On parallel pre-conditioners for pressure Poisson equation in LES of complex geometry flows

China and India Award of Royal Academy of Engineering, UK to Drs Eldad Avital and Krishna M. Singh. Grant Numbers: Grant No. SEMF1A4R, Grant No. EP/L000261/

Self similar flows in finite or infinite two dimensional geometries

This study is concerned with several problems related to self-similar flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order to calculate them. One common characteristic to all applications of self-similar flows in real problems is that they involve fluid domains with large aspect ratios. Self-similar flows are admissible solutions of the Navier-Stokes equations in unbounded domains, and in applications it is assumed that the effects of the boundary conditions at the edge of the domain will have only a local effect and that a self- similar solution will be valid in most of the fluid domain. However, it has been shown that some similarity flows exist only under a very restricted set of conditions which need to be inferred from numerical simulations. Our main interest is to study several self-similar solutions related to flows in oscillating channels and to investigate the hypothesis that these solutions are reasonable approximations to Navier-Stokes flows in long, slender but finite domains

A Fast Poisson Solver For The Finite Difference Solution Of The Incompressible Navier-Stokes Equations

In this paper, a fast direct solver for the Poisson equation on the half-staggered grid is presented. The Poisson equation results from the projection method of the finite difference solution of the incompressible Navier-Stokes equations. To achieve our goal, new algorithms for diagonalizing a semidefinite pair are developed. The fast solver can also be extended to the three-dimensional case. The motivation and related issues in using this half-staggered grid are also discussed

Large Eddy Simulations of complex turbulent flows

In this dissertation a solution methodology for complex turbulent flows of industrial interests is developed using a combination of Large Eddy Simulation (LES) and Immersed Boundary Method (IBM) concepts. LES is an intermediate approach to turbulence simulation in which the onus of modeling of “universal” small scales is appropriately transferred to the resolution of “problem-dependent” large scales or eddies. IBM combines the efficiency inherent in using a fixed Cartesian grid to compute the fluid motion, along with the ease of tracking the immersed boundary at a set of moving Lagrangian points. Numerical code developed for this dissertation solves unsteady, filtered Navier-Stokes equations using high-order accurate (fourth order in space) finite difference schemes on a staggered grid with a fractional step approach. Pressure Poisson equation is solved using a direct solver based on a matrix diagonalization technique. Second order accurate Adams-Bashforth scheme is used for temporal integration of equations. Dynamic mixed model (DMM) is used to model subgrid scale (SGS) terms. It can represent large scale anisotropy and back-scatter of energy from small-to-large scale through scale-similar term and maintain the energy drain through eddy viscosity term whose coefficient is allowed to change with in the computational domain. This code is validated for several bench-mark problems and is demonstrated to solve complex moving geometry problem such as stator-rotor interaction. A number of parametric studies on jets-in-crossflow are performed to understand complex fluid dynamics issues pertaining to film-cooling. These studies included effects of variation of hole-aspect ratio, jet injection angle, free-stream turbulence intensity and free-stream turbulence length scales on the coherent structure dynamics for jets-in-crossflow. Fundamental flow physics and heat transfer issues are addressed by extracting coherent structures from time-dependent three dimensional flow fields of film-cooling by inclined jet and studying their influence on the film-cooled surface heat transfer. A direct method to perform heat transfer calculations in periodic geometries is proposed and applied to internal cooling in rotating ribbed duct. Immersed boundary method is used to render complex geometry of trapped vortex combustor on Cartesian grid and fluid mixing inside trapped vortex cavity is studied in detail