Nonequilibrium regime of airflows in contoured nozzles - Theory and experiments.

Abstract

Experimental data are compared with theory for the expansion of high-temperature air through a 9.492-in. exit diameter, contoured nozzle. An exact numerical calculation of a one-dimensional equilibrium and nonequilibrium expansion based on the measured potential nozzle flow is included. Thermodynamic calculations are based on rotational, vibrational, and electronic partition functions with associated corrections for anharmonicity, rotational-vibrational coupling, and rotational stretching. Flow properties are calculated for an air model containing N£, C>2, NO, N, O, and argon. An experimental program utilizing a 3-Mw, d.c. arc heater provided design reservoir conditions of 114.7 atm and 4120°K to produce a Mach number 10.23 "near-equilibrium" flow. Fully instrumented nozzle exit surveys of mass flux, impact pressure, and steady-state calorimetry along with nozzle wall pressures were utilized to derive freestream velocity, density, and total enthalpy. A second case with reservoir conditions of 132.7 atm and 5725°K was found to be in good agreement with the nonequilibrium expansion process. A third case, reservoir conditions of 35.4 atm and 5361 °K, yielded a nonequilibrium, parallel flow resembling a gas nearly "frozen" directly after the nozzle throat. Nomenclature A= one-dimensional nozzle area, cm 2 or ft 2 AI = coeff in equilibrium const, Table 3 B = exp of T in equilibrium const, Table 3 CMJ = concentration of specie j, mole/cm 3 d* = nozzle throat diam, in. E 0i = zero point energy per mole of specie i, dyne cm/mole Ej)i = heat of reaction per mole of specie i, dyne cm/mole, or cal/mole HT = total enthalpy per unit mass of fluid, dyne cm/g or Btu/lbm Hi = enthalpy per mole of specie i, dyne cm/mole h = static enthalpy per unit mass of fluid, dyne cm/g or Btu/lbm K pr = equilibrium const for reaction r, Table 3 kb r -backward rate constant for reaction r, (cm s ) 2 /mole 2 -sec kf r = forward rate constant for reaction r, cm 3 /mole-sec, Table 1 M = Mach number MJ = molecular weight of species j, g/mole n = number of compounds m = mole number of species i, mole/g of mixture m° = mole number of reference species i, mole/g P T = reservoir pressure, atm p = local pressure, atm or dynes/cm 2

Mach 4 and Mach 8 axisymmetric nozzles for a high-enthalpy shock tunnel

“…In Ref. 18 it was indicated that such throats produce good quality source flow when used in conical nozzles. Also, it was found that these throats resisted erosion better than those with a shorter constant-diameter section or those manufactured from grade 316 stainless steel.…”