Parmar M, Haselbacher A, Balachandar S
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA.
Philos Trans A Math Phys Eng Sci. 2008 Jun 28;366(1873):2161-75. doi: 10.1098/rsta.2008.0027.
The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c(infinity)t/R approximately >10, where c(infinity) is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.
研究了亚临界可压缩流中圆柱和球体上的非定常无粘力。在不可压缩流的极限情况下，圆柱或球体上的非定常无粘力是所谓的附加质量力，它与物体排开的质量和瞬时加速度的乘积成正比。在可压缩流中，有限的声传播速度意味着由瞬时施加的恒定加速度产生的非定常无粘力是逐渐发展的，并且仅在无量纲时间c(∞)t/R大约>10时才达到稳定值，其中c(∞)是自由流声速，R是圆柱或球体的半径。在此极限下，可以定义一个有效附加质量系数。我们研究的主要结论是，自由流马赫数对非定常力的峰值和有效附加质量系数都有显著影响。在自由流马赫数为0.5时，球体的有效附加质量系数约为不可压缩值的两倍。与脉冲加速度相结合，可压缩流中的非定常无粘力可能比不可压缩理论预测的力大四倍以上。此外，随着马赫数的增加，比热比在非定常力上的影响变得更加明显。
