1. The following literature survey is a discussion of what has and has not been dealt with in the world of solid rocket motors. Selected studies are discussed in the following paragraph and are referenced chronologically in [1-29]. Slag deposition process through flow modeling and the subsequent accumulation and pooling of slag material within the Space Shuttle solid rocket motor (SRM) was first documented by Boraas. Flow field modeling consisted of a potential flow gaseous computation with a Lagrangian particle trajectory calculation. The separated flow region in the aft end of the submerged nozzle motor was approximated by a fictitious interface drawn between the submerged nozzle entrance and the aft dome recirculation region. Particle trajectories were computed by varying particle starting locations on the propellant surface. Murdock2discussed the ejection of a body that blocks the nozzle throat and may cause perturbation in the measured thrust-time histories of solid rocket motors. Traineau at al. conducted cold-flow simulation tests of a nozzleless solid rocket motor using a two-dimensional porous-walled duct with an impermeable-walled diverging section. Beddini4conducted theoretical analysis of the flow in porous-AIAA 2001-5236
2. walled tubes and channels with appreciable injection through the duct wall. The flow at large injection Reynolds numbers can undergo at least three flow regimes. Basset5compiled results of modeling of circumferential flow in the RSRM induced by potential non-axisymmetric flow sources. It describes analytical and experimental results. The numerical techniques utilized eight 3D fluid-flow codes and two 3D heat flow codes, while the testing media included water, cold air, and hot combustion gas. Salita suggested abimodal lognormal droplet size distribution at apressure of about 6.90 MPa (1000 psia) consisting of small droplets with 1.5 jjjm mean and large droplets with a 100 um mean. Whitesides et al.7conducted a series of subscale cold flow tests to quantify the gas flow characteristics at the aft end of the RSRM. These tests consisted of measurements of static pressure and gas velocities in the vicinity of the nozzle/case joint when nozzle is gimbaled at angles of 0, 3.5, and 7 degrees. Golafshani and Loh conducted a time-dependent, axisymmetric numerical solution of the Navier-Stokes to analyze the viscous coupled gas-particle non-reacting flow in solid rocket motors. The solution assumed laminar internal flow. Waesche et al. conducted flow-visualization tests in a 1/8-scale model of the RSRM in a water tunnel to simulate (1) circumferential flow induced by asymmetric inhibitor stub in the port of the RSRM, (2) vortex formation in the aft-dome cavity with and without nozzle vectoring. Burning propellant was simulated through the introduction of a uniform distribution of water along simulated burn-back patterns. Vortices shed from protruding inhibitor were found to diminish by wall injection. Circumferential flow resulting from a flawed inhibitor was limited to region near the missing portion of the inhibitor. Strong circumferential flow in the aftdome was observed toward the end of burn. Boraas10used the hydraulic analogy principle to simulate flow in the aft dome of the RSRM. Using a water table a thin layer of water was pumped across the table between sidewalls that simulated the motor centerline and its aftdome-nozzle boundary in non-vectoring condition and during late in the burn. Lightweight dye was injected uniformly across the flow field at an upstream location. Entrainment of the dye into the cavity revealed a counterrotating three vortices in the aft dome. Majumdar et al. conducted three-dimensional CFD analyses to calculate circumferential pressure and velocity gradients in the vicinity of an asymmetric inhibitor stub in the port of the RSRM. The numerical predictions were compared with the measurements from a 7.5% scale, cold-flow model of the RSRM. A maximum of 0.34 atm (5 psid) has been shown. Waesche et al.12conducted a series of cold-gas tests in a 1/8-scale (18-in. dia.) model of the forward segment of candidate grain designs for the Advanced Solid Rocket Motor (ASRM). It was found that the effects of grain slots on the downstream flow were minimal. Effects dissipate quickly because of rapid mixing with the core flow. Carrier et al.13used an approximate and simple model forparticle trajectories in a long-bore solid rocket motor. Heister and Landsbaum4described anomalies caused by mass ejection through the nozzle throat of Titan 34-D solid propellant rocket motor. Hess et al.15found that the accumulation of slag in the aft end for a short motor is less than accumulation of slag for the long motor. Numerical solution was obtained using a simple Eulerian potential flow / Lagrangian - particle tracking formulation. It was found that gravity acceleration would be discernible only for larger particle sizes, above 200-um diameter. Smith-Kent et al.16describe a potential flow based slag accumulation model with Lagrangian particle tracking. Key input parameters, namely, particle size, vortex definition, and capture criteria are based on empirical data. Johnston et al. conducted quasisteady axisymmetric, inviscid, coupled two-phase (combustion gas and molten AhOs) flow calculations in the Titan SRMU. Six burn back geometries (0, 30, 55, 80, 110, and 125 sec) that span the total burn time of 135 sec, and four different droplet sizes (10, 35, 60, and 100 jim) were analyzed. They simplified the bimodal distribution droplet size of Salita6to a flow withjust two droplet sizes, namely 1.5 and 100 jim. Loh and Chwalowski18used particles of diameters of 1to 100 jim in converging-diverging nozzles and amass loading of 28.8%. Acceleration between Ig and 3g had a minimal effect on the particles' behavior in the nozzle. Whitesides et al.19conducted combined analytical and experimental studies to develop an understanding of the effects of slag ejection on motor performance. A simplistic quasi-steady analytical model was formulated for the purpose of determining the instantaneous slag flow rate and the total quantity of slag required to produce a given pressure perturbation. Salita ° reported slag measurements of 58 kg (128 Ibm), 1980 kg (4366 Ibm), and 1102 to 4365 kg (500 to 3500 Ibm) in SICBM, SRMU, and RSRM, respectively. A flow model was proposed for use in predicting slag accumulation in these motors. Chauvot et al. developed amodel to predict slag weight deposited in the submerged nozzle of solid rocket motors. In-flight acceleration increases slag weight. Sabnis et al.22conducted two-phase three-dimensional flow field in the Titan IV SRM at 17.5 in.burn-back geometry using multiphase Navier-Stokes analysis using CELMINT (Combined Eulerian Lagrangian Multidimensional Implicit Navier-Stokes Time-dependent) code.23The geometry in the aft closure region is non-axisymmetric due to the nozzle being canted withrespect to the chamber axis. The purpose of the analyses was to understand asymmetric insulation erosion in the aft closure observed in static and flight tests. Asymmetric geometry in the aft
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4. closure results in secondary flows that can significantly affect the impingement pattern of the aluminum oxide droplets on the aft closure insulation. Several twodimensional axisymmetric calculations were performed before initiating the three-dimensional calculations. They were performed to (1) assess the grid resolution, (2) obtain consistent flow conditions at the inlet to the sixth segment so that the three-dimensional simulations could be limited to the region down-stream of the fifth segment. The two-dimensional axisymmetric analyses comprised segments 1 through 7, the aft closure propellant and the nozzle and solved on two grids. The first grid consisted of 900 and 90 cells in the axial and radial directions, respectively, yielding a total number of 81,000 cells. The second grid consisted of 1,175 and 90 cells in the axial and radial directions, respectively, yielding a total number of 105,750 cells. The viscous sub-layer wasresolved (i.e., the first point off the wall corresponds to y+< 1). Simulation 1of the present study utilized many more cells (Table 1) than in Sabnis et al. to obtain y+around 5. This author used up to 300 cells in the radial direction in the converging-diverging section of the nozzle. The size of the cell adjacent to the wall was 10"4m (3.94xlO"3in.). A smaller size than this would generate negative areas which CFD can not handle. Therefore, the iterative process between the grid and the calculated wall y+ceased. In the three-dimensional analyses,22a grid was used and consisted of 351, 90, and 19 in the axial, radial, and circumferential directions, respectively, yielding a total of 598,500 cells. A propellant combustion study conducted by Perkins et al.4has shown that propellant variability due to subtle raw ingredient can affect the quantity and distribution of slag formed. Quench bomb tests conducted by Brennan25at 3.44 MPa (500 psia) chamber pressure and particles were quenched at 0.0127 m (0.5 in.) from the burning surface. The resulting particle size distribution was bi-modal with 50-70% (Fig. 10 of Brennan ) of the particles by weight under 5 jim and designated as smoke. The rest of the fraction inthe 5-700 (urn range was designated as the coarse fraction. This coarse fraction comprised the discrete fraction used in the two-phase CFD analysis conducted by Whitesides et al. '7Whitesides et al.7conducted a two-dimensional axisymmetric two-phase flow analysis using CELMINT code. The overall objective was to determine the structure of the flow field in the recirculation region underneath the submerged nozzle nose and to define the gas flow and particle impingement environments alongthe surface of the aft case dome insulation. It was concluded that particles were impacting the area underneath the nozzle nose and forming a sheet of molten aluminum oxide or slag. The sheet flows afterwards, along the underneath nozzle nose surface as is the direction of the near surface velocity vector during the last half of motor burn. This slag layer is then sheared from the nozzle cowl/boot ring surface and impacts the aft dome case insulation atthe location of severe erosion.
5. Related heat transfer studies are given inRefs. (30-38). Bartz extended the well-known Dittus-Boelter correlation for turbulent pipe flow to account for mass flux and variations in velocity and temperature. Back etaj 31,33-35conducted analytical and experimental convective heat transfer studies in the Jet Propulsion Laboratory (JPL) nozzle. Moretti and Kays conducted experimental convective heat transfer to an essentially constant property turbulent boundary layer for various rates of free-stream acceleration. Back et al. and Moretti and Kays found that acceleration causes a depression in heat transfer rate below what would be predicted assuming a boundary-layer structure such as obtained for constant free-stream velocity. They attributed it to relaminarization of the turbulent boundary layer. Moretti and Kays state the above acceleration parameter was a result of experimental tests conducted in a twodimensional channel. They further state, it is by no means