University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 5-2012 Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using OpenFOAM Austin Barrett Kimbrell University of Tennessee, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Part of the Aerodynamics and Fluid Mechanics Commons, Computational Engineering Commons, and the Computer-Aided Engineering and Design Commons Recommended Citation Kimbrell, Austin Barrett, "Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using OpenFOAM. " Master's Thesis, University of Tennessee, 2012. https://trace.tennessee.edu/utk_gradthes/1173 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Austin Barrett Kimbrell entitled "Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using OpenFOAM." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Master of Science, with a major in Mechanical Engineering. John S. Steinhoff, Major Professor We have read this thesis and recommend its acceptance: K. C. Reddy, Joseph C. Yen Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using OpenFOAM A Thesis Presented for the Master of Science Degree The University of Tennessee, Knoxville Austin Barrett Kimbrell May 2012 Copyright © 2012 by Austin B. Kimbrell All rights reserved. ii ACKNOWLEDGEMENTS I would like to express sincere appreciation to my advisor Dr. John Steinhoff for his guidance in developing this work and providing a challenging, yet enjoyable experience. I would also like to thank my other advising committee members, Dr. K.C. Reddy and Dr. Joseph Yen, for their time and helpful comments. I would like to especially acknowledge Dr. Yen for all of the discussion, insight, and advice he has provided over the past few years on topics both work and school-related, which has helped grow my technical knowledge and expertise in computational methods and aerodynamics. He is not only a friend but a true mentor and I am very grateful to work with him. I offer special thanks and acknowledgement to Chris Connor and Dr. Ed Duell at Jacobs Technology for all of the support and opportunities for technical advancement given to me. Jacobs Technology has been an invaluable resource the past few years by providing funding for my continued education as well as the available computational resources to complete this work. The working environment at Jacobs is truly unique and I am thankful to be a part of it. Lastly, I owe the greatest thanks to my wife, Oxana, and my daughter, Sophia, for all of their support and understanding during this whole endeavor. It wasn’t always easy, but they were always there for me to provide encouragement and keep me on the path to success. iii ABSTRACT Vorticity Confinement (VC) is a numerical technique which enhances computation of fluid flows by acting as negative diffusion within the limit of vortical regions, preventing the inherent numerical dissipation present with conventional methods. VC shares similarities with large eddy simulation (LES), but its behavior is based on a stable negative dissipation of vortical structures controlled by the automatic balance between two parameters, μ [mu] and ε [epsilon]. In this thesis, three-dimensional, parallel-computing Navier-Stokes solvers with VC are developed using the OpenFOAM computational framework. OpenFOAM is an open-source collection of C++ libraries developed for computational fluid dynamics. Object-oriented programming concepts are used to develop the finite volume solvers, which introduce the VC source term into the governing equations as a body force. An immersed boundary method is implemented with the VC module to mitigate limitations of body-fitted grids. The developed solvers are examined using two-dimensional boundary layer simulations, which demonstrate that for a given range of confinement parameters the boundary layer can be relaxed to a desired height to approximate a turbulent boundary layer thickness. Unlike wall function models, however, the VC boundary layer can still separate in an adverse pressure gradient. The application of VC to a two-dimensional advecting compact vortex results in the propagation of the vortex without dissipation. Solutions for a three-dimensional backward-facing step are validated against experimental data. The VC simulations show excellent agreement with experimental data for a fixed value of μ [mu] and a given range of ε [epsilon]. Coarsening the mesh increases inherent numerical dissipation and requires using a smaller value of μ [mu] to show good agreement with experimental data. Turbulence kinetic energy spectra exhibit a -5/3 slope inertial wavenumber range indicating proper turbulence cascading using the VC model. Simulation of a Formula One racecar represented by an iv immersed surface demonstrates the suitability of VC for fast prototyping. A time- accurate VC analysis on a 3,400,000 cell coarse mesh appears more realistic in the wake region than a steady RANS simulation on a 30,000,000 cell mesh. The VC solution appears visually comparable to an LES solution but represents a fraction of the computational cost. v TABLE OF CONTENTS Chapter 1 Introduction .......................................................................................... 1 1.1 Objectives ................................................................................................... 3 1.2 General Approach ....................................................................................... 4 Chapter 2 Vorticity Confinement ........................................................................... 6 2.1 VC1 Formulation ......................................................................................... 7 2.1.1 Surface Confinement ............................................................................ 9 2.2 VC2 Formulation ....................................................................................... 10 2.3 Compressible Vorticity Confinement ......................................................... 11 2.4 Dimensional Analysis of ε .......................................................................... 13 2.4.1 Dynamic Vorticity Confinement ........................................................... 15 Chapter 3 Introduction to OpenFOAM ................................................................ 16 3.1 Introduction to Object-Oriented Programming ........................................... 17 3.2 Programming in OpenFOAM ..................................................................... 19 3.3 OpenFOAM Data Structure ....................................................................... 20 3.4 Standard Case Structure ........................................................................... 21 3.4.1 system Directory ................................................................................. 24 3.4.2 constant Directory ............................................................................... 24 3.4.3 Time Directories .................................................................................. 26 3.5 OpenFOAM Utilities ................................................................................... 26 3.5.1 Pre-processing .................................................................................... 27 3.5.2 Meshing .............................................................................................. 27 3.5.3 Domain Decomposition ....................................................................... 28 3.5.4 Post-processing .................................................................................. 29 3.5.5 Run-time Processing........................................................................... 30 3.5.6 Solution Monitoring ............................................................................. 30 3.5.7 Additional Community-developed Tools.............................................. 31 Chapter 4 Solution Methodology ......................................................................... 32 4.1 Finite Volume Approach ............................................................................ 33 vi 4.1.1 Conservation Equations in Integral Form ............................................ 34 4.2 Pressure-Correction Methods ................................................................... 37 4.2.1 PISO Algorithm for Time-Accurate Simulation .................................... 41 4.2.2 SIMPLE Algorithm for Steady-State Simulation .................................. 43 4.2.3 Rhie-Chow Treatment in OpenFOAM ................................................. 44 4.3 Vorticity Confinement Implementation ....................................................... 45 4.3.1 Parallelization ..................................................................................... 47 4.3.2 VC as an Immersed