic flow with strong shock waves. Detailed studies of the grid system and corresponding problems related to the boundary (inlet,exit and periodicity) conditions. Results are presented for the ECDEV transonic compressor cascade with prescribed pressure ratio and with a strong passage shock. The results obtained are compared with those obtained by an explicit method utilised at ONERA -:FRANCE.•

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“…The artificial compressibility methods utilizing a stream function equation (ref. 8,9) have also been developed. In ref.…”

Section: Introductionmentioning

confidence: 99%

“…In ref. 8 the method was used for a 2-D transonic flow calculation around an airfoil where the gas dynamic parameters far away from the airfoil were known; this enabled the density value for the flow to be determined uniquely. However, determining the proper density for an internal flow stream function solution is more difficult.…”

Section: Introductionmentioning

confidence: 99%

A Stream Function Relaxation Method for Solving Transonic S1 Stream Surface With Pre-Determination of the Density

Ge¹

1985

Volume 1: Aircraft Engine; Marine; Turbomachinery; Microturbines and Small Turbomachinery

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On the basis of Prof. Wu’s 3-D flow theory (ref.1, 2, 3, 4, 5), a general streamfunction equation in non-orthogonal curvilinear coordinates is developed. The equation can be used to calculate subsonic or transonic flows on S1 or S2 stream surfaces of turbomachinery. In this paper streamlines coordinates and a mixed difference scheme are adopted in solving the stream function equation. A procedure for pre-determination of the density is developed and used to determine the unique-value of density from the known value of the stream function. Numerical examples are given.

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Numerical solution of transonic stream function equation

Cited by 19 publications

References 6 publications

A Generalized Numerical Method for Solving Direct, Inverse and Hybrid Problems of Blade Cascade Flow by Using Streamline-Co-Ordinate Equation

A Generalized Numerical Method for Solving Direct, Inverse and Hybrid Problems of Blade Cascade Flow by Using Streamline-Co-Ordinate Equation

Implicit Time-Dependent Method for the Calculation of Transonic Blade-to-Blade Flows With Strong Shock Waves

A Stream Function Relaxation Method for Solving Transonic S1 Stream Surface With Pre-Determination of the Density

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