The problem relating to the small-amplitude free capillary oscillations of an encapsulated spherical drop is solved theoretically in the framework of asymptotic methods.Liquids are supposed to be inviscid and immiscib...The problem relating to the small-amplitude free capillary oscillations of an encapsulated spherical drop is solved theoretically in the framework of asymptotic methods.Liquids are supposed to be inviscid and immiscible.The formulas derived are presented for different parameters of the inner and outer liquids,including densities,thickness of the outer liquid layer,and the surface and interfacial tension coefficients.The frequencies of oscillation of the encapsulated drop are studied in relation to several“modes”which can effectively be determined in experiments by photo and video analysis.The results are presented in terms of oscillation frequencies reported as a function of the mode number,the spherical layer thickness and the relation between the(surface and interfacial)tension coefficients.It is revealed that the influence of the liquids’parameters(and related variations)on the drop oscillation changes dramatically depending on whether oscillations are“in-phase”or“out-of-phase”.Frequencies for“in-phase”type oscillations can be correlated with linear functions of the shell thickness and the relative values of interfacial tension coefficient whereas the analogous dependencies for the“out-of-phase”type oscillation are essentially non-linear.展开更多
In this article, the transonic inviscid flow over a deformable airfoil with plunging motion is studied numerically. A finite volume method based on the Roe scheme developed in a generalized coordinate is used along wi...In this article, the transonic inviscid flow over a deformable airfoil with plunging motion is studied numerically. A finite volume method based on the Roe scheme developed in a generalized coordinate is used along with an arbitrary Lagrangian-Eulerian method and a dynamic mesh algorithm to track the instantaneous position of the airfoil. The effects of different governing parameters such as the phase angle, the deformation amplitude, the initial angle of attack, the flapping frequency, and the Mach number on the unsteady flow field and aerodynamic coefficients are investigated in detail. The results show that maneuverability of the airfoil under various flow conditions is improved by the deformation. In addition, as the oscillation frequency of the airfoil increases, its aerodynamic performance is significantly improved.展开更多
The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite...The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu- tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.展开更多
In this paper,we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space.Both compressible inviscid fluid and viscous fluid are considered with suita...In this paper,we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space.Both compressible inviscid fluid and viscous fluid are considered with suitable boundary conditions.We develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes.The method is an extension of the inverse Lax-Wendroff(ILW)procedure in our works(Cheng et al.,Appl Math Mech(Engl Ed)42:841-854,2021;Liu et al.)for 2D problems.Different from the 2D case,the local coordinate rotation in 3D required in the ILW procedure is not unique.We give a theoretical analysis to show that the boundary treatment is independent of the choice of the rotation,ensuring the method is feasible and valid.Both translation and rotation of the body are taken into account in this paper.In particular,we reformulate the material derivative for inviscid fluid on the moving boundary with no-penetration condition,which plays a key role in the proposed algorithm.Numerical simulations on the cylinder and sphere are given,demonstrating the good performance of our numerical boundary treatments.展开更多
基金supported by the Russian Science Foundation(Project 19-19-00598“Hydrodynamics and energetics of drops and droplet jets:formation,motion,break-up,interaction with the contact surface”).
文摘The problem relating to the small-amplitude free capillary oscillations of an encapsulated spherical drop is solved theoretically in the framework of asymptotic methods.Liquids are supposed to be inviscid and immiscible.The formulas derived are presented for different parameters of the inner and outer liquids,including densities,thickness of the outer liquid layer,and the surface and interfacial tension coefficients.The frequencies of oscillation of the encapsulated drop are studied in relation to several“modes”which can effectively be determined in experiments by photo and video analysis.The results are presented in terms of oscillation frequencies reported as a function of the mode number,the spherical layer thickness and the relation between the(surface and interfacial)tension coefficients.It is revealed that the influence of the liquids’parameters(and related variations)on the drop oscillation changes dramatically depending on whether oscillations are“in-phase”or“out-of-phase”.Frequencies for“in-phase”type oscillations can be correlated with linear functions of the shell thickness and the relative values of interfacial tension coefficient whereas the analogous dependencies for the“out-of-phase”type oscillation are essentially non-linear.
文摘In this article, the transonic inviscid flow over a deformable airfoil with plunging motion is studied numerically. A finite volume method based on the Roe scheme developed in a generalized coordinate is used along with an arbitrary Lagrangian-Eulerian method and a dynamic mesh algorithm to track the instantaneous position of the airfoil. The effects of different governing parameters such as the phase angle, the deformation amplitude, the initial angle of attack, the flapping frequency, and the Mach number on the unsteady flow field and aerodynamic coefficients are investigated in detail. The results show that maneuverability of the airfoil under various flow conditions is improved by the deformation. In addition, as the oscillation frequency of the airfoil increases, its aerodynamic performance is significantly improved.
基金supported in part by the National Science Foundationthe Office of Naval Research
文摘The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu- tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.
基金National Numerical Windtunnel project(No.NNW2019ZT4-B10)National Natural Science Foundation of China(Nos.11901555,11901213,11871448,11732016).
文摘In this paper,we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space.Both compressible inviscid fluid and viscous fluid are considered with suitable boundary conditions.We develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes.The method is an extension of the inverse Lax-Wendroff(ILW)procedure in our works(Cheng et al.,Appl Math Mech(Engl Ed)42:841-854,2021;Liu et al.)for 2D problems.Different from the 2D case,the local coordinate rotation in 3D required in the ILW procedure is not unique.We give a theoretical analysis to show that the boundary treatment is independent of the choice of the rotation,ensuring the method is feasible and valid.Both translation and rotation of the body are taken into account in this paper.In particular,we reformulate the material derivative for inviscid fluid on the moving boundary with no-penetration condition,which plays a key role in the proposed algorithm.Numerical simulations on the cylinder and sphere are given,demonstrating the good performance of our numerical boundary treatments.
