物体在不可压缩流场中所受的流体动力表达式

(厦门大学航空航天学院,福建 厦门 361005)

飞艇; 非定常气动力; 不可压缩流场; 涡动力学

On the Fluid Dynamic Force of a Solid Body Moving in the Incompressible Flow
LIN Xinwu,LIN Xianwu*,LAN Weiyao

(School of Aerospace Engineering,Xiamen University,Xiamen 361005,China)

airship; unsteady state hydrodynamic force; incompressible flow field; vortical dynamics

DOI: 10.6043/j.issn.0438-0479.201705046

备注

为统一有粘和无粘不可压缩流场中的流体动力表达式,在允许滑移边界条件的情况下,重新推导了不可压缩流场中运动体的流体动力表达式.根据流场动量定理将流体动力表示为无穷远边界上流场应力的积分与流场动量变化率积分的代数和; 再利用导数矩转换(DMT)公式分别将这两个积分结果进行分解,并根据速度在无穷远处的渐近特性将这些分解结果组合并简化成流场第一涡量矩的积分及流场在物面边界上切向速度矩的积分之和,得到了新的流体动力表达式.理论分析和算例证明了这种新的流体动力表达式在无粘流的情况下收敛于Lamb的流体动力表达式,而在有粘流的情况下与涡动力学理论一致.

For unifying the expression of the fluid dynamic force in the viscous and inviscid incompressible flow field,the expression is re-deduced with the slip boundary condition is permitted.The fluid dynamic force is expressed as the algebraic sum of the integral of the flow stress on the infinity boundary and the integral of the change rate of the flow field momentum based on the momentum theorem.Then,the derivative moment transformation(DMT)is adopted to decompose these two integrals,then decomposition results are combined and simplified into the sum of the integral of the first vortex moment in the flow field and the integral of the tangent velocity moment on the solid surface based on the asymptotic property of the velocity at infinity,and the new expression of the fluid dynamic force is obtained.Theoretical analysis and the example show that this new expression of the fluid dynamic force not only converges to the Lamb's expression in the inviscid flow,but also is consistent with the theory of vortical dynamics in the viscous flow.