Subgrid-modelling in LES of compressible flow

Subgrid-models for Large Eddy Simulation (LES) of compressible turbulent flow are tested for the three-dimensional mixing layer. For the turbulent stress tensor the recently developed dynamic mixed model yields reasonable results.A priori estimates of the subgrid-terms in the filtered energy equation show that the usually neglected pressure-dilatation and turbulent dissipation rate are as large as the commonly retained pressure-velocity subgrid-term. Models for all these terms are proposed: a similarity model for the pressure-dilatation, similarity andk-dependent models for the turbulent dissipation rate and a dynamic mixed model for the pressure-velocity subgrid-term. Actual LES demonstrates that for a low Mach number all subgrid-terms in the energy equation can be neglected, while for a moderate Mach number the effect of the modelled turbulent dissipation rate is larger than the combined effect of the other modelled subgrid-terms in the filtered energy equation.     

Point-Particle DNS and LES of Particle-Laden Turbulent flow - a state-of-the-art review

Particle-laden or droplet-laden turbulent flows occur in many industrial applications and in natural phenomena. Knowledge about the properties of these flows can help to improve the design of unit operations in industry and to predict for instance the occurrence of rain showers. This knowledge can be obtained from experimental research and from numerical simulations. In this paper a review is given of numerical simulation methods for particle-laden flows. There are various simulation methods possible. They range from methods in which all details, including the flow around each particle, are resolved, via point-particle methods, in which for each particle an equation of motion is solved, to Eulerian methods in which equations for particle concentration and velocity are solved. This review puts the emphasis on the intermediate class of methods, the Euler-Lagrange methods in which the continuous phase is described by an Eulerian approach and the dispersed phase in a Lagrangian way with equations of motion for each individual particle.     

A 2D boundary element method for simulating the deformation of axisymmetric compound non‐Newtonian drops

The boundary integral formulation of the solution to the Stokes equations is used to describe the deformation of small compound non‐Newtonian axisymmetric drops suspended in a Newtonian fluid that is subjected to an axisymmetric flow field. The non‐Newtonian stress is treated as a source term in the Stokes equations, which yields an extra integral over the domains containing non‐Newtonian material. By transforming the integral representation for the velocity to cylindrical co‐ordinates and performing the integration over the azimuthal direction analytically, the dimension of the problem can be reduced from three to two. A boundary element method for the remaining two‐dimensional problem aimed at the simulation of the deformation of such axisymmetric compound non‐Newtonian drops is developed. Apart from a numerical validation of the method, simulation results for a drop consisting of an Oldroyd‐B fluid and a viscoelastic material are presented. Moreover, the method is extended to compound drops that are composed of a viscous inner core encapsulated by a viscoelastic material. The simulation results for these drops are verified against theoretical results from literature. Moreover, it is shown that the method can be used to identify the dominant break‐up mechanism of compound drops in relation to the specific non‐Newtonian character of the membrane. Copyright © 1999 John Wiley & Sons, Ltd.     

A boundary integral method for two-dimensional (non)-Newtonian drops in slow viscous flow

A boundary integral method for the simulation of the time-dependent deformation of Newtonian or non-Newtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term which yields an extra integral over the domain of the drop. The implementation of the boundary conditions is facilitated by rewriting the domain integral by means of the Gauss divergence theorem. To apply the divergence theorem smoothness assumptions are made concerning the non-Newtonian stress tensor. The correctness of these assumptions in actual simulations is checked with a numerical validation procedure. The method appears mathematically correct and the numerical algorithm is second order accurate. Besides this validation we present simulation results for a Newtonian drop and a drop consisting of an Oldroyd-B fluid. The results for Newtonian and non-Newtonian drops in two dimensions indicate that the steady state deformation is quite independent of the drop-fluid. The deformation process, however, appears to be strongly dependent on the drop-fluid. For the non-Newtonian drop a mechanical model is developed to describe the time-dependent deformation of the cylinder for small capillary numbers.