INVESTIGATION OF COMBUSTIVE FLOWS AND DYNAMIC MESHING IN COMPUTATIONAL FLUID DYNAMICS A Thesis by STEVEN B. CHAMBERS Submitted to the O–ce of Graduate Studies of Texas A&M University in partial fulflllment of the requirements for the degree of MASTER OF SCIENCE December 2004 Major Subject: Aerospace Engineering INVESTIGATION OF COMBUSTIVE FLOWS AND DYNAMIC MESHING IN COMPUTATIONAL FLUID DYNAMICS A Thesis by STEVEN B. CHAMBERS Submitted to Texas A&M University in partial fulflllment of the requirements for the degree of MASTER OF SCIENCE Approved as to style and content by: Paul G. A. Cizmas Leland A. Carlson (Chair of Committee) (Member) Raytcho D. Lazarov Othon K. Rediniotis (Member) (Member) Walter E. Haisler (Head of Department) December 2004 Major Subject: Aerospace Engineering iii ABSTRACT Investigation of Combustive Flows and Dynamic Meshing in Computational Fluid Dynamics. (December 2004) Steven B. Chambers, B.S., Texas A&M University Chair of Advisory Committee: Dr. Paul G. A. Cizmas Computational Fluid Dynamics (CFD) is a fleld that is constantly advancing. Its advances in terms of capabilities are a result of new theories, faster computers, and new numerical methods. In this thesis, advances in the computational (cid:176)uid dynamic modeling of moving bodies and combustive (cid:176)ows are investigated. Thus, the basic theory behind CFD is being extended to solve a new class of problems that are generally more complex. The flrst chapter that investigates some of the results, chapter IV, discusses a technique developed to model unsteady aerodynamics with moving boundariessuch as (cid:176)appingwinged (cid:176)ight. This will include mesh deformation and (cid:176)uid dynamics theory needed to solve such a complex system. Chapter V will examine the numerical modeling of a combustive (cid:176)ow. A three dimensional single vane burner combustion chamber is numerically modeled. Species balance equations along with rates of reactions are introduced when modeling combustive (cid:176)ows and these expressions are discussed. A reaction mechanism is validated for use with in situ reheat simulations. Chapter VI compares numerical results with a laminar methane (cid:176)ame experiment to further investigate the capabilities of CFD to simulate a combustive (cid:176)ow. A new method of examining a combustive (cid:176)ow is introduced by looking at the solutions ability to satisfy the second law of thermodynamics. All laminar (cid:176)ame simulations are found to be in violation of the entropy inequality. iv To Greg and Wendy v ACKNOWLEDGMENTS No proper acknowledgment can be written without thanking my adviser, Dr. Paul Cizmas. Every step of the way he has been a true mentor and a friend. Long after this work is forgotten, I will still remember the person he is. I also would like to thank the members of my committee: Leland Carlson, Raytcho Lazarov and Othon Rediniotis. They challenged me in ways I had never known or wanted and made me allthebetterbecauseofit. Additionally, IwouldliketothankDr. JohnSlattery. The many discussions with him assisted in my understanding of the material. I would like to thank my peers: Roshawn Bowers, Joaquin Gargolofi, Jason Guarnieri, Kyu-sup Kim, Aditya Murthi, Josh O’Neil, Celerino Resendiz, Amarnath Sambasivam, Leslie Weitz, and Tao Yuan. Lastly, I would like to thank my family. Without their love and support, none of this would be possible. vi NOMENCLATURE 2D Two-dimensional ¡ 3D Three-dimensional ¡ a Summation of the entropy inequality expression over ¡ all the cells in violation of the second law A Pre-exponential factor r ¡ c Total molar density ¡ C Molar concentration of species j in reaction r j;r ¡ cm Centimeters ¡ c Constant pressure speciflc heat of species j p;j ¡ CFD Computational (cid:176)uid dynamics ¡ D Diameter of circular cylinder ¡ D Rate of deformation tensor ¡ ~ d Intermediate term deflned on (p.450) of [Slattery] i ¡ Binary difiusion coe–cient ij D ¡ D Matrix of binary difiusion coe–cients ij ¡ D Difiusion coe–cient for species i in mixture i;m ¡ D Thermal difiusion coe–cient T;i ¡ E Activation energy for reaction r ¡ F(`) Spatial discretized function ¡ ~ F Force on mesh node i i ¡ vii ~g Gravitational acceleration ¡ h Enthalpy ¡ h0 Enthalpy of formation of species j j ¡ I Turbulence intensity ¡ I Identity matrix ¡ in Inches ¡ ~ J Mass difiusion (cid:176)ux for species i i ¡ k Turbulent kinetic energy, thermal conductivity ¡ k Boltzmann’s constant B ¡ k Efiective heat conductivity eff ¡ k Spring constant between nodes i and j ij ¡ k Forward rate constant for reaction r f;r ¡ k Backward rate constant for reaction r b;r ¡ K Reaction equilibrium constant for reaction r r ¡ L Hydraulic diameter ¡ m Meters ¡ mm Millimeters ¡ M Molecular mass of species i i ¡ N Number of chemical species present in the system ¡ n Number of neighboring nodes connected to node i i ¡ N Number of chemical species in reaction r r ¡ viii N Total number of chemical species in one chemical reaction s ¡ P Pressure ¡ Pa Pascals ¡ P Reduced pressure R ¡ q Total number of cells that violate the second law of ¡ thermodynamics r Mass rate of production of species i by chemical reaction r i;r ¡ R Universal gas constant ¡ ^ R Arrhenius molar rate of production of species i in reaction r i;r ¡ R Species mass rate of production by all chemical reactions i ¡ Re Reynolds number ¡ Sc Turbulent Schmidt number t ¡ S Heat energy due to chemical reaction h ¡ S Arbitrary speciflcation of chemical species i, i ¡ source term of component i in momentum equation St Strouhal number ¡ T Temperature ¡ T⁄ Dimensionless temperature ¡ T Reference temperature ref ¡ UDF User deflned function ¡ U Boundary layer edge velocity e ¡ ix U Freestream velocity 1 ¡ u Velocity vector using index notation i ¡ U Mean (cid:176)ow velocity ¡ u0 Root mean square of velocity (cid:176)uctuations ¡ ~v Velocity vector ¡ V Cell volume ¡ w Calculation of entropy inequality at a single cell ¡ X Mole fraction for species i i ¡ Y Mass fraction for species i i ¡ fi Cell height factor – ¡ fl Temperature exponent r ¡ – Cell height ¡ – Ideal cell height ideal ¡ ¢G– Gibbs energy change ¡ ¢H– Standard enthalpy change of reaction ¡ ¢t Time step ¡ ¢~x Displacement of node j j ¡ † Characteristic energy ¡ ~† Intermediate term deflned on (p.449) of [Slattery] ¡ ·0 Forward rate exponent of species j in reaction r j;r ¡ x ·00 Backward rate exponent of species j in reaction r j;r ¡ (cid:176) Activity coe–cient B ¡ „ Viscosity ¡ „ Viscosity of species i i ¡ „ Turbulent viscosity t ¡ ”0 Stoichiometric coe–cient for reactant i in reaction r i;r ¡ ”00 Stoichiometric coe–cient for product i in reaction r i;r ¡ › Collision integral D ¡ ` Arbitrary scalar quantity ¡ ` Values of ` convected through face f f ¡ ‰ Density ¡ (cid:190) Collision diameter i ¡ ¿„„ Viscous stress tensor used within FLUENT ¡ T General expression for stress tensor for a Newtonian (cid:176)uid ¡