热声板叠内低马赫数流动的数值方法研究

NUMERICAL RESEARCH ON THE LOW MACH NUMBER FLOW IN THERMODYNAMICS STACK PLATE

采用AUSMDV(P)格式研究热声制冷机板叠内的低马赫数可压缩流动问题,采用二阶隐式格式进行时间推进。考察了此格式在计算全马赫数可压缩流动问题上的准确性。并在此基础上,验证了界面质量流量采用AUS- MDV(P)格式求得,可以有效改善激波的捕捉能力;验证了格式中的预处理思想,解决了由低马赫数可压缩流动引起的压力和速度的失耦问题;验证了利用格式中将压力扩散的影响考虑到界面质量流量的方法,解决了由于激波的产生而引起的数值振荡和扩散问题。同时,分析了不同时刻,板叠附近沿轴线方向的速度变化以及封闭端附近速度随时间的变化规律。由模拟结果可以看出在t=0.065s时,活塞向左移动,此时速度u(0,0.065)<0,激波从封闭端向入口方向移动。在t=0.067s时,活塞向右移动,此时速度u(0,0.067)>0,激波从人口向封闭端移动。距封闭端x/L=0.98148,y/L=0.84处,不同时刻下,激波的出现会使速度急剧增大形成一个尖峰。为进一步探讨在新型制冷技术中广泛存在的流动和换热耦合的低马赫数可压缩交变流动问题奠定了一定基础。

The AUSMDV （P） scheme was applied for low Mach number compressible oscillating flow in the thermodynamics stack plate. And the two-order implicit scheme was used to advance the flow equations in time. In order to demonstrate the accuracy and applicability of the method, all Mach number compressible flows were computed. On the basis of validation, AUSMDV（P） scheme showed its shock capturing ability. And the precondition step in this scheme can improve the decoupling of pressure and velocity caused by low Mach number compressible flows. The results shown that the axial velocity at t = 0.065s at that time the piston is moving to left （u（0,0.065） 〈 0） and the shock wave is moving from the closed end to the piston and the axial velocity at t = 0.067s at that time the piston is moving to the right （ u（0, 0.067） 〉0） and the shock wave is moving toward the closed end. Near the closed end x/L =0.98148, y/L =0.84, at different times, the velocity increases sharply at interval because of shock waves.