Quasi-one-dimensional modeling of a free-piston shock tunnel

Abstract

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

Simulation of Oxford University Gun Tunnel performance using a quasi-one-dimensional model

“…For example, the reflected shock tunnel simulations of [Jacobs (1994)] and [Tani et al (1994)] typically produce pressure histories that are within 10% of the experimental measurements over the period of useful test flow produced by the facility. However, substantial differences between the simulated and experimental shock compression processes can usually be observed within either the pressure history or shock speed comparisons.…”

“…In the current article, the performance of the Oxford University Gun Tunnel is simulated using the Lagrangian formulation described by [Jacobs (1994)]. Paricular attention is given to the problem of modelling area changes for accurate simulation of both flow discharge and wave trans-mission/reflection processes.…”

“…The numerical model used in the present work is the Lagrangian formulation that has been described in some detail by [Jacobs (1994)]. Briefly however, the area variation along the length of the facility is specified as are the initial conditions of the gas slugs in each region.…”

“…A number of different quasi-one-dimensional numerical formulations for the solution of impulse facility operation have been described by [Groth et al (1991)], [Jacobs (1994)], and [Tani et al (1994)]. …”

“…A number of additional features have been developed since the original publication of [Jacobs (1994)] including a boundary layer mass entrainment model to improve the simulation of the contact surface trajectories in shock and expansion tubes, [Doolan and Jacobs (1996)]. …”