2013 1(12)

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   Long abstract

 

Pages:

111 - 116

Language:

RU

Ref.:

5


 


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2013_1(12)_19.pdf

 

 

THE STABILITY OF DISTURBANCES IN SUPERSONIC BOUNDARY LAYER OF A COMPRESSIBLE GAS WITH THE HEAT EXCHANGE ON THE WALL

Gaponov S.A., Terekhova N.M.

Khristianovich Institute Of Theoretical And Applied Mechanics SB RAS, Novosibirsk, Russia


Keywords:

supersonic boundary layer, hydrodynamic stability, laminar-turbulent transition


Introduction

Understanding the nature of the physical processes involved in the evolution of unstable disturbances in supersonic boundary layers is an important fundamental. Unfortunately, for supersonic flows the linear and nonlinear the wave development into the boundary layers  with the heat exchange on the wall  are still not investigated.

Purpose

The purpose of that work is theoretical investigation and numerical simulation of  the stability of  disturbances in supersonic boundary layer of a compressible gas with of the heat exchange on the wall for M=2 and M=5.35.

Method

In the linear and non-linear approximation (weakly nonlinear theory of stability) the interaction of disturbances in the boundary layer of a compressible gas while cooling the surface is studied. The moderate (Mach number M=2) and high (M =5.35) regimes of supersonic speeds is considered in the framework of the theory of hydrodynamic stability.

Results

It is established that the cooling of the surface leads to a significant change in the linear evolution of the perturbation: the vortex disturbances of the first mode stabilized and the acoustic disturbances of the second mode are destabilized, the degree of change is determined by the rate of change of the temperature factor.

The nonlinear interaction into a three-wave systems at high (M=5.35) supersonic velocities in the boundary layer of a compressible gas is between waves of different nature (acoustic and vortex) in the regime of the parametric resonance.

The pumping wave  is the plane acoustic wave  which exited three-dimensional sub-harmonic components of the vortex nature. At the same time, similar to the vortex interaction of waves with M=2 is considerably weaker.

For moderate M the nonlinear interaction between the vortex modes is very weak, at high Mach numbers it is carried out between the waves of different nature (acoustic and vortex) in the regime of the parametric resonance. This interaction takes place more rapidly if the subharmonic frequency are three-dimensional vortex waves. The pump wave is the plane acoustic wave, the intensity of which significantly increases during cooling streamlined surfaces. There is a threshold intensities beginning of nonlinear interactions.

 
     

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