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Blank, Henrik. "Numerical methods for compressible and incompressible flow." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300125.
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Yang, Zhiyan. "Numerical simulation of incompressible and compressible flow." Thesis, University of Sheffield, 1989. http://etheses.whiterose.ac.uk/3485/.
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This thesis describes the development of a numerical solution procedure which is valid for both incompressible flow and compressible flow at any Mach number. Most of the available numerical methods are for incompressible flow or compressible flow only and density is usually chosen as a main dependent variable by almost all the methods developed for compressible flow. This practice limits the range of the applicability of these methods since density changes can be very small when Mach number is low. Even for high Mach number flows the existing time-dependent methods may be inefficient and costly when only the finial steady-state is of concern. The presently developed numerical solution procedure, which is based on the SIMPLE algorithm, solves the steady-state form of the Navier-stokes equations, and pressure is chosen as a main dependent variable since the pressure changes are always relatively larger than the density changes. This choice makes it possible that the same set of variables can be used for both incompressible and compressible flows. It is believed that Reynolds stress models would give better performance in some cases such as recirculating flow, highly swirling flow and so on where the widely used two equation k-e model performs poorly. Hence, a comparative study of a Reynolds stress model and the k-e model has been undertaken to assess their performance in the case of highly swirling flows in vortex throttles. At the same time the relative performance of different wall treatments is also presented. It is generally accepted that no boundary conditions should be specified at the outflow boundary when the outflow is supersonic, and all the variables can be obtained by extrapolation. However, it has been found that this established principle on the outflow boundary conditions is misleading, and at least one variable should be specified at the outflow boundary. It is also shown that the central differencing scheme should be used for the pressure gradient no matter whether it is subsonic or supersonic flow.
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Wadey, Philip David. "Goetler vortex instabilities of incompressible and compressible boundary layers." Thesis, University of Exeter, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253560.
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Baghaei, Masoud. "Research on fluidic oscillators under incompressible and compressible flow conditions." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669607.
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One of the main advantages of fluidic oscillators is that they do not have moving parts, which brings high reliability whenever being used in real applications. To use these devices in real applications, it is necessary to evaluate their performance, since each application requires a particular injected fluid momentum and frequency. In this PhD., the performance of a given fluidic oscillator is evaluated at different Reynolds numbers via a 3D-computational fluid dynamics (CFD) analysis under incompressible and compressible flow conditions. In the first stage, the net momentum applied to the incoming jet is compared with the dynamic maximum stagnation pressure in the mixing chamber, to the dynamic output mass flow, to the dynamic feedback channels mass flow, to the pressure acting to both feedback channels outlets, and to the mixing chamber inlet jet oscillation angle. A perfect correlation between these parameters is obtained, therefore indicating the oscillation is triggered by the pressure momentum term applied to the jet at the feedback channels outlets. The stagnation pressure fluctuations appearing at the mixing chamber inclined walls are responsible for the pressure momentum term acting at the feedback channels outlets, thus it is proved that the oscillations are pressure-driven. In the second stage, several performance parameters were numerically evaluated as a function of different internal modifications via using 3D-CFD simulations. The evaluation is based on studying the output mass flow frequency and amplitude whenever several internal geometry parameters are modified. The geometry modifications considered were the mixing chamber inlet and outlet widths, and the mixing chamber inlet and outlet wall inclination angles. The concept behind this is, to evaluate how much the fluidic oscillator internal dimensions affect the device's main characteristics, and to analyze which parts of the oscillator produce a higher impact on the fluidic oscillator output characteristics. For the different internal modifications, evaluated, special care is taken in studying the forces required to flip the jet. The entire study is performed for three different Reynolds numbers, 8711, 16034 and 32068. Among the conclusions reached it is to be highlighted that, for a given Reynolds number, modifying the internal shape affects the oscillation frequencies and amplitudes. Any oscillator internal modification generates a much relevant effect as Reynolds number increases. Under all conditions studied, it was observed that the fluidic oscillator is pressure-driven under incompressible flow conditions as discussed in the first and second stages. In the third stage, the feedback channel effect on the oscillator output mass flow frequency and amplitude under compressible flow conditions were evaluated. In order to bring light to this point, a set of three dimensional Direct Numerical Simulations under compressible flow conditions, are introduced in the present stage, four different feedback channel lengths and two inlet fluid velocities are considered. From the results obtained, it was observed that as the inlet velocity increases, the fluidic oscillator output mass flow frequency and amplitude increase. An increase of the feedback channel length decreases the output mass flow oscillating frequency. At high feedback channel lengths, the form of the main oscillation tends to disappear, the jet inside the mixing chamber simply actuates at high frequencies, for these cases, the mass flow and pressure signals are very scattered due to the pressure waves appearing on mixing chamber converging surfaces and both feedback channels at the same time. Once the FC length exceeds a certain threshold, the oscillation stops. Under compressible conditions, the oscillations are pressure-driven as previously stated for the incompressible cases. The forces due to the pressure are much stronger than the mass flow flowing along the feedback channels.El principal avantatge dels oscil·ladors fluídics es que no te parts mòbils, i això fa que sigui més fiable en aplicacions reals. Per tal d'aplicar aquests oscil·ladors en un cas concret, es necessari avaluar el seu comportament, doncs cada cas concret necessita una freqüència i quantitat de moviment donades. En el present doctorat s'ha analitzat mitjançant 3D-CFD, una configuració de oscil·lador fluídic per diferents números de Reynolds, diferents geometries internes i considerant el fluid com incompressible i compressible. Inicialment, la quantitat de moviment aplicada al jet entrant a la cambra de barreja, es comparada amb la pressió d'estancament dinàmica a les parets convergents de la cambra de barreja, amb el cabal màssic dinàmic que surt del actuador, amb el cabal màssic dinàmic que passa per els canals de realimentació, amb la pressió dinàmica que hi ha a la sortida dels canals de realimentació i amb el angle de oscil·lació del jet a l'entrada de la cambra de barreja. Tots aquests paràmetres es va veure que estaven correlacionats i això indicava que el origen de les oscil·lacions del jet era únic i era la pressió d'estancament a les parets convergents de la cambra de barreja, provant que les oscil·lacions son dirigides per gradients de pressió. Posteriorment es va fer el mateix tipus de estudi però modificant la amplada i angle de inclinació a l'entrada de la cambra de barreja i també modificant la amplada i angle de inclinació de les parets de sortida de la cambra de barreja. Aquestes quatre modificacions de la geometria interna es van fer per tres números de Reynolds diferents, 8711, 16034 i 32068. Entre les conclusions obtingudes cal destacar que, la freqüència i amplitud de oscil·lació del jet a la sortida del actuador pot ser modificada al variar les dimensions i angles interns de la cambra de barreja. Independentment del número de Reynolds estudiat i de la modificació interna considerada, es va comprovar que les oscil·lacions estaven dirigides per els gradients de pressió existents entre les dos sortides dels conductes de realimentació. L'efecte generat per qualsevol modificació interna era sempre més rellevant a números de Reynolds alts. En la tercera fase de la tesi el fluid es va considerar com a compressible subsònic, i es va avaluar els efectes de la modificació de la longitud dels canals de realimentació, sobre la freqüència i amplitud del flux que surt del oscil·lador. Quatre diferents longituds i dos números de Mach van ser avaluats. Al augmentar la longitud del canal de realimentació, la freqüència i amplitud de la oscil·lació disminueix, la oscil·lació tendeix a ser mes caòtica, apareixen altes freqüències que fan que el jet fluctuï en lloc de oscil·lar, de fet a partir de una certa longitud les oscil·lacions desapareixen i només hi han fluctuacions. Aquestes fluctuacions apareixen abans per elevats números de Mach. Les oscil·lacions son degudes a gradients de pressió, al igual que en el cas de fluid incompressible. De fet, per fluid compressible, el cabal màssic que passa per els canals de realimentació, juga un paper menys rellevant que en el cas de fluid incompressible.
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RONZANI, ERNESTO RIBEIRO. "NUMERICAL SOLUTION OF COMPRESSIBLE AND INCOMPRESSIBLE FLOW IN IRREGULAR GEOMETRIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1996. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=18648@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOEste trabalho propõe um método numérico de solução de escoamentos de fluidos compressíveis e incompressíveis a qualquer número de Mach em geometrias irregulares. Um sistema bidimensional de coordenadas curvilíneas não-ortogonais,coincidentes com os contornos físicos é utilizado. Os componentes cartesianos de velocidade são usados nas equações da quantidade de movimento e os covariantes na equação da continuidade. Seleciona-se a técnica de volumes finitos para discretizar as equações de conservação relacionadas aos princípios físicos, em regime permanente devido esta preservar a propriedade conservativa das equações e a sua con sistência física no processo numérico. Adota-se a configuração de malha co-localizada, avaliando-se todas as variáveis dependentes nos pontos centrais dos volumes são avaliados com esquemas Power-Law e Quick. Especial atenção é dada ao tratamento numérico das condições de contorno. O problema do acoplamento massa específica-pressão-velocidade é solucionado usando-se uma combinação das equações da continuidade, de quantidade de movimento linear e de uma equação de estado, gerando duas equações de correção da pressão. A primeira corrige a massa específica e a pressão, a segunda, o fluxo de massa e a velocidade. Propõe-se uma modificação da equação da correção da velocidade usando um termo de compensação do erro obtido na sua avaliação a fim de acelerar a convergência. Utilizam-se vários tipos de interpolação da massa específica na face, para minimizar as atenuações das variáveis, causadas pela falsa difusão. Para a solução das equações algébricas resultantes usa-se o algoritmo TDMA linha por linha e um processo de correção por blocos para acelerar a convergência. O método proposto é verificado em seis problemas testes, através da comparação com os resultados analíticos e numéricos disponíveis na literatura.
The present work consists in the development of a numerical method of solution of compressible and incompressible fluid flow for all speed in iregular geometries. A boundary-fitted two-dimensional nonorthogonal curvilinear coordinate systeam is utilized. The cartesian velocity components are the dependent variables in the momentum equations and covariant velocity components are used in the continuity equation. The finite-volume technique was selected to discretuze the steady-state physical phenomenon conservation equations, since this method keeps the conservative property of the equations and its physical consistency in the numerical process. A nonstaggered grid was employed, and all dependent variables are evaluated at the cell center points, which divides the physical domain. The convection-diffusion fluxes at the control volumes faces are evaluated with the Power Law and Quick shemes. Special attention is paid to the numerical treatment of boundary conditions. The problem of velocity-pressure-density coupling is solved using a combination of continuity, momentum equations and state equation resulting in two pressure correction equations. The first equation corrects the density and the pressure, the second equation corrects the mass flux and the velocity. A modification in the velocity correction equations is proposed using a compensationterm to accelerate the convergence. Several types of interpolation of the face density are used to reduce variable atenuations, caused by false diffusion. For the solution of the resulting algebric equations,the line-by-line TDMA algorith is used as well as a block-correction method to accelerate the convergence. The proposed method is verified on six test problems,by comparing the present results with analytical and numerical results avaiable in the literature.
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Kho, Cedric. "A unified formulation for mixed incompressible/compressible flows." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0002/MQ44017.pdf.
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Tain, Ludovic. "Compressor leading edges in incompressible and compressible flows." Thesis, University of Cambridge, 1998. https://www.repository.cam.ac.uk/handle/1810/272432.
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Chinarak, Theerarak. "Development of a time-based mass flow controller for compressible and incompressible fluids." Thesis, University of Bristol, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.503923.
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In this thesis a new type of Mass Flow Controller (MFC) is designed, constructed and used. Whilst existing MFCs rely on either pressure loss or temperature rise measurements to estimate and control flows, this new device is based on measuring time, which is more easily and accurately monitored. The device adopts the 'bucket and stopwatch' method to deliver specific and constant masses at pre-set time intervals. By alerting the time intervals, the mass flow is precisely controlled.
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Huber, Jamison Jared. "Numerical Simulations of Incompressible and Compressible Transitional Turbine Flows." Thesis, North Dakota State University, 2014. https://hdl.handle.net/10365/27124.
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Accurate and reliable turbulence and transition models are needed for prediction heating loads in the hot section of the turbine, and predicting aerodynamic losses when designing new blade profiles. Two dimensional compressible flow simulations were conducted at North Dakota State University on a first stage turbine vane design. Surface pressure results were compared with experimental data collected at the University of North Dakota. Results showed an under prediction of the surface pressure on the suction surface of the vane. Two and three dimensional compressible flow simulations were also conducted at NDSU on an incident tolerant blade design to look at the effect of incidence angle, Reynolds number, and turbulence intensity on transition. Results from these simulations were compared with experimental data collected at UND. The results show good agreement at higher Reynolds numbers with discrepancies being seen on the suction surface of the blade at lower Reynolds numbers.
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Pattinson, John. "A cut-cell, agglomerated-multigrid accelerated, Cartesian mesh method for compressible and incompressible flow." Pretoria : [s.n.]m, 2006. http://upetd.up.ac.za/thesis/available/etd-07052007-103047.
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Hendriana, Dena. "A parabolic quadrilateral finite element for compressible and incompressible flows." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50060.
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Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (leaves 156-161).
A unified finite element solution scheme for incompressible and compressible flows would be most attractive in engineering practice. The objective in this thesis was to work toward this goal. A 9-node finite element for compressible and incompressible 2-D flow solutions is presented. In the compressible flow formulation, a new high-order derivative artificial diffusion and a new shock capturing term are employed to stabilize the formulation. The new upwinding term is shown numerically to stabilize the formulation and an inf-sup test is performed assuming idealized 1-D conditions. The new shock capturing term performed well in the solutions of various judiciously selected numerical examples. Various flow problems in which the Mach numbers range from about 0.0005 to 6 are considered. The numerical results indicate that the element is applicable to a wide range of analysis problems. For incompressible flows, the element must satisfy the relevant inf-sup condition, and an element is used with parabolic velocity and linear pressure interpolations (the 9/4c-element). An upwinding term in a similar form as for the compressible flow solution is introduced to stabilize the formulation. A convergence study with the formulation to estimate the order of convergence is performed. In addition, a new low order element is presented. The new solution schemes for compressible and incompressible flows provide effective solution techniques and the study provides insight into the difficulties encountered in the development of a unified scheme for incompressible and compressible flows.
by Dena Hendriana.
Sc.D.
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Denk, Kerem. "Development Of A Pressure-based Solver For Both Incompressible And Compressible Flows." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609100/index.pdf.
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The aim of this study is to develop a two-dimensional pressure-based Navier-Stokes solver for
incompressible/compressible flows. Main variables are Cartesian velocity components, pressure
and temperature while density is linked to pressure via equation of state. Modified SIMPLE algorithm
is used to achieve pressure-velocity coupling. Finite Volume discretisation is performed
on non-orthogonal and boundary-fitted grids. Collocated variable arrangement is preferred because
of its advantage on staggered arrangement in non-orthogonal meshes. Face velocities are
calculated using Rhie-Chow momentum interpolation scheme to avoid pressure checkerboarding
effect. The solver is validated by solving a number of benchmark problems.
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Choudhary, Aniruddha. "Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/51169.
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Code verification is the process of ensuring, to the degree possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. In this work, techniques are presented for performing code verification of boundary conditions commonly used in compressible and incompressible Computational Fluid Dynamics (CFD) codes. Using a compressible CFD code, this study assesses the subsonic inflow (isentropic and fixed-mass), subsonic outflow, supersonic outflow, no-slip wall (adiabatic and isothermal), and inviscid slip-wall. The use of simplified curved surfaces is proposed for easier generation of manufactured solutions during the verification of certain boundary conditions involving many constraints. To perform rigorous code verification, general grids with mixed cell types at the verified boundary are used. A novel approach is introduced to determine manufactured solutions for boundary condition verification when the velocity-field is constrained to be divergence-free during the simulation in an incompressible CFD code. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is employed here for code verification of the major components of an open-source, multiphase flow code - MFIX. The presence of two-phase governing equations and a modified SIMPLE-based algorithm requiring divergence-free flows makes the selection of manufactured solutions more involved than for single-phase, compressible flows. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX.
In a CFD simulation, truncation error (TE) is the difference between the continuous governing equation and its discrete approximation. Since TE can be shown to be the local source term for the discretization error, TE is proposed as the criterion for determining which regions of the computational mesh should be refined/coarsened. For mesh modification, an error equidistribution strategy to perform r-refinement (i.e., mesh node relocation) is employed. This technique is applied to 1D and 2D inviscid flow problems where the exact (i.e.,
analytic) solution is available. For mesh adaptation based upon TE, about an order of magnitude improvement in discretization error levels is observed when compared with the uniform mesh.Ph. D.
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Dyne, Barry Richard. "Finite element analysis of incompressible, compressible, and chemically reacting flows, with an emphasis on the pressure approximation." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185789.
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A finite element numerical method is developed for the modelling of compressible flows with locally incompressible regions, which avoids the pressure oscillations frequently exhibited in these areas. Unification of the modelling of pressure in the finite element approximation of compressible and incompressible flows is investigated through the appropriate combinations of approximation spaces and integration schemes. The penalty method for incompressible flows is re-examined in the context of a slightly compressible fluid, yielding a formulation that is consistent for both the Navier-Stokes and Stokes equations, and providing an accurate method for calculation of pressure that is faster than the solution of a pressure Poisson equation. Extension of concepts from the reformulated penalty method to the compressible Navier-Stokes equations leads to an algorithm using piecewise constant density and pressure, with bilinear velocity and temperature. Further investigation shows that bilinear density with selective reduced integration also avoids pressure oscillations, while providing improved shock capture. Selective reduced integration of all terms related to compressibility is shown to be a key element in the avoidance of pressure oscillations. The identification of the isotropic component of the stress tensor as a compressibility term, not to be combined with viscous terms, is emphasized. Reduced integration of divergence terms is shown to yield conservation of mass on the element level as well as on the assembled level, whereas full integration conserves mass only on the assembled level. The compressible flow algorithm is coupled with a chemistry solver, for the study of chemically reacting flows, where an oscillation free flow solution is essential since unphysical oscillations may cause premature ignition. Computational efficiency is obtained by iterating a fluid flow step with frozen chemistry, and a chemical reaction step with frozen flow. The algorithm is applied to the study of the ram accelerator concept, a technique for accelerating a projectile in a tube to extremely high velocities by using a shock wave to initiate combustion. The viability of the ram accelerator is demonstrated through calculations at various velocities, pressures, and gas mixtures.
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Pontaza, Juan Pablo. "Least-squares variational principles and the finite element method: theory, formulations, and models for solid and fluid mechanics." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/288.
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We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite elementmodelalways yields a discrete system ofequations witha symmetric positive definite coeffcientmatrix.These attributes, amongst manyothers highlightedand detailed in this work, allow the developmentofrobust andeffcient finite elementmodels for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.
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Pretorius, Johannes Jacobus. "A network approach for the prediction of flow and flow splits within a gas turbine combustor." Diss., University of Pretoria, 2005. http://hdl.handle.net/2263/26712.
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The modern gas turbine engine industry needs a simpler and faster method to facilitate the design of gas turbine combustors due to the enormous costs of experimental test rigging and detailed computational fluid dynamics (CFD) simulations. Therefore, in the initial design phase, a couple of preliminary designs are conducted to establish initial values for combustor performance and geometric characteristics. In these preliminary designs, various one-dimensional models using analytical and empirical formulations may be used. One of the disadvantages of existing models is that they are typically geometric dependant, i.e. they apply only to the geometry they are derived for. Therefore the need for a more versatile design tool exists. In this work, which constitutes the first step in the development of such a versatile design tool, a single equation-set network simulation model to describe both steady state compressible and incompressible isothermal flow is developed. The continuity and momentum equations are solved through a hybrid type network model analogy which makes use of the SIMPLE pressure correction methodology. The code has the capability to efficiently compute flow through elements where the loss factor K is highly flow dependant and accurately describes variable area duct flow in the case of incompressible flow. The latter includes ducts with discontinuously varying flow sectional areas. Proper treatment of flow related non-linearities, such as flow friction, is facilitated in a natural manner in the proposed methodology. The proposed network method is implemented into a Windows based simulation package with a user interface. The ability of the proposed method to accurately model both compressible and incompressible flow is demonstrated through the analyses of a number of benchmark problems. It will be shown that the proposed methodology yields similar or improved results as compared to other’s work. The proposed method is applied to a research combustor to solve for isothermal flows and flow splits. The predicted flows were in relatively close agreement with measured data as well as detailed CFD analysis.Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2005.
Mechanical and Aeronautical Engineering
unrestricted
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Torbjörnsson, Carl-Adam. "Modelling of a Variable Venturi in a Heavy Duty Diesel Engine." Thesis, Linköping University, Department of Electrical Engineering, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-1531.
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The objectives in this thesis are to present a model of a variable venturi in an exhaust gas recirculation (EGR) system located in a heavy duty diesel engine. A new legislation called EURO~4 will come into force in 2005 which affects truck development and it will require an On-Board Diagnostic system in the truck. If model based diagnostic systems are to be used, one of the advantages is that the system performance will increase if a model of a variable venturi is used.
Three models with different complexity are compared in ten different experiments. The experiments are performed in a steady flow rig at different percentage of EGR gases and venturi areas. The model predicts the mass flow through the venturi. The results show that the first model with fewer simplifications performs better and has fewer errors than the other two models. The simplifications that differ between the models are initial velocity before the venturi and the assumption of incompressible flow.
The model that shows the best result is not proposed by known literature in this area of knowledge and technology. This thesis shows that further studies and work on this model, the model with fewer simplifications, can be advantageous.
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Ahmed, Aqeel. "LES of atomization and cavitation for fuel injectors." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMR048/document.
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Cette thèse présente la Simulation des Grandes Echelles (LES) de l’injection, de la pulvérisation et de la cavitation dans un injecteur pour les applications liées aux moteurs à combustion interne. Pour la modélisation de l’atomisation, on utilise le modèle ELSA (Eulerian Lagrangian Spray Atomization). Le modèle résout la fraction volumique du combustible liquide ainsi que la densité de surface d’interface liquide-gaz pour décrire le processus complet d’atomisation. Dans cette thèse, l’écoulement à l’intérieur de l’injecteur est également pris en compte pour une étude ultérieure de l’atomisation. L’étude présente l’application du modèle ELSA à un injecteur Diesel typique, à la fois dans le contexte de RANS et de LES.Le modèle est validé à l’aide de données expérimentales disponibles dans Engine Combustion Network (ECN). Le modèle ELSA, qui est normalement conçu pour les interfaces diffuses (non résolues), lorsque l’emplacement exact de l’interface liquide-gaz n’est pas pris en compte, est étendu pour fonctionner avec une formulation de type Volume of Fluid (VOF) de flux à deux phases, où l’interface est explicitement résolu. Le couplage est réalisé à l’aide de critères IRQ (Interface Resolution Quality), qui prennent en compte à la fois la courbure de l’interface et la quantité modélisée de la surface de l’interface. Le modèle ELSA est développé en premier lieu en considérant les deux phases comme incompressibles. L’extension à la phase compressible est également brièvement étudiée dans cette thèse. Il en résulte une formulation ELSA compressible qui prend en compte la densité variable de chaque phase. En collaboration avec l’Imperial College de Londres, la formulation de la fonction de densité de probabilité (PDF) avec les champs stochastiques est également explorée afin d’étudier l’atomisation. Dans les systèmes d’injection de carburant modernes, la pression locale à l’intérieur de l’injecteur tombe souvent en dessous de la pression de saturation en vapeur du carburant, ce qui entraîne une cavitation. La cavitation affecte le flux externe et la formulation du spray. Ainsi, une procédure est nécessaire pour étudier le changement de phase ainsi que la formulation du jet en utilisant une configuration numérique unique et cohérente. Une méthode qui couple le changement de phase à l’intérieur de l’injecteur à la pulvérisation externe du jet est développée dans cette thèse. Ceci est réalisé en utilisant le volume de formulation de fluide où l’interface est considérée entre le liquide et le gaz; le gaz est composé à la fois de vapeur et d’airambiant non condensableThis thesis presents Large Eddy Simulation (LES) of fuel injection, atomization and cavitation inside the fuel injector for applications related to internal combustion engines. For atomization modeling, Eulerian Lagrangian Spray Atomization (ELSA) model is used. The model solves for volume fraction of liquid fuel as well as liquid-gas interface surface density to describe the complete atomization process. In this thesis, flow inside the injector is also considered for subsequent study of atomization. The study presents the application of ELSA model to a typical diesel injector, both in the context of RANS and LES. The model is validated with the help of experimental data available from Engine Combustion Network (ECN). The ELSA model which is normally designed for diffused (unresolved) interfaces, where the exact location of the liquid-gas interface is not considered, is extended to work with Volume of Fluid (VOF) type formulation of two phase flow, where interface is explicitly resolved. The coupling is achieved with the help of Interface Resolution Quality (IRQ) criteria, that takes into account both the interface curvature and modeled amount of interface surface. ELSA model is developed first considering both phases as incompressible, the extension to compressible phase is also briefly studied in this thesis, resulting in compressible ELSA formulation that takes into account varying density in each phase. In collaboration with Imperial College London, the Probability Density Function (PDF) formulation with Stochastic Fields is also explored to study atomization. In modern fuel injection systems, quite oftenthe local pressure inside the injector falls below the vapor saturation pressure of the fuel, resulting in cavitation. Cavitation effects the external flow and spray formulation. Thus, a procedure is required to study the phase change as well as jet formulation using a single and consistent numerical setup. A method is developed in this thesis that couples the phase change inside the injector to the external jet atomization. This is achieved using the volume of fluid formulation where the interface is considered between liquid and gas; gas consists of both the vapor and non condensible ambient air
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Billaud, Friess Marie. "Eléments finis stabilisés pour des écoulements diphasiques compressible-incompressible." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2009. http://tel.archives-ouvertes.fr/tel-00565815.
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Dans cette thèse, nous nous intéressons à la simulation numérique d'écoulements instationnaires de deux fluides visqueux non miscibles, séparés par une interface mobile. Plus particulièrement des écoulements sans choc constitués d'une phase gazeuse et d'une phase liquide sont considérés. Pour modéliser de tels écoulements, une approche dans laquelle le gaz est décrit par les équations de Navier-Stokes compressible et le liquide par les équations de Navier-Stokes incompressible est proposée. C'est le couplage de ces deux modèles qui constitue l'originalité et l'enjeu principal de de cette thèse. Pour traiter cette difficulté majeure, une méthode globale (i.e. la même dans chaque phase) et simple à mettre en \oe uvre est élaborée. L'utilisation des équations de Navier-Stokes formulées de façon unifiée pour les inconnues primitives (pression, vitesse et température) constitue le point de départ pour la construction de notre méthode qui repose sur les composants suivants: - une méthode d'éléments finis stabilisés pour la discrétisation spatiale des équations de Navier-Stokes; - une approche Level Set pour représenter précisément l'interface dont l'équation de transport a été résolue par une méthode de type Galerkin Discontinu; \item et des grandeurs moyennées pour traiter les discontinuités à l'interface. Le bon comportement de notre approche est illustré sur différents tests mono et bi-dimensionnels.
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Nersisyan, Hayk. "Contrôlabilité et stabilisation des équations d'Euler incompressible et compressible." Thesis, Cergy-Pontoise, 2011. http://www.theses.fr/2011CERG0531/document.
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Dans cette thèse, on étudie la contrôlabilité et la stabilisation de certaines équations aux dérivées partielles . On s'intéresse d'abord au problème du contrôle de l'équation d'Euler 3D incompressible par une force extérieure de dimension finie. Nous montrons que pour un choix approprié de l'espace de contrôle, la vitesse et la pression du fluide sont exactement contrôlables en projections. De plus, la vitesse est approximativement contrôlable. Nous montrons aussi que le système en question n'est pas exactement contrôlable par une force extérieure de dimension finie.On étudie aussi la contrôlabilité de l'équation d'Euler 3D compressible. Le contrôle est une force extérieure de dimension finie agissant uniquement sur l'équation de la vitesse. Nous montrons que la vitesse et la densité du fluide sont simultanément contrôlables. En particulier, le système est approximativement contrôlable et exactement contrôlable en projections. Dans la dernière partie, on étudie la stabilisation de l'équation d'Euler dans un cylindre infini.Nous montrons que pour toute solution stationnaire (c,0) du système d'Euler il existe un contrôle supporté dans une partie de la frontière du cylindre qui stabilise le système à (c,0)In this thesis, we study the controllability and stabilization of certain partial differential equations.We consider first the problem of control of the 3D incompressible Euler equationby an external force of finite dimension. We show that for an appropriate choice of control space, the velocity and the pressure of the fluid are exactly controllable in projections.Moreover, the velocity is approximately controllable. We also show that the system in question is not exactly controllable by a finite-dimensional external force.We also study the controllability of the 3D compressible Euler equation. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are simultaneously controllable. In particular, the system is approximately controllable and exactly controllable in projections.The last section of the thesis is devoted to the study of a stabilization problem for the 2D incompressible Euler system in an infinite strip with boundary controls. We show that for any stationary solution (c,0) of the Euler system there is a control which is supported in a given bounded part of the boundary of the strip and stabilizes the system to (c,0)
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Billaud, Marie. "Eléments finis stabilisés pour des écoulements diphasiques compressible-incompressible." Thesis, Bordeaux 1, 2009. http://www.theses.fr/2009BOR13872/document.
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Dans cette thèse, nous nous intéressons à la simulation numérique d'écoulements instationnaires de deux fluides visqueux non miscibles, séparés par une interface mobile. Plus particulièrement des écoulements sans choc constitués d'une phase gazeuse et d'une phase liquide sont considérés. Pour modéliser de tels écoulements, une approche dans laquelle le gaz est décrit par les équations de Navier-Stokes compressible et le liquide par les équations de Navier-Stokes incompressible est proposée. C'est le couplage de ces deux modèles qui constitue l'originalité et l'enjeu principal de de cette thèse. Pour traiter cette difficulté majeure, une méthode globale (i.e. la même dans chaque phase) et simple à mettre en oeuvre est élaborée. L'utilisation des équations de Navier-Stokes formulées de façon unifiée pour les inconnues primitives (pression, vitesse et température) constitue le point de départ pour la construction de notre méthode qui repose sur les composants suivants: une méthode d'éléments finis stabilisés pour la discrétisation spatiale des équations de Navier-Stokes; une approche Level Set pour représenter précisément l'interface dont l'équation de transport a été résolue par une méthode de type Galerkin Discontinu; et des grandeurs moyennes pour traiter les discontinuités à l'interface. Le bon comportement de notre approche est illustré sur différents tests mono et bi-dimensionnelsIn this work, we are interested in the numerical simulation of instationnary viscous flows of two immiscible fluids, separated by a mobile interface. In particular, flows without shock composed of a gas phase and a liquid phase are considered. In order to modelize such flows, an approach in which the gaz is described by compressible Navier-Stokes equations and the liquid by incompressible Navier-Stokes équations is proposed. The coupling between these two models is the originality and the stake of this thesis. To treat this important difficulty, a global (i.e. the same for each phase) and simple method is elaborated. In our procedure we propose, using the Navier-Stokes equations formulated in set of primitives unknowns (pressure, velocity and temperature), to elaborate a strategy that relies on the follow components: the stabilized finite element method to discretize spatially the Navier-Stokes equations; the Level Set method for tracking the interface precisely with a discontinuous Galerkin method to solve the associated transport equation; and some averaged quantities to treat the discontinuities at the interface. The good behaviour of this approach is performed on both one and two spatial dimensions
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Lin, Chi-Kun. "On the incompressible limit of the compressible Navier-Stokes equations." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185888.
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Many interesting problems in classical physics involve the behavior of solutions of nonlinear hyperbolic systems as certain parameter and coefficients becomes infinite. Quite often, the limiting solution (when it exits) satisfies a completely different nonlinear partial differential equation. The incompressible limit of the compressible Navier-Stokes equations is one physical problem involving dissipation when such a singular limiting process is interesting. In this article we study the time-discretized compressible Navier-Stokes equation and consider the incompressible limit as the Mach number tends to zero. For γ-law gas, 1 < γ ≤ 2, D ≤ 4, we show that the solutions (ρ(ε), μ(ε)/ε) of the compressible Navier-Stokes system converge to the solution (1, v) of the incompressible Navier-Stokes system. Furthermore we also prove that the limit also satisfies the Leray energy inequality.
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Enault, Séverine. "Modélisation de la propagation d'une tumeur en milieu faiblement compressible." Lyon, Ecole normale supérieure, 2010. http://www.theses.fr/2010ENSL0607.
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Dans cette thèse, on s’intéresse à la modélisation, à l’analyse mathématique et numérique de certains phénomènes biologiques. On a d’abord étudié l’effet de la compressibilité du tissu sain sur la progression d’une tumeur solide. Deux systèmes d’équations aux dérivées partielles découlent de cette modélisation selon la prise en compte de la compressibilité des cellules saines : un système incompressible et un système compressible. Après avoir étudié l'existence de solution pour ces deux systèmes, une comparaison numérique permet de quantifier l’effet de la compressibilité sur la croissance de la tumeur. Enfin, on s’est intéressé à la modélisation et à la simulation numérique du transport du mucus dans le poumon. L’étude numérique en 2D a mis en évidence l'importance du mouvement des cils de l'épithélium et a permis de préciser les termes dominants nécessaires à la mise en place d’un schéma numérique en 3DIn this thesis, we are interested in modeling, mathematical analysis and numerical simulation of some biological phenomena. We first study the compressibility effect of the healthy tissu on the invasivness of a tumor. Two systems of partial differential equations follow from this modeling depending on whether the compressibility of the healthy tissu is taken into account: an incompressible system and a compressible one. After the study of the existence of solution of both systems, a numerical comparison allows to quantify the compressibility effect on tumor growth. Finally, we model and simulate mucus motion in the lung. The numerical study in 2D shows the importance of the epithelium ciliated cells in this phenomenon and identifies the leading terms and the leads to follow for the 3D algorithm
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Welsh, Stephanie. "Compressible Taylor-Couette flow." Thesis, University of Leeds, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616475.
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Incompressible Taylor-Couette flow has been studied extensively over the years. However, the compressible system has been largely ignored with only a few notable studies. The present thesis aims to explore the compressible Taylor-Couette system for a large range of parameters. The compressible equations have been linearised and a spectral method was applied to solve the system using a MATLAB-routine. In Chapter 2, we discuss the analysis performed to solve the system and explain the basic concepts and phenomena we expect to find. We also explain the numerical methods used. Chapter 3 discusses the case in which the outer cylinder remains motionless. The most important parameters, the Mach and Prandtl number and the radius ratio, are varied. In Chapters 4 and 5, the same procedure is applied to the cases of the co- and counter-rotating cylinders, respectively.
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Brock, S. T. H. "Fractal dimensions and their relationship to filtration characteristics." Thesis, Loughborough University, 2000. https://dspace.lboro.ac.uk/2134/13486.
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Work has been performed to characterise filtration systems according to their fractal properties and to construct agglomerates to mimic the filtration systems under scrutiny. The first objective was achieved by carrying out experiments examining the dead-end filtration of two separate mineral suspensions, namely calcite and talc. These minerals were chosen to represent typical incompressible (calcite) and compressible (talc) filtration systems, undergoing filtration using a range of pressures. The experimental apparatus produced filter cakes that could be sampled, sectioned and examined under high magnification. The second objective was met by developing a computer application that could construct simulated particle agglomerates in both two and three dimensions, using a seed agglomeration model as well as simulating filtration by means of a virtua1 filter cell. A large number of simulations were completed to mimic both the dead-end filtration and other agglomerate models. The computer application was also capable of characterising the fractal and Euclidean spatial nature of both the simulated and experimental particulate systems, using a variety of techniques. Euclidean spatial attributes such as porosity as well as fractal properties including surface roughness and a number of density fractal dimensions have been measured for both types of system and demonstrate that the conditions under which the trials were performed have a bearing on the final configuration of the structures. Results from both experimental and simulation work show that fractal dimensions offer a valid method of measuring the properties of filtration systems. Experimental results showed that as the filtering pressure was increased, the density fractal dimension for the system appeared to increase. This change in fractal dimension was also accompanied by a decrease in the porosity of the system (more so for talc than the calcite), confirming the compressibility of the materials under scrutiny. The characterisation of the sampled cakes also showed that the spatial characteristics vary within the individual slices of the sample,in agreement with modem filtration theory. Results from the simulations show that both the physical and fractal properties of the resulting structures varied with the parameters used to construct them. As a rule, as the particles in the simulations were able to move in a more diffusive manner (akin to Brownian motion), the agglomerates they formed had a more open, rugged structure. The simulation of filtration systems also showed a variation within the individual cake structures. In the case of the filtration simulations, the probability assigned to the particles' sticking to the growing agglomerate was the controlling factor. In addition, it was found that the simulated cakes had similar spatial properties to the experimental systems they were designed to replicate.
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Pareja, Victor David. "IMPULSE FORMULATIONS OF THE EULER EQUATIONS FOR INCOMPRESSIBLE AND COMPRESSIBLE FLUIDS." Master's thesis, University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3265.
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The purpose of this paper is to consider the impulse formulations of the Euler equations for incompressible and compressible fluids. Different gauges are considered. In particular, the Kuz'min gauge provides an interesting case as it allows the fluid impulse velocity to describe the evolution of material surface elements. This result affords interesting physical interpretations of the Kuz'min invariant. Some exact solutions in the impulse formulation are studied. Finally, generalizations to compressible fluids are considered as an extension of these results. The arrangement of the paper is as follows: in the first chapter we will give a brief explanation on the importance of the study of fluid impulse. In chapters two and three we will derive the Kuz'min, E & Liu, Maddocks & Pego and the Zero gauges for the evolution equation of the impulse density, as well as their properties. The first three of these gauges have been named after their authors. Chapter four will study two exact solutions in the impulse formulation. Physical interpretations are examined in chapter five. In chapter six, we will begin with the generalization to the compressible case for the Kuz'min gauge, based on Shivamoggi et al. (2007), and we will derive similar results for the remaining gauges. In Chapter seven we will examine physical interpretations for the compressible case.M.S.
Department of Mathematics
Sciences
Mathematical Science MS
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McKay, Melanie. "Iterative methods for incompressible flow." Thesis, University of Ottawa (Canada), 2009. http://hdl.handle.net/10393/28063.
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The goal of this thesis is to illustrate the effectiveness of iterative methods on the discretized Navier Stokes equations. The standard lid-driven cavity in both 2-D and 3-D test cases are examined and compared with published results of the same type. The numerical results are obtained by reducing the partial differential equations (PDEs) to a system of algebraic equations with a stabilized P1-P1 Finite Element Method (FEM) in space. Gear's Backward Difference Formula (BDF2) and an adaptive time stepping scheme utilizing a first order Backward Euler (BE) startup and BDF2 are then utilized to discretizc the time derivative of the Javier-Stokes equations. The iterative method used is the Generalized Minimal Residual (GMRES) along with the selected preconditioners Incomplete LU Factorization (ILU), Jacobi preconditioner and the Block Jacobi preconditioner.
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Zwart, Philip J. "Grid turbulence in compressible flow." Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/10207.
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The flow downstream of a grid in a wind tunnel is of considerable interest for two reasons. Theoretically, it represents a good approximation to the idealized concept of homogeneous and isotropic turbulence, and therefore provides a benchmark to evaluate various analytical theories of turbulence. On the practical side, grids and screens are used extensively in the management of turbulence in a variety of applications. Experimental studies of grid turbulence are numerous in incompressible flow but far scarcer in compressible flow. The present study considers the characteristics of grid turbulence over a range of Mach numbers, M, ranging from the essentially incompressible (M = 0.16), through the moderate subsonic ($0.16 M 0.7)$ and high subsonic $(0.7 M 1.0),$ to the supersonic (M = 1.55). The experiments comprise flow visualization, performed with the shadowgraph method, and mean and fluctuating velocity measurements, made with a laser-Doppler velocimeter. Characteristics of the flow near the grid were visualized in a demonstration nozzle using the schlieren technique. In the moderate subsonic regime, flow visualization indicated that the flow near the grid underwent major changes as M increased. The turbulence intensity and decay characteristics were also found to be influenced, which was attributed to the changes in the flow near the grid. In the high subsonic regime, an unsteady quasi-normal shock was present in the test section. This induced relatively large velocity fluctuations and anisotropic turbulence. In the supersonic regime, stationary oblique shocks generated by the grid were present throughout the test section, which interfered with the turbulence and introduced errors in the measurement technique.
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FERREIRA, ANA LUISA AULER DA SILVA. "ULTRASONIC TECHNOLOGY IN FLOW MEASUREMENT OF INCOMPRESSIBLE FLOW." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=16724@1.
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O presente trabalho avalia a influência da instalação em medidores de vazão
ultrassônicos, utilizando simulação numérica. Foram apresentadas características
dos medidores ultrassônicos e questões sobre a configuração da modelagem do
escoamento que podem influenciar nos resultados numéricos. Foram descritos os
procedimentos utilizados para traçar as linhas e para calcular a velocidade média
no medidor e o erro de medição. Foi mostrado o efeito de uma curva, duas curvas
no mesmo plano e duas curvas em planos perpendiculares, em medidores
ultrassônicos de 1, 2, 3, 4, 5 e 8 canais, com diferentes arranjos. Também foi
analisado o efeito de um degrau no resultado do medidor ultrassônico por meio de
simulação de medidores 1 a 5 canais e por calibração de medidores de 3 canais.
Foram utilizados fatores, calculados pela razão entre a velocidade indicada pelo
medidor em um dado local e a velocidade que seria indicada pelo mesmo medidor
em escoamento completamente desenvolvido. Logo após uma curva, os fatores
para medidores de 1 canal variaram de 0,40 a 1,28; para medidores de 3 canais, de
0,5 a 1,42; e para medidores de 4 e 5 canais, as diferenças chegaram a ultrapassar
10%. A 20D após uma curva, medidores de 2 e 3 canais indicaram fatores de 0,9 a
1,08 e medidores de 4 e 5 canais, fatores de 0,99 a 1,04. Os parâmetros de
diagnóstico analisados não se mostraram eficazes e sua utilização não é
recomendada. Pela simulação, um degrau convergente de -4% gera diferenças na
ordem de 0,3% para medidores de 3 canais e, para degrau divergente de 4%, as
diferenças ultrapassam 0,5%. A diferença entre os resultados das calibrações com
e sem degrau ficou entre 0,18% a 0,3%. A simulação numérica é uma ferramenta
útil na análise dos medidores ultrassônicos e mostrou a sensibilidade desses
medidores a variações no perfil de velocidades.The present work evaluates the influence of the installation in ultrasonic flow meters, using numerical simulation. Ultrasonic meter characteristics and issues about the flow modeling configuration that may influence the numerical results were presented. Procedures used to draw the lines and to calculate the meter mean velocity and the measurement error were described. The effect of one curve, two curves at the same plane and two curves at perpendicular planes at 1, 2, 3, 4, 5 and 8-path meters with different arrangements were shown. Also, the effect of one step at the results of ultrasonic meters was analyzed by the simulation of 1 to 5-paths meters and by the calibration of a 3 path meters. Factors calculated by the ratio between the velocity indicated by the meter in a certain position and the velocity that would be indicated by the meter in a fully developed flow. Just after one curve, the factors for 1-path meters varied from 0.40 to 1.28; for 3-path meters, from 0.5 to 1.42; and for 4 and 5-path meters, the differences were higher than 10%. At 20D downstream of one curve, 2 and 3-path meters indicated factors equal to 0.9 and 1.08; and 4 and 5-path meters, factors equal to 0.99 to 1.04. The diagnostic parameters analyzed were not efficient and their use is not recommended. By the simulation, a convergent step of -4% generates differences about 0.3% for 3-path meters and for a divergent step -f 4%, the differences are higher than 0.5%. The differences between the calibration results with and without steps were from 0.18% to 0.3%. The numerical simulation is a useful tool in the ultrasonic meter analyses and showed the sensitivity of these meters to velocity profile variations.
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Bocchi, Edoardo. "Compressible-incompressible transitions in fluid mechanics : waves-structures interaction and rotating fluids." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0279/document.
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Ce manuscrit porte sur les transitions compressible-incompressible dans les équations aux dérivées partielles de la mécanique des fluides. On s'intéresse à deux problèmes : les structures flottantes et les fluides en rotation. Dans le premier problème, l'introduction d'un objet flottant dans les vagues induit une contrainte sur le fluide et les équations gouvernant le mouvement acquièrent une structure compressible-incompressible. Dans le deuxième problème, le mouvement de fluides géophysiques compressibles est influencé par la rotation de la Terre. L'étude de la limite à rotation rapide montre que le champ vectoriel de vitesse tend vers une configuration horizontale et incompressible.Les structures flottantes constituent un exemple particulier d'interaction fluide-structure, où un solide partiellement immergé flotte à la surface du fluide. Ce problème mathématique modélise le mouvement de convertisseurs d'énergie marine. En particulier, on s'intéresse aux bouées pilonnantes, installées proche de la côte où les modèles asymptotiques en eaux peu profondes sont valables. On étudie les équations de Saint-Venant axisymétriques en dimension deux avec un objet flottant à murs verticaux se déplaçant seulement verticalement. Les hypothèses sur le solide permettent de supprimer le problème à bord libre associé avec la ligne de contact entre l'air, le fluide et le solide. Les équations pour le fluide dans le domaine extérieur au solide sont donc écrites comme un problème au bord quasi-linéaire hyperbolique. Celui-ci est couplé avec une EDO non-linéaire du second ordre qui est dérivée de l'équation de Newton pour le mouvement libre du solide. On montre le caractère bien posé localement en temps du système couplé lorsque que les données initiales satisfont des conditions de compatibilité afin de générer des solutions régulières.Ensuite on considère une configuration particulière: le retour à l'équilibre. Il s'agit de considérer un solide partiellement immergé dans un fluide initialement au repos et de le laisser retourner à sa position d'équilibre. Pour cela, on utilise un modèle hydrodynamique différent, où les équations sont linearisées dans le domaine extérieur, tandis que les effets non-linéaires sont considérés en dessous du solide. Le mouvement du solide est décrit par une équation intégro-différentielle non-linéaire du second ordre qui justifie rigoureusement l'équation de Cummins, utilisée par les ingénieurs pour les mouvements des objets flottants. L'équation que l'on dérive améliore l'approche linéaire de Cummins en tenant compte des effets non-linéaires. On montre l'existence et l'unicité globale de la solution pour des données petites en utilisant la conservation de l'énergie du système fluide-structure.Dans la deuxième partie du manuscrit, on étudie les fluides en rotation rapide. Ce problème mathématique modélise le mouvement des flots géophysiques à grandes échelles influencés par la rotation de la Terre. Le mouvement est aussi affecté par la gravité, ce qui donne lieu à une stratification de la densité dans les fluides compressibles. La rotation génère de l'anisotropie dans les flots visqueux et la viscosité turbulente verticale tend vers zéro dans la limite à rotation rapide. Notre interêt porte sur ce problème de limite singulière en tenant compte des effets gravitationnels et compressibles. On étudie les équations de Navier-Stokes-Coriolis anisotropes compressibles avec force gravitationnelle dans la bande infinie horizontale avec une condition au bord de non glissement. Celle-ci et la force de Coriolis donnent lieu à l'apparition des couches d'Ekman proche du bord. Dans ce travail on considère des données initiales bien préparées. On montre un résultat de stabilité des solutions faibles globales pour des lois de pression particulières. La dynamique limite est décrite par une équation quasi-géostrophique visqueuse en dimension deux avec un terme d'amortissement qui tient compte des couches limitesThis manuscript deals with compressible-incompressible transitions arising in partial differential equations of fluid mechanics. We investigate two problems: floating structures and rotating fluids. In the first problem, the introduction of a floating object into water waves enforces a constraint on the fluid and the governing equations turn out to have a compressible-incompressible structure. In the second problem, the motion of geophysical compressible fluids is affected by the Earth's rotation and the study of the high rotation limit shows that the velocity vector field tends to be horizontal and with an incompressibility constraint.Floating structures are a particular example of fluid-structure interaction, in which a partially immersed solid is floating at the fluid surface. This mathematical problem models the motion of wave energy converters in sea water. In particular, we focus on heaving buoys, usually implemented in the near-shore zone, where the shallow water asymptotic models describe accurately the motion of waves. We study the two-dimensional nonlinear shallow water equations in the axisymmetric configuration in the presence of a floating object with vertical side-walls moving only vertically. The assumptions on the solid permit to avoid the free boundary problem associated with the moving contact line between the air, the water and the solid. Hence, in the domain exterior to the solid the fluid equations can be written as an hyperbolic quasilinear initial boundary value problem. This couples with a nonlinear second order ODE derived from Newton's law for the free solid motion. Local in time well-posedness of the coupled system is shown provided some compatibility conditions are satisfied by the initial data in order to generate smooth solutions.Afterwards, we address a particular configuration of this fluid-structure interaction: the return to equilibrium. It consists in releasing a partially immersed solid body into a fluid initially at rest and letting it evolve towards its equilibrium position. A different hydrodynamical model is used. In the exterior domain the equations are linearized but the nonlinear effects are taken into account under the solid. The equation for the solid motion becomes a nonlinear second order integro-differential equation which rigorously justifies the Cummins equation, assumed by engineers to govern the motion of floating objects. Moreover, the equation derived improves the linear approach of Cummins by taking into account the nonlinear effects. The global existence and uniqueness of the solution is shown for small data using the conservation of the energy of the fluid-structure system.In the second part of the manuscript, highly rotating fluids are studied. This mathematical problem models the motion of geophysical flows at large scales affected by the Earth's rotation, such as massive oceanic and atmospheric currents. The motion is also influenced by the gravity, which causes a stratification of the density in compressible fluids. The rotation generates anisotropy in viscous flows and the vertical turbulent viscosity tends to zero in the high rotation limit. Our interest lies in this singular limit problem taking into account gravitational and compressible effects. We study the compressible anisotropic Navier-Stokes-Coriolis equations with gravitational force in the horizontal infinite slab with no-slip boundary condition. Both this condition and the Coriolis force cause the apparition of Ekman layers near the boundary. They are taken into account in the analysis by adding corrector terms which decay in the interior of the domain. In this work well-prepared initial data are considered. A stability result of global weak solutions is shown for power-type pressure laws. The limit dynamics is described by a two-dimensional viscous quasi-geostrophic equation with a damping term that accounts for the boundary layers
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Roberts, William. "Techniques for modelling incompressible fluid flow." Thesis, University of Edinburgh, 1991. http://hdl.handle.net/1842/12857.
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The work presented in this thesis can be divided into two main parts: a study of Cellular Automaton (CA) models of incompressible fluid flow and work on the use of Renormalisation Group (RG) methods to derive an effective viscosity for use in subgrid modelling in Large Eddy Simulation of incompressible turbulence. The derivation of hydrodynamic equations for the behaviour of CA models is reviewed in the context of classical statistical mechanics. In computer simulations of such models, velocity and density values are found by calculating averages of appropriate microscopic quantities: the effect of this averaging on noise levels in such simulations is investigated. We verify the expected results that the noise level is proportional to N-1/2 where N is the number of space cells or time-steps in the average. A new CA model, the '2D multispeed model', is developed by considering the projection of the 4D face-centred hypercubic model into 2D. Optimal collision rules are obtained and computer simulations of flow through a channel are performed, which reproduce the well-known parabolic velocity profile. Kinematic viscosity is calculated as a function of particle density from the velocity profiles and the imposed pressure gradient: the results compare favourably with those of the FHP model in terms of maximum attainable Reynolds number for a given computational effort. After briefly summarising some important aspects of turbulent fluid flow, a conditional averaging procedure is presented, designed to deal with the problems of coupling between low-wavenumber and high-wavenumber modes in the filtered Navier-Stokes equation in k-space. The conditional average is precisely defined in terms of the turbulent ensemble and a method of evaluation is proposed, whereby the conditional average of moments of the velocity field is related to the full-ensemble average of the same quantities, with an explicit error term representing the effect of the coupling. The application of this averaging procedure to the modelling of small-scale motion in homogeneous isotropic turbulence is explained and the derivation of an effective viscosity, due to McComb and Watt (Phys. Rev. Lett. 65 (1990) p.3281) is outlined.
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Lanerolle, Lyon Werner John. "Numerical modelling of turbulent compressible flow." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362004.
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Oo, Htet Htet Nwe. "Actuator Disk Theory for Compressible Flow." DigitalCommons@CalPoly, 2017. https://digitalcommons.calpoly.edu/theses/1727.
Full textAbstract:
Because compressibility effects arise in real applications of propellers and turbines, the Actuator Disk Theory or Froude’s Momentum Theory was established for compressible, subsonic flow using the three laws of conservation and isentropic thermodynamics. The compressible Actuator Disk Theory was established for the unducted (bare) and ducted cases in which the disk was treated as the only assembly within the flow stream in the bare case and enclosed by a duct having a constant cross-sectional area equal to the disk area in the ducted case. The primary motivation of the current thesis was to predict the ideal performance of a small ram-air turbine (microRAT), operating at high subsonic Mach numbers, that would power an autonomous Boundary Layer Data System during test flights. The compressible-flow governing equations were applied to a propeller and a turbine for both the bare and ducted cases. The solutions to the resulting system of coupled, non-linear, algebraic equations were obtained using an iterative approach. The results showed that the power extraction efficiency and the total drag coefficient of the bare turbine are slightly higher for compressible flow than for incompressible flow. As the free-stream Mach increases, the Betz limit of the compressible bare turbine slightly increases from the incompressible value of 0.593 and occurs at a velocity ratio between the far downstream and the free-stream that is lower than the incompressible value of 0.333. From incompressible to a free-stream Mach number of 0.8, the Betz limit increases by 0.021 while its corresponding velocity ratio decreases by 0.036. The Betz limit and its corresponding velocity ratio for the ducted turbine are not affected by the free-stream Mach and are the same for both incompressible and compressible flow. The total drag coefficient of the ducted turbine is also the same regardless of the free-stream Mach number and the compressibility of the flow; but, the individual contributions of the turbine drag and the lip thrust to the total drag differs between compressible and incompressible flow and between varying free-stream Mach numbers. It was concluded that overall compressibility has little influence on the ideal performance of an actuator disk.
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Kanschat, Guido. "Discontinuous Galerkin methods for viscous incompressible flow." Wiesbaden : Deutscher Universitäts-Verlag, 2008. http://dx.doi.org/10.1007/978-3-8350-5519-3.
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Khobeiz, Mohamed Hussien. "Numerical simulation of viscous incompressible turbomachinery flow." Thesis, University of Sheffield, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338828.
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Kanschat, Guido. "Discontinuous Galerkin methods for viscous incompressible flow." Wiesbaden : Dt. Univ.-Verl, 2004. http://www.myilibrary.com?id=134464.
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Yao, H. "Incompressible flow over a three-dimensional cavity." Thesis, Queen's University Belfast, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.273119.
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Farooq, Muhammad Asif. "Cartesian Grid Method for Compressible Flow Simulation." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for energi- og prosessteknikk, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-16538.
Full textAbstract:
The Cartesian grid method is an alternative to the existing methods to solve a physical problem governed by partial differential equations (PDEs) computationally. Researchers are interested in this method due to its simplicity of grid generation, less computational effort and ease of implementation into a computer code. One of the other options to solve a physical PDE problem is by the body-fitted grid method. In the body-fitted grid method, the boundary points are grid points. This is not the case with the Cartesian grid method where the body wall is embedded as a boundary into a Cartesian grid resultingin irregular cells near the embedded boundary. These irregular cells near the embedded boundary are known as cut-cells. Instead of using special treatmentsof the cut-cells or enforcing the presence of the embedded boundary by adding source terms at the Cartesian grid points near the boundary, the kinematic and other boundary conditions can be introduced in the Cartesian grid method via ghost points. Those grid points which lie inside the embedded boundary and are also a part of computation are called ghost points. Inactive grid points inside the embedded boundary are referred to as solid points. In the present Cartesian grid method, based on a ghost point treatment, local symmetry conditions are imposed at the embedded wall boundary. The ghost point treatments available in the literature are difficult to implement due to complex procedures. We are introducing a new approach to approximate the kinematics of the embedded boundary by a very simple ghost point treatment called the simplified ghost point treatment. In this approach, we consider the grid lines in the x- and y- directions as approximations of the lines normal to the embedded boundary depending on whether the angle between the normal and the x- or y-directions is closer. For 1D hyperbolic nonlinear systems of conservation laws, we use the moving normal shock wave as a test case for the 1D compressible Euler equations.For the 2D compressible Euler equations, we test the simplified ghost point treatment for an oblique shock wave generated by a wedge. Then, we verified our approach for slender bodies, namely for supersonic flow over a circular arc airfoil and for transonic flow over a circular arc bump in a channel. In a final problem, we applied the simplified ghost point treatment to blunt body flow and considered supersonic flows over a cylinder using the 2D compressible Euler and Navier-Stokes equations. The results are good or comparable to those found in the existing literature.
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Lin, Hong-Chia. "Topics in Numerical Computation of Compressible Flow." Thesis, Cranfield University, 1990. http://dspace.lib.cranfield.ac.uk/handle/1826/4555.
Full textAbstract:
This thesis aims to assist the development of a multiblock
implicit Navier-Stokes code for hypersonic flow applications.
There are mainly three topics, which concern the understanding
of basic Riemann solvers, the implementing of implicit zonal
method, and grid adaption for viscous flow.
Three problems of Riemann solvers are investigated. The
post-shock oscillation problem of slowly moving shocks is
examined, especially for Roe's Riemann solver, and possible cures
are suggested for both first and second order schemes. The
carbuncle phenomenon associated with blunt body calculation is
cured by a formula based on pressure gradient, which will not
degrade the solutions for viscous calculations too much. The
grid-dependent characteristic of current upwind schemes is also
demonstrated.
Several issues associated with implicit zonal methods are
discussed. The effects of having different mesh sizes in
different zones when shock present are examined with first order
explicit scheme and such effects are shown to be unwanted
therefore big mesh size change should be avoided. Several
implicit schemes are tested for hypersonic flow. The
conservative DDADI scheme is found to be the most robust one. A
simple and robust implicit zonal method is demonstrated. A
proper treatment of the diagonal Jacobian and choosing the
updating method are found to be crucial.
The final topic concerns the calculation and grid adaption
of viscous flow. We study the linear advection-diffusion equation
thoroughly. The results are unfortunately not applicable to
Navier-Stokes equations directly. Nevertheless a suggestion on
the mesh size control for viscous flow is made and demonstrated.
An attempt to construct a cell-vertex TVD scheme is
described in the appendix.
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Wash, Nicholas D. "Upwind iteration techniques for compressible flow computations." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308589.
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Suddhoo, A. "Inviscid compressible flow past multi-element aerofoils." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356714.
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Batten, Paul. "Compressible flow simulation on a parallel computer." Thesis, University of Southampton, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358770.
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Svedholm, Matheus, and Josefine Gessl. "Laboratory exercise - Compressible flow, oblique shock waves." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-276595.
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When studying to become an engineer the education is mainly theoretical and to confirm the theory laboratory exercises are incorporated in the curriculum. Being able to visualize the phenomenons studied helps in giving the students a deeper understanding. The purpose of this report is to aid the department of fluid mechanics at KTH in designing an experiment to help the students understand the theory of oblique shock waves. The project is divided in two parts. Part one the design of the wedge and base plate and part two the creation of the actual experiment and lab PM. The design of the wedge is quite simple. It is a sharp wedge with two angles measured from the horizontal plane, 8° at the top and 4° at the bottom, this is so that two measurements can be made per experiment. Writing the PM and the design of the exercise is the main part of this project. The result is a laboratory exercise where the students compare the flow around a wedge in a shock tube for three different Mach numbers, subsonic, transonic and supersonic. Using shadowgraph optics and a high speed camera the image of the shock is captured. The different regimes are then discussed and compared with the help of theoretical calculations and the measured values.Inom ingenjörsutbildningar är utbildningen huvudsakligen teoretisk och för att bekräfta teorin integreras laborationer i läroplanen. Möjligheten att visualisera de studerade fenomenen hjälper studenterna att få en djupare förståelse. Syftet med denna rapport är att hjälpa den strömningsmekaniska avdelningen på KTH att ta fram ett experiment som hjälper studenterna att förstå teorin om sneda stötvågor. Projektet är uppdelat i två delar. Del ett, design av kilen och fästet och del två framtagningen av själva experimentet och lab PMet. Kilens design är ganska simpel. Det är en vass kil med två vinklar mätta från horisontalplanet , 8° på ovansidan och 4° på undersidan, detta så att man kan göra två mätningar per experiment. Utformandet av laborationen och labpeket är huvuddelen av detta projekt. Resultatet är en laboration där studenterna jämför flödet runt en kil i ett stötrör för tre olika machtal, subsoniskt, transoniskt och supersoniskt. Med hjälp av en höghastighetskamera och shadowgraph optik kan stötvågen fångas på bild. De olika scenarierna diskuteras och jämförs med hjälp av teoretiska beräkningar och de uppmätta värdena.
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Abou-Haidar, Nabil Ibrahim. "Compressible flow pressure losses in branched ducts." Thesis, University of Liverpool, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330238.
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Vilhelmsson, Carl. "Compressible Flow Modeling with Combustion Engine Applications." Thesis, Linköpings universitet, Fordonssystem, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-138434.
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The high demands on low fuel consumption and low emissions on the combustion engines of both today, and the future, is highly dependent on advanced control systems in order to fulfill these demands. The control systems and strategies are based on models which describe the physical system. The more accuratly the models describe the real world system, the more accurate the control will be, leading to better fuel economy and lower emissions. This master's thesis investigates and improves the mass flow model used for a compressible restriction, such as over the throttle valve, EGR valve, or the wastegate valve, for example. The standard model is evaluated and an improvement is proposed which does not assume isentropic flow. This seems to explain the deviation from the isentropic Psi-function shown in earlier research such as (Andersson:2005). Furthermore a throttle valve is analyzed in ANSYS in order to show the generation of entropy. The presence of pressure pulsations in a combustion engine is also evaluated, especially how they effect the otherwise assumed steady flow model. It is tested if a mean value pressure is sufficient or if one needs to take the pulsations in to account, and the result shows that a mean pressure is sufficient, at least for the throttle when typical intake manifold pulsations is present. A dynamic flow model is also derived which can be useful for pressure ratios close to one. The dynamic flow model is based on the standard equation but with an extra dynamic term, however it is not implemented and tested due to complexity and time limitation. The proposed new non-isentropic flow model has proven promising and can hopefully lead to lower emissions and better fuel economy.
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Bonner, Michael Patrick. "Compressible subsonic flow on a staggered grid." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/32290.
Full textAbstract:
This work focuses on numerically modelling the dynamics of a single phase
fluid at varying densities and pressures. We explore the potential of incompressible
flow simulation methods in modelling compressible flow, with
an eye towards computer animation applications. The methods developed
capture the interesting thermodynamic effects of compressible flow, and reduce
to the standard Marker and Cell incompressible flow Poisson matrix
in the incompressible limit. The method works well in modelling flows in
the subsonic range that normal incompressible techniques do not capture
and where compressible methods are inefficient. We have also investigated
adapting these techniques to granular elastic-plastic flow.Science, Faculty of
Computer Science, Department of
Graduate
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Mrabet, Ahmed Amine. "Accélérations algorithmiques pour la simulation numérique d’impacts de vagues. Modèles de type "roofline" pour la caractérisation des performances, application à la CFD." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLN010/document.
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Au cours de ces dernières années les processeurs sont devenus de plus en plus complexes (plusieurs niveaux de cache, vectorisation,...), l’augmentation de la complexité fait que l’étude des performances et les optimisations sont eux aussi devenus de plus en plus complexes et difficiles à comprendre. Donc développer un outil de caractérisation simple et facile d’utilisation des performances d’applications, serait de grande valeur. Le Modèle Roofline [17] promet un début de réponse à ces critères, mais reste insuffisant pour une caractérisation robuste et détaillée. Dans la première partie de cette thèse, Nous allons développer plusieurs versions améliorées du Roofline, robustes et précises, en passant par une version du Roofline en fonction du temps, des blocs et enfin la nouvelle version du Roofline introduite dans la suite de caractérisation Vtune d’Intel. Pour valider ces modèles, nous utilisons le benchmark LINPACK, STREAM ainsi qu’une mini-application développée au cours de cette thèse, qui résout l’équation de l’advection et qui servira de prototype pour l’évaluation de codes hydrodynamiques explicites. Nous portons aussi cette mini-application sur les co-processeurs d’Intel Xeon Phi KNL et KNC. Dans la deuxième partie de cette thèse nous nous intéressons à la simulation d’impact de vagues, à l’aide de codes industriels compressibles et incompressibles. Nous rajoutons plusieurs fonctionnalités dans le code compressible FluxIC, nous effectuons un chaînage de codes incompressible et compressible et enfin nous introduisons un nouveau schéma numérique appelé liquide incompressible et gaz quasi-compressible, qui permet de réaliser une simulation d’impact d’une vague via un code incompressible avec une correction compressible dans les zones où la compressibilité du gaz est importanteDuring recent years computer processors have become increasingly complex (multiple levels of cache, vectorization, etc), meaning that the study of performance and optimization is also becoming more complex and difficult to understand. So a simple and easy-to-use model aimed at studying the performance of applications would be of great value. The Roofline model [17] promises to meet this criteria, but it is insufficient for robust and detailed characterization.In the first part of this thesis, several improved versions of the Roofline model, that are more robust and accurate, are developed by going through theRoofline version as a function of time and block, and finally a new Rooflinemodel is implemented in the Intel Vtune characterization suite. To validate thenew models, the LINPACK andtextitSTREAM benchmarks are used, as wellas, a mini-application developed during this thesis that solves the advectionequation and serves as a prototype for the evaluation of explicit hydrodynamicsimulation codes. This mini-application is also ported to the new Intel XeonPhi KNL and KNC co-processors.Simulation of wave impact using compressible and incompressible industrialcodes is the focus of the second part of this thesis. Several functionalities are added to the compressible FluxIC code, and a chaining of compressible andincompressible codes is carried out. Finally, a new numerical scheme called"incompressible liquid and quasi-compressible gas" is introduced, which allowsthe simulation of wave impact using an incompressible code with a compressiblecorrection in areas where gas compressibility is significant
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Codina, Rovira Ramon. "A finite Element model for incompressible flow problems." Doctoral thesis, Universitat Politècnica de Catalunya, 1992. http://hdl.handle.net/10803/5915.
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Fithen, Robert Miller. "Adaptive finite element simulation of incompressible viscous flow." Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-170423/.
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Stoyanov, Miroslav Karolinov. "Optimal Linear Feedback Control for Incompressible Fluid Flow." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/33454.
Full textAbstract:
Linear feedback control is considered for large systems of differential algebraic equations
arising from discretization of saddle point problems. Necessary conditions are derived by
applying the Maximum Principle and have the form of constrained Riccati equations. We
consider two approaches for solving the feedback control problem as well as practical numerical
methods. Numerical studies using examples derived from a constrained heat equation
and Stokes equation confirms the effectiveness of the approaches we consider.Master of Science