Large Eddy Simulation of Flow Development in Chamber with Surface Mass Injection

Abstract

Motivated by the recent experimental observation of noticeable features of dimplelike surface roughness patterns on the hybrid fuel grain, the authors investigated a cold flow in a porous chamber with surface mass injection through a large eddy simulation technique. The main purpose is to understand the role of turbulent structures in generating those irregular, isolated roughness patterns found on the fuel surface. It was noted that the structural feature of nearwall coherent vortices has been considerably altered by the application of wall injection, resulting in isolated cell-like contours of streamwise velocity distributed all over the horizontal planes close to the wall. This sudden change of contour shape is reminiscent of the roughness patterns observed in the accompanying experiment. The rapid evolution of the kinematical configuration of near-wall turbulence structures is believed to be caused by the effect of vertical momentum given at the wall as in the regression process. NomenclatureC S = model coefficient for velocity field C T = model coefficient for passive scalar h = half-channel height L x = domain size in streamwise direction L y = domain size in wall-normal direction, 2h L z = domain size in spanwise direction Pr = molecular Prandtl number p = pressure q j = residual scalar flux vector R uu = two point or autocorrelation of streamwise velocity Re h = Reynolds number based on inlet bulk velocity and half-channel height S ij = strain rate tensor, u i;j u j;i =2 T = temperature (passive scalar) T w = wall temperature t = time U b = inlet bulk velocity u = velocity component in x direction v = velocity component in y direction w = velocity component in z direction x = Cartesian coordinate in streamwise direction y = Cartesian coordinate in wall-normal direction z = Cartesian coordinate in spanwise direction t = turbulent diffusivity = filter width ij = Kronecker delta function t = turbulent viscosity ij = residual stress tensor Subscripts b = bulk mean quantity mean = averaged quantity over time and spanwise direction Superscripts h i = grid filter h i t = test filter = fluctuating component due to turbulence

The characteristics of turbulent surface flow in planar channel with imposed wall blowing

“…For numerical convenience, a model rocket motor was idealized to be a simple channel and the regression process was approximated by the arti¦cial injection of the §uid through the motor surface as in [3].…”

“…The authors£ earlier results indicated that calculations with a higher resolution beyond 1025 × 193 × 513 grid size did not change the overall §ow characteristics and thus it was assumed that the mesh size with 1025 × 193 × 513 grids (about 101 million grids) was good enough for the purpose of the present work. The details of numerical calculations and computational grid can be found in [3,10]. Figure 1 shows a schematic of the three-dimensional (3D) computational domain.…”

“…The §uid density was assumed to be independent of temperature so that the heat was essentially transported as a passive scalar without producing the buoyant force. The details of the numerical procedures of getting the solution and LES algorithms using a dynamic mixed model (DMM) are described in [3,10].…”

“…Thus, in this subsection, some of the representative mean statistics from the earlier studies [3] are provided. The mean statistics were obtained by averaging the §ow variables over both time and homogeneous spanwise direction.…”

“…2b. Reference [3] could provide other statistics of turbulent structures including a passive scalar and the magnitude of turbulent transport terms such as Reynolds shear stress and turbulent heat §ux. Figure 3 shows that the instantaneous axial velocity pro¦les, u(y), in the mid plane (i. e., in the plane z/h = 3.25) at several streamwis locations, §uctu-ate signi¦cantly with time.…”