Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

https://math.berkeley.edu/~sethian/2006/Papers/sethian.levelsetreviewarticle.2001.pdf

Evolution, implementation, and application of level set and fast marching methods for advancing fronts

The hydrodynamics of anguilliform swimming motions was investigated using three-dimensional simulations of the fluid flow past a self-propelled body. The motion of the body is not specified a priori, but is instead obtained through an evolutionary algorithm used to optimize the swimming efficiency and the burst swimming speed. The results of the present simulations support the hypothesis that anguilliform swimmers modify their kinematics according to different objectives and provide a quantitative analysis of the swimming motion and the forces experienced by the body. The kinematics of burst swimming is characterized by the large amplitude of the tail undulations while the anterior part of the body remains straight. In contrast, during efficient swimming behavior significant lateral undulation occurs along the entire length of the body. In turn, during burst swimming, the majority of the thrust is generated at the tail, whereas in the efficient swimming mode, in addition to the tail, the middle of the body contributes significantly to the thrust. The burst swimming velocity is 42% higher and the propulsive efficiency is 15% lower than the respective values during efficient swimming. The wake, for both swimming modes, consists largely of a double row of vortex rings with an axis aligned with the swimming direction. The vortex rings are responsible for producing lateral jets of fluid, which has been documented in prior experimental studies. We note that the primary wake vortices are qualitatively similar in both swimming modes except that the wake vortex rings are stronger and relatively more elongated in the fast swimming mode. The present results provide quantitative information of three-dimensional fluid-body interactions that may complement related experimental studies. In addition they enable a detailed quantitative analysis, which may be difficult to obtain experimentally, of the different swimming modes linking the kinematics of the motion with the forces acting on the self-propelled body. Finally, the optimization procedure helps to identify, in a systematic fashion, links between swimming motion and biological function.

Simulations of optimized anguilliform swimming.

Mathematical and numerical modeling of two-phase compressible flows with micro-inertia

The present paper is devoted to the computation of two-phase flows using the two-fluid approach. The overall model is hyperbolic and has no conservative form. No instantaneous local equilibrium between phases is assumed, which results in a two-velocity two-pressure model. Original closure laws for interfacial velocity and interfacial pressure are proposed. These closures allow to deal with discontinuous solutions such as shock waves and contact discontinuities without ambiguity with the definition of Rankine–Hugoniot jump relations. Each field of the convective system is investigated, providing maximum principle for the volume fraction and the positivity of densities and internal energies are ensured when focusing on the Riemann problem. Two-finite volume methods are presented, based on the Rusanov scheme and on an approximate Godunov scheme. Relaxation terms are taken into account using a fractional step method. Eventually, numerical tests illustrate the ability of both methods to compute two-phase flows.

/pdf/numerical-modeling-of-two-phase-flows-using-the-two-fluid-272czs4szb.pdf

Numerical modeling of two-phase flows using the two-fluid two-pressure approach

We analyse and improve a recently-proposed two-phase flow model for the statistical evolution of two-fluid mixing. A hyperbolic equation for the volume fraction, whose characteristic speed is the average interface velocity v*, plays a central role. We propose a new model for v* in terms of the volume fraction and fluid velocities, which can be interpreted as a constitutive law for two-fluid mixing. In the incompressible limit, the two-phase equations admit a self-similar solution for an arbitrary scaling of lengths. We show that the constitutive law for v* can be expressed directly in terms of the volume fraction, and thus it is an experimentally measurable quantity. For incompressible Rayleigh–Taylor mixing, we examine the self-similar solution based on a simple zero-parameter model for v*. It is shown that the present approach gives improved agreement with experimental data for the growth rate of a Rayleigh–Taylor mixing layer.Closure of the two-phase flow model requires boundary conditions for the surfaces that separate the two-phase and single-phase regions, i.e. the edges of the mixing layer. We propose boundary conditions for Rayleigh–Taylor mixing based on the inertial, drag, and buoyant forces on the furthest penetrating structures which define these edges. Our analysis indicates that the compatibility of the boundary conditions with the two-phase flow model is an important consideration. The closure assumptions introduced here and their consequences in relation to experimental data are compared to the work of others.

J. Glimm

Papers

Two-phase modelling of a fluid mixing layer