Reynolds-Averaged Navier-Stokes Simulations of the HyShot II Scramjet

Abstract

The internal flow in the HyShot II scramjet is investigated through numerical simulations. A computational infrastructure to solve the compressible Reynolds-averaged Navier-Stokes equations on unstructured meshes is introduced. A combustion model based on tabulated chemistry is considered to incorporate detailed chemicalkinetics mechanics while retaining a low computational cost. Both nonreactive and reactive simulations have been performed, and results are compared with ground test measurements obtained at DLR, German Aerospace Center. Different turbulence models were tested, and the dependence on the mesh is assessed through grid refinement. The comparison with experimental data shows good agreement, although the computed heat fluxes at the wall are higher than measurements for the reactive case. A sensitivity analysis on the turbulent Schmidt and Prandtl numbers shows that the choice of these parameters has a strong influence on the results. In particular, variations of the turbulent Prandtl number lead to large changes in the heat flux at the walls. Finally, the inception of thermal choking is investigated by increasing the equivalence ratio, whereby a normal shock is created locally and moves upstream, leading to a large increase in the maximum pressure. Nevertheless, a large portion of the flow is still supersonic. Nomenclatureproportionality constant between turbulence and scalar time scales c p = specific heat capacity at constant pressure D = scalar diffusion coefficient d = injector diameter E = total specific energy e = specific internal energy F = convective flux vector F v = viscous flux vector h = specific enthalpy I = identity matrix k = turbulent kinetic energy Le = Lewis number Ma = Mach number N = number of species n = outward-pointing unit vector normal to surface P ref = reference pressure Pr = Prandtl number p = pressure Q = vector of primitives variables Q ref = reference wall heat flux R = residuum R = gas constant R u = universal gas constant r f = vector connecting cell center and center of cell face S = source-term vector S = wave speed in approximate Riemann solver S i = source term for scalar i Sc = Schmidt number T = temperature t = time U = vector of conserved variables U = inflow velocity V = cell volume v = Cartesian velocity vector W = species molecular weight x = Cartesian position vector Y = species mass fraction y = wall-normal direction Z = mixture fraction = exponent for the pressure correction of the source term of the progress variable = ratio of specific heat capacity h 0 = heat of formation ij = Kronecker delta @ = boundary of the physical domain = thermal diffusivity = viscosity = approximation of the triple correlation = stress tensor = density k = turbulent kinetic-energy Schmidt number ij = viscous stress tensor R ij = Reynolds stress tensor = generic scalar ' = equivalence ratio = scalar dissipation rate = slope limiter = physical domain ! = specific turbulent dissipation _ ! C = source term of the progress variable Subscripts F = fuel f = cell face inj = injector k ...

Incipient thermal choking and stable shock-train formation in the heat-release region of a scramjet combustor. Part II: Large eddy simulations

“…More importantly, in a mixing-controlled flow, details of the combustion model have less influence on the solution. The relative agreement between the computed pressure profiles by Karl et al [19] and Pecnik et al [21] (two studies which used very different turbulent combustion models) is consistent with this.…”

“…Thus the computational domain is 1/4 of the width of the full combustor, with periodic boundary conditions used in the spanwise direction. This approximation was investigated by Pecnik et al [21] using RANS, and was found to be reasonable.…”

“…Pecnik et al [21] extended the classic flamelet-based modeling approach to the supersonic regime, and applied this model to the HyShot II combustor within a RANS framework. One important contribution of Pecnik et al [21] was to assess the importance of the spanwise domain size on the RANS results.…”

“…The steady flamelet-based model of Pecnik et al [21], which is an extension of the steady flamelet/progress-variable model of Pierce and Moin [33] to supersonic flows, is used in this work. Laminar counterflow diffusion (non-premixed) flamelets are solved a priori at different strain-rates, with the results parametrized in terms of the mixture fraction Z and the reaction progress-variable C, taken here as the mass fraction of H 2 O.…”

“…One important contribution of Pecnik et al [21] was to assess the importance of the spanwise domain size on the RANS results. Specifically, they compared cases covering 1/2 and 1/8 of the combustor width using the appropriate symmetry boundary conditions, and showed that the differences in the results were small.…”