A Lagrangian formulation for the quasi-one-dimensional modeling of free-piston-driven shock tunnels is described. Three simulations of particular conditions for the T4 shock tunnel are then presented and compared with experimental measurements. The simulations provide very good estimates for both the shock speed and the nozzle-supply pressure obtained after shock reflection and also provide detailed information on the gasdynamic processes over the full length of the facility. This detailed information may be used to identify some of the causes for observed variations in nozzle-supply pressure.
NomenclatureA = duct or tube area, m 2 a = speed of sound, m/s C v = specific heat at constant volume, J/kg/K D = (effective) duct or tube diameter, m E = total energy per unit mass e + l/2« 2 , J/kg e = specific internal energy, J/kĝ loss = effective force due to pipe-fitting losses, N F p = piston friction force, N waii = wa U shear force due to viscous effects, N / = Darcy-Weisbach friction factor H = total enthalpy, J/kg h = heat transfer coefficient, J/s/m 2 /K j = cell index K = viscous loss coefficient L = length, m M = Mach number m = mass, kg P = pressure, Pa Pr = Prandtl number q = heat transfer rate, J/s R = gas constant, J/kg/K Re = Reynolds number r = duct or tube radius, m St = Stanton number T = temperature, K t = time, s U_ _ = state vector in the gasdynamics equations U L ,U R = Riemann invariants u = local velocity, m/s V = piston velocity, m/s x = position, m Y = ratio of specific heats A± = intermediate variable for interpolation A = compressibility factor X = compression ratio |i = viscosity, kg/m/s; friction coefficient n =3.14159... T = wall shear stress, Pa Q, = recovery factor Subscripts aw = adiabatic wall condition B = back of piston exit = nozzle exit plane Received