基于WENO-分段线性格式的旋翼流场数值模拟

为了降低二阶JST(Jameson-schmidt-turkel)格式导致的数值耗散,发展了一套适合于格心格式的基于加权本质无振荡(Weighted essentially non-oscillatory,WENO)-分段线性格式的旋翼流场数值模拟方法。采用运动嵌套网格方法生成围绕旋翼的网格系统,主控方程选择Navier-Stokes(N-S)方程。为了更加有效地对桨尖涡等流动细节进行捕捉,在笛卡尔背景网格上采用七阶Roe-WENO格式计算对流通量;在桨叶贴体非结构网格上采用二阶精度的Roe-分段线性格式计算对流通量。时间离散采用了高效的双时间隐式LU-SGS(Lower upper symmetric Gauss-Seidel)方法进行时间推进。最后,应用上述方法对悬停状态的C-T(Caradonna-tung)旋翼和Helishape 7A旋翼进行了数值模拟,将数值计算结果与实验数据进行了对比,计算值与实验值吻合较好;并将桨尖涡模拟效果与二阶JST格式的模拟效果进行了对比。对比结果表明:本文方法能有效对旋翼流场进行计算,且在相同计算条件下,WENO-分段线性格式能够更有效地捕捉旋翼涡流场的流动特性,表明在计算旋翼涡流场时WENO-分段线性格式相比传统二阶JST格式具有更低的数值耗散。

Numerical Simulation for Flow Field of Rotors Based on WENO-Piecewise Linear Scheme

A set of technology of numerical simulation for rotor flow field based on WENO (weighted essentially non-oscillatory)-piecewise linear scheme is developed to reduce the numerical dissipation of tip vortex caused by the second-order JST scheme. The moving overset grid method is selected to generate the grid system, the Navier-Stokes equation is selected to be the main control equation. In order to capture the flow details including the tip vortex more effectively, we use the seventh-order Roe-WENO scheme on the cartesian background grid, and the second-order Roe-piecewise linear scheme is adopted on the unstructured body fitted grid of blade. Temporal discretization method chooses the efficient dual-time implicit LU-SGS (lower upper symmetric Gauss-Seidel) scheme for time advancement. Finally, we use the method to numerically calculate the flow field of C-T(caradona-tung) model rotor in hover and the Helishape 7A model rotor in hover, and the comparison between the numerical results and the experimental data are good. Then we compare the results of WENO-piecewise linear scheme with the results of JST scheme. The comparison results verify the effectiveness of the WENO-piecewise linear scheme to calculate the flow field of rotor. And the results show that under the same calculation conditions, the proposed method can capture the flow characteristics of the rotor flow field more effectively, indicating that the WENO-piecewise linear scheme has lower numerical dissipation than the traditional second-order JST scheme when calculating the rotor flow field.