David M. Peterson

Unstructured grid approaches for accurate aeroheating simulations

The use of tetrahedral, prismatic, and hybrid hexahedral-prismatic-tetrahedral grids for the accurate prediction of aerodynamic heating at hypersonic conditions is investigated. We find that tetrahedral grids introduce significant error in the vicinity of strong shock waves, which results in unacceptable aeroheating predictions. The source of this error is studied with an idealized model, and it is found that a large spurious component of post-shock velocity is generated by triangular and tetrahedral elements. This type error is much smaller and easier to control on quadrilateral or hexahedral grids. Thus, we are very skeptical about the utility of tetrahedral grids for accurate hypersonic aeroheating predictions. Several comparisons of heating predictions for a three-dimensional sphere are made, and it is found that the stagnation region results are very sensitive to the grid design. Based on this work and our experience, we advocate the use of unstructured hexahedral grids which increase the grid design space, reduce the element count for many geometries, and result in accurate aeroheating predictions.

Detached Eddy Simulation of a Generic Scramjet Inlet and Combustor

Results are presented which detail progress toward building the capability of simulating full scramjet powered vehicles. Important issues involved in the design of hypersonic, inward-turning inlets are disscussed and a process by which the performance of the inlets can be optimized is outlined. The geometry of the inlet is defined in terms of cubic rational Bezier curves. This allows for automated generation of high quality grids, as well as providing parameters which drive the optimizaiton process. The simulations used in the optimization of the inlets use a steady-state Reynolds-averaged Navier-Stokes model for turbulence closure. Simulations of the combustor section of a scramjet engine require a different modeling approach. A hybrid Reynolds-averaged Navier-Stokes and large eddy simulation methodology based on the detached-eddy simulation formulation is used. This allows for the large-scale unsteadiness of the flow to be resolved, which is key in simulating this type of flow accurately. The RANS portion of the method provides wall-modeling for large eddy simulation regions as well as fully modeling the turbulence in regions away from where mixing and combustion occur. This reduces the cost over a full LES. Preliminary results from simulations of two combustor configurations are presented. The first configuration involves the combustion of hydrogen injected through a normal, circular injector downstream of a small step. The second configuration involves a hydrogen-fluorine reaction in an expansion-ramp combustor. Finite-rate chemistry is used in the simulations; however, the current simulations do not include the effects of a subgrid model for the chemical source term. The simulations demonstrate the large range of time scales involved in combustor flows, which make an efficient solver with implicit time integration necessary. A low-dissipation, kinetic energy conserving numerical scheme is used in the simulation of the second configuration. This scheme resolves a larger range of turbulent scales on the same grid at minimal additional cost over standard upwind-biased schemes.

Simulations of mixing in an inlet-fueled axisymmetric scramjet

An unsteady simulation of a simple axisymmetric inlet-fueled scramjet engine concept is performed using a hybrid Reynolds-averaged Navier–Stokes and large-eddy simulation approach. The freestream has a Mach number of 7.5 with Mach 8 flight enthalpy. The simulation is of a nonreacting case in which hydrogen is injected into nitrogen. The simulation is used to provide a detailed description of the structure of the flow. The simulation shows that a large-scale pair of counter-rotating vortices forms within the scramjet combustor, with rotation opposite to the rotation of the pair that forms further upstream due to the interaction of the fuel plume with the crossflow. This vortex pair is found to significantly alter the shape of the hydrogen fuel plume and increase the rate at which the hydrogen is mixing by more than a factor of 2 compared to before the vortex pair is formed. The distribution of hydrogen is examined in detail. The time-averaged and fluctuating wall pressures, the mean velocity field, and res...

Numerical Investigation of a Supersonic Cavity Flameholder

Simulation results are presented for non-reacting flow within a supersonic cavity flameholder. The freestream is air at Mach 2. A case is simulated with no fuel injection, and two cases are simulated with different rates of ethylene fuel injected through holes located on the back face of the cavity. The simulations correspond to a series of experiments for which particle image velocimetry measurements of two velocity components were made within the cavity. The flow within the cavity is computed using unsteady hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation, as well as steady-state Reynolds-averaged NavierStokes simulations. A thorough grid resolution study is presented in which the resolution required to resolve the flow within the cavity is determined. The effects of wall temperature and the thickness of the oncoming turbulent boundary on the solutions is examined and found not to affect the mean velocity and turbulence, and to affect mean mixing only slightly. For steady-state Reynolds-Averaged Navier-Stokes simulations, several turbulence models are used and compared to the hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation results, and the effects of the turbulent Schmidt number, are investigated. The influence of the side walls are investigated by comparing simulations of the full-width duct to simulations of a partial-width duct that uses periodic boundary conditions. The results of the simulations are also compared to the velocity measurements from the experiments, and the hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation results are found to compare well with the experiment in most locations.

Assessment of Synthetic Inflow Generation for Simulating Injection Into a Supersonic Crossflow

Detached eddy simulation is used to simulate the flow field around gaseous jets injected into supersonic crossflows. The simulations are done with and without the use of synthetic inflow generation, a method used to provide a realistic, time-varying boundary layer for the inflow condition of the simulations. The goal is to assess the ability of DES to simulate the complicated flow field around the injection location, and to assess the ability of synthetic inflow generation to capture the contribution of the preinjection boundary layer to the flow field. Reynolds stresses and turbulent kinetic energy predicted by the simulations are compared to experimentally measured values in one test case of normal injection of air into a Mach 1.6 freestream. A second test case compares predicted mean injectant mole fractions with measured values for a pair of staged injectors that inject air into a Mach 2 freestream. Unlike previous simulations of jets in supersonic crossflows done by the authors, the DES provides highly unsteady jet plumes, even without the synthetic inflow boundary layer. This is due partially to improved mesh resolution, but is mostly due to large and highly energetic separation regions upstream of the normal injectors, compared to smaller, less energetic regions upstream of the angled injectors simulated previously. As a result of the natural instability of these configurations, the role of the boundary layer structures is found to be small. However, the results show that DES reproduces the mean and fluctuating quantities very well compared to the measured values.

Simulating Turbulence and Mixing in Supersonic Combustors Using Hybrid RANS/LES

Simulation results are presented for non-reacting flow within a supersonic cavity flameholder. The freestream is air at Mach 2. A case is simulated with no fuel injection and with ethylene fuel injected through holes located on the back face of the cavity. The simulations correspond to a series of experiments for which particle image velocimetry measurements of two velocity components were made within the cavity. The flow within the cavity is computed using unsteady hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation. A thorough grid resolution study is presented in which the resolution required to resolve the flow within the cavity is determined. The influence of the level of turbulence within the oncoming boundary layer is examined and found to significantly affect the velocity field and mixing within the cavity. The effect of the side walls is investigated by comparing simulations of the full-width duct to simulations of a partial-width duct that uses periodic boundary conditions. Differences in resolved turbulence kinetic energy and mixing are seen between the full-width and partial width simulations. The results of the simulations are also compared to the velocity measurements from the experiments, and the hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation results are found to compare reasonably well with the experiment in most locations. Improved agreement with fluctuating velocity components is found when the simulation results are filtered to a resolution corresponding to the resolution of the velocity measurement technique.

Hybrid Reynolds-Averaged and Large-Eddy Simulations of a Supersonic Cavity Flameholder

Simulation results are presented for non-reacting flow within a supersonic cavity flameholder. The freestream is air at Mach 2. A case is simulated with no fuel injection, and two cases are simulated with different rates of ethylene fuel injected through holes located on the back face of the cavity. The simulations correspond to a series of experiments for which particle image velocimetry measurements of two velocity components were made within the cavity. Reynolds-averaged Navier-Stokes simulations are used to examine the influence of the finite-width, low-angled slot used to seed the flow for the particle image velocimetry. The simulations indicate that the seeder has little influence on the flow within the cavity, allowing for the seeder to be neglected in the remainder of the simulations. The flow within the cavity is simulated using steady-state Reynolds-averaged Navier-Stokes simulations, as well as unsteady hybrid Reynolds-averaged Navier-Stokes and large-eddy simulations. A thorough grid resolution study is presented in which the resolution required to resolve the flow within the cavity is determined. The results of the simulations on the final grids are compared to the velocity measurements from the experiments and the hybrid Reynolds-averaged Navier-Stokes and large-eddy simulation results are found to provide improved agreement with certain aspects of the flow. The simulation results are then used to investigate the mixing within the cavity, which was not measured in the experiments. The mixing information from the simulations provides further insight into the physics of the cavity flameholder flowfield.

DES investigations of transverse injection into supersonic crossflow using a hybrid unstructured solver

Numerical simulations of transverse injection through low-angled injector ports into a supersonic freestream are performed using a hybrid, unstructured solver. Two cases are investigated: air injected into a M=2.9 air freestream with a 25 injection angle, and heated helium injected into a M=4.0 air freestream with a 30 injection angle. Simulations were run in RANS and DES modes. A set of the DES simulations were run with an unsteady inflow boundary layer, where the perturbations are a statistically meaningful representation of a series of randomly placed hairpin eddies. This boundary condition was fed periodically into the domain, and was reused multiple times over the course of a simulation. The RANS and DES simulations are found to capture the salient features of the flow, though discrepancies with experimental data are found. While the DES simulations were found to give steady-state solutions for the flow fields, the addition of the unsteady inflow boundary layer was found to greatly impact the downstream flow field and to improve the overall agreement with experiment. In the case of the helium injection, it was found that the predicted mass fraction distributions of the DES simulations with the unsteady inflow boundary layer was far less dependent on the value of the turbulent Schmidt number. This result shows that the mixing found in DES simulation with the unsteady inflow boundary layer is a result of the large-scale turbulent motion of the flow, rather than because of the gradient diusion term. However, the ‘box of eddies’ used to create the unsteady inflow boundary layers were not long enough to ensure that no bias was introduced into the flow field, and future simulations will be run with larger boxes. The results of the study show a great deal of promise for the use of DES simulations in conjunction with unsteady inflow boundary layers for simulation of SCRAMjet fuel injection.

Supersonic combustor fuel injection simulations using a hybrid RANS/LES approach

The non-reacting injection of ethylene into a Mach 2 supersonic cross ow is simulated using a hybrid Reynolds-Averaged Navier-Stokes and Large-Eddy Simulation approach. Injection occurs through circular injector ports oriented at either 90 degrees or 30 degrees with respect to the freestream. For each injection angle, multiple jet-to-freestream momentum ux ratios are simulated. The results of the simulations are qualitatively compared to the mean and standard deviation of sequences of planar laser-induced uorescence intensity images. Results are quantitatively compared to mean ethylene mole fraction distributions obtained via Raman scattering. The simulation results compare very well to the experimental data. The simulation results are used to investigate the mixing properties of the di erent injector con gurations and conditions.

Hybrid RANS/LES of a Supersonic Combustor

Preliminary results from simulations modeling ush wall fuel injection in scramjet engines is presented. The simulations use a hybrid Reynolds-averaged Navier-Stokes and large eddy simulation methodology, where the primary function of the RANS mode is to act as a wall model for the large eddy simulation. The hybrid method is based on the delayed detached-eddy simulation formulation and includes improvements for functioning as a wall-modeled large eddy simulation. A seven species, eight reaction mechanism for hydrogen-air chemistry is coupled with the ow solver. The results presented here do not include the eects of subgrid turbulence-chemistry interaction. The instantaneous structure and ignition characteristics of a transverse jet of hydrogen in a supersonic crossow is compared to planar laser induced uorescence of OH radicals. The chemical mechanism used results in autoignition of the jet. The thin, wrinkled lament of OH observed in the experiment is reproduced well by the simulation. A model hydrogen-powered scramjet combustor for which there are internal measurements of temperature and species concentration, as well as wall pressure measurements, was also simulated. Well into the simulation a combustion front develops within the combustor that propagates upstream. As of the time this paper was written, the front is still moving upstream. The development of the combustion front it discussed and initial comparisons to the experimental data are made. The initial comparisons are promising, showing mean ow quantities that are qualitatively similar to what is measured experimentally.