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Heat Transfer Engineering, Vol.22, No.6, 40-61, 2001
Discharge coefficients and heat transfer for axisymmetric supersonic nozzles
Computational fluid dynamics (CFD) analysis was used to compute effective nozzle discharge coefficients for subscale sharp-edged converging/diverging nozzles, with a variety of convergence half-angles, motor operating conditions, and two propellants with different ballistics. Convergence half-angles ranged from 10 degrees to 90 degrees. Analysis was conducted at total temperatures from 2,946 K (5303 degreesR) to 3,346 K (6023 degreesR) and total pressures ranging from 2.72 MPa (395 psia) to 20.68 MAI (3,000 psia). Area ratios (A(e)/A*) ranged from 7.43 to 9.39. Ratio of specific heats (gamma) ranged from 1.13 to 1.18. The maximum throat and exit Reynolds' numbers based on axial diameter ranged from 6.73 x 10(5) to 3.61 x 10(6) and 3.26 x 10(5) to 1.99 x 10(6), respectively. Present results of nozzle discharge coefficients are reported and correlated as a function of nozzle convergence half-angle (theta (c)), area ratios (A(e)/A*), and pressure ratio (P-o/P-infinity) for a constant divergence half-angle (theta (d)) of 15 degrees. Computed discharge coefficients ranged from 0.88 to 0.97. They are compared with theory and experimental data available in the literature. Available turbulence models with respect to grid refinements and heat transfer are discussed. Heat transfer is calculated from a modified Reynolds' analogy for laminar flow over a flat plate, the Dittus-Boelter correlation for fully developed turbulent pipe flow, and the Bartz correlation for nozzle flows, and the results are compared with available experimental data.