Grid system (180 x 30) in the computational region. 

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... numerical simulations have been carried out with the help of a standard k-omega model. This turbulence model is an empirical model based on model transport equations for the turbulence kinetic energy (k) and the specific dissipation rate ( ω ). This code solves standard k-omega turbulence equations with shear flow corrections using the coupled second order implicit unsteady formulation. The turbulence kinetic energy, k, and the specific dissipation rate, ω , are obtained from the following two transport equations: In the equations, G k represents the generation of turbulent kinetic energy due to mean velocity gradient. G ω represents the generation of ω . Γ k and Γ ω represent the effective diffusivity of k and ω , respectively. Y k and Y ω represent the dissipation of k and ω due to turbulence. S and S are user-defined source terms. This model uses a control-volume based technique to convert the governing equations to algebraic equations, which can be solved numerically. The viscosity is determined from the Sutherland formula. An algebraic grid-generation technique is employed to discretize the computational domain. The present code has been validated and selected for capturing the fine flow features often observed in SRMs with non-uniform port. A typical grid system in the computational region is selected after the detailed grid refinement exercises. The grids are clustered near the solid walls using suitable stretching functions. In all the cases length of the first grid from the solid surfaces is taken as 0.1 mm. The motors geometric variables and material properties are known a priori . Initial wall temperature, inlet total pressure and temperature are specified. At the solid walls no-slip boundary condition is imposed. At the nozzle exit a pressure profile is imposed. The Courant-Friedrichs-Lewy number is initially chosen as 3.0 in all of the computations. Ideal gas is selected as the working fluid. The transient mass additions due to propellant burning are deliberately ignored in this model to examine the turbulent separated flow features discretely in solid rockets with non- uniform ports. The numerical results corresponding to the experimental configuration and propellant properties reproduce many qualitative features such as secondary ignition and backward flame spread. These results are succinctly reported in the previous connected papers [12, 13, 14, 15, 16]. In this study consideration is given to examine the geometrical influence on turbulent separated flows in SRMs without any mass addition. Results of interests such as reattachment length, size of the recirculation bubble and the axial velocity variations are reported to illustrate the influence of transition region on the flow characteristics of turbulent mixed convection downstream of a solid rocket motor with divergent port. Such detailed results are needed for an integrated design and optimization of the high-performance solid rockets port geometry and its allied igniters with confidence. In the present numerical simulation two different physical models with different port geometries are examined. In the first phase low-velocity transient (LVT) motors (A t /A p < 0.56, L/D < 10) and in the second phase HVT motors are considered. The grid system (baseline case) in the computational region for LVT motor is shown in figure 2. Baseline values are selected based on the geometric configuration of a typical LVT motor (L/D = 4, Figure 3 shows the comparison of the axial velocity variation at a particular time interval for five different test cases. In the first three cases divergent location (Xs) is varied, in the forth case inlet diameter is increased by 50% and in the fifth case divergence angle, α is increased from 45 o to 64 o . All the results reported are anticipated and giving corroborative evidences of the previous experimental and theoretical findings [10, 11, 12, 13, 14, 15, 16]. 14 Australasian Fluid Mechanics Conference Adelaide University, Adelaide, Australia 10-14 December 2001 recognized up to t = 0.001 s. This phenomenon is not observed in the forth case due to high inlet port area and low axial velocity. In the second phase attention is focused on HVT motors with sudden enlargement of port, as has been observed in the case of Space Shuttle’s Redesigned SRM. In the parametric study three different transition locations (X s ) are considered. Figure 5 shows the grid system in the computational region of the baseline case. An algebraic grid-generation technique is employed to discretize the computational domain. The total element in each case is fixed as 1328. The grids are clustered using suitable stretching functions for capturing the fine flow features during the transient period. Note that the inappropriate stretching of grids will lead to the inaccurate prediction of the reattachment point. An error in pinpointing the reattachment point will lead to the significant errors in the actual prediction of the location of secondary ignition, which will warrant the inaccurate performance prediction of HVT motors. The geometrical parameters are selected based on typical HVT motors. In all the cases, considered in this study, the length-to-diameter ratio and the throat-to-port area ratio are retained as constant values similar to a conventional HVT motor. The igniter jet flow and the material properties are retained as constant for examining the influence of location of the transition region on identical conditions. The ignition is not invoked in this analysis. At the solid walls no-slip boundary condition is imposed. Initial total pressure and temperature are prescribed at the inlet and a pressure profile is imposed at the nozzle exit. In the first numerical drill, for all the cases, the initial igniter total pressure is taken as 2.25 kgf/cm 2 , and temperature as 700 K. The turbulent intensity is assumed as 10% at the inlet and the exit. At the given inlet hydraulic diameter, using the standard k- ω model, the initial inlet turbulent kinetic energy is evaluated as 306.93 m 2 /s 2 and the corresponding specific dissipation rate is obtained as 62569.78 s -1 . The initial Courant-Friedrichs-Lewy number is chosen as 5 in all the cases. Figure 6 is demonstrating the difference in velocity magnitude along the axis of an HVT motor with three different divergent locations at two different time intervals but with same initial and boundary conditions. In all the cases the velocity magnitude is found maximum at the transition location. 14 Australasian Fluid Mechanics Conference Adelaide University, Adelaide, Australia 10-14 December 2001 motors. We also observed that in all the cases, due to the flow instability, the near wall temperature was found non-uniform along the curved surface and as a result the heat flux values will be discontinuous. This will warrant the discontinuous ignition leading for multiple flame fronts in HVT motors with divergent port. The velocity, density and temperature fluctuations are not independent, being related, also through pressure fluctuations, by the mass balance equation, the energy balance equation, and the constitutive equation of the fluid. So suppression and control of one parameter will be a meaningful objective for rocket motor design optimization. We also discerned that under certain conditions, the flow gets accelerated to a higher Mach number (M>1) near the transition region of an HVT motor with divergent port but without any geometrical-throat! A shock wave cannot exist unless the Mach number is supersonic; therefore the flow must have accelerated through a throat which is sonic. As argued above, owing to the viscous friction, boundary layer will be formed on the walls (before the transition region) and their thickness will increase in the down stream direction to the divergent location leading to the formation of a momentarily fluid-throat at the transition location. This might lead to the formation of shock waves in certain class of HVT motors with divergent port. Note that the downstream of the shock the flow has an adverse pressure gradient, usually leading to wall boundary-layer separation and reattachment. From these studies one can deduce that the thrust/pressure oscillations, pressure-rise rate and unexpected peak pressure often observed in solid rockets with ...