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Abstracts

Numerical solution of differential and integral equations

In this paper the results of numerical investigation of supersonic flows in 2-D plane channels of a complex geometry are presented. The necessity to study these flows is connected with a design of high-speed air intakes for perspective high-performance aircraft. The computations were performed on a basis of Favre-averaged Navier-Stokes equations closed by a two-equation turbulence model. The original numerical algorithm [1] has been used to compute various 2-D turbulent supersonic separated flows and shown a good potential to predict the properties of these flows [2, 3].

The first subject of inquiry is a flat plate with a sharp leading edge. The double ramp model with 11 and 9 angles was fixed so that transition could be detected far upstream of the ramp model. Incoming boundary layer is assumed to be turbulent. In the first step the question was to find the critical length of the first ramp to determine the beginning of separation of the second shock. In this case the length was varied with fixed unit Reynolds number Re=10^7 and a free-stream Mach number of 2.5. Thus, several geometric configurations were considered. For one of the configurations chosen as a basic one the calculations were carried out in the framework of Navier-Stokes approach and also on the basis of simplified approach to the boundary layer equations. The purpose of these calculations is to obtain initial data for solving of total Navier Stokes equations and analysis of peculiar properties of the flow.

Further we accomplished modelling of supersonic flows in 2-D air intake. The results of the simulation have been compared with the data of experiments carried out in the supersonic blow-down wind tunnel of ITAM SB RAS at Mach numbers 2 to 6 in a wide range of Reynolds numbers. The validation of the numerical results has been performed using the flowfield pictures, static pressure distributions along the central body surface, total pressure measurements in some cross-sections as well as the skin friction distributions. The parametric computations carried out in a wide range of geometric and gas-dynamic parameters permit one to choose the optimal design configuration and conditions as well as to explain some particularities of the flows investigated. The effect of a laminar-turbulent transition on the channel walls on the results of a flow simulation was investigated. The computations were carried out for a laminar, transitional and turbulent state of the boundary layer developed at a cowl. It was shown that the state of the boundary layer produced a significant effect on the wave picture of the channel flow as well as the main parameter distributions. The results of implementation of various two-equation turbulence models to simulate a transition are presented.

Bibliography

1. A.V. Borisov,. N.N. Fedorova Numerical simulation of turbulent flows near the forward-facing steps //Thermophisics and Aeromechanics. - 1996. -Vol. 4, No. 1. C. 69-83.

2. I.A. Bedarev, A.V. Borisov, N.N. Fedorova Numerical Simulation of the Supersonic Turbulent Separated Flows in Vicinity of the Backward- and Forward-Faced Steps // Computational Fluid Dynamics Journal.- 2001. - Vol.9, No.1, Pt.2. P. 194 - 202.

3. N.N. Fedorova, I.A. Fedorchenko, E. Shuelein Experimental and numerical study of oblique shock wave / turbulent boundary layer interaction at M=5 // Computational Fluid Dynamics Journal.- 2001. Vol.10, No.3. P. 376-381.

Note. Abstracts are published in author's edition

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