Compressible Fluid Dynamics

In this paper we write, analyze and experimentally compare three different numerical schemes dedicated to the one dimensional barotropic Navier-Stokes equations: • a staggered scheme based on the Rusanov one for the inviscid (Euler) system, • a staggered pseudo-Lagrangian scheme in which the mesh "follows" the fluid, • the Eulerian projection (on a fixed mesh) of the preceding scheme. All these schemes only involve the resolution of linear systems (all the nonlinear terms are solved in an explicit way). We propose numerical illustrations of their behaviors on particular solutions in which the density has discontinuities (hereafter called Hoff solutions). We show that the three schemes seem to converge to the same solutions, and we compare the evolution of the amplitude of the discontinuity of the numerical solution (with the pseudo-Lagrangian scheme) with the one predicted by Hoff and observe a good agreement.

A positivity-preserving variant of the Roe flux difference splitting method is here proposed. Positivity-preservation is attained by modifying the Roe scheme such that the coefficients of the discretization equation become positive, with a coefficient considered positive if all its eigenvalues are positive and if its eigenvectors correspond to those of the flux Jacobian. Because the modification does not alter the wave speeds at the interface, the appealing attributes of the Roe flux difference splitting schemes are retained, such as high-resolution capture of discontinuous waves, low amount of artificial dissipation within viscous layers, and ease of convergence to steady-state. The proposed flux function is advantaged over previous positivity-preserving variants of the Roe method by being written in general matrix form and hence by being readily deployable to arbitrary systems of conservation laws. The stencils are extended to second-order accuracy through a newly-derived positivity-preserving total-variation-diminishing limiting process that is applied to the characteristic variables and that yields positive coefficients. Also derived is a positivity-preserving restriction on the time step for flux difference splitting schemes that is shown to depart significantly from the CFL condition in regions with high property gradients.

We present a high fidelity Large-Eddy Simulation (LES) of a pseudo-shock system in the divergent part of a Laval nozzle with rectangular cross section. The parallel side walls are taken into account, all wall boundary layers are well resolved and no wall model is used. For the first time it was possible to perform a wall-resolved LES for the same parameter set of a reference experiment. The results are validated against experimental wall-pressure measurements and schlieren pictures. Detailed insight into the complex 3-D flow phenomena including corner vortices and recirculation zones is presented. Differences between our LES and RANS simulations are discussed.

This PhD thesis focuses on numerical and analytical methods for simulating the dynamics of volcanic ash plumes.
The study starts from the fundamental balance laws for a multiphase gas– particle mixture, reviewing the existing models and developing a new set of Partial Differential Equations (PDEs), well suited for modeling multiphase dispersed turbulence. In particular, a new model generalizing the equilibrium–Eulerian model to two-way coupled compressible flows is developed.
The PDEs associated to the four-way Eulerian-Eulerian model is studied, in- vestigating the existence of weak solutions fulfilling the energy inequalities of the PDEs. In particular, the convergence of sequences of smooth solutions to such a set of weak solutions is showed.
Having explored the well-posedness of multiphase systems, the three-dimensional compressible equilibrium–Eulerian model is discretized and numerically solved by using the OpenFOAM® numerical infrastructure. The new solver is called ASHEE, and it is verified and validated against a number of well understood benchmarks and experiments. It demonstrates to be capable to capture the key phenomena involved in the dynamics of volcanic ash plumes. Those are: turbulence, mixing, heat transfer, compressibility, preferential concentration of particles, plume entrainment.
The numerical solver is tested by taking advantage of the newest High Perfor- mance Computing infrastructure currently available.
Thus, ASHEE is used to simulate two volcanic plumes in realistic volcanological conditions. The influence of model configuration on the numerical solution is analyzed. In particular, a parametric analysis is performed, based on: 1) the kinematic decoupling model; 2) the subgrid scale model for turbulence; 3) the discretization resolution.
In a one-dimensional and steady-state approximation, the multiphase flow model is used to derive a model for volcanic plumes in a calm, stratified atmosphere. The corresponding Ordinary Differential Equations (ODEs) are written in a compact, dimensionless formulation. The six non-dimensional parameters characterizing a multiphase plume are then written. The ODEs is studied both numerically and analytically. Different regimes are analyzed, extracting the first integral of motion and asymptotic solutions. An asymptotic analytical solution approximating the model in the general regime is derived and compared with numerical results. Such a solution is coupled with an electromagnetic model providing the infrared intensity emitted by a volcanic ash plume. Key vent parameters are then retrieved by means of inversion techniques applied to infrared images measured during a real volcanic eruption.

A novel alteration to the Cauchy–Kowalevski procedure is here presented to obtain essentially monotonic solutions
for multidimensional flows. It is argued that this can be accomplished by splitting the cross-derivative terms among
the several dimensions, such that the coefficient of the cross derivatives remains small compared to the coefficient of
the normal derivatives. The approach naturally lends itself to extending the Roe flux difference splitting scheme to
multiple dimensions and is advantaged over previous Cauchy–Kowalevski-based methods by yielding a solution free
of spurious oscillations in the vicinity of oblique shock waves. Several test cases ranging from low-speed subsonic flows
in channels to hypersonic flows over ramp injectors indicate that the proposed genuinely multidimensional method
generally achieves a twofold or more increase in resolution along each dimension over the dimensionally split Roe
scheme while retaining its appealing attributes: the scheme has a compact three-node-bandwidth stencil, is a finite
volume flux function, yields essentially monotonic solutions, introduces minimal dissipation within viscous layers, and
is written in general matrix form. Although the method proposed is first-order accurate, it offers a resolution as high
or higher than the dimensionally split second-order total-variation-diminishing schemes for many problems of
interest and is expected to surpass significantly the latter when extended to second-order accuracy.

The project is about studying the whole rocket. We will work on comparing between analytical and theory results on the converging diverging (C-D) nozzle, also called de Laval nozzle for an isentropic flow, a normal shock wave in the diverging section, an oblique shock wave and an expansion at the exit. Then we will simulate the flow at the upper surface of the rocket by CFD, considering the upper area as diamond shaped. The aim of the simulation is to show the oblique shock wave created by supersonic speed and doesn’t intersect with the rest of the rocket, reducing overall the drag.

In this thesis, several novel numerical methods, including the high-order shock-capturing targeted Essentially Non-oscillatory (TENO) schemes, smoothed-particle hydrodynamics (SPH) based partitioning method and Centroidal Voronoi Particle (CVP) domain decomposition method, are proposed and validated. These methods can be used for high-resolution computational fluid simulations and high-performance scientific computing, which are important to study the physics of fluid dynamics.

The effects of compressibility are studied in low Reynolds number turbulent supersonic channel flow via a direct numerical simulation (DNS). A pressure-velocity-entropy formulation of the compressible Navier-Stokes equations which is cast in a characteristic, non-conservative form and allows one to specify exact wall boundary conditions, consistent with the field equations, is integrated using a fifth-order compact upwind scheme for the Euler part, a fourth-order Padé scheme for the viscous terms and a third-order low-storage Runge-Kutta time integration method. Coleman et al fully developed supersonic channel flow at M = 1.5 and Re = 3000 is used to test the method. The nature of fluctuating variables is investigated in detail for the wall layer and the core region based on scatter plots. Fluctuations conditioned on sweeps and ejections in the wall layer are especially instructive, showing that positive temperature, entropy and total temperature fluctuations are mainly due to sweep events in this specific situation of wall cooling. The effect of compressibility on the turbulence structure is in many respects similar to that found in homogeneous shear turbulence and in mixing layers. The normal components of the Reynolds stress anisotropy tensor are increased due to compressibility, while the shear stress component is slightly reduced. Characteristic of the Reynolds stress transport is a suppression of the production of the longitudinal and the shear stress component, a suppression of all velocity-pressure-gradient correlations and most of the dissipation rates. Comparison with incompressible channel flow data reveals that compressibility effects manifest themselves in the wall layer only.

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.

The unsteady behavior in shockwave turbulent boundary layer interaction is investi- gated by analyzing results from a LES of a supersonic turbulent boundary layer over a compression-expansion ramp. The interaction leads to a very-low-frequency motion near the foot of the shock, with a characteristic frequency that is three orders of magnitude lower than the typical frequency of the incoming boundary layer. Wall pressure data are first analyzed by means of Fourier analysis, highlighting the low-frequency phenomenon in the interaction region. Furthermore, the flow dynamics are analyzed by a dynamic mode decomposition which shows the presence of a low-frequency mode associated with the pulsation of the separation bubble and accompanied by a forward-backward motion of the shock.

We investigate a passive flow-control technique for the interaction of an oblique shock generated by an 8.8 ○ wedge with a turbulent boundary-layer at a free-stream Mach number of Ma ∞ = 2.3 and a Reynolds number based on the incoming boundary-layer thickness of Re δ0 = 60.5 ⋅ 10 3 by means of large-eddy simulation (LES). The compressible Navier-Stokes equations in conservative form are solved using the adaptive local deconvolution method (ALDM) for physically consistent subgrid scale modeling. Emphasis is placed on the correct description of turbulent inflow boundary conditions, which do not artificially force low-frequency periodic motion of the reflected shock. The control configuration combines suction inside the separation zone and blowing upstream of the interaction region by a pressure feedback through a duct embedded in the wall. We vary the suction location within the recirculation zone while the injection position is kept constant. Suction reduces the size of the separation zone with strongest effect when applied in the rear part of the separation bubble. The analysis of wall-pressure spectra reveals that all control configurations shift the highenergy low-frequency range to higher frequencies, while the energy level is significantly reduced only if suction acts in the rear part of the separated zone. In that case also turbulence production within the interaction region is significantly reduced as a consequence of mitigated reflected shock dynamics and near-wall flow acceleration.

This contribution presents a stability analysis for compressible boundary layer flows over indented surfaces. Specifically, the effects of increasing depth D /δ * and Ma  number on perturbation time-decay rates and spatial amplification factors are quantified and compared with those of an unindented configuration. The indented surfaces represent aeronautical lifting surfaces endowed with the smooth gap resulting when a filler material applied at the junction of leading-edge and wing-box components retracts upon its curing process. Since the configuration considered is such that the parallel/weakly-parallel assumptions are necessarily compromised, a global temporal stability analysis is considered in this study. Our analysis does not require a parallel flow constrain, and hence it is believed to be valid when two dimensional effects are relevant. We find that small surface modifications enhance certain flow instabilities. An increase in Ma ∞ enhances further this behaviour: for the D /δ * = 1.5, Ma  = 0.5 case, amplification factors at a given location can be up to 20 times larger than those corresponding to the unindented case.

Phone Number: 0 (+33) 232 959 794, Fax Number: 0 (+33) 232 959 780 ABSTRACT In a recent paper by Zhang et al. (2012), a Mach number-invariant scaling was proposed to account for the effect of variation of free-stream Mach number in supersonic turbulent boundary layers. The present work focuses on the effect of variation of wall temperature with strong heating and cooling at the wall. Direct numerical simulation is used to study scaling and turbulence structure of a spatially evolving Mach 2 supersonic boundary layer at a friction Reynolds number of 500. A new scaling law is proposed to account for temperature dependent fluid-property variations.

We investigate the shock-induced turbulent mixing between a light and heavy gas, where a Richtmyer-Meshkov instability (RMI) is initiated by a Ma = 1.5 shock wave. The prescribed initial conditions define a deterministic multimode interface perturbation between light and heavy gas which can be exactly imposed for different simulation codes and resolutions to allow for quantitative comparability. Well-resolved Large-Eddy Simulations are performed using two different and independent numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies the focus of the present investigation is to quantify uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and non-linear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient quantities, such as enstrophy and scalar dissipation rate, show stronger dependencies on the small-scale flow field structures in consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large scale, non-linear entrainment, to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ∼ t 7/12 before reshock, and ∼ (t − t 0 ) 2/7 long after re-shock. The decay rate of turbulence kinetic energy is consistently ∼ (t − t 0 ) −10/7 at late times, where the molecular mixing fraction approaches an asymptotic limit Θ ≈ 0.85. Spectra of density, turbulence kinetic energy, scalar dissipation rate and enstrophy are presented and show excellent agreement for the resolved scales. Probability density function of the heavy gas mass fraction and vorticity reveal that the light-heavy gas composition within the mixing zone is accurately predicted, whereas it is more difficult to capture the long-term behaviour of the vorticity. The established agreement for the large scales of the solution for two fundamentally different numerical methods is unprecedented and serves to establish a reference data set for further numerical analysis of the RMI evolution. †

We investigate a passive flow-control technique for the interaction of an oblique shock generated by an 8.8° wedge with a turbulent boundary-layer at a free-stream Mach number of Ma∞=2.3 and a Reynolds number based on the incoming boundary-layer thickness of Reδ0=60 500 by means of large-eddy simulation (LES). The compressible Navier–Stokes equations in conservative form are solved using the adaptive local deconvolution method (ALDM) for physically consistent subgrid scale modeling. Emphasis is placed on the correct description of turbulent inflow boundary conditions, which do not artificially force low-frequency periodic motion of the reflected shock. The control configuration combines suction inside the separation zone and blowing upstream of the interaction region by a pressure feedback through a duct embedded in the wall. We vary the suction location within the recirculation zone while the injection position is kept constant. Suction reduces the size of the separation zone with strongest effect when applied in the rear part of the separation bubble. The analysis of wall-pressure spectra reveals that all control configurations shift the high-energy low-frequency range to higher frequencies, while the energy level is significantly reduced only if suction acts in the rear part of the separated zone. In that case also turbulence production within the interaction region is significantly reduced as a consequence of mitigated reflected shock dynamics and near-wall flow acceleration.

The effect of new terms in the improved algorithm, the modified direct simulation Monte-Carlo (MDSMC) method, is investigated by simulating a rarefied binary gas mixture flow inside a rotating cylinder. Dalton law for the partial pressures contributed by each species of the binary gas mixture is incorporated into our simulation using the MDSMC method and the direct simulation Monte-Carlo (DSMC) method. Moreover, the effect of the exponent of the cosine of deflection angle (a) in the inter molecular collision models, the variable soft sphere (VSS) and the variable hard sphere (VHS), is investigated in our simulation. The improvement of the results of simulation is pronounced using the MDSMC method when compared with the results of the DSMC method. The results of simulation using the VSS model show some improvements on the result of simulation for the mixture temperature at radial distances close to the cylinder wall where the temperature reaches the maximum value when compared with the results using the VHS model.

Compressible fluid dynamics is of great practical interest in many industrial applications, ranging from chemistry to aeronautical industry, and to nuclear field as well. At the same time, modelling and simulation of compressible flows is a very complex task, requiring the development of specific approaches, in order to describe the effect of pressure on the fluid velocity field. Compressibility effects become even more important in the study of two-phase flows, due to the presence of a gaseous phase. In addition, compressibility is also expected to have a significant impact on other physics, such as chemical or nuclear reactions occurring in the mixture. In this perspective, multiphysics represents a useful approach to address this complex problem, providing a way to catch all the different physics that come into play as well as the coupling between them. In this work, a multiphysics model is developed for the analysis of the generation IV Molten Salt Fast Reactor (MSFR), with a specific focus on the compressibility effects of the fluid that acts as fuel in the reactor. The fuel mixture compressibility is expected to have an important effect on the system dynamics, especially in very rapid super-prompt-critical transients. In addition, the presence of a helium bubbling system used for online fission product removal could modify the fuel mixture compressibility, further affecting the system transient behaviour. Therefore, the MSFR represents an application of concrete interest , inherent to the analysis of compressibility effects and to the development of suitable modelling approaches. An OpenFOAM solver is developed to handle the fuel compressibility, the presence of gas bubbles in the reactor as well as the coupling between the system neutronics and fluid dynamics. The outcomes of this analysis point out that the fuel compressibility plays a crucial role in the evolution of fast transients, introducing delays in the expansion feedbacks that strongly affect the system dynamics. Moreover, it is found that the gas bubbles significantly alter the fuel compressibility, yielding even larger differences compared to the incompressible approximation usually adopted in the current MSFR solvers.

A new class of flux-limited schemes for systems of conservation laws is presented that is both high-resolution and positivity-preserving. The schemes are obtained by extending the Steger-Warming method to second-order accuracy through the use of component-wise TVD flux limiters while ensuring that the coefficients of the discretization equation are positive. A coefficient is considered positive if it has all-positive eigenvalues and has the same eigenvectors as those of the convective flux Jacobian evaluated at the corresponding node. For certain systems of conservation laws, such as the Euler equations for instance, this condition is sufficient to guarantee positivity-preservation. The method proposed is advantaged over previous positivity-preserving flux-limited schemes by being capable to capture with high resolution all wave types (including contact discontinuities, shocks, and expansion fans). Several test cases are considered in which the Euler equations in generalized curvilinear coordinates are solved in 1D, 2D, and 3D. The test cases confirm that the proposed schemes are positivity-preserving while not being significantly more dissipative than the conventional TVD methods. The schemes are written in general matrix form and can be used to solve other systems of conservation laws, as long as they are homogeneous of degree one.

The authors present a higher-order Godunov method for the solution of the two-and three-dimensional equations of ideal magnetohydrodynamics (MHD). This work is based both on a suitable operator-split approximation to the full multidimensional equations, and on a one-dimensional Riemann solver. TIlls Riemann solver is sufficiently robust to handle the nonstrictly hyperbolic nature of the MHD equations and the presence of local linear degeneracies. Results from a set of test problems show that this operator-split methodology has no problems handling any of the three MHD waves. yet resolves shocks to three or four computational zones. The advantages and limitations of this method are discussed. Key words. magnetohydrodynamics (MHD), Godunov methods, hyperbolic systems, finite difference equations AMS subject classifications. 65M06, 35L665, 3504, 76W05 1. Introduction. Conservative, finite-difference schemes based on higher-order Godunov methods have proven very effective at computing discontinuous solutions to hyperbolic systems of conservation laws. Several examples of such schemes are available for the equations of hydrodynamics (van Leer [23], Roe [20], Harten, Lax, and van Leer [13], and Colella and Woodward [9]

A Large Eddy Simulation (LES) methodology has been developed for supersonic turbulent flows with strong shock boundary layer interaction. Results are presented for an expansion-compression corner at Mach 3 and compared with experimental data.

In this paper, we develop an optimal particle setup method for initial condition with Centroidal Voronoi Particle (CVP) dynamics, which combines the Centroidal Voronoi Tessellation (CVT) and Voronoi Particle (VP) concept. CVT optimizes the energy function in terms of compactness and consequently ensures the isotropy of particle distribution. The CVT configuration is computed by Lloyd’s algorithm, which decreases the energy function monotonically. A physics-motivated model equation with tailored equation of state (EOS) is employed to relax the Voronoi particle system such that the convergent equilibrium matches the target configuration. The resulting particle distribution approximates the given analytical profiles of spatially adaptive density, smoothing-length and mass distribution with high interpolation accuracy. The level-set method is introduced to describe arbitrarily complex geometries. A set of Smoothed Particle Hydrodynamics (SPH) simulations is computed to demonstrate the performances of the proposed method. Without parameter tuning, good performance is obtained for presented benchmarks implying its promising potential.

The relationship between the three-dimensional vortex structures and flow-separation zones generated by a shock wave/boundary-layer interaction within a low-aspect-ratio duct was studied using stereoscopic particle imaging velocimetry measurements. In this configuration, the interaction of the incident shock with all walls was important in controlling the flowfield; the three interactions coupled to produce a strongly distorted flowfield. Conditional sampling was used to construct the local probability of reverse flow maps, and thus quantify the distribution of regions of intermittent separation on both bottom-walls and side-walls. The latter regions were found to be significantly larger and more likely to separate than the former. Thus, it was concluded that the sidewall and corner flow interactions dominate in this configuration. A triple decomposition of motion was used to construct a three-dimensional representation of the vortex features generated by the interaction. The results indicated that the flowfield was dominated by three vortex systems: 1) the vortex associated with the sidewall swept-shock interaction; 2) a complex, possibly branched, vortex pair induced on the bottom wall; and 3) a vortex pair induced by the flow at the corner, which coupled the two interactions. The role of the three vortex systems on the onset of flow separation was also explored and discussed.

Well-resolved Large-Eddy Simulations (LES) of a pseudo-shock system in the divergent part of a Laval nozzle with rectangular cross section are conducted and compared with experimental results. The LES matches the parameter set of a reference experiment. Details of the experiment, such as planar side walls, are taken into account, all wall boundary layers are well-resolved and no wall model is used. The Adaptive Local Deconvolution Method (ALDM) with shock sensor is employed for subgrid-scale turbulence modeling and shock capturing. The LES results are validated against experimental wall-pressure measurements and schlieren pictures. A detailed discussion of the complex flow phenomena of three-dimensional shock-wave–boundary-layer interaction, including corner vortices and recirculation zones, is presented. Limitations of RANS approaches are discussed with reference to the LES results.

The injection of choked gaseous jets into still air is investigated computationally and experimentally. The objective is to compare the performance of three turbulence models-Realizable k-, SST k- and Reynolds Stress Transport to resolve the effect of injection angle on the jet mixing with ambient air. The experimental methods consist of particle image velocimetry (PIV) using pulsed Nd:YAG lasers of a choked gas jet, seeded with aluminum oxide particles, injected into still air that has been seeded with water fog. The test conditions include injection angles of 0° and 15°. The results including jet velocities and the vorticity field are presented. The flow field is not symmetric along the injection axis due to the asymmetric triggering of expansion fans at the jet exit due to the inclined injection plane. Moreover, the numerical simulation reveals the complex interaction mechanism of the expansion fans and shockwaves within the injection port.

With the continuing miniaturization of technology happening a rapid pace, more and more compressible flows are occurring at the microscale. At the small length scales encountered in such microflows, the standard assumption of shockwaves having infinitesimal thickness may no longer apply. In this paper we therefore suggest the existence of " shock-plugs, " standing normal shocks with finite thickness. We model shock-plugs using the same methods and assumptions as seen in standard normal shockwave analysis. The inclusion of shock thickness necessitates the inclusion of additional parameters in the analysis, however, namely differing upstream and downstream cross sectional areas, as well the pressure on the sidewalls adjacent to the shock. Predictions for changes in Mach number, temperature, pressure, and entropy are presented, all of which show deviation from conventional shockwave analysis. The models presented here may provide better estimates of shock properties in microscale applications.

We study the hydrodynamic interactions between colloids suspended in a compressible fluid inside a rigid channel. Using lattice–Boltzmann simulations and a simplified hydrodynamic theory, we find that the diffusive dynamics of density perturbations (sound) in the confined fluid give rise to particle correlations of exceptionally long spatial range and algebraic temporal decay. We examine the effect of these sound-mediated correlations on two-particle dynamics and on the collective dynamics of a quasi-one-dimensional suspension. 1. Introduction Particles embedded in an unbounded fluid are dynamically correlated by hydrodynamic interactions that decay like 1/r (where r denotes the separation between particles) [1]. This result is understood in terms of the fundamental solution to the steady-state Stokes equation, η∇ 2 u = ∇p − bδ(r), supplemented by the fluid-incompressibility condition ∇ · u = 0. Here u is the flow velocity field, p the pressure field, b a point force, and η the shear viscosity. It follows from the first equation that the vorticity, ∇×u, satisfies the Laplace equation, leading in the case of an unbounded fluid to the 1/r slow decay of the velocity field. When particles are confined to a quasi-one-dimensional (q1D) channel, however, these long-range dynamic correlations are cut off [2], the screening being attributed to dissipation at the fluid-solid interface, i.e., to the loss of fluid momentum at the channel boundaries. The resulting screening length is comparable to the channel width. The dissipative effect of the boundaries can be incorporated through an additional friction term in an " effective fluid " model [3, 4], η∇ 2 u = ρ 0 ξu + ∇p − bδ(r). In the extra term ρ 0 is the fluid mass density and ξ an effective friction coefficient. The parameter ξ has units of inverse time and characterizes the rate of momentum loss to the boundaries. It can be estimated, therefore, as the inverse of the time it takes fluid momentum to diffuse to the channel boundary, ξ ∼ ν/h 2 , ν = η/ρ 0 being the kinematic shear viscosity and h the channel width. This simplified, phenomenological approach has been shown by simulations [5, 6, 7, 8] and analytical calculations [9] to correctly reproduce the qualitative behavior of confined fluids. The modified Stokes equation leads to a Helmholtz equation for the vorticity, whose regular solutions are exponentially screened functions. Yet, the friction that suppresses the vorticity (transverse fluid stress) does not similarly suppress the pressure field (longitudinal fluid stress) emanating from a locally applied force. Consequently, the application of a localized force generates a long-range pressure distribution, which may give rise to long-range flows and forces on embedded particles. For example, in a q2D suspension confined between two plates, the pressure distribution creates

We  investigate  the  role  of  a  viscous  compressible  sedimentarylayer underlying sea water on the formation, propagation and at-tenuation of hydro-acoustic waves. The analysis of low frequencypressure waves can be used for evaluation of stratified sedimentstructure.  Two models based on depth-integration, for rigid andpermeable sea bed are presented. The hydro-acoustic waves mod-eling,  hereinafter  presented  can  be  used  for  tsunami  predictionin large scale domains, overcoming computational diculties ofthree-dimensional models and therefore enhance the promptnessand accuracy of Tsunami Early Warning Systems (TEWS).KEYWORD:  Hydro-acoustic  waves;  Tsunami;  CompressibleFluid; Viscous Sediment; Peak Frequency; Damping term

The interaction of three-dimensional isotropic turbulence with a plane shock at Mach numbers of M = 2.0 and M = 3.0 is investigated via direct numerical simulation. The numerical scheme is based on a characteristic-type formulation of the Navier-Stokes equations and uses fifth-order upwind schemes in space, a fourth order Runge Kutta scheme in time and a shock-fitting as inlet condition. The isotropic turbulence was generated in a separate computation based on a prescribed energy spectrum. This turbulent flow is considered as frozen, and is convected through the shock with a prescribed average shock speed. An FFT interpolation is used to obtain the upstream values at the instantaneous shock location. Turbulence enhancement is observed, and the evolution of velocity fluctuations as well as turbulence microscales are in good agreement with the behaviour observed using shock-capturing. To cite this article: J. Sesterhenn et al., C. R. Mecanique 333 (2005).

The interaction of acoustic waves with a shock wave is simulated numerically. Both sound reflec- tion and refraction are investigated. Numerical simulations are performed with resolving the interior viscous structure of shock transition. A high-order compact-difference scheme is used to solve the compressible Navier-Stokes equations. It is shown that in the limiting case when the wavelength of incident disturbances is much greater than the shock thickness, the results of simulations within a wide range of Mach numbers and angles of incidence of disturbances correspond very accurately to the predictions of the classical linear inviscid theory. The results obtained enable an unambiguous conclusion on the incorrectness of the recently proposed alternative theory of interaction of shock waves with small disturbances to be made.

We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier-Stokes equations in cylindrical coordinates using high-order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point-flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up- and downstream. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Classical Mach-number (M) scaling in compressible wall turbulence was suggested by van Driest (Van Driest E R. Turbulent boundary layers in compressible fluids. J Aerodynamics Science, 1951, 18(3): 145-160) and Huang et al. (Huang P G, Coleman G N, Bradshaw P. Compressible turbulent channel flows: DNS results and modeling. J Fluid Mech , 1995, 305: 185-218). Using a concept of velocity-vorticity correlation structure (VVCS), defined by high correlation regions in a field of two-point cross-correlation coefficient between a velocity and a vorticity component, we have discovered a limiting VVCS as the closest streamwise vortex structure to the wall, which provides a concrete Morkovin scaling summarizing all compressibility effects. Specifically, when the height and mean velocity of the limiting VVCS are used as the units for the length scale and the velocity, all geometrical measures in the spanwise and normal directions, as well as the mean velocity and fluctuation (r.m.s) profiles become M-independent. The results are validated by direct numerical simulations (DNS) of compressible channel flows with M up to 3. Furthermore, a quantitative model is found for the M-scaling in terms of the wall density, which is also validated by the DNS data. These findings yield a geometrical interpretation of the semi-local transformation , and a conclusion that the location and the thermodynamic properties associated with the limiting VVCS determine the M-effects on supersonic wall-bounded flows. compressible channel flow, coherent structures, correlation structures, Morkovin's hypothesis PACS number(s): 47.27.nd, 47.27.De, 47.40.-x Citation: Pei J, Chen J, Fazle H, et al. New scaling for compressible wall turbulence. Sci China-Phys Mech Astron,

Results of a large-eddy simulation (LES) of a supersonic turbulent boundary layer flow along a compression–expansion ramp configuration are presented. The numerical simulation is directly compared with an available experiment at the same flow conditions. The compression–expansion ramp has a deflection angle of β = 25°. The flow is characterized by a free-stream Mach number of Ma∞ = 2.88 and the Reynolds number based on the incoming boundary layer thickness is Reδ0=132840. The Navier Stokes equations for compressible flows are solved on a cartesian collocated grid. About 32.5 × 106 grid points are used to discretize the computational domain. Subgrid scale effects are modeled implicitly by the adaptive local deconvolution method (ALDM). A synthetic inflow-turbulence technique is used, which does not introduce any low frequency into the domain, therefore avoiding any possible interference with the shock/boundary layer interaction system. Statistical samples are gathered over 800 characteristic time scales δ0/U∞. The numerical data are in good agreement with the experiment in terms of mean surface-pressure distribution, skin-friction, mean velocity profiles, velocity and density fluctuations. For the first time the full compression–expansion ramp configuration was taken into account. The computational results confirm theoretical and experimental findings on fluctuation-amplification across the shockwave/boundary layer interaction region and on turbulence damping through the interaction with rarefaction waves. The LES provide evidence of the existence of Görtler-like structures originating from the recirculation region and traveling downstream along the ramp. An analysis of the wall pressure field clearly shows the presence of a low frequency motion of the shock and strong influence of the Görtler-like vortices on the wall pressure spectra.

This contribution presents a stability analysis for compressible boundary layer flows over indented surfaces. Specifically, the effects of increasing depth D /δ * and Ma ∞ number on perturbation time-decay rates and spatial amplification factors are quantified and compared with those of an unindented configuration. The indented surfaces represent aeronautical lifting surfaces endowed with the smooth gap resulting when a filler material applied at the junction of leadingedge and wing-box components retracts upon its curing process. Since the configuration considered is such that the parallel/weakly-parallel assumptions are necessarily compromised, a global temporal stability analysis is considered in this study. Our analysis does not require a parallel flow constrain, and hence it is believed to be valid when two dimensional effects are relevant. We find that small surface modifications enhance certain flow instabilities. An increase in Ma ∞ enhances further this behaviour: for the D /δ * = 1.5, Ma ∞ = 0.5 case, amplification factors at a given location can be up to 20 times larger than those corresponding to the unindented case.

The turbulent spot propagation process in boundary layer flows of air, nitrogen, carbon dioxide, and air/carbon dioxide mixtures in thermochemical nonequilibrium at high enthalpy is investigated. Experiments are performed in a hypervelocity reflected shock tunnel with a 5-degree half-angle axisymmetric cone instrumented with flush-mounted fast-response coaxial thermocouples. Time resolved and spatially demarcated heat transfer traces are used to track the propagation of turbulent bursts within the mean flow, and convection rates at approximately 91, 74, and 63% of the boundary layer edge velocity, respectively, are observed for the leading edge, peak, and trailing edge of the spots. A simple model constructed with these spot propagation parameters is used to infer spot generation rates from observed transition onset to completion distance. Spot generation rates in air and nitrogen are estimated to be approximately twice the spot generation rates in air/carbon dioxide mixtures.

Turbulence affects the dynamics and the evolution of the turbulent mixing layer and its complex configuration is studied taking into account the dependence on the initial modes at the early stages and its spectral, self-similar information. Most models of the turbulent mixing evolution generated by hydrodynamics instabilities do not include any dependence on initial conditions, but in many relevant physical problems this dependence is very important, for instance, in Inertial Confinement Fusion target implosion. We discuss simple initial conditions with the aid of a numerical model developed at FIAN Lebedev which was compared with results of many simulations. The analysis of Kelvin-Helmholtz, Rayleigh-Taylor, Richtmyer-Meshkov and of accelerated instabilities is presented locally, and seen to dominate the turbulent cascade mixing zone differently under different initial conditions. Simulations and multi-fractal and neuron network analysis of Turbulent Mixing under RT and RM instabilities are presented for the different experiments and numerical simulations, further analysis on the numerical model is presented using wavelet preprocessing of the simulation results and neuron network presentation of the data. The aspect ratios of the bubble induced convective cells are seen to depend on the boundary and initial conditions applied to the front. The evolution of the Rayleigh-Taylor instability develops into a turbulent mixing front that may be investigated further using the information that the fractal dimensions or Kolmogorov Capacities give as the flow evolves in time. The basic self-similar characteristics of the flow are compared and the evolution of the multi-fractal dimensions of density, velocity and vorticity contours provides indication that most mixing takes place at the sides of the dominant convective blobs. In the context of determining the influence of structure on mixing ability and determine the regions of the front which contribute most to molecular mixing.

The interaction of three-dimensional isotropic turbulence with a plane shock at Mach numbers of M = 2.0 and M = 3.0 is investigated via direct numerical simulation. The numerical scheme is based on a characteristic-type formulation of the Navier-Stokes equations and uses fifth-order upwind schemes in space, a fourth order Runge Kutta scheme in time and a shock-fitting as inlet condition. The isotropic turbulence was generated in a separate computation based on a prescribed energy spectrum. This turbulent flow is considered as frozen, and is convected through the shock with a prescribed average shock speed. An FFT interpolation is used to obtain the upstream values at the instantaneous shock location. Turbulence enhancement is observed, and the evolution of velocity fluctuations as well as turbulence microscales are in good agreement with the behaviour observed using shock-capturing. To cite this article: J. Sesterhenn et al., C. R. Mecanique 333 (2005).