arXiv subjects

Linlin Kang

Publications and source records attributed to Linlin Kang.

3 recordsLinked to original sources

arXiv2017

Minimum-domain impulse theory for unsteady aerodynamic force

We extend the impulse theory for unsteady aerodynamics, from its classic global form to finite-domain formulation then to minimum-domain form, and from incompressible to compressible flows. For incompressible flow, the minimum-domain impulse theory raises the finding of Li and Lu (J. Fluid Mech., 712: 598-613, 2012) to a theorem: The entire force with discrete wake is completely determined by only the time rate of impulse of those vortical structures still connecting to the body, along with the Lamb-vector integral thereof that captures the contribution of all the rest disconnected vortical structures. For compressible flow, we find that the global form in terms of the curl of momentum, obtained by Huang (Unsteady Vortical Aerodynamics. Shanghai Jiaotong Univ. Press, 1994), can be generalized to having arbitrary finite domain, but the formula is cumbersome and in general the curl of momentum no longer has discrete structure and hence no minimum-domain theory exists. Nevertheless, as the measure of transverse process only, the unsteady field of vorticity may still have discrete wake. This leads to a minimum-domain compressible vorticity-moment theory in terms of density-weighted vorticity (but it is beyond the classic concept of impulse). These new findings and applications have been confirmed by our numerical experiments. The results not only open an avenue to combine the theory with computation-experiment in wide applications, but also reveals a physical truth that it is no longer necessary to account for all wake vortical structures in computing the force and moment.

physics.flu-dyn↗

arXiv2016

Lift and drag in three-dimensional steady viscous and compressible flow

In a recent paper, Liu, Zhu and Wu (2015, {\it J. Fluid Mech.} {\bf 784}: 304) present a force theory for a body in a two-dimensional, viscous, compressible and steady flow. In this companion paper we do the same for three-dimensional flow. Using the fundamental solution of the linearized Navier-Stokes equations, we improve the force formula for incompressible flow originally derived by Goldstein in 1931 and summarized by Milne-Thomson in 1968, both being far from complete, to its perfect final form, which is further proved to be universally true from subsonic to supersonic flows. We call this result the \textit{unified force theorem}, which states that the forces are always determined by the vector circulation $\pGamma_\phi$ of longitudinal velocity and the scalar inflow $Q_\psi$ of transverse velocity. Since this theorem is not directly observable either experimentally or computationally, a testable version is also derived, which, however, holds only in the linear far field. We name this version the \textit{testable unified force formula}. After that, a general principle to increase the lift-drag ratio is proposed.

physics.flu-dyn↗

arXiv2016

Zonal structure of unbounded external-flow and aerodynamics

This paper starts from the far-field behaviours of velocity field in externally-unbounded flow. We find that the well-known algebraic decay of disturbance velocity as derived kinematically is too conservative. Once the kinetics is taken into account by working on the fundamental solutions of far-field linearized Navier-Stokes equations, it is proven that the furthest far-field zone adjacent to the uniform fluid at infinity must be unsteady, viscous and compressible, where all disturbances degenerate to sound waves that decay exponentially. But this optimal rate does not exist in some commonly used simplified flow models, such as steady flow, incompressible flow and inviscid flow, because they actually work in true subspaces of the unbounded free space, which are surrounded by further far fields of different nature. This finding naturally leads to a zonal structure of externally-unbounded flow field. The significance of the zonal structure is demonstrated by its close relevance to existing theories of aerodynamic force and moment in external flows, including the removal of the difficulties or paradoxes inherent in the simplified models.

physics.flu-dyn↗