We conduct large-eddy simulations of a Mach 5.84 cold wall turbulent boundary layer over one-dimensional wavy walls with varying amplitudes and wavelengths. Across all wall topologies, a series of alternating shock and expansion waves is shown to influence the entire boundary layer, and generate repeating wave patterns in the turbulent stresses, dispersive stresses, and turbulent kinetic energy budget. The series of alternating shocks and expansions imposes repeating adverse and favourable pressure gradients across the wavy wall, and at sufficient wall amplitude, triggers flow separation in the trough of the wave. Flow separation is demonstrated to influence the behaviour of wall pressure fluctuations over the wavy wall. In attached flows, the prominent frequencies are consistent with integral-scale boundary layer turbulence, whereas in separated flows, a two-decade frequency range is present, akin to two-dimensional shock-boundary layer interactions. Counter-rotating streamwise-oriented structures are observed on the windward side of the wave, which diminish over the wave crest. A conditional analysis demonstrates that these structures are present in the upstream boundary layer, and are amplified with increasing wall amplitude. An examination of the G & ouml;rtler number and probability density function (PDF) of the fluctuating lateral wall shear stress demonstrates the strong correlation between a large G & ouml;rtler number and growth of the PDF tail density, suggesting that the amplification of the counter-rotating streamwise-oriented structures are linked to centrifugal instabilities in regions of streamline concavity.

A suite of wall-modeled large-eddy simulations (WMLES) is performed to assess the predictions of the wall pressure fluctuations induced by zero-pressure gradient turbulent boundary layers at Mach numbers ranging from 2 to 14. WMLES results are compared with accompanying large-eddy simulation (LES) results, as well as experimental measurements. It is shown that the wall pressure fluctuation dynamics are sensitive to the wall-model exchange location, wherein placing the exchange location away from the wall results in an upwards shift of the wall pressure fluctuation autospectra relative to experiment and LES. A detailed grid resolution study at Mach 9 conditions demonstrates modest sensitivity in the mean and unsteady flow quantities with respect to grid density, but notable sensitivity with respect to the WMLES exchange location.

Pressure fluctuations experienced by high-speed reentry vehicles impart significant loads onto the body, and much remains to be quantified particularly for finite angle of attack when separation occurs on the leeward side. To investigate these angle-of-attack effects, we examine the coherence of pressure fluctuations of a slender seven-degree half-angle cone at angles of attack alpha = 0 degrees, 8 degrees and 14 degrees at Mach 5 and Mach 8 experimentally using the Hypersonic Wind Tunnel facility at Sandia National Laboratories. Kulite sensors placed in T-shaped arrangements and approximately aligned with the streamlines are utilized to assess the spatial coherence of pressure fluctuations in the streamwise and lateral directions. The placement is determined a-priori using oil-based flow visualization. The coherence functions are quantified experimentally. The results indicate significantly higher coherence than anticipated from simulation, possibly due to delayed transition from the blunted nose cone. This result will be reexamined in upcoming wind tunnel tests.

The near wake flow field associated with hypersonic blunt bodies is characterized by complex physical phenomena resulting in both steady and time dependent pressure loadings on the base of the vehicle. Here, we focus on the unsteady fluid dynamic pressure fluctuation behavior as a vibratory input loading. Typically, these flows are characterized by a locally low-pressure, separated flow region with an unsteady formation of vortical cells that are locally produced and convected downstream into the far-field wake. This periodic production and transport of vortical elements is very-well known from classical incompressible fluid mechanics and is usually termed as the (Von) Karman vortex street. While traditionally discussed within the scope of incompressible flow, the periodic vortex shedding phenomenon is known for compressible flows as well. To support vehicle vibratory loading design computations, we examine a suite of analytical and high-fidelity computational models supported by dedicated experimental measurements. While large scale simulation approaches offer very high-quality results, they are impractical for design-level decisions, implying that analytically derived reduced order models are essential. The major portions of this effort include an examination of the DeChant-Smith Power Spectral Density (PSD) [1] model to better understand both overall Root Mean Square (RMS) magnitude and functional maximum associated with a critical vortex shedding phenomenon. The critical frequency is examined using computational, experiments and an analytical shear layer frequency model. Finally, the PSD magnitude maximum is studied using a theory-based approach connecting the PSD to the spatial correlation that strongly supports the DeChant-Smith PSD model behavior. These results combine to demonstrate that the current employed PSD models provide plausible reduced order closures for turbulent base pressure fluctuations for high Reynolds number flows over range of Mach numbers. Access to a reliable base pressure fluctuation model then permits simulation of bluff body vibratory input

: This work aims to assess the influence of blunt body base protuberances, such as a sting in an experiment, on near-wake unsteadiness using high-fidelity simulations. To evaluate the sensitivity of the near-wake dynamics to these geometrical features, three sting configurations are considered; a ‘no-sting’ case, a ‘centered-sting’ case (where the sting axis is aligned with the body axis), and an ‘offset-sting’ case (where the sting axis and body axis are offset by some distance). To generate a more comprehensive simulation database, two different types of flows are simulated, namely a Mach 2.49 cylinder wake, and a Mach 8 cone wake, thereby comprising six total cases. Flowfield visualizations highlight the influence of the sting on the near-wake structure, particularly the recirculation region, the separated shear layers, and the expansion/recompression process. Analysis of the unsteady base pressure field shows the presence of the sting suppresses dynamics that occur in the no-sting cases. A modal decomposition of the near-wake velocity field suggests the behavior of the recirculation region is associated with the suppression of these dynamics.

The near-field dynamics of a rectangular heated overexpanded jet of aspect ratio two is examined with an implicit large-eddy simulation using experimental data for validation purposes. The conical nozzle, representative of practical configurations, results in multiple shock trains from the throat region as well as the overexpanded operating condition. Each train introduces unsteadiness that influences the external shock cell and plume structure. A detailed analysis of the terms contributing to the turbulent kinetic energy (TKE) is performed to examine the evolution of the plume. The major-axis shear layer experiences significant amplification of the TKE compared with the minor axis, particularly near the core collapse region, and thus pressure fluctuations in the near acoustic field are correspondingly larger in that direction. The most prominent source of TKE in this region is associated with strong mean flow gradients across the major-axis shear layer, and larger corresponding cross-correlations of velocity fluctuations. These effects are shown to be consistent with protrusions of vortical perturbations arising in the minor-axis shear layer into the potential core. The evolution of pressure perturbations from asymmetric to axisymmetric occurs relatively quickly, to achieve agreement with far-field experimental data.

Rectangular nozzles are receiving increased attention because of, among other reasons, the ease with which they may be integrated into the airframe. However, their dynamics have not been examined in as much detail as circular configurations, particularly at operating conditions relevant to practical applications. The present work investigates the nearfield dynamics of a rectangular heated overexpanded jet of aspect ratio 2 using a high-fidelity Large-Eddy Simulation (LES). The LES is validated through comparisons of nearfield as well as farfield measurements with corresponding experiments. Since the nozzle is not contoured in order to represent practical configurations, multiple shock trains arise; the first from a separation bubble slightly downstream of the sharp throat, a second from the reattachment of the flow downstream of the throat, and a third from the overexpanded operating condition. The first shock train displays significant unsteadiness and generates shocklets that destabilize the downstream shock cells. As the plume evolves downstream, the major axis shear layer of the jet experiences significant amplification of turbulent kinetic energy (TKE) compared to the minor axis, with the primary effect being manifested in peak fluctuations of the streamwise component of velocity. This is shown to be related to the more rapid lateral collapse of the potential core along the major axis, where the jet is relatively wider. The most prominent source of TKE on the major axis is shown to result from the strong mean flow gradients across the shear layer, and larger corresponding cross-plane components of Reynolds stress. In the very nearfield, the pressure perturbations from the turbulent fluctuations are shown to be asymmetric; however a symmetric distribution is recovered by approximately 2.25 equivalent diameters from the jet centerline. This is consistent with an azimuthally symmetric farfield acoustic signature in both computation and experiment.

Large-eddy simulations are employed to analyze the flowfield generated by a multistream propulsion system, comprised of a core Mach 1.6 single-sided expansion ramp stream separated by a splitter plate from a sonic stream evolving on an aft-deck. The emphasis is on deriving a fundamental understanding of three-dimensional unsteadiness due to the different interacting free and wall-bounded shear layers. Simulation results on several grids compare well to data from a companion experiment, including particle image velocimetry measurements, time-resolved Schlieren images, and deck pressure spectra, thereby confirming simulation fidelity for the primary physics of interest. Even at design conditions, the asymmetry induced by the single-sided expansion and the aft-deck results in a complex three-dimensional shock train, whose interactions with the bounding shear layers yield many of the principal observations, including local separation of boundary layers developing on the expansion ramp and aft-deck, as well as plume unsteadiness. The mean transverse deflection of the plume, whether upward or downward, is shown to be related to the nature of the shock train components at the aft-deck trailing edge. As the plume develops downstream, three-dimensional characteristics become prominent, including corner effects and asymmetric entrainment. Spectral analyses and space-time correlations demonstrate that the signature of a shedding instability initiated at the splitter plate trailing edge permeates the entire flowfield, and influences the development of the shock train, deck pressure, and shear layers.

•Improved synthetic digital filtering method described for generation of turbulence.•Boundary layer equilibration with streamwise development quantified in detail.•Development length criteria established for various quantities of interest.•Performance using modeled (RANS) versus simulated (DNS or LES) statistics compared.•Effectiveness demonstrated for complex internal multi-stream flows, jets, and wakes.

Low-dimensional models of experimental and simulation data for a complex supersonic jet were fused to reconstruct time-dependent proper orthogonal decomposition (POD) coefficients. The jet consists of a multistream rectangular single expansion ramp nozzle, containing a core stream operating at Mach number M-j,M- 1 = 1.6 and bypass stream at M-j,M-3 = 1.0 with an underlying deck. Proper orthogonal decomposition was applied to schlieren and particle image velocimetry data to acquire the spatial basis functions. These eigenfunctions were projected onto their corresponding time-dependent large-eddy simulation (LES) fields to reconstruct the temporal POD coefficients. This reconstruction was able to resolve spectral peaks that were previously aliased due to the slower sampling rates of the experiments. Additionally, dynamic mode decomposition was applied to the experimental and LES data sets and the spatiotemporal characteristics were compared to POD.

Large eddy simulations (LES) are performed on a cold rectangular supersonic multistream jet with an aft-deck to understand the interaction of multiple streams in the presence of the deck boundary layer. The primary (core) stream has a single expansion ramp on the upper side. Between the core stream and the deck is the deck stream issuing from a convergent nozzle. The design exit Mach numbers of the core and deck streams are M=1.6 and M=1 respectively. Results are obtained using the structured, high-fidelity FDL3DI solver. A favorable comparison is obtained with available Schlieren and PIV visualizations. Even at design nozzle pressure and temperature ratios, a shock train arises in the core stream due to the single-sided expansion, but the deck stream is shock-free. Instantaneous and mean velocity profiles display the upward vectoring effect of the plume as observed in previous and ongoing experiments. A Kelvin-Helmholtz instability occurs in the shear layer formed by the core and deck streams. The resulting spanwise coherent structures breakdown in the presence of the deck boundary layer. The frequency associated with this instability is observed at downstream locations, including through the shock train and greatly influences the flow near the deck in the centerline region of the configuration. The shocks are weaker near the sidewalls and the spectrum becomes broadband.