Investigation into transition modeling

Abstract

h Enthalpy Transition from laminar to turbulent flow is modeled using several turbulence and transition models in the Navier-Stokes code GASP. The Baldwin-Lomax algebraic model and Wilcox's k w model with low Reynolds number corrections are the turbulence models used to model transition. The Lam and Bremhorst k c model is used with the modification to the turbulent kinetic energy production term from Schmidt and Patankar. The linear combination model of Dey and Narasimha as well as the algebraic model of ONERA/CERT are the transition models used in conjunction with a given turbulence model to simulate transition. Calculations of heat transfer data are compared against experimental results for a simple cone flow, a supersonic compression ramp with an adverse pressure gradient and a supersonic flared cone producing a favorable pressure gradient. Nomenclature turbulent kinetic energy a Baldwin-Lomax constant = 0.0168 surface roughness height non-dimensional surface roughness height, pressure gradient parameter Mach number non-dimensional turbulent-spot formation rate for zero pressure gradients non-dimensional turbulent-spot formation rate production term in TKE equation free stream turbulence level, $ Wall heat transfer rate Wilcox k w constant = 6 Wilcox k w constant = 8 Wilcox k w constant = 27/10 Reynolds number based on transition location Reynolds number based on momentum thickness Re, Reynolds number based on x A+ Baldwin-Lomax constant = 26 St Stanton Number, , (Stainback) A Schmidt and Patankar transition parameter QW ~ w U w ( h 0 h w ) (Kimmel) B Schmidt and Patankar transition parameter TW Temperature a t the wall C~ Specific heat a t constant pressure , Taw Adiabatic temperature a t the wall Ccp Baldwin-Lomax constant = 1.6 d m C t skin friction coefficient Tu, turbulence intensity, Uch Heat Transfer coefficient, -* CKlea Baldwin-Lomax constant = 0.3 Cmutm Baldwin-Lomax constant = 14 Cwk Baldwin-Lomax constant = 0.25 velocity in j direction, t e k o r notation U Reynolds averaged steady state velocity U T friction velocity, P velocity vector xj coordinate in j direction, tensor notation * Research Assistant, Student Member AIAA X t o stream wise distance to start of transition t professor, Associate Fellow AIAA xt2 stream wise location of subtransition i ~ e n i o r Aeronautical Engineer, Member AIAA X axial distance Copyright Q 1995 by Scott McKeel. Published by y normal distance to wall the American Institute of Aeronautics and Astronauy+ non-dimensional distance to wall, 7 tics, Inc. with permission. 1128 American Institute of Aeronautics and Astronautics time Wilcox k w constant = 1 / 1 0 Wilcox k w constant = 1 / 4 0 boundary layer thickness length of Wilcox roughness strip transition function intermittency KArmAn constant = .41 molecular viscosity effective viscosity molecular viscosity turbulent eddy viscosity density Wilcox k w constant = 112 Wilcox k w constant = 112 Reynolds stress tensor momentum thickness momentum thickness of laminar flow field momentum thickness a t xto dynamic viscosity, Momentum thickness parameter vorticity or specific dissipation rate ( e l k )