Compressible Fluid Dynamics

Large-eddy simulations (LES) of a transitional shock wave boundary layer interaction (TrSBLI) are carried out to investigate the origin of the low-frequency unsteadiness in an incident-reflecting shock configuration. The separated region is characterised by low-frequency breathing and is associated with a fluidic feedback originating from the vicinity of the reattachment point, in agreement with previous investigations. The non-linear spectral analysis reveals a quadratic coupling between the low-frequency feedback and the unstable modes developing within the separated shear layer. The chronological sequence of the phenomena is retrieved in the physical space through the bicorrelation statistical tool.

Although several mechanisms have been suggested as explanations for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions, questions remain on causes and effects. In this effort, we examine the observed asymmetry in large-scale shock motions to highlight which of the suggested mechanisms is most consistent with shock-speed observations and accompanying separation dynamics. The analysis is based on a flowfield obtained from a validated large eddy simulation of a fully separated interaction. A statistical analysis is used to determine the speed of bubble collapse relative to dilation. The low-pass filtering required to separate upstream from downstream motions in the presence of higher-frequency jitter is accomplished with a relatively new technique, empirical mode decomposition, that is very appropriate for this purpose. The dynamics of bubble dilation versus collapse are then elaborated with conditional dynamic mode decomposition (DMD) analyses on the respective pressure fields. Bubble breathing is shown to have a different structure during dilation than during collapse-larger structures are observed during collapse when fluid is expelled from the bubble. The nature of the DMD mode associated with Kelvin-Helmholtz (K-H) shedding in the mixing layer also differs between dilation and collapse: When the bubble is dilating, the structures at the dominant K-H frequency are larger than when the bubble is collapsing. Additionally, a link is established between the convecting K-H structures and corrugation observed along the reflected shock. Some aspects of the nature of the asymmetry are linked to the ease of eddy formation (K-H structures), which plays an important role in the collapse of the bubble. Shock unsteadiness • SWBLI • LES • Conditional analysis • Bubble breathing • Kelvin-Helmholtz shedding • Dynamic mode decomposition • Empirical mode decomposition Communicated by H. Olivier and A. Higgins.

Large-eddy simulations (LES) of transitional shock wave boundary layer interactions (TrSBLIs) are carried out and results are compared with available experimental databases from the TFAST project. The separated region is characterised by low-frequency breathing and it is associated with a fluidic feedback originating from the vicinity of the reattachment point, in agreement with previous investigations. The non-linear spectral analysis reveled a quadratic coupling between the lowfrequency feedback and the linear unstable modes developing within the mixing layer.

Although several mechanisms have been suggested as explanations for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions, questions remain on causes and effects. In this effort, we examine the observed asymmetry in large-scale shock motions to highlight which of the suggested mechanisms is most consistent with shock-speed observations and accompanying separation dynamics. The analysis is based on a flowfield obtained from a validated large eddy simulation of a fully separated interaction. A statistical analysis is used to determine the speed of bubble collapse relative to dilation. The low-pass filtering required to separate upstream from downstream motions in the presence of higher-frequency jitter is accomplished with a relatively new technique, empirical mode decomposition, that is very appropriate for this purpose. The dynamics of bubble dilation versus collapse are then elaborated with conditional dynamic mode decomposition (DMD) analyses on the respective pressure fields. Bubble breathing is shown to have a different structure during dilation than during collapse-larger structures are observed during collapse when fluid is expelled from the bubble. The nature of the DMD mode associated with Kelvin-Helmholtz (K-H) shedding in the mixing layer also differs between dilation and collapse: When the bubble is dilating, the structures at the dominant K-H frequency are larger than when the bubble is collapsing. Additionally, a link is established between the convecting K-H structures and corrugation observed along the reflected shock. Some aspects of the nature of the asymmetry are linked to the ease of eddy formation (K-H structures), which plays an important role in the collapse of the bubble. Shock unsteadiness • SWBLI • LES • Conditional analysis • Bubble breathing • Kelvin-Helmholtz shedding • Dynamic mode decomposition • Empirical mode decomposition Communicated by H. Olivier and A. Higgins.

A general procedure for deriving effective large-scale fluid equations is presented. It is applicable to a large class of non-linear systems. Starting from the original dynamical equations, the formalism determines closed equations governing the large-scale component of the fields. In this way, complex flows can be numerically simulated with moderate computational resources. The procedure is applied to the twodimensional Navier-Stokes equation for incompressible flow and to a decaying one dimensional Burgers flow. The resulting systems are numerically solved on a coarse grid. The solutions are compared to direct numerical simulations of the Navier-Stokes equation and of Burgers equation, which require a much finer grid. The characteristic features of the flow at all stages of its evolution are well reproduced, including a correct energy exchange between large and small scales.

Investigation of fuel compressibility effects on the Molten Salt Fast Reactor (MSFR) dynamics. Modelling of the MSFR helium bubbling system. Development of a coupled neutronics and fluid dynamics model for the MSFR. Modelling of both liquid fuel and helium bubbles as compressible fluids. Effects on compressibility due to presence and distribution of helium bubbles are investigated.

The dissimilarity between the Reynolds stresses and the heat fluxes in perturbed turbulent channel and plane Couette flows was studied using direct numerical simulation. The results demonstrate that the majority of the dissimilarity was due to the difference between the wall-normal fluxes, while the difference between the streamwise fluxes was lower. The main causes for the dissimilarity were the production terms, followed by the velocity-pressure interaction terms. Further insights into the importance of the velocity-pressure interaction in the origin of the dissimilarity are provided using two-point correlation. Furthermore, an octant conditional averaged dataset reveals that not only the wall-normal heat flux but also the streamwise heat flux is strongly related to the wall-normal gradient of the mean temperature. A simple Reynolds-averaged Navier–Stokes (RANS) heat flux model is proposed as a function of the Reynolds stresses. A comparison of the direct numerical simulation data...

This study focuses on the effect of a sweep angle between the upstream mean flow direction and the shock plane normal in a canonical oblique shock wave/boundary layer interaction. We study a configuration based on the experiments of : an incident shock impinges on a turbulent boundary layer developing at free stream Mach number M = 2.7 and a Reynolds number Re θ = 3200. The sweep angle is implemented by adding a spanwise velocity component (crossflow) at the inflow and enforcing periodicity conditions on the side boundaries. Several sweep angles are investigated and compared to a canonical unswept case. A viscosity is selected for each case in an effort to keep a constant Re θ across the whole range of sweep angles. The mean flow structure is analyzed, showing a strongly skewed flow around the separation zone that increases in size compared to a reference unswept case. Pressure loads on the wall surface are also higher for swept cases; and the characteristic low-frequencies of the flow separation also slightly increase.

We investigate in this study how the height h and distance to the interaction d of microramp vortex generators (mVGs) placed upstream of a shock wave/boundary layer interaction (SBLI) may influence the efficiency of such passive devices in controlling the unsteady mechanisms and shock-induced separation suffered by this kind of flow configuration. To this end, high-fidelity Large Eddy Simulations (LES) are carried out on four different micro-vortex generators geometries in order to assess the effectiveness of low-profile microramp vortex generators (h < 0.4δ ) and medium size devices (0.5δ < h < 0.8δ ) to alleviate the detrimental unsteadiness of SBLI, see . All computations are performed at the same flow conditions as in the experiment of Wang et al. (2012) with a freestream Mach number of M = 2.7 and a Reynolds number of Re θ = 3600. The medium size microramps are found to generate the shedding of large scale structures in their wake triggering a high-frequency unsteadiness in the flow, two orders of magnitude higher than the low-frequency unsteadiness related to the reflected shock foot motion and leaving it unaffected in terms of frequency content. This family of medium size micro-vortex generators is however shown to significantly reduce the area of the separated region induced by the SBLI, as well as the pressure loads intensity on the wall surface. These improved performances come with very limited drag penalty. On the contrary, low-profile devices do display any significant change in the SBLI features.

In this study we propose a new experimental and methodological approach dedicated to the analysis of the development of a turbulent mixing zone produced by the Richtmyer-Meshkov Instability. A brief description of the experimental device dedicated to the generation of the initial interface is first presented. An overview of the main results obtained by means of strioscopic, Particle Image Velocimetry (PIV) and tomoscopic time-resolved measurements are then provided. The spatio-temporal evolution of the macroscopic scale based on the thickness of the mixing zone is discussed on the basis of the time-resolved Schlieren data. A first step into a more comprehensive analysis of finer, local scales of the flow is introduced, based on the qualitative analysis of the velocity and density fields during the development of the mixing zone.

We investigate in this study how the height h and distance to the interaction d of microramp vortex generators (mVGs) placed upstream of a shock wave/boundary layer interaction (SBLI) may influence the efficiency of such passive devices in controlling the unsteady mechanisms and shock-induced separation suffered by this kind of flow configuration. To this end, high-fidelity Large Eddy Simulations (LES) are carried out on four different micro-vortex generators geometries in order to assess the effectiveness of low-profile microramp vortex generators (h &lt; 0:4d) and medium size devices (0.5d &lt; h &lt; 0.8d) to alleviate the detrimental unsteadiness of SBLI, see Panaras & Lu (2015). All computations are performed at the same flow conditions as in the experiment of Wang et al. (2012) with a freestream Mach number of M = 2.7 and a Reynolds number of Req = 3600. The medium size microramps are found to generate the shedding of large scale structures in their wake triggering a high-freq...

This paper provides a comprehensive introduction to compressible flow, exploring key concepts such as Mach number and the conditions that define compressible flow. It delves into the historical evolution of compressible flow research, including one-dimensional compressible flow theory, choked flow, and the behavior of normal and oblique shockwaves. The Mach-area relationship is examined in detail, highlighting its importance in the design and analysis of high-speed flows. Finally, real-world applications are discussed, showcasing how these principles are essential in modern engineering, from aerospace design to propulsion systems.

Проведено прямое численное моделирование развития турбулентных пятен в пограничном слое на плоской пластине под нулевым углом атаки при числе Маха набегающего потока $\mathrm{M}_\infty=6$. Рассмотрено распространение искусственно возбуждeнных локализованных трeхмерных вихревых возмущений с различными начальными амплитудами, которые при распространении вниз по потоку развиваются в турбулентные пятна. Моделирование выполнено в рамках решения уравнений Навье--Стокса для пространственных течений сжимаемого газа с помощью авторского расчeтного кода, реализующего неявный метод сквозного счeта. Показано, что универсальная квазимонотонная численная схема позволяет корректно оценивать основные характеристики турбулентных пятен - угол поперечного раскрытия и скорости переднего и заднего фронтов. Продемонстрировано согласование полученных параметров пятен с результатами других авторов.

A three-dimensional (3D) strongly under expanded hydrogen jet flow is numerically investigated with a storage pressure of 82 MPa and a tiny jet orifice diameter of 0.2 mm. The full compressible NaviereStokes equations are utilized in a domain with a size of about 3 Â 3 Â 6 m which is discretized by employing adaptive mesh refinement (AMR) technology to reduce the number of grid cells. The highly under expanded hydrogen jet flow with a nozzle pressure ratio (NPR) of about 809 is then captured from the very beginning when hydrogen is ejected out of the jet orifice. The starting transient evolution and Mach disk stabilization are then discussed in details. It is found that with the AMR technology, the grid number can be greatly reduced and high resolutions can be easily installed to deal with the small jet orifice size together with those flow microscales. Jet flow is numerically captured and discussed. It is found that over expansion occurs in this under expanded jet. The secondary shock is generated to match the pressure which plays the most important physics in the starting transient period of an under expanded hydrogen jet. The Mach shock and the lateral barrel shock which are originated from the secondary shock play central roles. The jet flow is divided into subsonic and supersonic branches in the nearnozzle region, which makes the highly under-expanded jets have two annular shear layers, the inner and outer layer, in this region.

We investigate the effectiveness of the semi-local Reynolds number Re τ to parametrize wall-bounded flows with strong density, ρ, and viscosity, µ, gradients. Several cases are considered, namely, volumetrically heated low-Mach-number turbulent channel flows, a simultaneously heated and cooled flow with CO 2 at supercritical pressure, and heated and cooled supersonic boundary layer flows. The mean density and viscosity in some of these cases vary up to a factor of nine and six, respectively. We show that, even for such high gradients in mean properties, the velocity transformation based on the semi-local Reynolds number is able to collapse the mean streamwise velocity profiles. We furthermore provide evidence that the turbulent kinetic energy and streamwise vorticity budget equations are also governed by the semi-local Reynolds number. For cases with strong property variations, additional mechanisms appear that are caused by individual density (e.g., baroclinicity) or viscosity gradients. However, in the cases investigated herein, these additional mechanisms are small. The insights gained are used to improve a wall model, which is then tested in a wall-modeled large-eddy simulation (LES) of a compressible channel flow with isothermal walls.

We present Implicit Large-Eddy Simulations of a shockwave-turbulent boundary layer interaction with and without localized heat addition. The flow is complex and involves boundary layer separation under the adverse pressure gradient imposed by the shock, turbulence amplification across the interaction and low frequency oscillation of the reflected shock. For an entropy spot generated ahead of the shock, baroclinic vorticity production occurs when the resulting density peak passes the shock. The objective of the present study is to analyze the shock-separation interaction and turbulence structure of such a configuration. The effect of the addition of an entropy spot to the flow field is assessed in terms of turbulence amplification.

Wall pressure fluctuations, schlieren imaging, oil flow visualization and PIV measurements have been performed on the shock boundary layer interaction (SBLI) formed by a 10 • compression ramp. The incoming Mach number and boundary layer characteristics are varied to examine their influence on the SBLI. Focus is placed on understanding the effect of these parameters on the structure and unsteadiness of the resultant interaction. Lower Mach numbers M = 2.3 (δ 0 = 1.7 mm, θ = 0.29 mm, Re θ = 3115, H = 1.4) and M = 3 (δ 0 = 1.3 mm, θ = 0.25 mm, Re θ = 1800, H = 1.8) show a turbulent or transitional approach boundary layer with no apparent separation at the ramp. Mach 4 has a large separated region which is seemingly a result of a now laminar or transitional approach boundary layer. Pulsations in the separated region correspond to the expected low frequency SBLI dynamics showing a broad peak around a Strouhal number of St = f L int /U ∞ = 0.27 which is lower than the characteristic frequency of the turbulent boundary layer. Additional results examining the influence of boundary layer modifications (e.g. sweep) and wind tunnel side-walls are also included.

In the present study, we investigate the influences of shock intensity on wall pressure fluctuations by performing direct numerical simulations of the supersonic turbulence boundary layers over compression ramps with different turning angles. We found that as the turning angle increases, the low-frequency motions of the separation shock are enhanced, accompanied by the enlarged energetic pressure structures with the lower convection velocities. By inspecting wavenumber-frequency spectra under the assumption of streamwise homogeneity, we further identified two energetic modes convected at different velocities. The one with the lower convection velocity, namely the 'slow mode', inherited from the upstream pressure fluctuations of the turbulent boundary layer, is decelerated when passing through the oblique shock, during which the 'rapid mode' with pressure fluctuations convected at higher speeds are generated. The increasing turning angle decelerates the slow mode and intensifies the fast mode. The reconstruction of the flow field suggests that the rapid mode is associated with the shear layer generated adjacent to the interaction zone while the slow mode with the Görtler vortices on the ramp.

In the hybrid RANS-LES simulations, proper turbulent fluctuations should be added at the RANS-to-LES interface to drive the numerical solution restoring to a physically resolved turbulence as rapidly as possible. Such turbulence generation methods mostly need to know the distribution of the characteristic length scale of the background RANS model, which is important for the recovery process. The approximation of the length scale for the Spalart-Allmaras (S-A) model is not a trivial issue since the model's one-equation nature. As a direct analogy, the approximations could be obtained from the definition of the Prandtl's mixing length. Moreover, this paper proposes a new algebraic expression to approximate the intrinsic length scale of the S-A model. The underlying transportation mechanism of S-A model are largely exploited in the derivation of this new expression. The new proposed expression is employed in the generation of synthetic turbulence to perform the hybrid RANS-LES simulation of canonical wall-bounded turbulent flows. The comparisons demonstrated the feasibility and improved performance of the new length scale on generating synthetic turbulence at the LES inlet.

In this numerical study, a film-cooling flow with shock-wave interaction is analyzed using large-eddy simulation (LES). A laminar cooling film at an injection Mach number of Mai = 1.8 is injected through a slot into a fully turbulent boundary layer at a freestream Mach number of Ma1 = 2.44. An oblique shock, generated by a flow deflection of = 5 or 8 , impinges upon the cooling film within the potential-core region. At a deflection angle of = 5 , the cooling effectiveness downstream the shock impingement is decreased by 4.6% compared to the undisturbed flow configuration. A flow deflection of = 8 leads to a decrease in cooling effectiveness of 13.4%. The separation bubble at the shock impingement position causes a strong negative peak of the Reynolds shear stress near the wall. With increasing shock strength, the separation bubble significantly grows in size. The separation length of the strong shock configuration is increased by a factor of 4.6 compared to the weaker shock configur...

We focus on the use of a meshless numerical method called Smooth Particle Hydrodynamics (SPH), to solve fragmentation issues as Hyper Velocity Impact (HVI) cases. Firstly applied to fluid flow simulations, this method can be extended to the solid dynamics framework. However it suffers from a lack of accuracy when evaluating state variables as the pressure field. And such inaccuracy generally generates non-physical processes (as numerical fragmentation). In the hydrodynamic context, SPH-ALE methods based on Riemann solvers significantly improve this evaluation, but increase the scheme complexity and low-Mach issues are difficult to prevent. We propose an alternative scheme called γ-SPH-ALE, firstly implemented to solve multi-regime barotropic flows, and secondly extended to solid dynamic cases. It relies on the combination of the SPH-ALE formalism and a finite volume stabilizing low-Mach scheme. Its characteristics are detailed and evaluated through a nonlinear stability analysis, hi...

An entrainment model for lazy turbulent plumes is proposed, the resulting solutions of the plume conservation equations are developed and the implications for plume behaviour are considered and compared with the available experimental data. Indeed the applicability of the classic solutions of the conservation equations subject to source conditions that produce lazy plumes, i.e. those with suitably high source Richardson number, contain an essential weakness: the underlying assumption of a constant entrainment coefficient. Whilst entrainment models prescribing the dependence of the entrainment coefficient with local Richardson number have been proposed for forced plumes, corresponding formulations for lazy plumes have not until now been considered. In the context of saline plumes, the model is applied directly. For hot gaseous plumes, we use a modified definition of buoyancy flux to recover a constant buoyancy flux in a non-stratified environment, despite specific heat varying with temperature, as shown in the appendix. After a rapid review of existing forced plume formulations of entrainment, a power-law variation is adopted for the lazy plume. The plume equations are solved for the parameter 0 ≤ ω < 1, where ω denotes the exponent of the power law. The cases of pure plumes and lazy plumes are then analysed in more detail; to our knowledge this represents the first modelling of variable entrainment for lazy plumes. Specifically, it is shown that classic plume theory is recovered for ω = 0, while for ω = 1/5 the plume equations may be solved using usual functions (notably polynomials) only. The results of the models for these cases are very similar, which advocates the idea of selecting systematically ω = 1/5, instead of ω = 0, for cases where the effect of variation of entrainment is weak, since the new model leads to simple calculations. In the case of very lazy plumes it is shown that, provided a relevant value of ω is chosen, the new model reproduces well the available experimental results.

Shock wave-turbulent boundary layer interaction is a critical problem in aircraft design. Therefore, a thorough understanding of the processes occurring in such flows is necessary. The most important task is to study the unsteady phenomena, in particular, the low-frequency ones, for this interaction. An experimental study of separated flow has been performed in the zone of interaction of the incident oblique shock wave with a turbulent boundary layer at Mach 2. Twopoint correlation data in the separation zone and the upstream flow were obtained and showed that low-frequency oscillations of the reflected shock waves are related to pulsations in the inflow turbulent boundary layer. Keywords Boundary layer • Separated flow • Shock wave • Turbulence • Unsteady List of symbols a w Overheat ratio C xy = |Pxy(f)| 2 P xx P yy , spectra of coherence CTA Constant temperature anemometry e Voltage F CTA Mass flow sensitivity coefficient for CTA f Frequency Communicated by H. Kleine.

The dynamics of shock-induced unsteady separated flow past a three-dimensional square-faced protuberance is investigated through wind tunnel experiments. Time-resolved schlieren imaging and unsteady surface pressure measurements are the diagnostics employed. Dynamic Mode Decomposition (DMD) of schlieren snapshots, and analysis of spectrum and correlations in pressure data are used to characterize and resolve the flow physics. The mean shock foot in the centreline is found to exhibit a Strouhal number of around 0.01, which is also the order of magnitude of the Strouhal numbers reported in the literature for two-dimensional shock-boundary layer interactions. The wall pressure spectra, in general, shift towards lower frequencies as we move away from (spanwise) centreline with some variation in the nature of peaks. The cross-correlation analysis depicts the strong dependence of the mean shock oscillations to the plateau region, and disturbances are found to travel upstream from inside the separation bubble. Good coherence is observed between the spanwise mean shock foot locations till a strouhal number of about 0.015 indicating that the 3-D shock foot largely moves to-and-fro in a coherent fashion.

The unsteady three-dimensional separated flow on a wall induced by a square protrusion (approximately twice the local boundary layer thickness in width and height), and its control by means of passive suction through holes, is investigated using wind tunnel experiments at Mach 2.87. The baseline flow without any control was characterized and compared against the cases with bleed. A bow-shaped separation line on the wall with a mid-span separation length of 5.57δ from protrusion face was traced from oil-flow visualization. The averaged pressure distribution surveyed using static pressure ports placed on the wall has mapped plateau, high-pressure, and a low-pressure region in the separated flow, distinctive to three-dimensional interactions. Ten control configurations were tested with suction holes placed along mid-span in the different pressure zones. Significant spanwise 'Mean Reduction in Separation Length' of up to 0.93δ was observed from oil-flow visualization. A comparison of observations from various control configurations suggested that bleeding the flow from the high-pressure region could in general delay the separation and reduce the bubble size. Further, time-resolved schlieren visualizations have confirmed reduction in both 'mid-span separation length' and 'shock-intermittent-region' with the introduction of suction in high-pressure region. Fourier and Proper Orthogonal Decomposition analysis done on the schlieren data has confirmed the presence of low-frequency separationshock oscillations at Strouhal Numbers of order 10 −2 , both with and without control. Furthermore, the amplitudes of separation-shock oscillations in the spectrum were reduced with the introduction of suction simultaneously from two holes placed in high and low-pressure regions.

The unsteady 3-dimensional separated flow induced by a square protrusion (measuring twice the local boundary layer thickness in both its width and height denoted by h), and its control by means of boundary layer suction through holes, is investigated using wind tunnel experiments and computations. Surface oil flow visualization, time resolved schlieren using high speed camera and surface static pressure measurements using pressure scanner are the diagnostics used to study the 3-dimensional shock boundary layer interaction. Unsteady-RANS computations are validated using the experimental data, and are used to complement the understanding of the flow field. It was observed from the oil-flow visualizations that at the span-wise centre, the separation location was at 2.6h from the protrusion. The time averaged foot of the separation shock measured from the schlieren images was at 2.80h from the protrusion. The computational results compared well with the visualizations as well as the surface pressure data. The computation of flow field with suction through holes upstream of protrusion suggested the emergence of interesting 3-dimensional flow patterns.

The unsteady three-dimensional separated flow on a wall induced by a square protrusion (approximately twice the local boundary layer thickness in width and height), and its control by means of passive suction through holes, is investigated using wind tunnel experiments at Mach 2.87. The baseline flow without any control was characterized and compared against the cases with bleed. A bow-shaped separation line on the wall with a mid-span separation length of 5.57δ from protrusion face was traced from the oil-flow visualization. The averaged pressure distribution surveyed using static pressure ports placed on the wall has mapped plateau, high-pressure, and low-pressure regions in the separated flow, distinctive to three-dimensional interactions. Ten control configurations were tested with suction holes placed along mid-span in the different pressure regions. Significant spanwise “Mean Reduction in Separation Length” of up to 0.93δ was observed from oil-flow visualization. A comparison ...

The unsteady three-dimensional separated flow on a wall induced by a square protrusion (approximately twice the local boundary layer thickness in width and height), and its control by means of passive suction through holes, is investigated using wind tunnel experiments at Mach 2.87. The baseline flow without any control was characterized and compared against the cases with bleed. A bow-shaped separation line on the wall with a mid-span separation length of 5.57δ from protrusion face was traced from oil-flow visualization. The averaged pressure distribution surveyed using static pressure ports placed on the wall has mapped plateau, high-pressure, and a low-pressure region in the separated flow, distinctive to three-dimensional interactions. Ten control configurations were tested with suction holes placed along mid-span in the different pressure zones. Significant spanwise 'Mean Reduction in Separation Length' of up to 0.93δ was observed from oil-flow visualization. A comparison of observations from various control configurations suggested that bleeding the flow from the high-pressure region could in general delay the separation and reduce the bubble size. Further, time-resolved schlieren visualizations have confirmed reduction in both 'mid-span separation length' and 'shock-intermittent-region' with the introduction of suction in high-pressure region. Fourier and Proper Orthogonal Decomposition analysis done on the schlieren data has confirmed the presence of low-frequency separationshock oscillations at Strouhal Numbers of order 10 −2 , both with and without control. Furthermore, the amplitudes of separation-shock oscillations in the spectrum were reduced with the introduction of suction simultaneously from two holes placed in high and low-pressure regions.

A cylindrical, initially diffuse density interface is formed by injecting a laminar jet of heavy gas into the test section of a shock tube. The injected gas is mixed with a fluorescent gaseous tracer, small liquid droplets, or smoke particles. The shock tube is tilted with respect to the horizontal. Thus the axis of the gravitystabilized heavy gas jet is at an oblique angle with the plane of the arriving shock front. The flow structure forming after the oblique shock wave interaction with the column of heavy gas is revealed by visualization in multiple planes. We observe the formation of the well-known counter-rotating vortex columns (same as caused by normal shock waves). However, along with them, periodic co-rotating vortices form in the vertical plane in the flow downstream of the oblique shock. The size of these vortices varies both with the Mach number and with the initial angle between the column and the shock front.

A novel multi-dimensional upwind bias formulation is presented. Designed to solve accurately the Euler and Navier-Stokes conservation-law systems on arbitrary grids, this new formulation is developed within the continuous conservation-law systems ahead of any discretization in space and time. This formulation utilizes shock-jump surface integrals, which emerge within integral weak statements for these conservation laws. The mean value theorem is then applied to express these surface integrals in terms of differences of gradients of differentiable entropy solutions. In the continuum, this process yields shock-capturing entropy weak statements with embedded upwind bias that are consistent with the theory of characteristics. These entropy weak statements are then discretized in space through a Galerkin finite element method, an inherently centered dissipation-free discretization. This automatically generates an intrinsically multi-dimensional upstreamed discrete system on any grid without the need for any further upwinding within the discrete equations. The computational solutions crisply capture shocks and reflect available exact solutions.

The evolution of a two-phase, air and unsaturated water vapor, time-decaying, shearless, and turbulent layer has been studied in the presence of both stable and unstable perturbations of the normal temperature lapse rate. The top interface between a warm vapor cloud and clear air in the absence of water droplets was considered as the reference dynamics. Direct, three-dimensional, and numerical simulations were performed within a 6 × 6-m-wide and 12-m-high domain, which was hypothesized to be located close to an interface between the warm cloud and clear air. The Taylor microscale Reynolds number was 250 inside the cloud portion. The squared Froude&#39;s number varied over intervals of [0.4; 981.6] and [−4.0; −19.6]. A sufficiently intense stratification was observed to change the mixing dynamics. The formation of a sublayer inside the shearless layer was observed. The sublayer, under a stable thermal stratification condition, behaved like a pit of kinetic energy. However, it was obs...

instability in the light-to-heavy and heavy-to-light cases. The model includes mixture molecular transport terms, enthalpy diffusion terms, pressure-dilatation and dilatation dissipation models, and a molecular diffusion flux with contributions from baro-and thermodiffusion. The four-equation models couple transport equations for the mass flux a i and the negative densityspecific volume correlation b to the K-ϵ or K-L equations, while the three-equation models use an algebraic closure for b. The evolution of various turbulence statistics, fields, and turbulent transport equation budgets are compared among these models to identify any differences in the turbulence production, dissipation and diffusion physics represented by the closures used in these models.

on the development and validation of a new K-ϵ multicomponent Reynolds-averaged Navier-Stokes model is discussed. The model includes mixture molecular dissipation and diffusion terms, molecular and turbulent enthalpy diffusion terms, and models for pressure-dilatation and dilatation dissipation. The model has successfully been applied to a set of ten reshocked Richtmyer-Meshkov mixing experiments, and more recently to experiments with larger Mach numbers and various Atwood numbers. An extension of the model to include a modeled density variance transport equation is described. The threeequation model is applied to various Rayleigh-Taylor mixing cases with complex accelerations. The evolution of various turbulence statistics, fields, and turbulent transport equation budgets are compared among these cases to elucidate differences in the turbulence production, dissipation and diffusion mechanisms. It is also shown that the mechanical turbulence timescale is poorly correlated with the molecular mixing timescale determined by the time-evolution of the molecular mixing parameter.

instability are combined with observed values of the growth parameters in these instabilities to derive coefficient sets for K-ϵ and K-L-a Reynolds-averaged turbulence models. It is shown that full numerical solutions of the model equations give mixing layer widths, fields, and budgets in good agreement with the corresponding self-similar quantities for small Atwood number. Both models are then applied to Rayleigh-Taylor instability with increasing density contrasts to estimate the Atwood number above which the self-similar solutions become invalid. The models are also applied to a reshocked Richtmyer-Meshkov instability, and the predictions are compared with data. The expressions for the growth parameters obtained from the similarity analysis are used to develop estimates for the sensitivity of their values to changes in important model coefficients. Numerical simulations using these modified coefficient values are then performed to provide bounds on the model predictions associated with uncertainties in these coefficient values.

instability-induced mixing is developed using a general buoyancysheardrag model. Analytical solutions are used to calibrate the coefficients to predict specific values of the mixing growth parameters and exponents. The model is applied to the three instability cases to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results.

code to a set of experiments fielded under this campaign in order to characterize the properties of turbulence and mixing. The evolution of the turbulent mixing layer width and of quantities such as the turbulent kinetic energy are investigated to determine how well the models predict the development and further growth of turbulence, especially following reshock of the layer. Flow features that can be more carefully explored using direct numerical simulation, largeeddy simulation and related numerical techniques that could potentially improve the modeling are also discussed.

The conference format consisted of several one hour review talks at the beginning of experimental, computational, and theoretical sessions. These talks were followed by shorter 20-min talks. Two staggered poster sessions were also held at the end of two of the days. There were a total of 126 presentations: 67 oral presentations and 59 poster presentations. Discussion sessions were also held during the poster sessions. The "workshop" provides a common international forum for the exchange of ideas and results and for establishing scientific collaborations. An objective of the conference is to cross-fertilize several disciplines by bringing together experimentalists, numericists, and theorists working in highly diverse areas: high-energy density physics, inertial confinement fusion, astrophysics, and fluid dynamics. Although the sessions were organized according to experimental, computational, and theoretical categories, most of the presentations combined at least two of these. There were 123 participants representing Canada~2!, France~8!, Israel~8!, Japan~4!, Russia~20!, Spain~1!, the United Kingdom~6!, and the United States~74!. Of these, one-third were from universities and the remainder were from national laboratories. The conference was also established as a forum for younger scientists~graduate students

Turbulent Richtmyer–Meshkov instability (RMI) is investigated through a series of high resolution three-dimensional simulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regimes combined. Overall, the growth rate exponent is determined as θ=0.292±0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is s...

The interaction of double-layer density stratified interfaces with initial non-uniform velocity shear is investigated theoretically and numerically, taking the incompressible Richtmyer-Meshkov instability as an example. The linear analysis for providing the initial conditions in numerical calculations is performed, and some numerical examples of vortex double layers are presented using the vortex sheet model. We show that the density stratifications (Atwood numbers), the initial distance between two interfaces, and the distribution of the initial velocity shear determine the evolution of vortex double layers. When the Atwood numbers are large, the deformation of interfaces is small, and the distance between the two interfaces is almost unchanged. On the other hand, when the Atwood numbers are small and the initial distance between two interfaces is sufficiently close (less than or equal to the half of the wavelength of the initial disturbance), the two interfaces get closer to each other and merge at the last computed stage due to the incompressibility. We confirm this theoretically expected fact numerically.