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The direct molecular simulation method is used to obtain viscosity data from ab initio potential energy surfaces for air over a wide range of temperatures. These data are important for constitutive laws used to simulate hypersonic flows.

High-fidelity numerical results have been obtained for low-disturbance wind-tunnel tests of transitional flow including isolated, discrete roughness elements on a 7 deg half-angle cone. Solutions f...

The design of an inward-turning high-speed three-dimensional streamline-traced intake is presented from osculating axisymmetric theory. To satisfy the osculating intake design criteria, a stitched Busemann diffuser and internal conical flow-A solution are used as the basic isentropic compressive streamline. This new contour provides efficient compression, high flow uniformity, and straight leading-edge shocks of equal strength. Additionally, a novel method for constructing the inlet cowl is presented. The combined process leads to a new method of high-speed intake design. A generic shape-transitioned intake is constructed and named the Indiana inlet for the Indiana universities that contributed to the project. Computational fluid dynamic results are assessed to validate the design method for the two-dimensional parent flowfields and the full three-dimensional design.

We present two-dimensional direct molecular simulation (DMS) results for high-enthalpy nitrogen flows in thermochemical non-equilibrium around a circular cylinder. The simulations are carried out using accurate ab initio potential energy surfaces (PES) to describe N2 + N and N2 + N2 interactions. Select comparisons with the direct simulation Monte Carlo method are presented to demonstrate how the high-fidelity DMS data, both at the level of bulk flow quantities and local molecular distributions, can be used to thoroughly inform or validate simplified reduced-order descriptions. Then, a partially dissociated nitrogen flow around a circular cylinder is obtained from two successive refinements of a well-established ab initio nitrogen PES. The only input in both calculations is the respective PESs, all other simulation parameters being precisely equal. This work, enabled by large scale computing, represents the first attempt at establishing a rigorous methodology for (i) the validation of lower-fidelity, computationally efficient models using ab initio, assumption-free calculations (DMS) as benchmarks and (ii) a systematic assessment of ab initio PES accuracy using entire flow field results.

A numerical investigation of low-frequency unsteadiness in a Mach 2.9 turbulent, reattaching shear layer was carried out with delayed detached-eddy simulation. The results were compared to data fro...

Reynolds-averaged Navier–Stokes simulations were carried out for sharp fin-induced shock wave/turbulent boundary-layer interactions at Mach 5. Calculations were executed for two fin angles of attack, with each case employing four turbulence models. The computational results were compared with vetted experimental data. For all the cases considered, the calculations replicated the experimentally observed flow structure, which is primarily determined by inviscid, rotational flow effects. Predictions of parameters dominated by viscous effects tended to be less accurate. The predictions of the different turbulence models were qualitatively consistent, but the predicted peak skin friction and wall heat flux varied by as much as a factor of two between the models. The discrepancies between computation and experiment are believed to be a result of large-scale unsteadiness and three dimensionality, which are not captured well by conventional turbulence models.

This paper presents the first systematic study of resolution in compressible, turbulent boundary simulations, and the best-resolved simulation carried out to date. Direct numerical simulation (DNS) and wall-resolved, implicit large-eddy simulation (ILES-NWR) were carried out for a turbulent boundary layer at a Mach number of M = 2.3 and maximum momentum thickness Reynolds number of Re θ i = 2 × 10 3 . The wall temperature was fixed at a constant value corresponding to the nominal adiabatic wall temperature. The flow was developed spatially from a laminar boundary layer similarity solution specified at the inflow, and transition to turbulence was promoted with an artificial body force trip. The effects of spatial resolution in the range of ILES-NWR, conventional DNS, and very strict DNS were considered. The finest grid in the spatial resolution study consisted of 3.3 × 1010 points, and maintained max ( Δ x 1 + , Δ x 2 + , Δ x 3 + ) ≤ 1 everywhere. With the resolution at the wall held at ( Δ x 2 + ) w 1 , statistics characterizing large-scale flow features converged for max ( Δ x i + ) ≤ 10 , and agreed well with experimental data. Velocity spectra in the outer part of the boundary layer agreed well at low wavenumber for all grids in this range of mesh spacing, and increasing resolution acted to fill out the high-wavenumber end of the spectrum. In all cases, the resolved region of the spectrum agreed well with a well-validated model of the spectrum of isotropic turbulence. Thus, ILES-NWR can be concluded to converge seamlessly to DNS as the spatial resolution is increased. The low-wavenumber aspect of spatial resolution was examined by varying the width of the computational domain, with a fixed level of small-scale resolution. The primary influence of increasing domain width was to capture additional spectral content in low spanwise wavenumbers; other statistics were found to be identical. Further, turbulence statistics were found to be essentially independent of the domain width for values between two and eight times the maximum boundary layer thickness. This work predicts computationally, for the first time, the full velocity spectrum in the outer part of the boundary layer. In doing so, it justifies use of the ILES-NWR approach as long as the maximum grid spacing is less than 10 in inner units, and the domain width is at least two times the maximum boundary layer thickness.

Spectra of wall-pressure fluctuations caused by separation shock unsteadiness were compared for data obtained from wind-tunnel experiments, the Hypersonic International Flight Research Experimentation flight test 1, and large-eddy simulations. The results were found to be in generally good agreement, despite differences in Mach number and two orders of magnitude difference in Reynolds number. Relatively good agreement was obtained between these spectra and the predictions of a theory developed by Plotkin. The predictions of this theory are also qualitatively consistent with the results of experiments in which the shock motion was synchronized to controlled perturbations. The results presented here support the idea that separation unsteadiness has common features across a broad range of compressible flows and that it behaves as a selective amplifier of large-scale disturbances in the incoming flow.

The properties of spectral subranges of scales in a boundary layer at Mach=2.3 and friction Reynolds number Reτ = 570 are investigated by analysing DNS data. One major aim is to examine whether footprinting and modulation of small-scale near-wall motions by outer large structures, observed at high Reynolds numbers, also pertain to this low-Reynolds-number case, or whether the logarithmic layer simply contains a continuous hierarchy of motions without specific outer scales playing a distinctive role. To this end, the spectrum of scales is decomposed into modes by application of the “Empirical Mode Decomposition”. The properties of different scales are then investigated by means of spectra, maps of isotropy/anisotropy parameters, the premultiplied derivative of the second-order structure function, correlation coefficients and joint probability density function (PDF), the last constructed from conditionally sampled data for the small-scale motions within the large-scale footprints. A clear commonality is identified between interactions in high-Reynolds-number channel flow and the present low-Reynolds-number boundary layer.

A dipole magnet was used to locally reduce surface heating on a fin that extended from a blunt elliptic cone geometry traveling in air at hypersonic speeds. The concept relies on magnetohydrodynamics to generate a force in the weakly ionized postshock air, which decelerates the incoming flow. A three-dimensional, compressible, thermochemical nonequilibrium, fluid code was loosely coupled to a magnetohydrodynamics module to compute the resultant flowfield, which included the electric field. The results showed that the resultant electric field had a minor contributor to the current and consequently to the magnetic body force. In the baseline scenario, the applied magnet was ineffective at perturbing the local shock due to the unseeded flow’s level of electrical conductivity. A potassium-infused ablator was incorporated into the vehicle’s nose to improve the flow’s low electrical conductivity and protect the geometry from the high thermal loads experienced at the stagnation point. A one-dimensional equilibri...

The Navier–Stokes equations were solved using a high-fidelity time-implicit numerical scheme and an implicit large-eddy simulation approach to investigate plasma-based flow control for supersonic flow over a compression ramp. The configuration included a flat-plate region to develop an equilibrium turbulent boundary layer at Mach 2.25, which was validated against a set of experimental measurements. The fully turbulent boundary-layer flow traveled over a 24 deg ramp and produced an unsteady shock-induced separation. A control strategy to suppress the separation through a magnetically-driven surface-discharge actuator was explored. The size, strength, and placement of the model actuator were based on recent experiments at the Princeton University Applied Physics Group. Three control scenarios were examined: steady control, pulsing with a 50% duty cycle, and a case with significant Joule heating. The control mechanism was very effective at reducing the time-mean separation length for all three cases. The ste...

Newly developed computational tools are used to compute hypersonic flowaround a hemisphere cylinder that uses a magnet located within the body as a means of heat flux mitigation. These tools include an improved electrical conductivity model and a parallelized three-dimensional magnetohydrodynamic module that is loosely coupled to a three-dimensional fluid code. Several electrical conductivity models are explored for a range of magnetic field strengths. Results show the shock standoff distance increases when the magnetic field is applied, but the distance is highly dependent on the conductivitymodel selected. The increase in shock standoff distance reduces the gradients in the shock layer, thereby reducing the peak heat flux to the body. However, the total heat flux slightly increases due to additional heating to the aft section of the geometry.

different volumetric energy deposition patterns are considered: a spherical pattern, a “pancake” pattern (oblate spheroid), and a “bean” pattern (prolate spheroid). The effectiveness of volumetric energy deposition for flight control appears to scale strongly with a nondimensional parameter based on the freestream flow kinetic energy flux.

This report describes numerical modeling work carried out on high Mach number flows. Three main technical areas were addressed: seamless transition of implicit large eddy simulation to direct numerical simulation, the development of secondary motion in corner flows, and large-scale unsteadiness of separated shock-wave/boundary-layer interactions. High-order numerical simulations of a Mach 2.3 turbulent equilibrium boundary-layer flow were performed with increasing resolution until all fluid scales in the domain were fully resolved. It was found that the high-fidelity implicit large-eddy simulations converged seamlessly to direct numerical simulation and the turbulent statistics were found to be essentially independent of the domain width for values greater than twice the maximum boundary layer thickness. Numerical simulations of turbulent equilibrium boundary layer flow in the presence of a second wall yielded the development of secondary motion, which significantly increased the three-dimensionality of the subsequent shock boundary-layer interaction in the system. Inclusion of both sidewalls was required to accurately predict the separation location. Introduction of the quadratic relationship into Reynolds-averaged Navier-Stokes models did generate secondary motion for compressible corner flows. However, the improved low-fidelity results did not fully match the high-fidelity implicit large eddy simulations. These results emphasize the need for and use of higher fidelity methods to reduce uncertainty and risk.

High-fidelity computational laser differential interferometry analysis was performed on flow in a supersonic isolator which had a turbulent equilibrium boundary-layer present on all four walls. A high-order implicit large-eddy simulation was used to generate the numerical flow-field. The beam projection simulations were performed by solving the high-fidelity paraxial beam equation. Several lower-order virtual laser beam models were also solved and compared with the high-fidelity simulations. The high-fidelity computations were performed in parallel with experimental laser differential interferometry measurements for a similar flow. This included replicating the post-measurement signal processing technique to minimize procedural differences between the computations and the experiment. The goals of this work are to better understand and validate the experimental technique for this flow while obtaining validation-quality measurements for the high-order high-fidelity implicit large-eddy simulations. Several parameters about the virtual beam and the accompanying virtual photosensor were varied to better understand their sensitivity to the resultant spectrum. One conclusion from the parametric study showed that the radius of the virtual laser beam can act to filter the flow’s spectral content, especially as the beam’s diameter approaches the size of the boundary-layer thickness. The results from the highfidelity beam study also found that a long wavelength beam can not respond to fine-scale structures in the boundary-layer when the wavelength is much greater then the feature size. This observation was not predicted in the low-order virtual beam models since they do not have a mechanism to account for the beam’s wavelength only its diameter. Overall, laser differential interferometry was seen to represent the spectrum of turbulent density fluctuations fairly accurately, despite averaging the fluctuations over the entire optical path that is inherent in the technique.

A series of Reynolds-averaged Navier–Stokes simulations is performed for a supersonic wall-bounded turbulent corner flow. These simulations are compared to a high-order implicit large-eddy simulation for the same geometry and flow conditions. Inclusion of the quadratic constitutive relation in the Reynolds-averaged Navier–Stokes simulation results in significant improvement in qualitative agreement with the large-eddy simulation: specifically, the presence of secondary flow (a counter-rotating vortex pair). The range of valid values for the constant in the quadratic constitutive relation formulation is explored. Additionally, the effects on this range from different turbulence models and momentum thickness Reynolds numbers for the corner are also examined. These effects of the quadratic constitutive relation are explored using both the finite difference fluid solver OVERFLOW and the finite volume fluid solver US3D. The results indicate that the quadratic constitutive relation term directly affects the str...

Large-eddy simulations were performed for a Mach 2.25 turbulent airflow as it travels over a 24◦ compression ramp in the presence of a sidewall. Two flat plates were joined perpendicular to each other to form the corner with each plate having sufficient computational extent to developed an equilibrium turbulent boundary layer profile far from the corner junction. The turbulent flow on each plate propagated into the corner and aided in its transition. On the bottom plate, the turbulent equilibrium boundary-layer flow traveled over a 24◦ compression ramp which lead to an unsteady oblique shock and subsequent separation bubble. At the same time, the inclusion of the sidewall led to the development of a corner vortex and an increasingly three-dimensional shock front. The complex corner flow included a nodal attachment point and separation vortex that traveled along the sidewall with the oblique shock. Theses features interacted with the sidewall turbulent boundary-layer, forming a smaller, swept, separation bubble. The solutions were obtained using a high-fidelity time-implicit numerical scheme and an implicit large-eddy simulation approach. Time mean and instantaneous flow quantities were collected and evaluated. The results were compared with a spanwise periodic scenario performed at the same conditions. In both scenarios, the mean flow separated upstream of the compression ramp, but in the current scenario the separation length varied significantly with distance from the sidewall. Since separation length correlates with the unsteady frequency of the shock boundarylayer interaction, the inclusion of the sidewall not only yielded a highly three-dimensional shock system, but also changed the local frequency of the unsteady shock boundary-layer interaction.

Large-eddy simulations are used to investigate a supersonic wall-bounded turbulent corner flow. Solutions are obtained using a high-fidelity time-implicit numerical scheme and an implicit large-eddy simulation approach. The inclusion of the sidewall leads to the development of a corner core flow which grows in size as the flow progresses downstream. A grid resolution study, with over a billion cells for the fine grid, is performed and both mean and time-accurate statistics are analyzed. The solutions are compared to a spanwiseperiodic flat-plate turbulent boundary layer developed at the same conditions and yield similar results when measured sufficiently far from the corner. Two-point autocorrelations verify that the domain’s cross-sectional area is sufficient to de-correlate the corner core flow front eh turbulent equilibrium boundary-layer developed on each of the adjoining flat-plate walls. In addition, triple products are collected and demonstrate that the corner-dominated flow is significantly different from the rest of the domain.

A physics-based model was developed for nanosecond-pulse discharges, including realistic air kinetics, electron energy transport, and compressible bulk gas flow. A reduced plasma kinetic model (23 species and 50 processes) was developed to capture the dominant species and reactions for energy storage and thermalization in the discharge. The kinetic model included electronically and vibrationally excited species, and several species of ions and ground state neutrals. The governing equations included the Poisson equation for the electric potential, diffusion equations for each neutral species, conservation equations for each charged species, and mass-averaged conservation equations for the bulk gas flow. The results of calculations with this model highlighted the path of energy transfer in the discharge. At breakdown, the input electrical energy was transformed over a timescale on the order of 1 ns into chemical energy of ions, dissociation products, and vibrationally and electronically excited particles. About 30% of this energy was subsequently thermalized over a timescale of 10 μs. Since the thermalization time scale was faster than the acoustic time scale, the heat release led to the formation of weak shock waves originating near the sheath edge, consistent with experimental observations.

High-order implicit large-eddy simulations were performed for supersonic turbulent ow over a 24 compression ramp. The interaction between the turbulent ow and the corner led to a low-frequency, unsteady, shock-induced separation. A magnetically-driven plasma-based ow controller was modeled and applied to the ow to minimize the separated region and its adverse eects. The controller consisted of two streamwise separated segments pulsed 180 out of phase at a 50% duty-cycle. The results show that this controller conguration was very eective at reducing the separation while only using 80% of the power reported for previous studies.

The Navier-Stokes equations are solved using a high-fidelity time-implicit numerical scheme and an implicit large-eddy simulation approach to investigate plasmabased flow control for supersonic flow over a compression ramp. The configuration includes a flat-plate region to develop an equilibrium turbulent boundary layer at Mach 2.25, which is validated against a set of experimental measurements. The fully turbulent boundary-layer flow interacts with a 24◦ ramp and produces an unsteady shock-induced separation. A control strategy to suppress the separation through a magnetically-driven gliding-arc actuator is explored. The size, strength, and placement of the actuator are developed based on recent experiments. Three control scenarios were examined: steady control, pulsing with a 50% duty cycle, and Joule heating. The results show the control mechanism is very effective at reducing the mean separation length for all three situations. The case without pulsing and Joule heating was the most effective, with a reduction in the separation length by more than 75%. Control was also found to significantly reduce the low-frequency content of the turbulent kinetic energy spectrum.

A computational study is performed for Mach 5 air flow over a cylinder with a dielectric barrier discharge actuator set into the cylinder surface. The actuator is pulsed at nanosecond time scales, which rapidly adds energy to the flow, thereby creating a shock wave that travels away from the pulse source. As the shock wave travels upstream, it interacts with the standing bow-shock and momentarily increases the bow-shock standoff distance. This phenomenon is also observed in phase-locked schlieren photography captured duriing the experiment. The focus of this paper is to reproduce flow phenomena observed in the experiment using high-fidelity computations in order to provide additional insight into the shock-shock interaction, the effect the dielectric barrier discharge pulse has on the surface properties of the cylinder, and develop a reduced-order phenomenological model representative of the nanosecond pulse discharge system. Experimental and high-fidelity modeling studies of the nanosecond pulse dielectric barrier discharge plasma actuators are known to operate with relatively low temperatures. This work explores the possibility that the induced compression wave is generated by rapid thermalization of the discharge which results in a local temperature rise occurring on longer time scales. Two-dimensional simulations are performed and provide many useful details about the discharge event while comparing with many measurements captured by the experiment.

ow. In order to increase the electrical conductivity and protect the geometry from the high thermal loads experienced at the stagnation point a potassium-impregnated ablator is incorporated into vehicle’s nose. A one-dimensional equilibrium material response code is developed and used to model the ablative surface. The seed particles from the impregnated ablator increase the electrical conductivity such that the magnetic force moves the triple point up the n face and, consequently, changes the surface properties.

A three-dimensional fluid code was loosely coupled to a low magnetic Reynolds number magnetohydrodynamics module to compute hypersonic air flow around a blunt elliptic cone with a fin protruding from the top centerline. A dipole magnet was positioned within the protrusion to reduce local heating on the fin, but had minimal effect because of the low electrical conductivity of the air. Two approaches were explored to increase the effectiveness of the magnet for local heat flux mitigation: increasing the flight Mach number, and using an impregnated ablator to introduce seed particles into the flow. Both approaches increased the electrical conductivity near the fin, making the magnet more effective at heat flux mitigation. However, the seeding approach does not require modification to the trajectory nor does it increase the baseline heat load on the fin, making it a more viable configuration for a magnetohydrodynamic flight experiment.