In the present work, a second throat ejector using nitrogen as the primary fluid is considered for the creation of a low vacuum in a high-altitude testing facility for large-area-ratio rocket motors. Detailed numerical investigations have been carried out to evaluate the performance of the ejector for various operational conditions and geometric parameters during the nonpumping and pumping modes of operation. In the nonpumping mode, the lowest vacuum chamber pressure is attained when the primary jet just expands up to the mixer throat and the resulting single shock cell seals the throat against any backflow. The study illustrates how each geometric and operational parameter of the ejector can be optimized to meet the test requirements in a high-altitude testing facility by ensuring that the primary jet completely expands without a strong impact on the duct wall. When the rocket motor is fully started, due to the self-pumping action, the required vacuum is almost maintained by the exhaust flow itself and the external nitrogen ejector plays only a supplementary role. Numerical predictions for both nonpumping and pumping modes of operation have been validated with experimental data obtained from a scaled-down model of a high-altitude testing facility.Nomenclature d 0 = ejector inlet diameter d 1 = primary nozzle throat diameter d 2 = primary nozzle exit diameter d 3 = mixer throat diameter L 1 = length of the entry duct L 2 = length of the mixing cone L 3 = length of the mixer throat L 4 = length of the divergent duct L 5 = length from primary nozzle exit to mixer throat entrance _ m 1 = flux of secondary flow (rocket exhaust water spray) _ m 2 = flux of primary flow (gaseous nitrogen) P = pressure q = heat transfer per unit area v = velocity = mixing cone convergent angle = entrainment ratio (ratio of secondary mass flux to primary mass flux) = density rr = normal stress in radial direction zr , rz = tangential stress zz = normal stress in axial direction = hoop stress = viscous dissipation Subscripts c = chamber p = primary r = radial s = suction (secondary) v = vacuum z = axial
The performance of a second-throat ejector-diffuser system employed in high-altitude testing of large-area-ratio rocket motors is considered under various steady and transient operating conditions. When the diffuser attains started condition, supersonic flow fills the entire inlet section and a series of oblique shock cells occurring in the diffuser duct seal the vacuum environment of the test chamber against backflow. The most sensitive parameter that influences the stagnation pressure needed for diffuser starting is the second-throat diameter. Between the throat and exit diameters of the nozzle, there exists a second-throat diameter value that corresponds to the lowest stagnation pressure for starting. When large radial/axial gaps exist between the nozzle exit and diffuser duct, significant reverse flow occurs for the unstarted cases, which spoils the vacuum in the test chamber. However, the starting stagnationpressure value remains unaffected by the axial/radial gap. Numerical simulations establish that it is possible to arrive at an optimum diffuser geometry that facilitates early functioning of the high-altitude-test facility during motor ignition phase. The predicted axial variations of static pressure and temperature along the diffuser for the testing of a cryogenic upper-stage motor agree well with available experimental data. Nomenclature= diffuser exit diameter e = specific internal energy G v = rate of production of turbulent viscosity k = thermal conductivity L = length in axial direction L 1 = entry duct length L 2 = convergent duct length L 3 = second-throat length L 4 = divergent duct length M = Mach number M i = area-averaged diffuser inlet Mach number P o = stagnation pressure p = static pressure p e = diffuser backpressure p v = vacuum pressure in the test chamber q = heat transfer per unit area r = radial coordinate T = static temperature T o = stagnation temperature t = time v = velocity Y v = rate of destruction of turbulent viscosity z = axial coordinate r = radial gap z = axial gap = convergence angle = absolute viscosity = density rr = normal stress in radial direction zr , rz = tangential stresses zz = normal stress in axial direction = hoop stress = viscous dissipation function Subscripts l = laminar r = radial t = turbulent z = axial
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