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Geometrical optics ray-tracing is used to derive schlieren and shadowgraph images from large-eddy simulation (LES) data of a jet in supersonic crossflow and to compare with experimental data. Including the components of the optical system that forms the image in the simulation is found to be important. The technique produces images that replicate flow physics more faithfully than straight-line path integration and other techniques, and more efficiently than physical-optics techniques. Applications of these simulated images are demonstrated in supersonic flows. Time-correlated pairs of shadowgraph images taken from the LES using this technique are used in conjunction with an image-correlation velocimetry technique to compare the estimated convection velocity field in the LES to that of experiments of the same flow. Agreement between the two is good with a maximum variance of 5% by some metrics. This technique can aid in the validation of LES results, allowing quantitative comparison between experiment and simulation, and to extract information unattainable by experiment alone. Comparisons of simulated and experimental jet penetration into the supersonic freestream are also made.

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Simulations of combustion in high-speed and supersonic flows need to account for autoignition phenomena, compressibility, and the effects of intense turbulence. In the present work, the evolution-variable manifold framework of Cymbalist and Dimotakis ("On Autoignition-Dominated Supersonic Combustion," AIAA Paper 2015-2315, June 2015) is implemented in a computational fluid dynamics method, and Reynolds-averaged Navier-Stokes and wall-modeled large-eddy simulations are performed for a hydrogen-air combustion test case. As implemented here, the evolution-variable manifold approach solves a scalar conservation equation for a reaction-evolution variable that represents both the induction and subsequent oxidation phases of combustion. The detailed thermochemical state of the reacting fluid is tabulated as a low-dimensional manifold as a function of density, energy, mixture fraction, and the evolution variable. A numerical flux function consistent with local thermodynamic processes is developed, and the approach for coupling the computational fluid dynamics to the evolution-variable manifold table is discussed. Wall-modeled large-eddy simulations incorporating the evolution-variable manifold framework are found to be in good agreement with full chemical kinetics model simulations and the jet in supersonic crossflow hydrogen-air experiments of Gamba and Mungal ("Ignition, Flame Structure and Near-Wall Burning in Transverse Hydrogen Jets in Supersonic Crossflow," Journal of Fluid Mechanics, Vol. 780, Oct. 2015, pp. 226-273). In particular, the evolutionvariable manifold approach captures both thin reaction fronts and distributed reaction-zone combustion that dominate high-speed turbulent combustion flows.Nomenclature a = speed of sound, m∕s C; X ; Z = progress variable, nonfuel mass fraction, and fuel mass fraction c v ; c v;s = mixture and s-species specific heats, J∕kg ⋅ K D = diffusion coefficient, m 2 ∕s E = total energy per unit volume, J∕m 3 e; e s = mixture and s-species specific energy, J∕kg F = convective flux vector h; h 0 = enthalpy and total enthalpy, J∕kg i = grid index J = jet momentum ratio j h = diffusive enthalpy flux k = kinetic energy, J∕kg L; R = values obtained from left and right data M s = s-species molar mass, kg∕kmol N s = number of species in detailed kinetics model n; n x ; n y ; n z = element face unit normal vector and components p = pressure, Pa q j = heat flux vector= vectors of conserved and primitive variables u; u; v; w = velocity vector and components, m∕s u 0 = face-normal velocity component, m∕s x; x j = position vector and its components, m Y s = s-species mass fraction α = dissipative flux factor δ R = reaction-zone thickness, m ε = dissipation rate ζ = evolution-variable source term, 1∕s η k = Kolmogorov length scale, m Λ; λ = diagonal matrix of eigenvalues and eigenvalue ν t ; ν = turbulence field variable and kinematic viscosity ρ; ρ s = density and s-species density, kg∕m 3 σ ij = viscous and Reynolds stress τ = evolution variable ϕ = stoichiometric fuel-air ratio χ = subgrid-s...

The simulation of low-speed combustion flows is well established. However, at highspeed conditions where radical formation and ignition delay are important, there is much less experience with turbulent combustion modeling. In the present work, a novel evolution variable manifold (EVM) approach of Cymbalist and Dimotakis 1,2 is implemented in a production CFD code and preliminary RANS and large-eddy simulations are computed for a hydrogen combustion test case. The EVM approach solves a scalar conservation equation for the induction time to represent ignition delay. The state of the combustion products is tabulated as a function of density, energy, mixture fraction, and the evolution variable. A thermodynamically-consistent numerical flux function is developed and the approach for coupling the EVM table to CFD is discussed. Initial simulations show that the EVM approach produces good agreement with full chemical kinetics model simulations. Work remains to be done to improve the numerical stability, extend the grid, and increase the order of accuracy of the simulations.