滑移边界条件的收敛性分析及应用

Convergence analysis and application of the slip boundary conditions

用速度滑移与温度跳跃边界条件代替通常假定的无滑移边界条件,可有效地提高计算流体力学模型对高空滑移流区域流动的预测精度。应用Maxwell滑移边界条件时,通过直接计算速度梯度及温度梯度而得到速度滑移和温度跳跃量的处理方法在网格较密的时候会出现迭代计算发散的问题。理论分析表明,直接计算梯度的方法使边界条件的时间推进过程等价于雅克比迭代过程,因此必须满足相应的收敛性条件。为了消除收敛性条件的限制,给出了一种在任意网格密度下均收敛的边界条件处理方法并通过数值算例验证了该方法的正确性。针对高空高超声速流动,以空天飞机为例,对比了滑移/无滑移边界条件所得结果的差异,分析了滑移效应对飞行器气动特性及热环境的影响。

By replacing the typical no-slip boundary conditions with velocity slip and temperature jump boundary conditions, the predicting accuracy of the CFD modeling is improved effectively for high altitudes flow in the slip regime. The numerical iterations usually suffer form divergence when the Maxwell slip boundary conditions are implemented with very great number of grid points by the numerical method, which the velocity slip and temperature jump are evaluated through explicit calculation of the velocity and temperature gradient terms. In the theoretical analysis, it is shown that the explicit calculation of gradient terms displays the time advancement process of the Maxwell slip boundary conditions similar to a Jacobian iteration scheme, hence it must satisfy the condition of convergence. In order to remove the limitation from the condition of convergence, a numerical treatment which is convergent for arbitrary grid density was derived for the slip boundary conditions. Numerical tests were calculated to demonstrate the validity of the derived method. A space shuttle model was studied numerically for hypersonic flow at high altitudes. The results disagreement between the slip and no-slip conditions was compared and the influence of slip effects on vehicle aerodynamic characteristics and aerothermodynamic properties was analyzed.