<p>This dissertation covers a computational investigation into hypersonic flight vehicle geometric imperfections, with a focus on wing-elevon-cove configurations. The primary region of focus for the overall research was the cove region at the juncture of the main wing element and the elevon. This region is associated with the shock-wave/boundary-layer interaction produced by the control surface deflection. There also exists a centrifugal instability at the cove, due to streamline curvature, which is associated with the production of Görtler vortices. The content includes three projects revolving around hypersonic wing-elevon-cove flows. These flows were computed with improved delayed detached-eddy simulation.</p> <p><br></p> <p>The first project was a computational investigation simulating the NASA experimental study done by W.D. Deveikis and W. Bartlett in 1978. This experiment consisted of hypersonic high Reynolds number wind tunnel tests for a shuttle-type reentry vehicle. The computational aerothermodynamic surface loadings for this project were compared to the experimental published data. Grounded with the agreement with mean surface data, this project expanded on the topics explored in the experimental study to include topics such as flow visualization and statistical analysis. The second and third project are extensions of this work and were done in collaboration with Purdue University and the University of Tennessee Space Institute (UTSI). A swept wing-elevon-cove model was designed by Carson Lay, of Purdue University, and is currently being employed in ongoing experiments in the Purdue Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) and at the Tennessee Aerothermodynamics Laboratory (TALon). A computational investigation on hypersonic high Reynolds number wing-elevon-cove flows was conducted with this model, where both corresponding experimental facility conditions were employed. At this time, the experimental data are limited; however, future experimental and computational collaboration is expected.</p> <p><br></p> <p>The motivation behind this research was to expand the knowledge on hypersonic wing-elevon-cove flows, gap heating, and the low-frequency unsteadiness in shock-wave/boundary-layer interactions. Therefore, the intended goal of this work was to provide an accurate characterization of the three hypersonic wing-elevon-cove flows. This was accomplished by using computational data to produce flowfield visualizations, analyze aerothermodynamic loadings, and conduct statistical flow analyses. The results on the three hypersonic wing-elevon-cove computations are presented, analyzed, and discussed throughout this dissertation.</p>

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Thesis (PhD) -- Stellenbosch University, 2014. / ENGLISH ABSTRACT: With increasing environmental concerns and the drive for a greener economy comes an increased desire to improve turbine engine fuel efficiency and reduce emissions. Unfortunately weight reduction techniques used increase the blade loading, which in turn increases the losses. Non-axisymmetric endwall contouring is one of several techniques being investigated to reduce loss in a turbine. An investigation at Durham University produced a non-axisymmetric endwall design for a linear cascade. An adaption of the most promising endwall was investigated in an annular rotating test rig at the CSIR using steady state instrumentation. The current investigation extends those investigations into the unsteady time domain. Previous investigations found that a generic rotor endwall contour improved efficiency by controlling the endwall secondary flow vortex system in both a linear cascade and an annular 1½ stage rotating test turbine. The current research was aimed at determining if there were any unsteady effects introduced by the contoured endwall. The approach was unique in that it investigated the unsteady effects of an endwall contour originally designed for a linear cascade both experimentally and numerically at three incidence angles (positive, zero and negative to represent increased load, design load and decreased load respectively), the results of which are openly available. Unsteady experimental hotfilm results showed that the endwall contour made the velocity profile more radially uniform by reducing the strength of the endwall secondary flow vortex system. The fluctuations in the velocity were also reduced producing a more temporally uniform velocity profile. The FFT magnitude of the velocity at the blade passing frequency below midspan was also reduced. It was found that the reduction in the endwall secondary flow vortex system due to the contour increased with increasing loading. Numerical results showed that the oscillations in the flow were small and did not penetrate the boundary layer. The contoured rotor was forward and aft loaded when compared to the annular rotor, resulting in a weaker cross passage pressure gradient which allowed the endwall secondary flow vortex system to be less tightly wrapped. Numerical results did not show a significant difference in the oscillations observed in the annular and contoured rotor. A new objective function for use in the endwall optimisation process was proposed that acts as a proxy for efficiency, but is less prone to uncertainty in the results. When used on the current results it shows the same trend as efficiency. It remains to be used to design an endwall for full validation. / AFRIKAANSE OPSOMMING: Met ’n toenemende omgewingsbesorgdheid en die strewe na ’n groener ekonomie kom ’n toenemende behoefte om turbine enjin brandstofdoeltreffendheid te verbeter en vrystellings te verlaag. Ongelukkig het gewigsbesparingstegnieke wat gebruik is die lemlading verhoog, wat op sy beurt die verliese verhoog. Nie-assimmetriese endwandprofilering is een van verskeie tegnieke wat ondersoek word om verliese in ’n turbine te verminder. ’n Ondersoek by die Universiteit van Durham het ’n nie-assimmetriese endwandontwerp vir ’n lineêre kaskade gelewer. ’n Aanpassing van die mees belowende endwand is in ’n annulêre roterende toetsopstelling by die WNNR getoets, deur gebruik te maak van bestendige toestand instrumentasie. Die huidige ondersoek brei daardie ondersoeke uit na die nie-bestendige verwysingsraamwerk . Vorige ondersoeke het bevind dat die generiese rotor endwandprofiel doeltreffendheid verbeter as gevolg van die beheer van die endwand sekondêre vloei draaikolkstelsel in beide ’n lineêre kaskade sowel as ’n annulêre 1½ stadium roterende toetsturbine. Die huidige navorsing was daarop gemik om vas te stel of die endwandprofiel enige onbestendige effekte tot gevolg gehad het. Die benadering was uniek in die sin dat dit die onbestendige effekte ondersoek het van ’n endwandprofiel wat oorspronklik ontwerp is vir ’n lineêre kaskade beide eksperimenteel en numeries op drie invalsshoeke (positief, nul en negatief om onderskeidelik verhoogde lading, ontwerplading en verlaagde lading te verteenwoordig), waarvan die resultate algemeen beskikbaar is. Onbestendige eksperimentele warmfilm resultate het getoon dat die endwandprofiel die snelheidsprofiel meer radiaal uniform gemaak het deur die vermindering van die sterkte van die endwand sekondêre vloei werwelstelsel. Die skommelinge in die snelheid is ook verminder wat ’n meer tyduniforme snelheidsprofiel gelewer het. Die FFT (Fast Fourier Transform) grootte van die snelheid van die lem verbygaan frekwensie onder lem midbestek het ook verminder. Daar was bevind dat die vermindering in die endwand sekondêre vloei draaikolkstelsel as gevolg van die endwandprofiel toeneem met toenemende lading. Numeriese resultate het getoon dat die ossilasie in die vloei klein was en nie die grenslaag binnegedring het nie. Die rotor met gevormde wand het ’n voor- en agterlading gehad in vergelyking met die rotor met annulêre wand, wat tot ’n laer drukgradient dwarsop die vloeirigting gelei het, die endwand sekondêre vloei draaikolkstelsel minder beperk het. Numeriese resultate het nie ’n beduidende verskil in die ossilasies tussen die annulêre en gevormde rotorwand getoon nie. ’n Nuwe doelwitfunksie vir gebruik in die endwand optimersproses is voorgestel wat dien as ’n plaasvervanger vir doeltreffendheid, maar minder geneig is tot onsekerheid in die resultate. Wanneer dit gebruik word op die huidige resultate toon dit dieselfde tendens as doeltreffendheid. Dit moet nog gebruik word in die ontwerp van ’n endwand vir volledige bevestiging.

Highly loaded single stage gas turbines are being developed to minimize the turbine size and weight. Such highly loaded turbines often result in transonic flows, which imply a reduction in the efficiency due to the shock losses. The efficiency of a turbine is defined as the ratio between the real work extracted by the turbine rotor from the fluid and the maximum available enthalpy for a given pressure ratio. The relationship between turbine performance and design parameters is not yet fully comprehended due to the complexity of the flow field and unsteady flow field interactions. Hence, experimental and numerical studies remain necessary to understand the flow behavior at different conditions to advance the state of the art of the prediction tools. The purpose of the current research is to develop a methodology to determine the efficiency with an accuracy better than 1 % in a cooled and uncooled high pressure (HP) turbine tested in a short duration facility with a running time of about 0.4s. Such low level of uncertainty requires the accurate evaluation of a large number of quantities simultaneously, namely the mass flow of the mainstream, the coolant, and leakage flows properties, the inlet total pressure and total temperature, the stage exit total pressure, the shaft power, the mechanical losses and the heat transfer. The experimental work is carried out in a compression tube facility that allows testing the turbine at the temperature ratios, Re and Mach numbers encountered in real engines. The stage mass flow is controlled by a variable sonic throat located downstream of the stage exit. Due to the absence of any brake, the turbine power is converted into rotor acceleration. The accurate measurement of this acceleration as well as those of the inertia and the rotational speed provides the shaft power. The inertia of the whole rotating assembly was accurately determined by accelerating and decelerating the shaft with a known energy. The mass-flow is derived from the measured turbine inlet total pressure and the vane sonic throat. The turbine sonic throat was evaluated based on a zero-dimensional model of the turbine. The efficiencies of two transonic turbines are measured at design and off-design conditions. The turbine design efficiency is obtained as 91.8 %. The repeatability of the measurements for 95% confidence level varies between 0.3 % and 1.1 % of the efficiency depending on the test case. The theoretical uncertainty level of 1.2 % is mainly affected by the uncertainty of exit total pressure measurements. Additionally, the effect of vane trailing edge shock formations and their interactions with the rotor blade are analyzed based on the experimental data, the numerical tools and the loss correlations. The changes of blade and vane performances are measured at mid-span for three different pressure ratios which influence the vane and rotor shock mechanisms. Moreover, the unsteady forces on the rotor blades and the rotor disk were calculated by integration of the unsteady static pressure field on the rotor surface.

This project is intended to demonstrate the current state of knowledge in the prediction of the tonal and broadband noise radiation from a Sevik rotor. The rotor measurements were made at the Virginia Tech Stability Wind Tunnel. Details of the rotor noise and flow measurements were presented by Wisda et al(2014) and Murray et al(2015) respectively. This study presents predictions based on an approach detailed by Glegg et al(2015) for the broadband noise generated by a rotor in an inhomogeneous flow, and compares them to measured noise radiated from the rotor at prescribed observer locations. Discrepancies between the measurements and predictions led to comprehensive study of the flow in the wind tunnel and the discovery of a vortex upstream of the rotor at low advance ratios. The study presents results of RANS simulations. The static pressure and velocity profile in the domain near the rotor's tip gap region were compared to measurements obtained from a pressure port array and a PIV visualization of the rotor in the wind tunnel. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection

Cette étude vise à caractériser en soufflerie les mécanismes aérodynamiques à l’origine de la génération puis la transmission des fluctuations de bruit dans un modèle d’habitacle automobile. Le banc d’essai conçu en soufflerie anéchoïque consiste en un écoulement dont la vitesse incidente est modulée par un volet mobile, et qui par interaction avec une marche montante rayonne un bruit aéroacoustique transmis à travers une vitre dans un caisson anéchoïque. L’approche retenue consiste, pendant le temps de maniement du volet, à mesurer et relier le champ de vitesse externe mesuré à l’aide de la technique de vélocimétrie laser par images de particules (TR-PIV échantillonnée à 20 kHz) à la pression pariétale d’une part, puis au champ acoustique interne obtenu par transmission d’autre part. Des outils de corrélation spatio-temporelle sont alors utilisés pour mettre en évidence les zones de l’écoulement les plus corrélées avec les fluctuations d’énergie de la pression pariétale et celles du niveau de bruit intérieur. La fluctuation du chargement aérodynamique de la vitre sous la bulle de recirculation est logiquement liée à l’activité instationnaire de cette dernière, puis plus en aval, au lâcher tourbillonnaire. Quant au bruit transmis dans le modèle d’habitacle, il semble principalement lié aux fluctuations de vitesse dans la couche de cisaillement. Enfin, une procédure spécifique a permis d’évaluer le caractère quasi-stationnaire des variations temporelles des quantités fluctuantes ainsi que la réponse acoustique de la vitre. / This study aims at characterizing in a wind tunnel the aerodynamic mechanisms contributing to the generation and transmission of the noise fluctuations into a car interior model. The test bench designed in anechoic wind tunnel consists of a flow whose incoming flow velocity is modulated by a mobile flap, and which by interaction with a forward-facing step radiates an aeroacoustic noise transmitted through a glass into an anechoic box. The adopted approach consists, during the flap handling time, in measuring and connecting the external velocity field measured using the Time-Resolved laser Particle Image Velocimetry technique (TR-PIV at sampling frequency 20 kHz) to the wall pressure on the one hand, and then to the internal acoustic field obtained by transmission on the other hand. Spatio-temporal correlation tools are then used to highlight the flow areas that are the most correlated with the energy fluctuations of the wall pressure and with those of the internal noise level. The fluctuation of the aerodynamic loading of the window under the recirculation bubble is logically related to the unsteady activity of the latter, then further downstream to the vortex stream. As for the noise transmitted into the cabin model, it seems mainly related to the speed fluctuations in the shear layer. Finally, a specific procedure allows to evaluate the quasi-steady nature of the temporal variations of the fluctuating quantities, as well as the acoustic response of the window.

These thesis review some recent results on the construction of very high order multidimensional upwind schemes for the solution of steady and unsteady conservation laws on unstructured triangular grids. We also consider the extension to the approximation of solutions to conservation laws containing second order dissipative terms. To build this high order schemes we use a sub-triangulation of the triangular Pk elements where we apply the distribution used for a P1 element. This manuscript is divided in two parts. The first part is dedicated to the design of the high order schemes for scalar equations and focus more on the theoretical design of the schemes. The second part deals with the extension to system of equations, in particular we will compare the performances of 2nd, 3rd and 4th order schemes. The first part is subdivided in four chapters: The aim of the second chapter is to present the multidimensional upwind residual distributive schmes and to explain what was the status of their development at the beginning of this work. The third chapter is dedicated to the first contribution: the design of 3rd and 4th order quasi non-oscillatory schemes. The fourth chapter is composed of two parts: We start by understanding the non-uniformity of the accuracy of the 2nd order schemes for advection-diffusion problem. To solve this issue we use a Finite Element hybridisation. This deep study of the 2nd order scheme is used as a basis to design a 3rd order scheme for advection-diffusion. Finally, in the fifth chapter we extend the high order quasi non-oscillatory schemes to unsteady problems. In the second part, we extend the schemes of the first part to systems of equations as follows: The sixth chapter deals with the extension to steady systems of hyperbolic equations. In particular, we discuss how to solve some issues such as boundary conditions and the discretisation of curved geometries. Then, we look at the performance of 2nd and 3rd order schemes on viscous flow. Finally, we test the space-time schemes on several test cases. In particular, we will test the monotonicity of the space-time non-oscillatory schemes and we apply residual distributive schemes to acoustic problems.

The design parameters axial gap and stator count of highpressure turbine stages are evaluated numerically towards theirinfluence on the unsteady aerodynamic excitation of rotorblades. Of particular interest is if and how unsteadyaerodynamic considerations in the design could reduce the riskofhigh cycle fatigue (HCF) failures of the turbine rotor. A well-documented 2D/Q3D non-linear unsteady code (UNSFLO)is chosen to perform the stage flow analyses. The evaluatedresults are interpreted as aerodynamic excitation mechanisms onstream sheets neglecting 3D effects. Mesh studies andvalidations against measurements and 3D computations provideconfidence in the unsteady results. Three test cases areanalysed. First, a typical aero-engine high pressure turbinestage is studied at subsonic and transonic flow conditions,with four axial gaps (37% - 52% of cax,rotor) and two statorconfigurations (43 and 70 NGV). Operating conditions areaccording to the resonant conditions of the blades used inaccompanied experiments. Second, a subsonic high pressureturbine intended to drive the turbopump of a rocket engine isinvestigated. Four axial gap variations (10% - 29% ofcax,rotor) and three stator geometry variations are analysed toextend and generalise the findings made on the first study.Third, a transonic low pressure turbine rotor, known as theInternational Standard Configuration 11, has been modelled tocompute the unsteady flow due to blade vibration and comparedto available experimental data. Excitation mechanisms due to shock, potential waves andwakes are described and related to the work found in the openliterature. The strength of shock excitation leads to increasedpressure excitation levels by a factor 2 to 3 compared tosubsonic cases. Potential excitations are of a typical wavetype in all cases, differences in the propagation direction ofthe waves and the wave reflection pattern in the rotor passagelead to modifications in the time and space resolved unsteadypressures on the blade surface. The significant influence ofoperating conditions, axial gap and stator size on the wavepropagation is discussed on chosen cases. The wake influence onthe rotorblade unsteady pressure is small in the presentevaluations, which is explicitly demonstrated on the turbopumpturbine by a parametric study of wake and potentialexcitations. A reduction in stator size (towards R≈1)reduces the potential excitation part so that wake andpotential excitation approach in their magnitude. Potentials to reduce the risk of HCF excitation in transonicflow are the decrease of stator exit Mach number and themodification of temporal relations between shock and potentialexcitation events. A similar temporal tuning of wake excitationto shock excitation appears not efficient because of the smallwake excitation contribution. The increase of axial gap doesnot necessarily decrease the shock excitation strength neitherdoes the decrease of vane size because the shock excitation mayremain strong even behind a smaller stator. The evaluation ofthe aerodynamic excitation towards a HCF risk reduction shouldonly be done with regard to the excited mode shape, asdemonstrated with parametric studies of the mode shapeinfluence on excitability. <b>Keywords:</b>Aeroelasticity, Aerodynamics, Stator-RotorInteraction, Excitation Mechanism, Unsteady Flow Computation,Forced Response, High Cycle Fatigue, Turbomachinery,Gas-Turbine, High-Pressure Turbine, Turbopump, CFD, Design

The thesis deals with the development of a new residual error estimator and adaptive algorithms based on the error estimator for steady and unsteady fluid flows in a finite volume framework. The aposteriori residual error estimator referred to as R--parameter, is a measure of the local truncation error and is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. A detailed and systematic study of the R--parameter on linear and non--linear hyperbolic problems, involving continuous flows and discontinuities is performed. Simple theoretical analysis and extensive numerical experiments are performed to establish the fact that the R--parameter is a valid estimator at limiter--free continuous flow regions, but is rendered inconsistent at discontinuities and with limiting. The R--parameter is demonstrated to work equally well on different mesh topologies and detects the sources of error, making it an ideal choice to drive adaptive strategies. The theory of the error estimation is also extended for unsteady flows, both on static and moving meshes. The R--parameter can be computed with a low computational overhead and is easily incorporated into existing finite volume codes with minimal effort. Adaptive refinement algorithms for steady flows are devised employing the residual error estimator. For continuous flows devoid of limiters, a purely R--parameter based adaptive algorithm is designed. A threshold length scale derived from the estimator determines the refinement/derefinement criterion, leading to a self--evolving adaptive algorithm devoid of heuristic parameters. On the other hand, for compressible flows involving discontinuities and limiting, a hybrid adaptive algorithm is proposed. In this hybrid algorithm, error indicators are used to flag regions for refinement, while regions of derefinement are detected using the R--parameter. Two variants of these algorithms, which differ in the computation of the threshold length scale are proposed. The disparate behaviour of the R--parameter for continuous and discontinuous flows is exploited to design a simple and effective discontinuity detector for compressible flows. For time--dependent flow problems, a two--step methodology is proposed for adaptive grid refinement. In the first step, the ``best" mesh at any given time instant is determined. The second step involves predicting the evolution of flow phenomena over a period of time and refines regions into which the flow features would progress into. The latter step is implemented using a geometric--based ``Refinement Level Projection" strategy which guarantees that the flow features remain in adapted zones between successive adaptive cycles and hence uniform solution accuracy. Several numerical experiments involving inviscid and viscous flows on different grid topologies are performed to illustrate the success of the proposed adaptive algorithms. Appendix 1 Candidate's response to the comments/queries of the examiners The author would like to thank the reviewers for their appreciation of the work embodied in the thesis and for their comments. The clarifications to the comments and queries posed in the reviews are summarized below. Referee 1 Q: The example of mesh refinement for RANS solution with shock was performed with isotropic mesh, while the author claims that it is appropriate with anisotropic mesh. If this is the case, why did he not demonstrate that ? As the author knows well, in the case of full 3--D configuration, isotropic adaptation will lead to substantial grid points. The large mesh will hamper timely turnaround time of simulation. Therefore it would be a significant contribution to the aero community if this point is investigated at a later date. Response: The author is of the view that for most practical situations, a pragmatic approach to mesh adaptation for RANS computations would merely involve generating a viscous padding of adequate fineness around the body and allowing for grid adaptation only in the outer potential region. Of course, this method would allow for grid adaptation in the outer layers of viscous padding only to the extent the smoothness criterion is satisfied while adapting the grids in the potential region. This completely obviates point addition to the wall (CAD surface) and there by avoids all complexities (like loss in automation) resulting from the interaction with the surface modeler while adding point on the wall. This method is expected to do well for attached flows and mildly separated flows. This method is expected to do well even for problems involving shock - boundary layer interaction, owing to the fact that the shock is normal to the wall surface (recall, a flow aligned grid is ideal to capture such shocks), as long as the interaction does not result in a massive separation. This approach has already been demonstrated in section 4.5.3 where in adaptive high-lift computations have been performed. Isotropic adaptation retains the goodness of the zero level grid and therefore the robustness of the solver does not suffer through successive levels of grid adaptation. This procedure may result in large number of volumes. On the other hand, the anisotropic refinement may result in significantly less number of volumes, but the mesh quality may have badly degenerated during successive levels of adaptation leading to difficulties in convergence. Therefore, the choice of either of these strategies is effectively dictated by requirements on grid quality and grid size. Also, it is generally understood that building tools for anisotropic adaptation are more complicated as compared to those required for isotropic adaptation, while anisotropic refinement may not require point addition on the wall. Considering these facts, in the view of the author, this issue is an open issue and his personal preference would be to use isotropic refinement or a hybrid strategy employing a combination of these methodologies, particularly considering aspects of solution quality. Finally, in both the examples cited by the reviewer (sections 6.4.5 & 6.4.6) the objective was to demonstrate the efficacy of the new adaptive algorithm (using error indicators and the residual estimator), rather than evaluating the pros & cons of isotropic and anisotropic refinement strategies. In the sections cited above, the author has merely highlighted the advantages of the refinement strategies in specific context of the problem considered and these statements need not be considered as general. Referee 2 Q: For convection problems, a good error estimator must be able to distinguish between locally generated error and convected error. The thesis says the residual error estimator is able to do this and some numerical evidence is presented, but can the candidate comment how the estimator is able to achieve this ? Response: The ultimate aim of any AMR strategy is to reduce the global error. The residual error estimator proposed in this work measures the local truncation error. It has been shown in the context of a linear convective equation that the global error in a cell consists of two parts--the locally generated error in the cell (which is the R--parameter) and the local error transported from other cells in the domain. Either of these errors are dependent on the local error itself and any algorithm that reduces the local truncation error (sources of error) will reduce the global error in the domain. This conclusion is supported by the test case of isentropic flow past an airfoil (Chapter 3, C, Pg 79), where refinement based on the R--parameter leads to lower global error levels than a global error based refinement itself. Q: While analysing the R--parameter in Section 3.3, the operator δ2 is missing. Response: The analysis in Section 3.3 is based on Eq.(3.3) (Pg 58) which provides the local truncation error. As can be seen from Eq.(3.14), the LHS represents the discrete operator acting on the numerical solution (which is zero) and the first term on the RHS is the exact operator acting on the numerical solution (which is I[u]). Consequently the truncation terms T1 and T2 contribute to the truncation error R1 . However, from the viewpoint of computing the error estimate on a discretised domain, we need to replace the exact operator I by a higher order discrete operator δ2 . This gives the R-parameter, which has contributions from R1 as well as discretisation errors due to the higher order operator, R2 . When the latter is negligible compared to the former, the R--parameter is an estimate of the local truncation error. The truncation error depends on the accuracy of the reconstruction procedure used in obtaining the numerical solution and hence on the discrete operator δ1. On very similar lines, it can be shown that operator δ2 leads to a formal second order accuracy and this operator is only required in computing the residual error estimate. Q: What does the phrase "exact derivatives of the numerical solution" mean ? Response: This statement exemplifies the fact that the numerical solution is the exact solution to the modified partial differential equation and that the truncation terms T1 and T2 that constitute the R--parameter are functions of the derivatives of this numerical solution. Q: For the operator δ2 quadratic reconstruction is employed. Is the exact or numerical flux function used ? Response: The operator δ2 is a higher order discrete approximation to the exact operator I. Therefore, a quadratic polynomial with a three--point Gauss quadrature has been used in the error estimation procedure. Error estimation does not involve issues with convergence associated with the flow solver and therefore an exact flux function has been employed with the δ2 operator. Nevertheless, it is also possible to use the same numerical flux function as employed in the flow solver for error estimation also. Q: The same stencil of grid points is used for the solution update and the error estimation. Does this not lead to an increased stencil size ? Response: In comparison to reconstruction using higher degree polynomials such as cubic and quartic reconstruction, quadratic reconstruction involves only a smaller stencil of points consisting of the node--sharing neighbours of a cell. The use of such a support stencil is sufficient for linear reconstruction also and adds to the robustness of the flow solver, although a linear reconstruction can, in principle, work with a smaller support stencil. A possible alternative to using quadratic reconstruction (and hence a slightly larger stencil) is to adopt a Defect Correction strategy to obtain derivatives to higher order accuracy and needs to be explored in detail. Q: How is the R--parameter computed for viscous flows ? Response: The computation of the R--parameter for viscous flows is on the same lines as for inviscid flows. The gradients needed for viscous flux computation at the face centers are obtained using quadratic reconstruction. The procedure for calculation of the R--parameter for steady flows (both inviscid and viscous) is the step--by--step algorithm in Section 3.5. Q: In some cases, regions ahead of the shock show no coarsening. Response: The adaptive algorithm proposed in this work does not allow for coarsening of the initial mesh, and regions ahead of the shock remain unaffected (because of uniform flow) at all levels of refinement. Q: Do adaptation strategies terminate automatically atleast for steady flows ? Response: The adaptation strategies (RAS and HAS) must, in principle by virtue of construction of the algorithm, automatically terminate for steady flows. In the HAS algorithms though, there are certain heuristic criteria for termination of refinement especially at shocks/turbulent boundary layers. In this work, a maximum of four cycles of refinement/derefinement have only been carried out and therefore an automatic termination of the adaptive strategies were no studied. Q: How do residual--based adaptive strategies compare and contrast with adjoint--based approaches which are now becoming popular for goal--oriented adaptation ? Adjoint--based methods involve solution to the adjoint problem in addition to solving the primal problem, which represents a substantial computational cost. A timing study for a typical 3D problem[2] indicates that the solution of the adjoint problem (which needs the computation of the Jacobian and sensitivities of the functional) could require as much as one--half of the total time needed to compute the flow solution. On the contrary, R--parameter based refinement involves no additional information than that required by the flow solver and is roughly equivalent to one explicit iteration of the flow solver (Section 3.5.1). For practical 3--D applications, adjoint--based approaches will lead to a prohibitively high cost, and more so for dynamic adaptation. This is also exemplified by the fact that there has been only few recent works on 3D adaptive computations based on adjoint error estimation (which consider only inviscid flows)[1,2]. Goal--oriented adaptation involves reducing the error in some functional of interest. This can be achieved within the framework of R--parameter based adaptation, by introducing additional termination criteria based on integrated quantities. Within an automated adaptation loop, such an algorithm would terminate when the integrated quantities do not change appreciably with refinement levels. This is in contrast to the adjoint--based approach which strives to reduce the error in the functional below a certain threshold. Considering the fact that reducing the residual leads to reducing the global error itself, the R--parameter based adaptive algorithm would also lead to accurate estimates of the integrated quantities (which depend on the numerical solution). This is also reflected in the fact that the R--parameter based adaptation for the three--element NHLP configuration predicts the lift and drag coefficients to reasonable accuracy, as shown in Section 4.5.3. The author is of the belief that the R--parameter based adaptive algorithm holds huge promise for adaptive simulations of flow past complex geometries, both in terms of computational cost and solution accuracy. This is exemplified by successful adaptive simulations of inviscid flow past ONERA M6 wing as well as a conventional missile configuration[3]. A more concrete comparison of the R--parameter based and adjoint--based approaches would involve systematically solving a set of problems by both approaches and has not been considered in this thesis. [1] Nemec and Aftosmis,``Adjoint error estimation and adaptive refinement for embedded--boundary cartesian meshes", AIAA Paper 2007--4187, 2007. [2] Wintzer, Nemec and Aftosmis,``Adjoint--based adaptive mesh refinement for sonic boom prediction", AIAA Paper 2008--6593, 2008. [3] Nikhil Shende, ``A general purpose flow solver for Euler equations", Ph.D. Thesis, Dept. of Aerospace Engg., Indian Institute of Science, 2005.