Large eddy simulation of turbulent flows in complex and moving rigid geometries using the immersed boundary method

Abstract

SUMMARYA large eddy simulation (LES) methodology for turbulent ows in complex rigid geometries is developed using the immersed boundary method (IBM). In the IBM body force terms are added to the momentum equations to represent a complex rigid geometry on a ÿxed Cartesian mesh. IBM combines the e ciency inherent in using a ÿxed Cartesian grid and the ease of tracking the immersed boundary at a set of moving Lagrangian points. Speciÿc implementation strategies for the IBM are described in this paper. A two-sided forcing scheme is presented and shown to work well for moving rigid boundary problems. Turbulence and ow unsteadiness are addressed by LES using higher order numerical schemes with an accurate and robust subgrid scale (SGS) stress model. The combined LES-IBM methodology is computationally cost-e ective for turbulent ows in moving geometries with prescribed surface trajectories.Several example problems are solved to illustrate the capability of the IBM and LES methodologies. The IBM is validated for the laminar ow past a heated cylinder in a channel and the combined LES-IBM methodology is validated for turbulent ÿlm-cooling ows involving heat transfer. In both cases predictions are in good agreement with measurements. LES-IBM is then used to study turbulent uid mixing inside the complex geometry of a trapped vortex combustor. Finally, to demonstrate the full potential of LES-IBM, a complex moving geometry problem of stator-rotor interaction is solved.

A divergence‐free interpolation scheme for the immersed boundary method

“…This is shown to result in a consistent set of equations; however, the present work shows that using the pseudo-velocity to define the force density can result in poor satisfaction of the boundary conditions on the surface of the object, which may result in permeability of an impermeable surface. However, the poor satisfaction of boundary conditions on the surface of the object may not greatly impact gross metrics such as drag coefficients; the authors and others [3,7,8,12,15] have computed drag coefficients for blunt body flows such as cylinders and spheres that have closely matched those obtained experimentally and from computational work involving body-fitted meshes. The present work demonstrates that satisfaction of the boundary conditions on the surface of the object is strongly a function of the time step, if the pseudo-velocity is used to define the force density.…”

Turbulent flow simulation using LES with dynamical mixed one‐equation subgrid models in complex geometries

“…Though LES has been successfully applied to simulate the turbulence flows with complex geometry [20][21][22], relatively few studies have been reported using LES for simulating the flow in a strong three-dimensional (3D) skew Francis hydro-turbine passage. A few studies of DNS and LES of fully turbulent flow in a low pressure turbine passage have been done, only for two-dimensional (2D) blade cascade simplifications [23][24][25].…”

A robust direct-forcing immersed boundary method with enhanced stability for moving body problems in curvilinear coordinates

“…The same condition is only first-order accurate in the p-form, but has nonetheless been used in the literature (e.g. [29,14]). Following a similar analysis to Kim and Moin [26], a second order accuracy can be achieved in the p−form by enforcing the immersed boundary condition,û Γ = U n Γ + ∆tGφ n−1 Γ (the derivation is deferred to Appendix A).…”