<p>In this work, we have focused on the jamming properties of systems composed of semi-2D elliptical shaped particles. In order to study these systems, we have performed three types of experiments: Couette shear, biaxial isotropic compression, and biaxial pure shear. In each experimental scheme, we take data for both systems of ellipses an bi-disperse disks, in order to probe the effect of broken spherical symmetry at the particle scale, on the global behavior. We use two synchronized cameras to capture the flow of particles and the local stress at the same time.</p><p>In Couette experiments, we study the rheological properties, as well as the stress fluctuations for very large strains (up to 20 revolutions of the inner wheel). The system is sheared for densities below the isotropic jamming point (point J). From these studies we learn that over a small range of packing fractions, ($0.85 \leq \phi \leq 0.86$),</p><p>systems of ellipses demonstrate exceptionally slow dynamical evolution when they are sheared. For</p><p>fixed density, and starting from an essentially unstressed state, the application of shear strain leads to</p><p>first a growth of average particle displacements in the system through a Reynolds dilatancy effect,</p><p>and then for very large strains, a steady decrease in particle displacements. In an intermediate</p><p>range of shear strains, the system exists in effectively meta-stable states for a very long time</p><p>before relaxing to an unjammed state, in which the flow of particles stops completely, and the</p><p>stress fluctuations drop to zero. The strain scale for this relaxation depends on the global packing</p><p>fraction. We characterize this slow dynamics by measuring the evolution of mean velocity, density,</p><p>and orientational order throughout the experiments. In a similar set of experiments performed on</p><p>disks, slow relaxation was observed as well. However, the increasing average displacement build-up</p><p>before relaxation, which was observed in ellipses, did not occur for disks. This suggests that the</p><p>slow relaxation towards an unjammed state in ellipses is associated with the possibility of small and</p><p>slow changes in their orientations, which then allow a more efficient packing.</p><p>In order to study the stress fluctuations, we implement photoelastic properties of the particles. We are able to track the $g^{2}$ (a measure of local stress) of each particle throughout the entire experiment. </p><p>Unlike disks, the power spectra of $g^2$, $P(\omega)$, is not rate invariant for ellipses. In other words, all curves of $R P(\omega)$ vs. $\omega / R$ (where $R$ is the shear rate) with different values of $R$, collapse to a single curve for disks, but not for ellipses.</p><p>The rate invariance of spectra was previously studied for sheared spherical glass beads and semi-2D pentagonal particles. This is the first experimental work in which the fluctuations of granular systems composed of elongated particles is addressed. </p><p>We have also studied the formation and destruction of stress avalanches during Couette shear in both systems of disks and ellipses. In particular, we introduce measures which characterize the size and shape of stress avalanches. Analysis of these measures shows that the build-up and release of stress in both systems of disks and ellipses have similar distributions which indicates that the deformation of particles in a Couette cell does not resemble stick-slip behavior. We also find that the build-up and release of stress is faster is larger avalanches.</p><p>Cyclic isotropic compression is performed on semi-2D systems of bi-disperse disks and identical ellipses with aspect ratio 2, which are composed of photoelastic particles. In each compression cycle, the system is compressed with a total strain of $1.6\%$ and then expanded to the initial state. After completion of each half cycle, the system is allowed to relax, then imaged by two synchronized cameras. The packing fraction, $\phi$, of compressed states are chosen above the isotopic jamming point (point J). In both systems of disks and ellipses, we observed relaxation of global stress over long compression cycles. We find that the global stress drops with a power law over time ($\sigma \sim C t^{-A}$). The exponent of decay, $A$, drops linearly with increasing $\phi$, and hits zero at $\phi \simeq 0.89$ for disks, and $\phi \simeq 0.93$ for ellipses. Above these packing fractions, the system is stable with respect to its global stress. </p><p>In order to understand the origin of this slow stress dilation, we have studied the structural changes of the system, including Falk-Langer measures of affine and non-affine deformations, as well as average contact per particle.</p> / Dissertation

Techn. Hochsch., Diss., 2001--Aachen.

La reología de suspensiones concentradas es un tema complejo tanto en la experimentación como en la teoría. La correcta caracterización de estas mezclas es un campo de investigación activo que tiene gran relevancia científica e industrial y donde la aplicación de la mecánica matemática permite desarrollar diseños de ingeniería más seguros y eficientes. El presente Trabajo de Título es un estudio teórico dividido en dos secciones, ambas en el marco de la reología aplicada a relaves mineros. La primera parte está dirigida al estudio de la construcción adecuada de la curva reológica de un material a partir de mediciones experimentales obtenidas utilizando un Reómetro de Cilindros Coaxiales. El procedimiento matemático involucrado se denomina Problema Inverso de Couette y en esta Memoria se prueba que es un problema mal puesto en el sentido de la estabilidad. Además, se revisan distintas estrategias que han sido utilizadas históricamente para buscar soluciones numéricas, a saber, la aproximación newtoniana, la norma DIN, la fórmula de Krieger y Elrod, la fórmula de diferencias finitas y la regularización de Tikhonov. Estos métodos de aproximación fueron implementados computacionalmente para ser aplicados tanto al estudio de modelos teóricos como a información experimental de relaves. En general, los resultados obtenidos fueron muy similares para todas las suspensiones de variada concentración de sólido que se analizaron. En la segunda parte de esta Memoria se propone un modelo reológico original que da cuenta de la compleja fenomenología observada a partir de las curvas construidas en la sección anterior. El comportamiento tixotrópico que se desprende de los experimentos sugiere la existencia de un parámetro de microestructura cuya variabilidad temporal con- trola la superposición relativa entre un régimen viscoelástico inicial y un comportamiento posterior viscoso tipo Bingham. El modelo resultante es de difícil empleo dada la gran cantidad de parámetros libres. Mediante la integración de los ensayos reológicos Vane y los de cilindros coaxiales es posible reducir el problema a la estimación numérica de sólo una o dos constantes. La validación de este modelo se lleva a cabo contrastando con amplia información experimental. Para el rango de datos estudiados, se observa en todos los casos un ajuste satisfactorio y resultados consistentes físicamente.

L’écoulement de Taylor-Couette entre deux cylindres concentriques (cylindre interne en rotation et cylindre externe fixe) est actuellement mis à profit au CEA pour étudier les performances d’extraction d’une colonne liquide/liquide pour le retraitement du combustible nucléaire. Ces performances étant fortement liées au mélange, il est important de le quantifier. En monophasique, les propriétés de mélange ont été étudiées dans une thèse précédente, à la fois expérimentalement et numériquement, et ont été reliées aux paramètres hydrodynamiques de l’écoulement. L’effet du nombre de Reynolds, du régime d’écoulement et de la taille des rouleaux (longueur d’onde axiale) ont notamment été prouvés. Le but de ce travail est d’étendre les précédentes études aux écoulements de Taylor-Couette diphasiques. Pour des raisons pratiques et afin de s’affranchir des phénomènes de coalescence et de rupture, des billes de PMMA de diamètres 800 µm à 3 mm sont choisies pour simuler la phase dispersée, en suspension dans une solution aqueuse de Dimethylsulfoxyde (DMSO) et de Thiocyanate de Potassium (KSCN). Le montage expérimental couple les méthodes de PIV et de PLIF afin d’obtenir en simultané les informations concernant l’hydrodynamique de l’écoulement et le mélange. Cependant la mise en place du diphasique impose un certain nombre de contraintes qui doivent être prises en compte. Bien que les deux phases soient soigneusement choisies afin d’être adaptées en indice et en densité, le recours à une deuxième chaine d’acquisition PLIF est nécessaire afin d’améliorer la qualité des mesures. Ainsi, une première voie de PLIF classique suit l’évolution au cours du temps de la concentration de Rhodamine WT, injectée au centre de la colonne au début de l’expérience. La voie supplémentaire visualise un autre fluorophore, de la Fluorescéine répartie de manière homogène dans la colonne, permettant ainsi de créer un masque dynamique des billes. Grâce à ce montage expérimental, une étude paramétrique (taille, rétention des billes) a été menée. Un double effet des billes sur le mélange a ainsi été observé. D’une part, la présence d’une phase dispersée modifie les propriétés hydrodynamiques de l’écoulement : les régimes (Couette, Taylor Vortex Flow et Wavy Vortex Flow) sont d’autant plus déstabilisés que la rétention ou la taille des billes augmente. De plus un régime supplémentaire, inhabituel dans le cas du cylindre externe fixe, apparait, forcé par la phase dispersée : le régime Spiral Vortex Flow, dans lequel le mélange est très efficace. D’autre part, une influence propre des billes sur le mélange a été mise en évidence, en fonction de leur taille et de leur concentration. Ces deux effets se combinent pour expliquer une forte augmentation du mélange en présence de la phase dispersée. Les mécanismes physiques liés à ces résultats sont ensuite discutés, et leur influence relative est comparée. Enfin, le rôle du mélange local sur le coefficient de dispersion global, paramètre classiquement utilisé en génie chimique afin de prédire les performances des colonnes d’extraction, est discuté. / In the scope of the nuclear fuel reprocessing, Taylor-Couette flows between two concentric cylinders (the inner one in rotation and the outer one at rest) are used at laboratory scale to study the performances of new liquid/liquid extraction processes. Separation performances are strongly related to the mixing efficiency, the quantification of the latter is therefore of prime importance. A previous Ph.D. work has related the mixing properties to the hydrodynamics parameters in single-phase flow, using both experimental and numerical investigations. The Reynolds number, flow state and vortices height (axial wavelength) impacts were thus highlighted. This Ph.D. work extends the previous study to two-phase configurations. For experimental simplification, and to avoid droplets coalescence or breakage, spherical solid particles of PMMA from 800 µm to 1500 µm diameter are used to model rigid droplets. These beads are suspended in an aqueous solution of dimethyl sulfoxide (DMSO) and potassium Thiocyanate (KSCN). The experimental setup uses coupled Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF) to access simultaneously the hydrodynamic and the mixing properties. Although the two phases are carefully chosen to match in density and refractive index, these precautions are not sufficient to ensure a good measurement quality, and a second PLIF channel is added to increase the precision of the mixing quantification. The classical PLIF channel monitors the evolution of Rhodamine WT concentration, while the additional PLIF channel is used to map a Fluorescein dye, which is homogeneously concentrated inside the gap. This way, a dynamic mask of the bead positions can be created and used to correct the Rhodamine WT raw images. Thanks to this experimental setup, a parametric study of the particles size and concentration is achieved. A double effect of the dispersed phase is evidenced. On one hand, the particles affect the flow hydrodynamic properties : the more the particles size and concentration grows, the more the studied flow regimes (Couette, Taylor Vortex Flow and Wavy Vortex Flow) are destabilized. In addition, a new flow state appears in presence of a dispersed phase, that is unusual in the configuration we use where the outer cylinder is at rest. This Spiral Vortex Flow is characterized by an enhanced mixing. On the other hand, for given hydrodynamic properties and depending on the particles size and concentration, a specific effect of the particles on mixing is highlighted. Both the “hydrodynamic” and “intrinsic“ effects are responsible for the significant increase of the global mixing observed in two-phase configuration. Possible physical mechanisms are proposed to analyze these results, and their relative influence is compared. At last, an attempt is made to relate the local mixing properties to a global dispersion coefficient of the flow, data commonly used in chemical engineering to predict the performances of extraction columns.

No description available.

The main focus of this work is to investigate thermal performance of self-contained drum motor drive systems (SCDMDS). All components of a SCDMDS are contained inside a rotating drum including the electric motor, gearbox, and an air/oil multiphase flow. A considerable amount of heat is generated within the SCDMDS from various sources, namely, the electric motor losses, the oil viscous dissipation and the gearbox losses. In meantime, a limited amount of heat is dissipated through the surface of the rotating drum and the side flanges. Therefore, a SCDMDS sometimes encounters a serious overheating problem, which often results in electric motor failure. The different heat generation and dissipation mechanisms as well as the two-phase flow within the SCDMDS have been studied experimentally and numerically under different operating parameters, namely, the oil level (OV), the drum rotational speed (N), the torque (ζ), the number of motor poles (n) and the electric motor dimensions. The effects of rubber lagging material and thickness as well as the use of rubber belts have been investigated as well. The numerical part of the present study has been carried out using Ansys-CFX and was validated using experimental data. Results showed that the optimum oil level (OV) for the best thermal performance is about 65%. The increase in the rotational speed (N) enhanced the heat transfer within the SCDMDS due to the improved oil splashing. Viscous dissipation (VD) between the motor stator and the rotating drive drum was found to be almost negligible. However, oil viscous dissipation within the gap between the motor rotor and stator was found to have an important effect on the thermal performance. An analytical model has been developed and implemented using MATLAB to estimate VD within the motor. The losses from the gearbox were studied experimentally and numerically considering planetary and co-axial gear trains. The numerical work was carried out using the KISSsoft and KISSsys software. Results showed that the increase in the drum rotational speed (N) or the drum torque (ζ) increased the gearbox losses. In the planetary gearbox, any increase in the OV increases the churning losses, however, the increase in OV increased the losses in the co-axial gearbox up to OV = 31% beyond which the losses remained constant. After understanding the complex interplay between all the heat generating and dissipating mechanisms within the SCDMDS, a number of possible modifications have been proposed in order to resolve the overheating problem. The effect of cooling the electric motor by using an axial air flow has been investigated. The effect of adding fins along the inner surface of the outer rotating drum has also been studied. Correlations of the various contributing mechanisms have been developed. Based on a thermal resistance network, a SCDMDS sizing and performance assessment computer software tool in the form of a digital twin (DT) has been developed. A user-friendly interface has been developed using Visual Basics and Excel. The DT estimates temperature distribution and the amount of heat generated and dissipated from each component within the SCDMDS and hence it identifies whether the case is considered safe to operate or overheating is expected. In overheated cases, the DT also suggests several possible modifications the user could consider to resolve the overheating problem. The DT has been validated against several experimental case studies and found to be very reasonably accurate. / Thesis / Doctor of Philosophy (PhD) / This study is focused on investigating heat transfer and fluid flow inside a self-contained drum motor drive system (SCDMDS). The problem of interest involves multiple heat sources enclosed inside a tight space of the rotating drum. There is an electrical motor, gearbox and a multiphase (oil/air) flow inside the rotating drum of the SCDMDS. In this thesis, experimental test rigs were constructed to investigate the effect of a number of operating and geometrical parameters. In addition, numerical analysis of the multiphase oil/air flow was carried out using Ansys - CFX. The KISSsoft and KISSsys software packages were used to determine various types of heat losses within the geartrain. Due to the presence of multiple heat sources inside a confined space, overheating of a number of SCDMDS has been reported. The overheating problem worsened even more when rubber lagging is used to increase traction between the drive drum and the belt. Several correlations have been developed for various heat transfer mechanisms governing the overall thermal performance of the entire SCDMDS. An analytical model (a digital twin) has been developed using Visual Basics and Excel. The digital twin estimates the temperature distribution and the amount of heat generated and dissipated inside the SCDMDS. It has been validated against many case studies provided by the industrial partner. The model identifies the possibility of overheating and provides the user with several potential modifications to resolve it. Hence, the model can be used as a performance and design tool of various models of SCDMDS.

No description available.

Lors du phénomène d’hémostase primaire ou de thrombose vasculaire, les plaquettes sanguines doivent adhérer aux parois afin de remplir leur fonction réparatrice ou pathologique. Pour ce faire, certains facteurs rhéologiques et hémodynamiques tels que l’hématocrite, le taux de cisaillement local et les contraintes de cisaillement pariétal, entrent en jeu afin d’exclure les plaquettes sanguines de l’écoulement principal et de les transporter vers le site endommagé ou enflammé. Cette exclusion pourrait aussi être influencée par l’agrégation de globules rouges qui est un phénomène naturel présent dans tout le système cardiovasculaire selon les conditions d’écoulement. La dérive de ces agrégats de globules rouges vers le centre des vaisseaux provoque la formation de réseaux d’agrégats dont la taille et la complexité varient en fonction de l’hématocrite et des conditions de cisaillement présentes. Il en résulte un écoulement bi-phasique avec un écoulement central composé d’agrégats de globules rouges avoisinés par une région moins dense en particules où l’on peut trouver des globules rouges singuliers, des petits rouleaux de globules rouges et une importante concentration en plaquettes et globules blancs. De ce fait, il est raisonnable de penser que plus la taille des agrégats qui occupent le centre du vaisseau augmente, plus il y aura de plaquettes expulsées vers les parois vasculaires. L'objectif du projet est de quantifier, in vitro, la migration des plaquettes sanguines en fonction du niveau d’agrégation érythrocytaire présent, en faisant varier l’hématocrite, le taux de cisaillement et en promouvant l’agrégation par l’ajout d’agents tels que le dextran à poids moléculaire élevé. Cependant, le comportement non Newtonien du sang dans un écoulement tubulaire peut être vu comme un facteur confondant à cause de son impact sur l’organisation spatiale des agrégats de globules rouges. De ce fait, les études ont été réalisées dans un appareil permettant de moduler, de façon homogène, la taille et la structure de ces agrégats et de quantifier ainsi leur effet sur la migration axiale des plaquettes. Du sang de porc anti coagulé a été ajusté à différents taux d’hématocrite et insérer dans un appareil à écoulement de Couette, à température ambiante. Les plaquettes sanguines, difficilement isolables in vitro sans en activer certains ligands membranaires, ont été remplacées par des fantômes en polystyrène ayant un revêtement de biotine. La quantification de la migration de ces fantômes de plaquettes a été réalisée grâce à l’utilisation de membranes biologiques fixées sur les parois internes de l’entrefer du rhéomètre de Couette. Ces membranes ont un revêtement de streptavidine assurant une très forte affinité d’adhésion avec les microparticules biotynilées. À 40% d’hématocrite, à un cisaillement de 2 s-1, 566 ± 53 microparticules ont été comptées pour un protocole préétabli avec du sang non agrégeant, comparativement à 1077 ± 229 pour du sang normal et 1568 ± 131 pour du sang hyper agrégeant. Les résultats obtenus suggèrent une nette participation de l’agrégation érythrocytaire sur le transport des fantômes de plaquettes puisque l’adhésion de ces derniers à la paroi du rhéomètre de Couette augmente de façon quasi exponentielle selon le niveau d’agrégation présent. / During the primary hemostatis or thrombosis phenomenon, the human blood platelets must adhere to the vascular wall in order for them to perform their repairing or pathological function. To do so, certain rheological and hemodynamic factors such as the hematocrit, local shear rate and the wall shear stress, must come into play to exclude blood platelets from the main blood stream and transport them to the vicinity of the damaged or inflamed site. This exclusion could also be influenced by red blood cell aggregation which is a natural process present throughout the entire cardiovascular system under certain flow conditions. The displacement of these rouleaux of red blood cells towards the centre of the vessel induces the formation of 3D networks of aggregates whose size and complexity vary as a function of the hematocrit and the shearing conditions present. It results in a two phase flow with an inner core composed of red blood cell aggregates surrounded by single red blood cells or small aggregates and large numbers of white blood cells and platelets. It is therefore reasonable to believe that the larger the inner core becomes, the more platelets will be expulsed towards the vascular wall. The objective of the study was to quantify, in vitro, the lateral migration of blood platelets as a function of the level of red blood cell aggregation present, by changing the hematocrit, the shear rate and by promoting red blood cell aggregation with the use of agents such as high molecular weight dextran. However, the non Newtonian behavior of blood in tube flow can be seen as a confounding factor to the understanding of the spatial organization of the red blood cell aggregates. In this study, whole blood was circulated in a simple shear flow apparatus, which allowed to homogeneously modulate the red blood cell aggregate sizes and structure, and quantify their effect on the axial migration of blood platelets. Anticoagulated porcine bloods were adjusted to different hematocrits and inserted into a Couette flow apparatus, at room temperature. Blood platelets, difficult to isolate in vitro without activating in a non reproducible manner specific membrane ligands, were replaced with biotin coated fluorescent polystyrene beads. The quantification of the migration of these platelet ghosts was conducted with the use of biological membranes fixed on the interior walls of the Couette apparatus. These streptavidin coated membranes ensure a strong adhesive affinity with the biotynilated beads. At 40% hematocrit and at a shear of 2 s-1, 566 ± 53 micro particles were counted for non aggregated erythrocytes, 1077 ± 229 for aggregating red blood cells and 1568 ± 131 for hyper aggregating blood. The results obtained suggest a strong participation of the red blood cell aggregation on the transport of platelet ghosts since the number of ghost cells fixed on the wall of the Couette rheometer increases almost exponentially with the level of aggregation present.

EDF exploite sur son parc de production de nombreuses machines électriques tournantes. Les contraintes thermiques subies par celles-ci engendrent des échauffements locaux qui nuisent à leur intégrité. Le présent travail contribue à fournir des méthodes de calcul adaptées à la détection et à la localisation des points chauds. Il participe à améliorer la compréhension des écoulements en rotation et leurs effets sur les transferts thermiques. Plusieurs dispositifs expérimentaux, de complexité ascendante, ont été utilisés pour comprendre et valider les simulations numériques. Une première étude sur une marche descendante (demi-pôle) parcourue par un jet de paroi non-confiné a mis en avant des différences par rapport à un jet confiné ; ces deux cas existent dans un alternateur. Une seconde étude menée sur une cavité tournante confinée a analysé l’impact d’un écoulement de Taylor-Couette-Poiseuille sur la température et la position des points chauds créés, en balayant l’ensemble des régimes d’écoulement. Ces études ont mis en exergue une première méthode de calcul fiable, fondée sur l’étude numérique CHT. Une autre méthode, basée sur la FEM couplée à une méthode inverse, a été testée sur une maquette d’alternateur hydraulique afin de pallier aux temps de calcul longs de la première. Cette méthodologie remonte aux coefficients d’échanges convectifs numériques à partir des mesures du champ thermique du rotor, mais n’est envisageable que lorsque l’on dispose de données expérimentales suffisantes. Ces travaux ont aussi mis en évidence de nouvelles techniques de mesures sans contact, comme l’utilisation d’un pyromètre à haute fréquence pour la mesure de température sur des machines tournantes. / EDF operates a large number of electrical rotating machines in its electricity generation capacity. Thermal stresses which affect them can cause local heating, sufficient to damage their integrity. The present work contributes to provide methodologies for detecting hot spots in these machines, better understanding the topology of rotating flows and identifying their effects on heat transfer. Several experimental scale model were used by increasing their complexity to understand and validate the numerical simulations. A first study on a turbulent wall jet over a non-confined backward-facing step (half-pole hydrogenerator) notes significant differences compared to results from confined case : both of them are present in an hydrogenerator. A second study was done on a small confined rotating scale model to determinate the effects of a Taylor-Couette-Poiseuille on temperature distribution and position of hot spots on the heated rotor, by studying the overall flow regimes flow. These studies have helped to obtain a reliable method based on conjugate heat transfer (CHT) simulations. Another method, based on FEM coupled with the use of an inverse method, has been studied on a large model of hydraulic generator so as to solve the computation time issue of the first methodology. It numerically calculates the convective heat transfer from temperature measurements, but depends on the availability of experimental data. This work has also developped new no-contact measurement techniques as the use of a high-frequency pyrometer which can be applied on rotating machines for monitoring temperature.

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.