Research On Physical Properties And Calculation Method Of Apparent Mass Based On Vorticity Field

When a rigid body accelerates in the fluid,it will move with the nearby fluid,equivalent to increase an additional mass of the body,i.e.,apparent mass.The role of apprent mass effects in coastal dynamics,flapping-wing aerodynamics theory,and large-scale airships,submarine maneuverability and other research areas is very important.The concept of apprent mass is raised very early,but for a long time its definition and calculation methods are based on the ideal fluid and potential flow hypothesis,which are not conducive to understanding its physical properties or using it to carry on hydrodynamic analysis,and even the apparent mass is influenced by external fluid environment or not is controversial.This paper abandons the ideal fluid and potential flow hypothesis,re-examine the apparent mass from the perspective of vorticity in real fluid conditions and obtains some valuable conclusions in theory,calculation and application.First is the aspect of theory.Starting from the definition of apparent mass,this paper points out that the essence of apparent mass is to change the vorticity moments of the vorticity layer on the surface of the body.It is theoretically proved that the apparent mass determined by the potential function method is mathematically equivalent to the apparent mass defined by the vorticity method when there is no vorticity exsits in the interior fluid.Further,the vorticity moment theory is used to study the influence of the external vortex and the motion state of the body on the apparent mass.It is found that the apparent mass is not affected by the external fluid environment and motion state of the body.With the help of vorticity theory,the influence of thickness,curvature,fineness ratio and trailing edge shape on the apparent mass is also analyzed on mechanism.In the aspect of calculation,the vorticity layers of two-dimensional,axisymmetric and three-dimensional bodies are approximate to point vortices,axisymmetric vorticity loops and quadrangular vorticity loops respectively.The vorticity element method for calculating the two-dimensional vortex point and the sub-vorticity loop method are developed to improve the accuracy of the calculation of the surface vorticity.The apprent mass calculation formulas of two-dimensional,axisymmetric and three-dimensional arbitrary shape bodies are deduced based on the vorticity moment theorem.The comparison with the potential function method and the experimental results shows that the formulas have higher accuracy and rapid convergence.In the aspect of application,the two-dimensional unsteady discrete vortex program is developed.The vorticity theory is used to analyze the effect of apparent mass and starting vortex on the lift generation in the acceleration of the airfoil.It is found that the lift increaseing effect of the apparent mass is very obvious in the early stage of acceleration motion.In the middle and late stages of acceleration motion,the effect of apparent mass is gradually reduced to zero.On the other hand,the starting vortex contributes most of the lift in the middle and late stages of acceleration motion,and the contribution of the magnitude of the lift is proportional to the angle of attack.So increase angle of attack,start with a lower acceleration is the most effective way to get a stable and lasting high lift.