Non-intrusive acoustic instruments that measure fluid velocity and temperature have been restricted to low subsonic Mach number applications due to increased complexities associated with acoustic refraction, low signal-to-noise ratios, and a limited range of practical applications. In the current work, the use of acoustics for non-intrusive flow monitoring in compressible flows is explored and a novel sonic anemometry and thermometry (SAT) technique is developed. Using multiple arrangements of SAT equipment, a compressible acoustic tomography technique was also developed to resolve flow non-uniformities. Three validation experiments were used to investigate the novel SAT technique performance, and a fourth validation experiment was used to explore compressible flow tomography capabilities. In the first experiment, an unheated jet was used to verify that the acoustic technique could measure fluid velocities in high subsonic Mach number flows. The application demonstrated velocity root mean square (RMS) errors of 9 m/s in unheated jet flows up to Mach 0.83. Next, a heated jet facility was used to assess the impact of fluid temperature on measurement accuracy. Using jet Mach numbers up to 0.7 and total temperatures up to 700 K, RMS velocity and static temperature errors up to 8.5 m/s (2.4% of maximum jet velocity) and 23.3 K (3.3% of total temperature) were observed. Finally, the acoustic technique was implemented at the exhaust of a JT15D-1A turbofan engine to investigate technique sensitivity to bypass engine conditions. A mass flow rate and thrust estimation approach was developed and RMS errors of 1.1 kg/s and 200 N were observed in conditions up to an exhaust Mach number of 0.48. Since modern acoustic tomography techniques require an incompressible flow assumption for velocity detection, advancements were made to extend acoustic tomography methods to compressible flow scenarios for the final experiment. The approach was tested in the heated jet operating at Mach 0.48 and 0.72 (total temperature of 675 K, approximately 2.25 times the ambient) and numerical simulations were used to identify technique sensitivity to input variables and system design. This research marks the first time an acoustic method has been used to estimate compressible flow velocities and temperatures. / Ph. D. / Traditionally, intrusive instruments such as pressure and temperature probes have been used to measure flow conditions. While these instruments are effective and widely used, they generate turbulence and produce blockage which could be undesirable in a variety of applications. In the current work, the use of non-intrusive acoustic measurements for flow velocity and temperature detection in compressible flow (Mach>0.3) environments was investigated. First, a novel acoustic technique was developed for compressible flow applications. The new approach was used to measure jet velocities and temperatures in compressible flow conditions for the first time. Later, this technique was implemented at the exhaust of a turbofan gas turbine engine. The results of this experiment demonstrated that acoustic measurements could be used to estimate engine mass flow rate and thrust in a non-intrusive manner. The final portion of this research focuses on the non-intrusive detection of fluid velocity and temperature gradients. Since existing acoustic techniques require an incompressible flow assumption, a novel approach was identified and used to perform a validation experiment. The experimental findings confirmed that non-intrusive acoustic measurements could be used to measure velocity and temperature gradients in compressible flow environments.

Cette thèse est consacrée à l’analyse mathématique de trois problèmes d’écoulements de fluides viscoélastiques de type Oldroyd. Tout d’abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d’écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d’existence et d’unicité des solutions. Nous étudions également le cas d’un écoulement non stationnaire. Nous montrons un résultat d’existence locale et un résultat d’existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous démontrons aussi la convergence du modèle d’écoulement viscoélastique compressible à faible nombre de Mach vers le modèle incompressible lorsque les données initiales sont "bien préparées" / In this PHD thesis, we study three problems for viscoelastic flows of Oldroyd type. First, we study steady flows of slightly compressible in a bounded domain with non-zero velocities on the boundary ; the pressure and the extra-stress tensor are prescribed on the part of the boundary corresponding to entering velocity. This causes a weak singularity in the solution at the junction of incoming and outgoing flows. We also study the problem of steady flows of slightly compressible fluids with zero boundary conditions in a domain with an isolated corner point. Using a method of fixed point (first and second problems) and a Helmoltz decomposition (second problem), we show some results of existence and uniqueness of solutions. In the last part, we study the case of a non-steady flow : we show some results of local and of global existence, with sufficiently small initial data, for compressible flows. The zero-Mach number limit is also established

Le SPS (Spark plasma sintering) ou frittage flash est une technique innovante de compaction de poudre. Ce procédé fait intervenir le courant électrique pour chauffer l'échantillon en appliquant simultanément une pression. Grâce à la vitesse de chauffage, le procédé SPS apparaît comme étant une technologie prometteuse dans le secteur aéronautique servant à produire des matériaux denses à microstructure fine, composés par des intermétalliques difficiles à fondre, à former et à usiner avec les procédés conventionnels. Cependant, la fabrication de formes complexes est problématique à cause des hétérogénéités en densité qui peuvent apparaître lors de la compaction et qui proviennent de la distribution de la température et des contraintes dans la poudre compactée. La distribution du courant, de la température et des contraintes, ainsi que leurs différents effets, font l'objet d'une large étude, étant responsables de l'homogénéité de la microstructure. Une modélisation numérique 3D du procédé est réalisée, dans le cadre de la librairie CimLib. Elle englobe trois problèmes physiques fortement couplés : électrique, thermique et mécanique. Nous utilisons une approche monolithique qui consiste à résoudre une équation pour chaque problème sur un maillage unique représentant outils et poudre. Tout d'abord le couplage électrique-thermique est modélisé et les simulations numériques sont validées. Une loi de comportement viscoplastique compressible s'appuyant sur un modèle d'Abouaf est utilisée pour modéliser la densification de la poudre de TiAl. Ce modèle est validé par plusieurs cas tests de compaction de poudre dans un contexte lagrangien puis eulérien avant de passer à une simulation complète de couplage électrique-thermique-mécanique. Dans ce contexte monolithique, nous développons un modèle pour prendre en compte les effets du frottement entre la poudre et le moule. Enfin, la loi de comportement utilisée est identifiée pour la poudre intermétallique de TiAl. Le frittage par SPS d'échantillons de différentes tailles est simulé. Les résultats en termes de distribution de densité et déplacement sont validés grâce à une comparaison avec l'expérience. / Spark plasma sintering process (SPS) is a breakthrough technology for producing high quality sintered materials. An electric current is applied simultaneously with a vertical load to sinter the powder placed in a graphite mould. Joule effect leads to high heating rates which are favorable for enhancing the microstructure and physical properties. However, manufacturing complex shapes is problematic due to heterogeneities in density distribution that may appeari during compaction. For that reason, the development of a numerical model to predict sintering is necessary. The model should help controlling temperature and stress distributions, which are responsible for the microstructure homogeneity. A 3D numerical model is developed to ensure a predictive tool for SPS using CimLib, a code developed at CEMEF. The numerical model presents three physical problems strongly coupled: an electric problem, a thermal problem and a mechanical problem. A monolithic approach is used which consists in solving one equation for each problem using one unique mesh for tools and powder. First the electric thermal coupling is modeled and the numerical simulations are validated by comparison with commercial codes. A viscoplastic compressible law based on Abouaf model is implemented to model the densification of TiAl powder. This model is validated by comparing the numerical results of different compaction tests with analytic solutions using a Lagrangian and Eulerian framework. Then a fully coupled electric-thermal-mechanical simulation is carried out. In the monolithic framework, a model is developed to take into account friction effects between powder and mould. Finally, the parameters of the selected material law are identified for TiAl powder using our numerical model and SPS experiments. Sintering of different samples is then simulated. Results are compared with the experiments in terms of density distribution and displacement.

Les écoulements décollés sont fortement instationnaires, l'objectif de cette thèse a été de localiser et d'identifier les phénomènes à la source de ces instationnarités et de comprendre les processus physiques permettant le transfert de l'information de ces zones sources au reste de l'écoulement. Pour ce faire une analyse des résultats issus de simulations numériques a été réalisée. En étudiant la corrélation et la cohérence entre les positions de choc et les fluctuations de pression, l'interaction a pu être séparée en plusieurs parties distinctes. A l'aide de la théorie des caractéristiques définissant les directions et les cinématiques de propagation de l'information, les liens spatio-temporels entre ces différentes régions ont pu être déterminés. Les résultats de ces études couplés avec ceux issus des expériences ont montré clairement que les phénomènes se produisant à l'intérieur de la zone de recirculation existant en aval du choc de décollement gouvernent la dynamique de la totalité de l'interaction, aussi bien à basse fréquence qu'à moyenne fréquence. Ainsi les mouvements de choc apparaissent comme le miroir des phénomènes se produisant à l'intérieur de la zone décollée. Une représentation équivalente en fluide non visqueux permettant une description du comportement instationnaire de l'interaction a aussi été proposée. / Separated flow are often strongly unsteady; the aim of this thesis is to localize and identify the sources of the unsteadiness and to understand the physical phenomena governing the information transfer from these source zones to the rest of the flow. To do this, data used for this analysis have been obtained from numerical simulations (LES). Both cross-correlation and coherence between shock motion and pressure fluctuations have shown that the interaction can be split in several distinct zones. The theory of characteristics is used to define the information paths and the propagation velocities, so that the space-time links between these regions have been determined. Both numerical and experimental studies have clearly shown that phenomena present within the recirculation buble govern the whole of the interaction, at low and intermediate frequencies. Indeed the shock motions appears as the mirror of phenomena present in the separated zone. An inviscid equivalent scenario has been proposed to represent the interaction.

Ce travail porte sur la simulation numérique et la modélisation du comportement thermo-mécanique des matériaux composites renforcés par des fibres. Spécifiquement les matériaux SMC (Sheet Moulding Compound) sont utilisés dans le processus de moulage par compression pour construire des pièces automobiles de haute performance. Ce travail est divisé en quatre chapitres, décrivant tout d’abord un modèle thermo-mécanique entièrement couplé pour les matériaux SMC standards et innovants à haute concentration en fibres (> 25% en volume). Le SMC est traité comme un mélange incompressible de fibre et de résine complété éventuellement par une phase de porosité compressible. Son anisotropie est modélisée au moyen de tenseurs structurels. La cinétique de réaction et de consolidation de la pièce est également modélisée et étudiée. Les données expérimentales mécaniques et thermiques enregistrées sur des échantillons de matériaux SMC sont comparées au modèle et à la solution numérique fournie par ce travail. D’un point de vue numérique, nous utilisons la méthode des domaines immergées o`u chaque phase est distinguée par une fonction distance signée. Nous décrivons le procédé de moulage par compression en proposant une résolution compressible anisotrope unifiée capable de décrire la transition compressible / incompressible du matériau SMC sous déformation. Cela permet de décrire la réponse mécanique du SMC et de prédire localement la consolidation (durcissement) de la pièce le long du cycle thermique. / This work deals with the numerical simulation and modeling of thermomechanical analysis of fiber reinforcedcomposites materials. Specifically for SMC (Sheet Molding Compound) materials that are used in compression molding processes to build automotive high performance parts. The work is divided into fourchapters, firstly describing a fully coupled thermo-mechanical model for standard SMC materials and for innovative SMC with high fiber concentration (> 25% in volume). The SMC is treated as an incompressible mixtureof fibers and paste complemented by a compressible porosity phase. Its anisotropy is modeled by means of structural tensors. Kinetic of reaction and consolidation of the part is also modeled and studied. Mechanicaland thermal experimental data recorded on samples of SMC materials are compared to the model and numerical solution provided in this work. A numerical framework, we use the immersed boundary method and the level set method. We describe the compression molding process by proposing an unified anisotropic compressible resolution able to describe the transition between compressible/ incompressible of SMC materials under deformation. We are able to describe the mechanical response of the SMC and to predict locally the consolidation (curing) of thepart throughout the thermal cycle.

Dans ce travail, on s'intéresse au développement d'une méthode hybride qui couple spatialement les schémas d'intégration temporelle explicite et implicite. Afin de répondre aux contraintes du solveur industriel FLUSEPA, les schémas explicite Heun et implicite Crank-Nicolson ont été hybridés via un paramètre de transition : l'approche mise en place est appelée schéma AION. Cette dernière est étudiée en détails avec une attention particulière sur son comportement spectral et sa capacité à maintenir l'ordre de précision. On montre que le traitement hybride a d'intéressants comportements dissipatif et dispersif tout en empêchant la réflexion d'ondes parasites et en maintenant la précision attendue. De plus, l'approche hybride est validée sur plusieurs cas académiques à la fois pour les flux convectifs et pour les flux diffusifs. Et comme espéré, la méthode est plus intéressante en terme de temps de calcul que les méthodes standards d'intégration temporelle. Pour l'extension de cette approche à la méthode temporelle adaptative présente dans FLUSEPA, il a été nécessaire d'améliorer le traitement qui permet à la méthode d’être conservative tout en obtenant des propriétés spectrales acceptables. Finalement l'approche hybride a été aussi étendue pour la modélisation RANS/LES de la turbulence avec des temps de calcul intéressants tout en capturant la physique de l'écoulement / This work deals with the design of a hybrid time integrator that couples spatially explicit and implicit time integrators. In order to cope with the industrial solver of Ariane Group called FLUSEPA, the explicit scheme of Heun and the implicit scheme of Crank-Nicolson are hybridized using the transition parameter : the whole technique is called AION time integration. The latter is studied into details with special focus on spectral behaviour and on its ability to keep the accuracy. It is shown that the hybrid technique has interesting dissipation and dispersion properties while maintaining precision and avoiding spurious waves. Moreover, this hybrid approach is validated on several academic test cases for both convective and diffusive fluxes. And as expected the method is more interesting in term of computational time than standard time integrators. For the extension of this hybrid approach to the temporal adaptive method implemented in FLUSEPA, it was necessary to improve some treatments in order to maintain conservation and acceptable spectral properties. Finally the hybrid time integration was also applied to a RANS/LES turbulent test case with interesting computational time while capturing the flow physics.

Ce travail de thèse concerne l’étude des écoulements de fluides gazeux compressibles laminaires subsonique-supersonique dans une tuyère de type convergent-divergent. Les écoulements étudiés sont à nombres de Reynolds modérés et s’affranchissent de l’hypothèse de condition adiabatique de paroi couramment utilisée afin de mieux prendre en compte les phénomènes de transfert de chaleur par convection et rayonnement avec le milieu extérieur. Cette étude des phénomènes de transferts conjugués a permis de déterminer le comportement dynamique simultané du fluide et de la paroi de la tuyère. Enfin, compte tenu des niveaux élevés de températures mis en jeu dans ces systèmes, une analyse concernant le comportement thermomécanique de l’ensemble de la structure de paroi avec des matériaux monocouches et multicouches a été réalisé. De nombreuses configurations géométriques, propriétés physiques et conditions aux limites sur le fluide et la paroi ont été analysées. Les résultats présentés montrent, la structure des écoulements à travers les iso-contours de vitesses, des nombres de Mach, des pressions dans le fluide, des températures dans le fluide et dans la paroi ainsi que les déformations et les contraintes de la paroi qui résultent des couplages thermomécaniques. Une analyse des performances de la tuyère, en termes de force de poussée et de coefficient de débit spécifique, est largement discutée dans ce travail. / This work concerns the study of flows of compressible gaseous laminar subsonic-supersonic nozzle in a convergent-divergent type. The flows are studied to moderate Reynolds numbers and free themselves from the assumption of adiabatic wall conditions commonly used to better take into account the phenomena of heat transfer by convection and radiation with the external environment. This study combined transfer phenomena was determined simultaneously the dynamic behavior of the fluid and the wall of the nozzle. Finally, given high levels of temperatures at stake in these systems, an analysis of the thermomechanical behavior of the entire wall structure with monolayer and multilayer materials was performed. Many geometric configurations, physical properties and boundary conditions on the fluid and the wall were analyzed. The results presented show the structure of the flow through the iso-contours of speed, Mach numbers, pressures in the fluid, temperatures in the fluid and in the wall as well as the deformations and stresses resulting from the wall thermomechanical couplings. A performance analysis of the nozzle, in terms of thrust coefficient and specific yield, is widely discussed in this work.

Compressible plane Couette flow is studied with superposed small perturbations. The steady mean flow is characterized by a non-uniform shear-rate and a varying temperature across the wall-normal direction for an appropriate perfect gas model. The studies are broadly into four main categories as said briefly below. Nonmodal transient growth studies and estimation of optimal perturbations have been made. The maximum amplification of perturbation energy over time, G max, is found to increase with Reynolds number Re, but decreases with Mach number M. More specifically, the optimal energy amplification Gopt (the supremum of G max over both the streamwise and spanwise wavenumbers) is maximum in the incompressible limit and decreases monotonically as M increases. The corresponding optimal streamwise wavenumber, αopt, is non-zero at M = 0, increases with increasing M, reaching a maximum for some value of M and then decreases, eventually becoming zero at high Mach numbers. While the pure streamwise vortices are the optimal patterns at high Mach numbers (in contrast to incompressible Couette flow), the modulated streamwise vortices are the optimal patterns for low-to-moderate values of the Mach number. Unlike in incompressible shear flows, the streamwise-independent modes in the present flow do not follow the scaling law G(t/Re) ~ Re2, the reasons for which are shown to be tied to the dominance of some terms (related to density and temperature fluctuations) in the linear stability operator. Based on a detailed nonmodal energy anlaysis, we show that the transient energy growth occurs due to the transfer of energy from the mean flow to perturbations via an inviscid algebraic instability. The decrease of transient growth with increasing Mach number is also shown to be tied to the decrease in the energy transferred from the mean flow (E1) in the same limit. The sharp decay of the viscous eigenfunctions with increasing Mach number is responsible for the decrease of E1 for the present mean flow. Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for the uniform shear flow with constant viscosity. For a given M, the critical Reynolds number (Re), the dominant instability (over all stream-wise wavenumbers, α) of each mean flow belongs different modes for a range of supersonic M. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean-flow to perturbations. It is shown that the energy-transfer from mean-flow occurs close to the moving top-wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II”.For the Non-modal transient growth anlaysis, it is shown that the maximum temporal amplification of perturbation energy, G max,, and the corresponding time-scale are significantly larger for the uniform shear case compared to those for its non-uniform counterpart. For α = 0, the linear stability operator can be partitioned into L ~ L ¯ L +Re2Lp is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t/Re) ~ Re2 . In contrast , the dominance of Lp is responsible for the invalidity of this scaling-law in non-uniform shear flow. An inviscid reduced model, based on Ellignsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and non-modal instability, the viscosity-stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow. Modal and nonmodal spatial growths of perturbations in compressible plane Couette flow are studied. The modal instability at a chosen set of parameters is caused by the scond least-decaying mode in the otherwise stable parameter setting. The eigenfunction is accurately computed using a three-domain spectral collocation method, and an anlysis of the energy contained in the least-decaying mode reveals that the instability is due to the work by the pressure fluctuations and an increased transfer of energy from mean flow. In the case of oblique modes the stability at higher spanwise wave number is due to higher thermal diffusion rate. At high frequency range there are disjoint regions of instability at chosen Reynolds number and Mach number. The stability characteristics in the inviscid limit is also presented. The increase in Mach number and frequency is found to further destabilize the unstable modes for the case of two-dimensional(2D) perturbations. The behaviors of the non-inflexional neutral modes are found to be similar to that of compressible boundary layer. A leading order viscous correction to the inviscid solution reveals that the neutral and unstable modes are destabilized by the no-slip enforced by viscosity. The viscosity has a dual role on the stable inviscid mode. A spatial transient growth studies have been performed and it is found that the transient amplification is of the order of Reynolds number for a superposition of stationary modes. The optimal perturbations are similar to the streamwise invariant perturbations in the temporal setting. Ellignsen & Palm solution for the spatial algebraic growth of stationary inviscid perturbation has been derived and found to agree well with the transient growth of viscous counterpart. This inviscid solution captures the features of streamwise vortices and streaks, which are observed as optimal viscous perturbations. The temporal secondary instability of most-unstable primary wave is also studied. The secondary growth-rate is many fold higher when compared with that of primary wave and found to be phase-locked. The fundamental mode is more unstable than subharmonic or detuned modes. The secondary growth is studied by varying the parameters such as β, Re, M and the detuning parameter.

Lors du développement d’un nouvel avion, l’estimation des échanges d’énergie entre l’air ambiant et les parois est une donnée cruciale pour la conception aérothermique. Cette conception repose de plus en plus sur des simulations numériques mais certains phénomènes d’aérothermique externe, comme le jet débouchant du système de dégivrage des nacelles moteur, montrent les limites des modèles RANS classiques. La simulation des grandes échelles (LES) se révèle bien adaptée à ce type de phénomène mais se heurte à un coût de calcul extrêmement élevé pour ces écoulements pariétaux à très grand nombre de Reynolds. Pour lever cette limitation, cette thèse propose l’étude de deux briques fondamentales : la LES avec loi de paroi (WMLES) conjuguée à l’injection d’une couche limite turbulente à l’entrée du domaine. Pour une meilleure compréhension et une utilisation fiable de l’approche loi de paroi, on se concentre tout d’abord sur les sources d’erreur qui lui sont associées. Après les avoir identifiées, on propose une correction de l’erreur de sous-maille ainsi qu’une loi de paroi adaptée aux écoulements compressibles. Grâce à ces deux éléments, on obtient une estimation correcte du flux de chaleur pariétal sur des simulations WMLES de canal plan supersonique sur parois froides. Puis, pour préparer la transition vers des applications plus industrielles, on introduit un schéma numérique plus dissipatif ce qui nous permet d’étudier l’influence de la méthode numérique sur l’approche loi de paroi. Dans une seconde partie dédiée à l’injection de couche limite pour la WMLES, on sélectionne une méthode basée sur l’injection de perturbations combinée à un terme de contrôle volumique. On montre que des simulations WMLES utilisant cette méthode d’injection permettent d’établir une couche limite turbulente réaliste à une courte distance en aval du plan d’entrée, à la fois sur une plaque plane mais également sur un écoulement de jet débouchant à la géométrie plus complexe, représentative d’un cas avion. / During the design of a new aircraft, the prediction of energy exchanged between the ambient air and the aircraft walls is crucial regarding aerothermal design. Numerical simulations plays a role of increasing importance in this design. However classical RANS models reach their limits on some external aerothermal flows, like the jet-in-cross-flow from the anti-icing system oh the engine nacelles. The large eddy simulation (LES) is well suited to this kind of flow but faces an extremely large computational cost for such high Reynolds number wall-bounded flows. To remove this limitation, we propose two building blocks: the Wall Modeled LES (WMLES) combined with a turbulent inflow generation. For a better understanding and a reliable use of the WMLES, we first focus on the sources of error related to this approach. We propose a correction to the subgrid-scale error as well as a wall model suitable for compressible and anisothermal flows. Thanks to these two elements, we correctly predict the wall heat flux in WMLES computations of a supersonic isothermal-wall channel flow. Then, to allow the computation of more industrial flows, we introduce some numerical dissipation and study its effect on the wall modeling approach. The last part is dedicated to turbulent inflow generation for WMLES. We select a method based on synthetic perturbation combined with a dynamic control term. We validate this method on WMLES computations of a flat plate turbulent boundary layer and a hot jet-in-cross-flow representative of an industrial configuration. In both cases, we show that a realistic turbulent boundary layer is generated at a small distance downstream from the inlet plane.

Lattice Boltzmann Method has been quite successful for incompressible flows. Its extension for compressible (especially supersonic and hypersonic) flows has attracted lot of attention in recent time. There have been some successful attempts but nearly all of them have either resulted in complex or expensive equilibrium function distributions or in extra energy levels. Thus, an efficient Lattice Boltzmann Method for compressible fluid flows is still a research idea worth pursuing for. In this thesis, a new Lattice Boltzmann Method has been developed for compressible flows, by using the concept of a relaxation system, which is traditionally used as semilinear alternative for non-linear hypebolic systems in CFD. In the relaxation system originally introduced by Jin and Xin (1995), the non-linear flux in a hyperbolic conservation law is replaced by a new variable, together with a relaxation equation for this new variable augmented by a relaxation term in which it relaxes to the original nonlinear flux, in the limit of a vanishing relaxation parameter. The advantage is that instead of one non-linear hyperbolic equation, two linear hyperbolic equations need to be solved, together with a non-linear relaxation term. Based on the interpretation of Natalini (1998) of a relaxation system as a discrete velocity Boltzmann equation, with a new isotropic relaxation system as the basic building block, a Lattice Boltzmann Method is introduced for solving the equations of inviscid compressible flows. Since the associated equilibrium distribution functions of the relaxation system are not based on a low Mach number expansion, this method is not restricted to the incompressible limit. Free slip boundary condition is introduced with this new relaxation system based Lattice Boltzmann method framework. The same scheme is then extended for curved boundaries using the ghost cell method. This new Lattice Boltzmann Relaxation Scheme is successfully tested on various bench-mark test cases for solving the equations of compressible flows such as shock tube problem in 1-D and in 2-D the test cases involving supersonic flow over a forward-facing step, supersonic oblique shock reflection from a flat plate, supersonic and hypersonic flows past half-cylinder.