Mathematical and Numerical Modeling of Turbulent Flows.

The present work is devoted to the development and implementation of a computational framework to perform numerical simulations of low Mach number turbulent flows over complex geometries. The algorithm under consideration is based on a classical predictor-corrector time integration scheme that employs a projection method for the momentum equations. The domain decomposition strategy is adopted for distributed computing, displaying very satisfactory levels of speed-up and efficiency. The Immersed Boundary Methodology is used to characterize the presence of a complex geometry. Such method demands two separate grids: An Eulerian, where the transport equations are solved with a Finite Volume, second order discretization and a Lagrangian domain, represented by a non-structured shell grid representing the immersed geometry. The in-house code developed was fully verified by the Method of Manufactured Solutions, in both Eulerian and Lagrangian domains. The capabilities of the resulting computational framework are illustrated on four distinct cases: a turbulent jet, the Poiseuille flow, as a matter of validation of the implemented Immersed Boundary methodology, the flow over a sphere covering a wide range of Reynolds numbers, and finally, with the intention of demonstrating the applicability of Large Eddy Simulations - LES - in an industrial problem, the turbulent flow inside an industrial fan.

[1]  Miltiadis V. Papalexandris,et al.  Time-accurate calculation of variable density flows with strong temperature gradients and combustion , 2006, J. Comput. Phys..

[2]  Patrick J. Roache,et al.  Symbolic manipulation and computational fluid dynamics , 1983 .

[3]  Ionut Danaila,et al.  Direct numerical simulation of bifurcating jets , 2000 .

[4]  Charles Meneveau,et al.  Generalized Smagorinsky model for anisotropic grids , 1993 .

[5]  João Marcelo Vedovoto,et al.  Application of the method of manufactured solutions to the verification of a pressure-based finite-volume numerical scheme , 2011 .

[6]  C. Pierce,et al.  Progress-variable approach for large-eddy simulation of turbulent combustion , 2001 .

[7]  P. Comte,et al.  Large-Eddy Simulations of Turbulence: Vortex dynamics , 2005 .

[8]  S. L. Yilmaz,et al.  RANS/PDF and LES/FDF for prediction of turbulent premixed flames , 2008 .

[9]  D. Lilly,et al.  A proposed modification of the Germano subgrid‐scale closure method , 1992 .

[10]  João Marcelo Vedovoto.  Mathematical and numerical modeling of turbulent reactive ows using a hybrid LES / PDF methodology , 2011 .

[11]  D. Haworth.  Progress in probability density function methods for turbulent reacting flows , 2010 .

[12]  Gerry E. Schneider,et al.  A MODIFIED STRONGLY IMPLICIT PROCEDURE FOR THE NUMERICAL SOLUTION OF FIELD PROBLEMS , 1981 .

[13]  Jianren Fan,et al.  Combined multi-direct forcing and immersed boundary method for simulating flows with moving particles , 2008 .

[14]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[15]  Boyce E. Griffith,et al.  On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems , 2005 .

[16]  J. Pereira,et al.  A new incompressible Navier-Stokes solver combining Fourier pseudo-spectral and immersed boundary methods , 2010 .

[17]  Rubens Campregher Junior.  Modelagem matemática tridimensional para problemas de interação fluido-estrutura , 2005 .

[18]  Norbert Peters,et al.  The detailed flame structure of highly stretched turbulent premixed methane-air flames , 1996 .

[19]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[20]  I. Celik,et al.  Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling , 2001 .

[21]  Server L. Yilmaz,et al.  An Irregularly Portioned Lagrangian Monte Carlo Method for Turbulent Flow Simulation , 2011, J. Sci. Comput..

[22]  H. V. D. Vorst,et al.  Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems☆ , 1981 .

[23]  M. Lesieur,et al.  New Trends in Large-Eddy Simulations of Turbulence , 1996 .

[24]  Bengt Fornberg,et al.  Steady viscous flow past a sphere at high Reynolds numbers , 1988, Journal of Fluid Mechanics.

[25]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[26]  Marcel Lesieur,et al.  A numerical investigation of the coherent vortices in turbulence behind a backward-facing step , 1993, Journal of Fluid Mechanics.

[27]  T. Poinsot,et al.  Theoretical and numerical combustion , 2001 .

[28]  P. Moin,et al.  A dynamic subgrid‐scale model for compressible turbulence and scalar transport , 1991 .

[29]  M. Uhlmann.  An immersed boundary method with direct forcing for the simulation of particulate flows , 2005, 1809.08170.

[30]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[31]  C. Meneveau,et al.  A Lagrangian dynamic subgrid-scale model of turbulence , 1994, Journal of Fluid Mechanics.