考虑黏性及压缩效应的旋涡运动特性

The motion characteristics of vortices considering the viscousand compressible effects

采用扩散速度法处理黏性作用项的离散涡法,数值模拟了旋涡在黏性不可压流场中的运动;推导了可压缩流中的旋涡运动方程,对不可压缩流中的Biot-Savart方程进行了可压缩修正,进而用离散涡方法求解出非定常、不稳定、可压缩流场中的旋涡运动. 分析了胀量及黏性扩散作用对旋涡运动的影响,通过大量长时间行为的数值试验得出了一系列结果. 结果表明: 为了真实地反映旋涡在实际流体中的运动规律,必须考虑黏性及压缩性的影响.

Recently the vortex method has been developed to simulate two dimensional incompressible separated flows at high Reynolds number. The motion of the vortex couple is studied in bounded and unbounded incompressible flow with the diffusion velocity method. The results show that little variation of viscous coefficient will change the motion of the vortex couple seriously. When the distance between the vortex couple is bigger than one certain distance, the viscous diffusion of the two vortices can be neglected. The diffusion velocity of the couple becomes bigger and dissipates. The Biot-Savart formulation of the compressible flow is deduced. The induced velocity of the vortices in the compressible flow is different from that in the incompressible flow due to the dilatation. The variation of the vorticity and the divergence of the velocity influence the vortices motion. When the divergence of the velocity is zero, the compressible Biot-Savart equation is degenerated to the incompressible Biot-Savart formulation. The revised Biot-Savart law of the compressible flow simulates the motion of the vortex couple in the unbounded flow. The motion of the vortex couple in the compressible flow is different from that in the incompressible flow. The vortex couple of the same direction moves outward along a circle that is not accurately a real circle. The vortex couple of the opposite direction moves inward or outward along with two parallel lines when the dilatation is negative or positive. The vortices will dissipate faster when the absolute magnitude of the dilatation is bigger.