Effects of acoustic oscillations on turbulent flowfield in a porous chamber with surface transpiration

Turbulent compressible flows in a porous chamber with acoustic oscillations have been analyzed numerically. Emphasis is placed on the interactions between turbulence and periodic motions, and their effect on mean flow properties. The impetus for the current work is to investigate the velocity-coupled combustion response of the propellant grain. Specifically, interactions between chamber gas dynamics and transient combustion responses of the propellants can be further explored based on present cold-flow analysis. The formulation treats the complete conservation equations of mass, momentum, and energy for the large energy-carrying turbulent structures. The effect of small, unresolved scales is modeled in this large eddy simulation (LES) technique. A stationary turbulent flowfield is first obtained and the coupling between the acoustic oscillations and turbulence are studied by imposing traveling waves over the mean flowfield. Loss of acoustic energy in a motor due to the flow-turning phenomenon is studied using a onedimensional analytical model. Turbulence characteristics and their effects on the mean flow properties are validated against available experimental data The impact of mean velocity transition and the turbulence kinetic energy transition on the turbulence structure are elucidated using time evolution of the voiticity and scalar fields. The flow in the duct undergoes three successive regimes of development governed by the injection, the turbulence, and the compressibility effect, respectively. The acoustic fields obtained in these regimes are quite different because of the turbulence-enhanced transport and dissipation rates. The shear waves obtained from periodic motions are damped in the turbulent region and serves as an additional mechanism for energy transfer to the turbulent flow. Enhanced production of vorticity in oscillatory flows may increase turbulence intensity in various parts of the chamber. The time-averaged effect of dynamical motions associated with the turbulence production in non-stationary flowfield is quite different from the stationary turbulent flow indicating strong interactions with acoustic excitations. The present work is a major step towards a complete analysis of the transient combustion response of propellants to the imposed periodic oscillations in turbulent environmenments. G = spatial filter function Nomenclature Gk u = amplification factor per time step cs =Smagorinsky constant f = flux vector in y-direction of Naviers ° J Stokes equations D = near wall damping function h = duct half-height, m B = filtered total energy per unit volume, i— —=• p/(Y-l)+0.5p(u+v) ,J/m l = turbulence intensity, Vu'u'+W, m/s E = flux vector in x-direction of Navierj = number of time steps required for one Stokes equations . E = turbulence energy , eddy life time f = frequency, Hz k = wave number, 1/m L = duct length, m * This work was performed under ONR Grant No. NOOO14-95-1-1338 1 Ph.D. Student, Department of Mechanical Engineering. 2 Professor, Department of Mechanical Engineering. m" = mass flux per unit area, kg/ ms M = mean cross-sectional-averaged Mach number Mc = mean centerline Mach number p = pressure, N/m Q = conservation variables vector of Navier-Stokes equations q = large scale velocity, m/s Re = Reynolds number S = strain-rate tensor, jo. = dynamic viscosity, kg/ms v = kinematic viscosity, m /s vs = subgrid-scale kinematic viscosity, m /s p = density, kg/m cr = CFL number T = viscous shear stress, N/m \ = grid parameter for LES T = temperature, K t = time coordinate, s u = velocity in x direction, m/s v = velocity in y direction, m/s vw = injection velocity, m/s y = ratio of specific heats A = filter width Sjj = Kronecker delta 8 = a constant* 0.0025 & dissipation rate of turbulence kinetic energy, m/s TI = Kolmogorov length scale, m K = thermal conductivity, W/mK