Heat transfer of gas-particle flow in a supersonic convergent-divergent nozzle

Summary Heat flux, wall heat transfer coefficients, and wall pressures are determined for high velocity flow of gas-solid mixtures in a converging-diverging nozzle. Flow separation accompanied with oblique shock formation occurs in the diverging section of the nozzle. The shock strength is reduced upon the addition of solid particles. The wall pressure in the convergent section of the nozzle appears unaffected by the presence of solid particles. In the divergent section, however, the wall pressure is slightly lowered. At the maximum ratio of solid to air flow used in the experiments (3.7) increases in the heat transfer rate of up to 20 and 50 percent are obtained in the convergent and separated (divergent) regions of the nozzle, respectively. Slightly larger increases in the wall heat transfer coefficients are also obtained. It is concluded that the wall heat flux and heat transfer coefficients are influenced strongly by the presence of disturbances upstream of the nozzle inlet.Nomenclature W_a air flow rate - W_s solids flow rate - x axial distance from nozzle entrance - L axial length of nozzle - specific heat ratio of fluid - A_e exit cross section of flow - A_* throat cross section of flow - P₀ inlet pressure - P_s wall separation pressure - P_a ambient exhaust pressure - shock wave angle - shock wave deflection angle - M₁ Mach number upstream of shock wave - Mach number normal to shock wave - q heat flux - k_f thermal conductivity of fluid - T_wi inside wall temperature - T_wo outside wall temperature - T_ad adiabatic wall temperature - h wall heat transfer coefficient - C nozzle constant - A local cross section of flow - c_p specific heat of fluid - Pr Prandtl number - viscosity of fluid - r_c throat radius of curvature - factor accounting for variation of and Units absolute temperature °R(ankine) °F+459.7 - conductivity 1 BTU (hr ft °F)^–1 4.137×10^–3 cal (s cm °C)^–1 - specific heat 1 BTU (1b °F)^–1 1 cal (g °C)^–1 - absolute pressure 1 psia 0.0680 atmSupported in part by aid provided by the UCLA Space Science Center (Grant NsG 236-62 Libby).Listed for readers not familiar with the units adopted in this paper (editor).