A three-order finite volume method and its applicationto under-expanded jet shock wave structure simulation
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摘要: 以喷管出口欠膨胀射流为研究对象，在Lagrange坐标系下建立欠膨胀射流二维积分形式的流动方程。通过在单元交接面处进行三阶ENO(essentially nonoscillatory)格式插值，构造得到一种适用于求解该方程的三阶ENO有限体积法。采用该格式对一维Sod激波管算例和喷管出口欠膨胀射流进行数值计算。计算结果表明，该方法具有高精度、基本无振荡的特点，能很好地捕捉包含激波、滑移线以及三波交点等复杂流场波系结构。计算得到的波系结构中马赫盘的位置与实验结果吻合很好，相对误差小于1.1%。Abstract: By considering the under-expanded jet flow from nozzle exit, the integral form Euler equations for unsteady compressible flow in the Lagrange coordinates of a moving control volume was developed. By using three-order essentially non-oscillatory (ENO) interpolations at cell interfaces, a three-order ENO finite volume method for the integral form Euler equations was presented. The Sod shock tube case and nozzle outlet under-expanded jet shock wave structures were used to test the proposed scheme. The numerical results demonstrate that the method is accurate and non-oscillatory, and it can capture the wave structures of jet flow fields including shock cell structure, slip lines, jet boundary and the triple point well. Meanwhile, the simulated Mach disk locations in wave structures coincide with the experimentally measured ones, especially the error of the first Mach disk locations in wave structures between the numerical results and the experimental results was less than 1.1%.
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表 1 三阶ENO有限体积法密度误差
Table 1. Density error for third-order ENO finite volume method
网格尺度 L1误差 计算时间/s 收敛精度 0.02 3.03×10-3 0.072 6 0.01 4.09×10-4 0.296 2 2.89 0.005 3.90×10-4 1.102 2 2.96 
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