Turbulence models for compressible flow are investigated in this thesis. A limiter for turbulence model variables is proposed from the realizability condition and a compressible turbulence model for pressurestrain correlation is developed to account for compressibility effects on turbulence.
When two-equation turbulence models are used, unrealistically large values of turbulence variables can appear due to the infringement of a realizability condition or numerical error. To cure this in practical calculations, various limiters are often employed. In the present work, a mathematically correct bound for eddy viscosity is obtained from the realizability condition. From this, realizability bounds for several terms of model equations are given. The effects of various bounds including the present one are investigated on the predictions of fundamental flows including the simple shear flows, supersonic compression ramp flow and supersonic base flow. It is shown that the limiter affects the prediction very significantly.
Performance of Ristorcelli's model for dilatational terms is investigated by simulating a supersonic boundary layer and a supersonic base flow in which it was known that the existing compressible turbulence models deteriorale the prediction performance of the turbulence models. Comparing the results of the other dilatational models. it is found that the Ristorcelli's model is in better agreement with the experimental data and this is due to the effect of gradient Mach number, which is another significant parameter in addition to the turbulent Mach number in compressible turbulence.
Recent results of DNS indicate that main compressibility effect comes from the reduced pressure-strain term due to reduced pressure fluctuations and not from the explicit dilatational terms. Using the concept of moving equilibrium in compressible homogeneous shear flow, a new compressible pressure-strain model is developed by modifying the incompressible pressure-strain model. It is characterized by a decrease in primary redistribution term but an increase in secondary redistribution term The model is applied to compressible mixing layer and the predicted results show that the growth rate is reduced with increasing convective Mach number and the Reynolds shear stress are reduced. All the components of the pressure-strain term and the shear stress anisotropy are reduced with the increase of the compressibility, whereas the normal stress anisotropy is increased, which are in accord with the experimental and DNS results.
2-방정식 난류 모형에 대해 realizability 조건으로부터 수학적으로 정확한 제한자를 제시하였다. Ristorcelli의 dilatational 항들에 대한 압축성 모형을 이용하여 기존의 압축성 모형의 적용이 오히려 난류모형의 예측성능을 떨어뜨리는 것으로 알려진 초음속경계층유동과 초음속기저유동의 해석을 하였다. Ristorcelli의 모형은 이러한 유동에서 기존의 모형들이 가지는 문제점을 거의 나타내지 않으며, 이러한 특징은 난류마하수 외에 중요한 압축성 변수인 gradient 마하수의 효과를 모형이 반영하고 있기 때문이다. 최근의 DNS 연구결과에 의하면, 난류에서의 주된 압축성 효과는 압력-분산의 감소로 인한 압력-변형율 항의 감소에 기인한다. 압축성균일전단난류에서의 moving equilibrium의 개념을 이용하여 새로운 압축성 압력-변형율항에 대한 모형을 개발하였다. 모형은 압축성 혼합층유동에 적용되었으며, 예측된 결과는 DNS나 실험의 결과와 잘 일치한다.