Flow Analysis of a Solid Propellant Rocket Motor with Aft Fins

Chaouat, Bruno

doi:10.2514/2.5169

Cited by 20 publications

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“…Equation (1) shows that the axial velocity increases linearly with the axial distance and satises the no-slip condition of the Navier-Stokes equations because u 1 .±/ D u 1 .¡±/ D 0. Because of the progress in computing power, channel ows with uid injection through porous walls have been studied numerically by several authors.…”

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confidence: 96%

Numerical Predictions of Channel Flows with Fluid Injection Using Reynolds-Stress Model

Chaouat

2002

Journal of Propulsion and Power

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Numerical predictions of channel ows with uid injection through a porous wall are performed by solving the time-dependent Navier-Stokes equations using a Reynolds-stress turbulent model. In uence of the turbulence injected uid is investigated. Numerical results with experimental data indicate that the ows evolve signi cantly vs the distance from the front wall such that different regimes of ow development can be observed. In the rst regime the velocity eld is developed in accordance with the laminar theory. The second regime is characterized by the development of turbulence, which occurs at different locations in the channel because of the presence of impermeable and permeable walls, and by the transition process of the mean axial velocity when a critical turbulence threshold is attained. Computed results are compared with existing experimental data including axial mean velocity pro les and full turbulent stresses. As a result for the simulations, the Reynolds-stress model predicts the mean velocity pro les, the transition process, and the turbulent stresses, in good agreement with experimental data. Nomenclature= total speci c energy, m 2 /s 2 , J/kg H = total speci c enthalpy, h C u i u i =2, m 2 /s 2 h = speci c enthalpy, m 2 /s 2 J i j = tensor of diffusion for the Reynolds stress ¿ i j k = speci c turbulent kinetic energy, ¿ ii =2, m 2 /s 2 L = channel length, m M = Mach number m = injection mass ux, kg/(m 2 ¢ s) n i = normal to the wall P i j = production rate of ¿ i j caused by mean shear P rt = turbulent Prandtl number p = static pressure, Pa q i = total heat ux vector, W/m 2 R s = injection Reynolds number, ½ s u s ±=¹ s R t = turbulent Reynolds number k 2 =º² R u = universal gas constant S i j = strain-rate tensor s = speci c entropy, J/(kg ¢ K)velocity vector, m/s u m = bulk velocity, m/s u s = injection velocity, m/s u ¿ = friction velocity, m/s x i = Cartesian coordinate, m x C i = dimensionless distance from walls, x i u ¿ =º ® = coef cient for planar or axisymmetric geometryratio of speci c heats ± = channel height, m ± i j = Kronecker tensor ² = dissipation rate, m 2 /s 3 ² i j k = permutation tensor · = thermal conductivity, W/(m ¢ K) ¹ = dynamic viscosity, kg/(m ¢ s) º = kinematic viscosity, m/s 2 ½ = density, kg/m 3 6 i j = total stress tensor ¾ i j = viscous stress tensor ¾ s = surface-generatedpseudoturbulence,. ] u 00 2 u 00turbulent stress tensor, ] u 00 i u 00 j 8 i j = pressure-strain uctuations, p 0 S 00 i j ! i = vorticity tensor, ² i jk @u k =@ x j , (1/s) Subscripts m = bulk mean quantity s = condition at injection surface w = wall Superscripts N = Reynolds averaged of variable Q = Favre averaged of variable 0 = Reynolds turbulent uctuating value of variable 00 = Favre turbulent uctuating value of variable

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Numerical Predictions of Channel Flows with Fluid Injection Using Reynolds-Stress Model

Chaouat

2002

Journal of Propulsion and Power

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“…The difference is due to the asymmetric mass flux distributions caused by the slots. Moreover, as described in detail by Chaouat [7], for the threedimensional nature of the SRM internal flow due to aft slots of the propellant grain, the vortices shed from grain slots create asymmetric cross-sectional flow. Because the vortical flow affects the diffusion velocity of the mass and the heat crossing the surface boundary layer on the liner materials, it causes circumferentially asymmetric erosion over the converging part of the nozzle.…”

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“…For example, the research of Chaouat [7] indicated that vortices shed from slots created asymmetric cross-sectional flow. Three dimensionality of the flow or vortical flow is caused by mixing of the flows from slots with the core flow in the port, and is intensified at the converging part of the submerged nozzle.…”

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Effects of Propellant Gases on Thermal Response of Solid Rocket Nozzle Liners

Hwang

Yim

2008

Journal of Propulsion and Power

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The propellant formulations, the gas properties in motor chamber, and the aluminum oxide particle sizes for two kinds of solid propellants with approximately 20% aluminum powder have been investigated. The scanning electron microscope photographs of aluminum oxide particles taken from a nozzle entrance show that the aluminized polycaprolactone polyol propellant with 47% volumetric fraction ammonium perchlorate/hexanitro hexaazaisowurtzitane and the bimodal oxidizers, 200=5 m, can offer greater possibility for increasing aluminum agglomeration than the aluminized hydroxy-terminated polybutadiene propellant with 64% volumetric fraction ammonium perchlorate and the trimodal oxidizers, 400=200=6 m. The aluminized polycaprolactone polyol propellant with energetic plasticizers results in locally greater mechanical erosion in four circumferential sections of the nozzle entrance in line with grain slots, due to the impingement of large particles. However, the hydroxyterminated polybutadiene propellant results in greater thermochemical ablation at the blast tube, the throat insert, and the exit cone of rocket nozzle, due to 2.3 times more water and carbon dioxide oxidizing species in exhaust gases than the polycaprolactone polyol propellant. Nomenclature A = cross-sectional flow area c p = specific heat of gases at constant pressure d p = diameter of aluminum oxide particle E 0 = activation energy of a chemical reaction h = convective heat transfer coefficient K 0 = preexponential factor of a chemical reaction k = mass fraction of the solid residue of material M 0 = molecular weight of gas mixture M c = molecular weight of carbon P w = pressure at nozzle wall R = ideal gas constant T w = temperature at nozzle wall CO 2 = mole fraction of CO 2 H 2 O = mole fraction of H 2 O 0 = initial density Subscripts t = conditions at nozzle throat w = wall conditions

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A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows

2005

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A new subgrid-scale turbulence model involving all the transport equations of the subgrid-scale stresses and including a dissipation rate equation is proposed for large-eddy simulation (LES) of unsteady flows which present nonequilibrium turbulence spectra. Such a situation in flow physics occurs when unsteadiness is created by forced boundary conditions, but also in more complex situations, when natural unsteadiness develops due to the existence of organized eddies. This latter phenomenon explains the instability found in a porous-walled chamber with mass injection. Due to the high value of Reynolds number, the presence of wall boundaries, and the use of relatively coarse grids, the spectral cutoff may be located before the inertial zone of the energy spectrum. The use of transport equations for all the subgrid-scale stress components allows us to take into account more precisely the turbulent processes of production, transfer, pressure redistribution effects, and dissipation, and the concept of turbulent viscosity is no longer necessary. Moreover, some backscatter effects can possibly arise. As a result of modeling in the spectral space, a formally continuous derivation of the model is obtained when the cutoff location is varied, which guaranties compatibility with the two extreme limits that are the full statistical Reynolds stress transport model of Launder and Shima and direct numerical simulation. In the present approach, due to the presence of the subgrid-scale pressure-strain correlation term in the stress equations, the new subgrid model is able to account for history and nonlocal effects of the turbulence interactions, and also to describe more accurately the anisotropy of the turbulence field. The present model is first calibrated on the well-known fully turbulent channel flow. For this test case, the LES simulation reveals that the computed velocities and Reynolds stresses agree very well with the DNS data. The application to the channel flow with wall mass injection which undergoes a transition process from laminar to turbulent regime and the development of natural unsteadiness is then considered for illustrating the potentials of the method. LES results are compared with experimental data including the velocity components, the turbulent stresses, and the transition location. A satisfactory agreement is obtained for both the mean quantities and the turbulent field. In addition, structural information of the flow is provided

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Flow Analysis of a Solid Propellant Rocket Motor with Aft Fins

Cited by 20 publications

References 3 publications

Numerical Predictions of Channel Flows with Fluid Injection Using Reynolds-Stress Model

Numerical Predictions of Channel Flows with Fluid Injection Using Reynolds-Stress Model

Effects of Propellant Gases on Thermal Response of Solid Rocket Nozzle Liners

A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows

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