基于混合网格多维梯度重构的热流预测方法研究

高超声速气动热环境的数值计算对算法和网格的敏感度极高. 随着高超声速飞行器外形日益复杂, 生成高质量的结构网格时间成本呈指数增加, 难以满足工程应用的需求. 非结构/混合网格因具有很强的复杂外形适应能力, 为了缩短任务周期, 有必要在非结构/混合网格上开展高精度的气动热环境数值计算方法研究. 梯度重构方法是影响非结构/混合网格热流计算精度的重要因素之一. 本文通过引入多维梯度重构方法, 发展了基于常规的非结构/混合网格的高精度热流计算方法, 对典型的高超声速Benchmark算例(二维圆柱)进行了模拟, 并与气动力计算广泛采用的Green-Gauss类方法和最小二乘类方法进行了对比. 计算结果表明, 多维梯度重构方法能有效提高非结构/混合网格热流预测精度, 其鲁棒性和收敛性更好. 最后将多维梯度重构方法应用于常规混合网格的三维圆柱和三维双椭球绕流问题, 得到了与实验值吻合较好的热流计算结果, 展现了良好的应用前景. 

ACCURATE AERO-HEATING PREDICTIONS BASED ON MUL-TI-DIMENSIONAL GRADIENT RECONSTRUCTION ON HYBRID UNSTRUCTURED GRIDS1)

The prediction of hypersonic aerodynamic environment is highly sensitive to numerical algorithms and computational grids. Due to the geometry complexity of modern lifting-body hypersonic vehicles, the time cost of generating high quality structured grids increases horribly, and it is difficult to meet the need of engineering applications. In order to shorten the task cycle, it is necessary to develop numerical methods for accurate aero-heating prediction on hybrid unstructured grids, due to the capability for complex configurations. Gradient reconstruction method is one of the important factors influencing the accuracy of heat flux prediction on unstructured grids. In this work, a multi-dimensional gradient reconstruction was introduced into the second-order cell-centered unstructured finite-volume solver developed by the authors, and compared with the widely used Green-Gauss methods and least squares methods in aerodynamic force simulations. The benchmark cases of hypersonic flows over a 2D cylinder, were tested to validate the multi-dimensional approach. The numerical results demonstrate that the multi-dimensional approach can improve the accuracy of aero-heating prediction and the convergence performance. Finally, the multidimensional gradient reconstruction method is applied to predict the heat flux over a 3D cylinder and the double ellipsoid configuration on the general hybrid grids. The numerical results agree well with experimental data, which demonstrates the potential capability for complex engineering applications.