Implicit Large-eddy Simulation Approach Research Articles

An accurate and practical numerical solver for simulations of shock, vortices and turbulence interaction problems

Numerical simulations of high-speed compressible flows remain challenging in engineering as the appearance of shock waves poses difficulties for high-resolution schemes as well as explicit large eddy simulation methods. Therefore, in this work, we propose a practical numerical solver for simulations of shock-vortex and shock-turbulence problems with the implicit large eddy simulation approach and newly developed low-dissipative schemes. In order to handle the multi-scale raised in the shock-vortex and shock-turbulence problems, it is required that the flow solver can simultaneously solve the large-scale flow structures such as shock waves with numerical oscillation-free, the resolvable flow structures above the grid scale with low-dissipation, and the under-resolve isotropic sub-grid scale with numerical stability. To this end, a low-dissipative, structure-preserving scheme with rigorously adjusted numerical dissipation is employed in the proposed solver. The structure-preserving property of this scheme can ensure that the large-scale structure is solved without numerical oscillations and the low-dissipative property of this scheme can produce high-resolution results for the resolvable flow scales. Moreover, the sub-grid scale is solved and stabilized by the inherent numerical dissipation in the shock-capturing scheme. The proposed numerical solver is then applied to simulate a wide range of shock-vortex and shock-turbulence interaction problems including supersonic planar jets, transonic flows past a deep cavity and impingement of a supersonic jet on a cone mounted on a flat plate. A comparison is also made with the solver using conventional total variation diminishing schemes. The numerical results of the supersonic planar jet have demonstrated that the proposed solver can resolve the small-scale structure such as Kelvin–Helmholtz instability involved in shock and shear layer with high-resolution. Through the results of transonic flow past a deep cavity and comparisons with the experimental data, it is verified that the proposed solver can reproduce the turbulence statistical data. Furthermore, the proposed solver resolves the complex turbulent fluid mechanical phenomena in the impingement of a supersonic jet on a cone, which demonstrates the proposed solver can robustly handle irregular geometry. The proposed solver also enjoys simplicity without using the explicit sub-grid scale model and involving the complexity of very high-order schemes. Thus, this work provides an accurate and practical numerical solver for shock-vortex and shock-turbulence problems in high-speed flows.

An embedded strategy for large scale incompressible flow simulations in moving domains

In this work we describe a methodology to approximate the incompressible Navier-Stokes equations in time dependent domains. To deal with the motion of the domain, we employ a fixed mesh method that we call fixed-mesh ALE. It consists of writing the equations in a moving ALE reference system but then projecting them onto a fixed background mesh. This implies that the boundaries of the elements do not necessarily coincide with the physical boundaries, and thus there is the possibility of badly cut elements. We use a Nitsche's type formulation to prescribe the boundary conditions and stabilise the bad cuts by introducing a term that penalises the gradient of the unknown orthogonal to the finite element space in a patch that contains the badly cut element. The flow formulation is a stabilised finite element method that allows one to treat convection dominated flows and to use equal velocity–pressure interpolation. Furthermore, this formulation can be shown to behave as an implicit large eddy simulation approach. A key issue is that the sub-grid scales on which the formulation depends are allowed to be time dependent; this fact has proved to be crucial for the robustness of the approach. The calculation of the velocity and the pressure is segregated by using a fractional step scheme designed at the pure algebraic level, and the conditioning of the pressure equation is improved by using an artificial compressibility technique. Finally, an adaptive mesh refinement strategy is described. All the algorithms are implemented in a parallel environment. The strategy described can be applied to complex flow problems, and in particular here we show the simulation of the air flow generated by a train moving inside a tunnel.

A new paradigm of dissipation-adjustable, multi-scale resolving schemes for compressible flows

The scale-resolving simulation of high speed compressible flow through direct numerical simulation (DNS) or large eddy simulation (LES) requires shock-capturing schemes to be more accurate for resolving broadband turbulence and robust for capturing strong shock waves. In this work, we develop a new paradigm of dissipation-adjustable, shock capturing scheme to resolve multi-scale flow structures in high speed compressible flow. The new scheme employs a polynomial of n-degree and non-polynomial THINC (Tangent of Hyperbola for INterface Capturing) functions of m-level steepness as reconstruction candidates. These reconstruction candidates are denoted as PnTm. From these candidates, the piecewise reconstruction function is selected through the boundary variation diminishing (BVD) algorithm. Unlike other shock-capturing techniques, the BVD algorithm effectively suppresses numerical oscillations without introducing excess numerical dissipation. Then, an adjustable dissipation (AD) algorithm is designed for scale-resolving simulations. This novel paradigm of shock-capturing scheme is named as PnTm−BVD−AD. The proposed PnTm−BVD−AD scheme has following desirable properties. First, it can capture large-scale discontinuous structures such as strong shock waves without obvious non-physical oscillations while resolving sharp contact, material interface and shear layer. Secondly, the numerical dissipation property of PnTm−BVD−AD can be effectively adjusted between n+1 order upwind-biased scheme and non-dissipative n+2 order central scheme through a simple tunable parameter λ. Thirdly, with λ=0.5 the scheme can recover to n+2 order non-dissipative central interpolation for smooth solution over all wavenumber, which is preferable for solving small-scale structures in DNS as well as resolvable-scale in explicit LES. Finally, the under-resolved small-scale can be solved with the dissipation adjustable algorithm through the so-called implicit LES (ILES) approach. Through simulating benchmark tests involving multi-scale flow structures and comparing with other central-upwind schemes, the superiority of the proposed scheme is evident. For instance, the simulation results of the supersonic planar jet show that PnTm−BVD−AD schemes can achieve competitive results as Pn+2Tm−BVD schemes which utilize a higher degree of reconstruction polynomial. Thus, in comparison with the previous work, the proposed PnTm−BVD−AD schemes have the benefit of a more compact stencil and lower cost. In summary, this work provides an alternative scheme for solving multi-scale problems in high speed compressible flows.

Gap-induced transition via oblique breakdown at Mach 6

It is well known that hypersonic boundary-layer transition is sensitive to a surface roughness since the roughness may either trigger an early transition or delay the transition. Hypersonic transition is still poorly understood as there are a very limited number of studies in the literature. In the present work, we conduct a computational study on the transition process of a hypersonic Mach 6 flow over a flat plate with a gap. An implicit large eddy simulation approach based on the flux reconstruction/correction procedure via a reconstruction method is used to investigate the interaction between the hypersonic boundary layer and a gap. Flow structures with and without the gap are compared to analyze the local skin friction coefficient overshoots before and after the gap. Two inlet angles of attack are investigated. The evolution of the skin friction coefficient shows that the gap has a very limited influence on the oblique transition at a zero angle of attack. In contrast, the gap can trigger an early transition at a negative angle of attack. In this case, the transverse feedback mechanism is believed to be the main cause, which amplifies the broadband instability waves.

Scale-Adaptive Simulation of Unsteady Cavitation Around a Naca66 Hydrofoil

The present paper focuses on the numerical simulation of unsteady cavitation around a NACA66 hydrofoil to improve the understanding of the cavitation effects on hydraulic machinery. For this aim, the Zwart–Gerber–Belamri cavitation model was updated and uploaded as a library file for OpenFOAM’s solvers using C++ language. Furthermore, the hybrid Reynold average Navier–Stokes (RANS)–large eddy simulation (LES) model k - ω SST scale adaptive simulation (SAS) was implemented as a turbulence model for the present study of scale adaptive simulation. For validation, numerical results were compared with experimental results obtained by Leroux at the Naval Academy Research Institute in France. In order to highlight the benefits in terms of computational consumption and reproduction of the phenomenon the k - ω SST SAS model was compared against implicit large eddy simulation (ILES). Results show that the cavitation evolution including the maximum vapor length, the detachment and the oscillation frequency were reproduced satisfactorily using k - ω SST SAS. Moreover, k - ω SST SAS results predicted a lower total vapor volume on time than ILES, which is related to observed pulses of pressure coefficient, C p , and those match fairly well with the experimental results. To summarize, the k - ω SST SAS model predicts with good accuracy unsteady cavitation behavior around hydrofoils and shows improved versatility over the ILES approach.

LES study of turbulence intensity impact on spark ignition in a two-phase flow

The paper presents large eddy simulation (LES) study aiming at investigations of an influence of flow conditions on a spark ignition process in a two-phase shear dominated flow. Implicit LES approach is applied for the combustion modelling and the spark is modelled using the energy deposition model of Lacaze et al. [20]. We examine an impact of turbulence intensities and randomness of initial distributions of velocity fluctuations on a flame development during the spark duration and shortly after it is switched off. It is found that for a strong spark, as used in IC engines, the turbulence intensity has little effect on the ignition and flame kernel growth and no significant differences are seen even if the turbulence intensities differ four times. It is observed that weak turbulent structures cannot affect fast flame propagation mechanism and its development is conditioned by evaporation and rapid thermal expansion. In such regimes, the turbulence seems to be too weak to significantly alter the flame dynamics. It is found that at the initial stage of the flame development it grows toward the fuel-rich region and spread over the fuel-lean side only after the evaporated fuel diffuses and mixes with the oxidizer stream. The flame size and its shape turn out to be equally dependent on the initial distribution of the turbulence fluctuations and turbulence intensity.

Numerical analysis of an impact of spray characteristics and co-flow temperature on a flame lift-off height

In the current work the jet spray combustion reflecting an experimental piloted spray burner is simulated numerically. In the simulations the diluted ethanol spray evaporates in the hot surrounding, the gaseous fuel diffuses from spray fuel-rich core into the oxidizer fuel-lean region and autoignites. An in-house high-order compact difference LES solver is used to carry out the computations. The reaction rates are modelled using Implicit LES approach based on the single-step global reaction. The continuous phase is modelled in the Eulerian reference frame while the droplets in the Lagrangian form. The studies are focused on the influence of the co-flow temperature and spray initial Sauter mean diameter (SMD) on the flame lift-off height, autoignition delay and the reaction zone features. The results are compared with the experimental data and show good agreement in terms of lift-off height. It is almost linearly related to the co-flow temperatures. It is found that for the same fuel mass loading, droplets with smaller SMDs significantly shorten the autoignition delay. Moreover the autoignition delay and the lift-off heights are influenced mostly by the droplets SMD rather than by the co-flow temperature.

Stratified Kelvin–Helmholtz turbulence of compressible shear flows

Abstract. We study scaling laws of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin–Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16 3842) and three-dimensional (with a spatial resolution of 5123) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both the kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k-5/3 inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k-5/3 scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum yields a k-5/3 scaling. This difference may be assumed to be a reason for the k-7/3 scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k−3 scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of the Helmholtz decomposition of both the kinetic velocity and density-weighted velocity fields. We observe that the scaling results are invariant with respect to the compressibility parameter when the density-weighted definition is used. Our two-dimensional results also confirm that a large inertial range of the solenoidal component with the k−3 scaling can be obtained when we simulate with a lower compressibility parameter; however, the compressive spectrum converges to k−2 for a larger compressibility parameter.

A priori and a posteriori analysis of the flow around a rectangular cylinder

The definition of a correct mesh resolution and modelling approach for the Large Eddy Simulation (LES) of the flow around a rectangular cylinder is recognized to be a rather elusive problem as shown by the large scatter of LES results present in the literature. In the present work, we aim at assessing this issue by performing an a priori analysis of Direct Numerical Simulation (DNS) data of the flow. This approach allows us to measure the ability of the LES field on reproducing the main flow features as a function of the resolution employed. Based on these results, we define a mesh resolution which maximize the opposite needs of reducing the computational costs and of adequately resolving the flow dynamics. The effectiveness of the resolution method proposed is then verified by means of an a posteriori analysis of actual LES data obtained by means of the implicit LES approach given by the numerical properties of the Discontinuous Galerkin spatial discretization technique. The present work represents a first step towards a best practice for LES of separating and reattaching flows.

Analysis of Dynamic Stall on a Pitching Airfoil Using High-Fidelity Large-Eddy Simulations

The onset of unsteady separation and dynamic stall vortex formation over a constant-rate pitching airfoil is analyzed by means of high-fidelity large-eddy simulations. The flowfields are computed by employing a previously developed and extensively validated high-fidelity implicit large-eddy simulation approach based on high-order compact schemes. A NACA 0012 airfoil section is considered at a freestream Mach number of and chord-based Reynolds numbers of . The wing is pitched about its quarter-chord axis at a nominally constant nondimensional rate of from a small initial incidence to an angle of attack beyond the onset of dynamic stall. The unsteady boundary-layer behavior that precedes the dynamic stall vortex formation is described in detail. It is found that the process is characterized by the presence of a laminar separation bubble that contracts with increasing angle of attack as leading-edge suction builds up. Beyond a critical incidence, the laminar separation bubble breaks down and rapid suction collapse ensues. Abrupt turbulent separation follows, allowing the turbulent boundary-layer vorticity to coalesce into a coherent dynamic stall vortex. The remaining turbulent boundary-layer vorticity rolls up into a shear-layer vortex that imparts a much weaker signature on the surface pressure. Maximum surface pressure fluctuations of very high frequency are observed near the leading edge just before laminar separation bubble bursting. The fluctuation level drops significantly as the shear layer moves away from the airfoil surface.

Numerical simulation of detonation failure and re-initiation in bifurcated tubes

A numerical approach is developed to simulate detonation propagation, attenuation, failure and re-initiation in hydrogen–air mixture. The aim is to study the condition under which detonations may fail or re-initiate in bifurcated tubes which is important for risk assessment in industrial accidents. A code is developed to solve compressible, multidimensional, transient, reactive Navier–Stokes equations. An Implicit Large Eddy Simulation approach is used to model the turbulence. The code is developed and tested to ensure both deflagrations (when detonation fails) and detonations are simulated correctly. The code can correctly predict the flame properties as well as detonation dynamic parameters. The detonation propagation predictions in bifurcated tubes are validated against the experimental work of Wang et al. [1,2] and found to be in good agreement with experimental observations.

Implicit Large-Eddy Simulation for the High-Order Flux Reconstruction Method

High-order methods have demonstrated their potential in large-eddy simulations of turbulent flows with relatively low Reynolds numbers. The cost becomes a serious limiting factor for high-Reynolds-number problems. A promising approach to reduce the cost of these simulations is the hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation approach. In this paper, a new hybrid Reynolds-averaged Navier–Stokes implicit large-eddy simulation approach for the high-order flux reconstruction/correction procedure via reconstruction method is developed based on a simple algebraic version of the Spalart–Allmaras model in the vicinity of solid walls and an implicit large-eddy simulation approach elsewhere. Despite its simplicity, this approach has demonstrated good performance in simulating turbulent flow at relatively high Reynolds numbers.

Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae

AbstractIn the implicit large eddy simulation (ILES) paradigm, the dissipative nature of high-resolution shock-capturing schemes is exploited to provide an implicit model of turbulence. The ILES approach has been applied to different contexts, with varying degrees of success. It is the de-facto standard in many astrophysical simulations and in particular in studies of core-collapse supernovae (CCSN). Recent 3D simulations suggest that turbulence might play a crucial role in core-collapse supernova explosions, however the fidelity with which turbulence is simulated in these studies is unclear. Especially considering that the accuracy of ILES for the regime of interest in CCSN, weakly compressible and strongly anisotropic, has not been systematically assessed before. Anisotropy, in particular, could impact the dissipative properties of the flow and enhance the turbulent pressure in the radial direction, favouring the explosion. In this paper we assess the accuracy of ILES using numerical methods most commonly employed in computational astrophysics by means of a number of local simulations of driven, weakly compressible, anisotropic turbulence. Our simulations employ several different methods and span a wide range of resolutions. We report a detailed analysis of the way in which the turbulent cascade is influenced by the numerics. Our results suggest that anisotropy and compressibility in CCSN turbulence have little effect on the turbulent kinetic energy spectrum and a Kolmogorov $k^{-5/3}$ k − 5 / 3 scaling is obtained in the inertial range. We find that, on the one hand, the kinetic energy dissipation rate at large scales is correctly captured even at low resolutions, suggesting that very high “effective Reynolds number” can be achieved at the largest scales of the simulation. On the other hand, the dynamics at intermediate scales appears to be completely dominated by the so-called bottleneck effect, i.e., the pile up of kinetic energy close to the dissipation range due to the partial suppression of the energy cascade by numerical viscosity. An inertial range is not recovered until the point where high resolution ∼5123, which would be difficult to realize in global simulations, is reached. We discuss the consequences for CCSN simulations.

Numerical investigation of throttle flow under cavitating conditions

The present paper shows the importance of the resolution of large unsteady flow structures in numerical simulations of cavitating flows. Three-dimensional simulations of the flow through a throttle geometry representative for fuel injectors have been performed to characterise the inception and development of cavitation, adopting the implicit Large Eddy Simulation approach. The two-phase flow has been handled by the Volume of Fluid method; whilst the simplified Rayleigh equation has been adopted to handle bubble dynamics. The mathematical model has been solved in the open source C++ toolbox OpenFOAM 2.0.1. Results obtained with the mathematical model are compared with those from RANS-based simulations and validated against experimental measurements. The performed Large Eddy Simulations not only are able to reproduce vortex cavitation, but also give further insight into the complex interaction between cavitation and turbulence through the assessment of the different terms of the vorticity equation.

Numerical study of three dimensional acoustic resonances in open cavities at high Reynolds numbers

We present two and three dimensional numerical simulations over open cavities at high Reynolds (Re=8.6×105) and various Mach numbers (0.2<M<0.8). Various turbulence closures are compared and the effect of the Mach number and three-dimensionality assessed. Results show that an implicit LES approach provides more accurate results that classic RANS models (e.g. k–epsilon variants) when analyzing the spectra associated to Rossiter's acoustic resonances (regular self-sustained oscillations). In addition, we show that the simulations require relatively high Mach numbers to compare favorably to experimental data, showing the importance of compressibility effects. Finally, to capture qualitatively the dynamical content, we show that 2D simulations are not accurate enough and three dimensional simulations are necessary.

Implicit LES of free and wall‐bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method

SummaryThis paper presents the second validation step of a compressible discontinuous Galerkin solver with symmetric interior penalty (DGM/SIP) for the direct numerical simulation (DNS) and the large eddy simulation (LES) of complex flows. The method has already been successfully validated for DNS of an academic flow and has been applied to flows around complex geometries (e.g. airfoils and turbomachinery blades). During these studies, the advantages of the dissipation properties of the method have been highlighted, showing a natural tendency to dissipate only the under‐resolved scales (i.e the smallest scales present on the mesh), leaving the larger scales unaffected. This phenomenon is further enhanced as the polynomial order is increased. Indeed, the order increases the dissipation at the largest wave numbers, while its range of impact is reduced. These properties are spectrally compatible with a subgrid‐scale model, and hence DGM may be well suited to be used for an implicit LES (ILES) approach. A validation of this DGM/ILES approach is here investigated on canonical flows, allowing to study the impact of the discretisation on the turbulence for under‐resolved computations. The first test case is the LES of decaying homogeneous isotropic turbulence (HIT) at very high Reynolds number. This benchmark allows to assess the spectral behaviour of the method for implicit LES. The results are in agreement with theory and are even slightly more accurate than other numerical results from literature, obtained using a pseudo‐spectral (PS) method with a state‐of‐the‐art subgrid‐scale model. The second benchmark is the LES of the channel flow. Three Reynolds numbers are considered: Reτ=395, 590 and 950. The results are compared with DNS of Moser et al. and Hoyas et al., also using PS methods. Both averaged velocity and fluctuations are globally in good agreement with the reference, showing the ability of the method to predict equilibrium wall‐bounded flow turbulence. To show that the method is able to perform accurate DNS, a DNS of HIT at Reλ=64 and a DNS of the channel flow at Reτ=180 are also performed. The effects of the grid refinement are investigated on the channel flow at Reτ=395, highlighting the improvement of the results when refining the mesh in the spanwise direction. Finally, the modification of the ILES parameters, that is the Riemann solver and of the SIP coefficient, is studied on both cases, showing a significant influence on the choice of the Riemann solver. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Impact of flexibility on the aerodynamics of an aspect ratio two membrane wing

Development of an aeroelastic solver with application to flexible membrane wings for micro air vehicles is presented. A high-order (up to sixth order) Navier–Stokes solver is coupled with a geometrically nonlinear p-version Reissner–Mindlin finite element plate model to simulate the highly flexible elastic membrane. An implicit LES approach is employed to compute the mixed laminar/transitional/turbulent flowfields present for the low Reynolds number flows associated with micro air vehicles. Computations are performed for an aspect ratio two membrane wing at angles of attack α=10°, 16° and 23° for a Reynolds number, Re=24300. Comparisons of the computational results with experimental PIV and surface deflection measurements demonstrated reasonable agreement. Reduced separation and enhanced lift are obtained due to favorable interactions between the flexible membrane wing and the unsteady flow over the wing. The impact of flexibility on the aerodynamic performance comes primarily from the development of mean camber with some further effects arising from the interaction between the dynamic motion of the membrane and the unsteady flowfield above. At lower angles of attack this lift enhancement comes at the cost of reduced L/D. The nose-down pitching moment increases with flexibility at the lowest angle of attack but is reduced for the higher two angles of attack. These results suggest that membrane flexibility might provide a means to reduce the impact of a strong gust encounter by maintaining lift and reducing the effect of the gust on pitching moment.

DIFFERENTIAL ROTATION IN SOLAR-LIKE STARS FROM GLOBAL SIMULATIONS

To explore the physics of large-scale flows in solar-like stars, we perform 3D anelastic simulations of rotating convection for global models with stratification resembling the solar interior. The numerical method is based on an implicit large-eddy simulation approach designed to capture effects from non-resolved small scales. We obtain two regimes of differential rotation, with equatorial zonal flows accelerated either in the direction of rotation (solar-like) or in the opposite direction (anti-solar). While the models with the solar-like differential rotation tend to produce multiple cells of meridional circulation, the models with anti-solar differential rotation result in only one or two meridional cells. Our simulations indicate that the rotation and large-scale flow patterns critically depend on the ratio between buoyancy and Coriolis forces. By including a subadiabatic layer at the bottom of the domain, corresponding to the stratification of a radiative zone, we reproduce a layer of strong radial shear similar to the solar tachocline. Similarly, enhanced superadiabaticity at the top results in a near-surface shear layer located mainly at lower latitudes. The models reveal a latitudinal entropy gradient localized at the base of the convection zone and in the stable region, which however does not propagate across the convection zone. In consequence, baroclinicity effects remain small and the rotation iso-contours align in cylinders along the rotation axis. Our results confirm the alignment of large convective cells along the rotation axis in the deep convection zone, and suggest that such "banana-cell" pattern can be hidden beneath the supergranulation layer.

Numerical exploration of the origin of aerodynamic enhancements in [low-Reynolds number] corrugated airfoils

This paper explores the flow structure of a corrugated airfoil using a high-fidelity implicit large eddy simulation approach. The first three-dimensional simulations for a corrugated wing section are presented considering a range of Reynolds numbers of Rec = 5 × 103 to 5.8 × 104 bridging the gap left by previous numerical and experimental studies. Several important effects are shown to result from the corrugations in the leading-edge region. First, interaction between the detached shear layer and the first corrugation peak promotes recirculation upstream and enhances transition to turbulence due to flow instabilities. Thus, early transitional flow develops on the corrugated wing which helps to delay stall even at Reynolds numbers as low as Rec = 1 × 104. Transition is shown to occur as early as Rec = 7.5 × 103 and quickly advances toward the leading-edge as Reynolds number is increased. Modification of the first corrugation peak height produces significantly reduced separation and improved aerodynamic forces demonstrating the sensitivity of flow behavior to leading-edge geometry. Second, the unusual orientation of the corrugated surface and strong suction resulting from rapidly turning fluid over the separated region upstream of the first corrugation produces a new effect which serves to reduce drag. This effect was amplified through the enhanced interaction produced by a modified geometry. Corrugations were found to be most advantageous in the leading-edge region and could be optimized to properly take advantage of the flow field under different operating conditions.

Plasma Control of a Turbulent Shock Boundary-Layer Interaction

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 steady control case was the most effective, with a reduction in the separation length of more than 75%. The controller was also found to significantly reduce the low-frequency content of the turbulent kinetic energy spectra within the separated region and reduce the total turbulent kinetic energy downstream of reattachment.