基于浸入式边界法的叶栅颤振数值模拟

Numerical simulation of an oscillating cascade based on immersed boundary method

基于浸入式边界法建立了求解振荡叶栅非定常流动的快速计算模型,并在模型中添加湍流模型,使之能够考虑更加接近实际流动的情况。具体的方法是求解目前为止最常用的雷诺时均Navier-Stokes方程并添加低雷诺数湍流模型(Lam-Bremhorst模型,k-ε模型的一种)进行计算,为了验证该方法的正确性,分别对层流边界层和湍流边界层进行了数值模拟,计算结果与布拉修斯解和壁面率吻合得很好,证明了湍流模型的可靠性。在此基础上,对高雷诺数条件下的振荡叶栅进行了数值模拟。结果表明,折合速度是影响叶栅振荡的重要因素,这与层流计算的结论类似。值得注意的是耦合过程没有生成贴体网格,减小了计算时间,可以准确快速地模拟真实的叶栅流动情况。

A fast explicit numerical method is established to solve the unsteady flow with an oscillating cascade on the basis of the immersed boundary method. In order to consider more practical problems, a turbulence model is introduced into this method. The specific method is to solve the Reynolds averaged Navier-Stokes equations with low Reynolds number turbulence model, i. e. , Lam-Bremhorst model, which is one of the k-ε models. In order to validate the method, two simulation cases, laminar boundary layer and turbulent boundary layer are carried out and results agree well with the Blasius solution and the law of wall. Based on these benchmark cases, a numerical simulation at high Reynolds number for an oscillating cascade is then established, it is found that the oscillating of cascade is greatly influenced by the reduced velocity which is just the same solution of the laminar results. It is worth noting that the coupling process is not necessary to generating any bodyfitting grid, which makes it much faster in computational process for such a cascade problem.