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1
Essel, Emmanuel Kwame. "Homogenization of Reynolds equations." Licentiate thesis, Luleå : Luleå University of Technology, 2007. http://epubl.ltu.se/1402-1757/2007/30/.
Повний текст джерела
2
Роговий, Андрій Сергійович. "Розробка теорії та методів розрахунку вихорокамерних нагнітачів". Thesis, Харківський національний автомобільно-дорожній університет, 2017. http://repository.kpi.kharkov.ua/handle/KhPI-Press/29275.
Повний текст джерелаАнотація:
Дисертація на здобуття наукового ступеня доктора технічних наук за спеціальністю 05.05.17 – гідравлічні машини та гідропневмоагрегати. – Національний технічний університет "Харківський політехнічний інститут", Харків, 2017.
У дисертаційній роботі розв'язано науково-практичну проблему підвищення техніко-економічної ефективності гідравлічних і пневматичних нагнітачів, що перекачують рідини в несприятливих умовах експлуатації або гетерогенні середовища, за рахунок розробки і використання принципово нового типу струминних нагнітачів відцентрової дії. Їх конструкція не містить рухомих механічних частин, а також ущільнень, завдяки чому вони мають високі показники надійності і довговічності притаманні струминній техніці. Концепція нагнітачів базується на новому для струминних нагнітачів принципі – поєднанні позитивних якостей процесів у відцентрових і струминних нагнітачах та особливостях гідродинаміки обмежених обертових потоків. Використання вихорокамерних нагнітачів дозволяє підвищити енергоефективність гідравлічних і пневматичних систем, збільшити обсяг переміщуваних вантажів в гідравлічному і пневматичному трубопровідному транспорті, підвищити продуктивність праці і якість продукції, знизити її собівартість, поліпшити умови роботи. Розроблені нагнітачі є більш енергоефективними, внаслідок передачі енергії в полі відцентрової сили. Таким чином, створено наукові основи проектування струминних вихорокамерних нагнітачів для перекачування середовищ різних агрегатних станів.Thesis for degree of Doctor of Science in Technique for speciality 05.05.17 – hydraulic machines and hydropneumatic units. – National Technical University "Kharkiv Polytechnical Institute", Kharkiv, 2017. In dissertational work the scientifically-practical problem of technical and economic efficiency increase of the hydraulic and pneumatic superchargers which are pumping over liquids in adverse service conditions or heterogeneous environments, at the expense of designing and use of essentially new type of jet superchargers of centrifugal action is solved. Their design does not contain mobile mechanical parts, and also sealing due to the fact that they have high indicators of reliability and durability inherent in jet technics. Conception of superchargers is based on a principle new to jet superchargers – unification of processes properties in centrifugal and jet superchargers and hydrodynamics features of the limited rotating streams. Use of vortex chamber superchargers allows to raise power efficiency of hydraulic and pneumatic systems, to increase volume of moved cargoes in hydraulic and pneumatic pipeline transport, to raise productivity of work and quality of production, to lower its cost price, to improve working conditions. The developed superchargers are more power effective, owing to transmission of energy in the field of centrifugal force. Thus, scientific bases of designing jet vortex chamber superchargers for transportation environments of different aggregation states are created.
3
Роговий, Андрій Сергійович. "Розробка теорії та методів розрахунку вихорокамерних нагнітачів". Thesis, НТУ "ХПІ", 2017. http://repository.kpi.kharkov.ua/handle/KhPI-Press/29269.
Повний текст джерелаАнотація:
Дисертація на здобуття наукового ступеня доктора технічних наук за спеціальністю 05.05.17 – гідравлічні машини та гідропневмоагрегати. – Національний технічний університет "Харківський політехнічний інститут", Харків, 2017.
У дисертаційній роботі розв'язано науково-практичну проблему підвищення техніко-економічної ефективності гідравлічних і пневматичних нагнітачів, що перекачують рідини в несприятливих умовах експлуатації або гетерогенні середовища, за рахунок розробки і використання принципово нового типу струминних нагнітачів відцентрової дії. Їх конструкція не містить рухомих механічних частин, а також ущільнень, завдяки чому вони мають високі показники надійності і довговічності притаманні струминній техніці. Концепція нагнітачів базується на новому для струминних нагнітачів принципі – поєднанні позитивних якостей процесів у відцентрових і струминних нагнітачах та особливостях гідродинаміки обмежених обертових потоків. Використання вихорокамерних нагнітачів дозволяє підвищити енергоефективність гідравлічних і пневматичних систем, збільшити обсяг переміщуваних вантажів в гідравлічному і пневматичному трубопровідному транспорті, підвищити продуктивність праці і якість продукції, знизити її собівартість, поліпшити умови роботи. Розроблені нагнітачі є більш енергоефективними, внаслідок передачі енергії в полі відцентрової сили. Таким чином, створено наукові основи проектування струминних вихорокамерних нагнітачів для перекачування середовищ різних агрегатних станів.Thesis for degree of Doctor of Science in Technique for speciality 05.05.17 – hydraulic machines and hydropneumatic units. – National Technical University "Kharkiv Polytechnical Institute", Kharkiv, 2017. In dissertational work the scientifically-practical problem of technical and economic efficiency increase of the hydraulic and pneumatic superchargers which are pumping over liquids in adverse service conditions or heterogeneous environments, at the expense of designing and use of essentially new type of jet superchargers of centrifugal action is solved. Their design does not contain mobile mechanical parts, and also sealing due to the fact that they have high indicators of reliability and durability inherent in jet technics. Conception of superchargers is based on a principle new to jet superchargers – unification of processes properties in centrifugal and jet superchargers and hydrodynamics features of the limited rotating streams. Use of vortex chamber superchargers allows to raise power efficiency of hydraulic and pneumatic systems, to increase volume of moved cargoes in hydraulic and pneumatic pipeline transport, to raise productivity of work and quality of production, to lower its cost price, to improve working conditions. The developed superchargers are more power effective, owing to transmission of energy in the field of centrifugal force. Thus, scientific bases of designing jet vortex chamber superchargers for transportation environments of different aggregation states are created.
4
Abell, Martha Louise. "Symmetry reduction of Reynold's equation and applications to film lubrication." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/28669.
Повний текст джерела
5
Zhang, Yunzh. "Contribution à la résolution des équations de Navier-Stokes par la méthode des équations intégrales." Palaiseau, Ecole polytechnique, 2003. http://www.theses.fr/2003EPXX0006.
Повний текст джерела
6
Tobias, Brännvall. "Source Term Estimation in the Atmospheric Boundary Layer : Using the adjoint of the Reynolds Averaged Scalar Transport equation." Thesis, Umeå universitet, Institutionen för fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-103671.
Повний текст джерелаАнотація:
This work evaluates whether the branch of Reynolds Averaging in Computational Fluid Dynamics can be used to, based on real field measurements, find the source of the measured gas in question. The method to do this is via the adjoint to the Reynolds Averaged Scalar Transport equation, explained and derived herein. Since the Inverse is only as good as the main equation, forward runs are made to evaluate the turbulence model. Reynolds Averaged Navier Stokes is solved in a domain containing 4 cubes in a 2x2 grid, generating a velocity field for said domain. The turbulence model in question is a union of two modifications to the standard two equation k-ε model in order to capture blunt body turbulence but also to model the atmospheric boundary layer. This field is then inserted into the Reynolds Averaged Scalar Transport equation and the simulation is compared to data from the Environmental Flow wind tunnel in Surrey. Finally the adjoint scalar transport is solved, both for synthetic data that was generated in the forward run, but also for the data from EnFlo. It was discovered that the turbulent Schmidt number plays a major role in capturing the dispersed gas, three different Schmidt numbers were tested, the standard 0.7, the unconventional 0.3 and a height dependent Schmidt number. The widely accepted value of 0.7 did not capture the dispersion at all and gave a huge model error. As such the adjoint scalar transport was solved for 0.3 and a height dependent Schmidt number. The interaction between measurements, the real source strength (which is not used in the adjoint equation, but needed to find the source) and the location of the source is intricate indeed. Over estimation and under estimation of the forward model may cancel out in order to find the correct source, with the correct strength. It is found that Reynolds Averaged Computational fluid dynamics may prove useful in source term estimation.Detta arbete utvärderar hurvida Reynolds medelvärdesmodellering inom flödessimuleringar kan användas till att finna källan till en viss gas baserat på verkliga mätningar ute i fält. Metoden går ut på att använda den adjungerade ekvationen till Reynolds tidsmedlade skalära transportekvationen, beskriven och härledd häri. Då bakåtmodellen bygger på framåtmodellen, måste såleds framåtmodellen utvärderas först. Navier-Stokes ekvationer med en turbulensmodell löses i en domän, innehållandes 4 kuber i en 2x2 orientering, för vilken en hastighetsprofil erhålles. Turbulensmodellen som användes är en union av två olika k-ε modeller, där den ena fångar turbulens runt tröga objekt och den andra som modellerar atmosfäriska gränsskiktet. Detta fält används sedan i framåtmodellen av skalära transportekvationen, som sedan jämförs med körningar från EnFlo windtunneln i Surrey. Slutligen testkörs även den adjungerade ekvationen, både för syntetiskt data genererat i framåtkörningen men även för data från EnFlo tunneln. Då det visade sig att det turbulenta Schmidttalet spelar stor roll inom spridning i det atmosfäriska gränsskiktet, gjordes testkörningar med tre olika Schmidttal, det normala 0.7, det väldigt låga talet 0.3 samt ett höjdberoende Schmidttal. Det visade sig att det vanligtvis använda talet 0.7 inte alls lyckas fånga spridningen tillfredställande och gav ett stort modellfel. Därför löstes den adjungerade ekvationen för 0.3 samt för ett höjdberoende Schmidttal. Interaktionen mellan mätningar, den riktiga källstyrkan (som är okänd i den adjungerade ekvationen) samt källpositionen är onekligen intrikat. Över- samt underestimationer av framåtmodellen kan ta ut varandra i bakåtmodellen för att finna rätt källa, med rätt källstyrka. Det ter sig som Reynolds turbulensmodellering mycket möjligt kan användas inom källtermsuppskattning.
7
Yeo, In-Wook. "Anisotropic hydraulic properties of a rock fracture under normal and shear loading." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286893.
Повний текст джерела
8
Chang, Huakang. "The steady Navier-Stokes problem for low Reynolds' number viscous jets." Thesis, University of British Columbia, 1991. http://hdl.handle.net/2429/30968.
Повний текст джерелаАнотація:
The classical existence theorem for the steady Navier-Stokes equations, based on a bound for the solution's Dirichlet integral, provides little qualitative information about the solution.
In particular, if a domain is unbounded, it is not evident that the solution will be unique even when the data are small. Inspired by the works of Odqvist for the interior problem and of Finn for the problem of flow past an obstacle, we give a potential theoretic construction of a solution of the steady Navier-Stokes equations in several domains with noncompact boundaries. We begin by studying a scalar quasilinear elliptic problem in a half space, which serves as a model problem for the development of some of the methods which are later applied to the Navier-Stokes equations. Then, we consider Navier-Stokes flow in a half space, modeling such phenomena as a jet emanating from a wall, with prescribed
boundary values. The solution which is obtained decays like |x|⁻² at infinity and has a finite Dirichlet integral. Finally, we solve the problem of flow through an aperture in a wall between two half spaces, with a prescribed net flux through the aperture, or with a prescribed pressure drop between the two half spaces. A steady solution is constructed which decays like |x|⁻² at infinity. For small data, uniqueness is proven within the class of functions which decay like |x|⁻¹ at infinity and have finite Dirichlet integrals.Science, Faculty of
Mathematics, Department of
Graduate
9
Essel, Emmanuel Kwame. "Homogenization of Reynolds equations and of some parabolic problems via Rothe's method /." Luleå : Luleå University of Technology, 2008. http://epubl.luth.se/1402-1544/2008/40.
Повний текст джерела
10
Waywell, M. N. "Predictions of wave and tidally induced oscillatory flows with Reynolds stress turbulence models." Thesis, University of Salford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308264.
Повний текст джерела
11
Oshida, Takeshi. "Surface equation of falling film flows with moderate Reynolds number and large but finite Weber number." 京都大学 (Kyoto University), 2000. http://hdl.handle.net/2433/181170.
Повний текст джерела
12
Almqvist, Torbjörn. "Numerical simulation of elastohydrodynamic and hydrodynamic lubrication using the Navier-Stokes and Reynolds equations." Licentiate thesis, Luleå, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-17230.
Повний текст джерелаАнотація:
The work presented in this thesis concerns computer simulations of the lubrication process. The main subject of interest is elastohydrodynamic lubrication (EHL) and, to some extent, hydrodynamic lubrication (HD). The thesis comprises an introductory section and three papers; referred to as A, B and C. Simulation of EHL is an inter-disciplinary task, incorporating the fields of fluid mechanics, solid mechanics, thermodynamics and rheology. In almost all numerical simulations of lubrication performed today, the hydrodynamics are modelled using the Reynolds equation. This equation is derived from the equations of momentum and continuity and using the thin film approximation. However, the assumptions made when deriving this equation limits the size of the computational/spatial domain and the equation cannot predict pressure variations across the lubricating oil film. The subject of papers A and B are numerical simulations using the full equations of momentum and continuity, (Paper B), and the equation of energy (Paper A). The main aim of the work was to investigate the possibilities of carrying out numerical simulations based on the above equations. The rheology was assumed to be Newtonian; the equations are then commonly referred to as the Navier-Stokes equations (N-S). The second aim of the work was to investigate the possibilities of using a commercial software, CFX 4.3 [1], to carry out the numerical simulations. The results in Paper A show that it is possible to simulate thermal EHL line contacts up to pressures of approximately 1 GPa. The limitations of the approach are due to a singularity that can occur in the equation of momentum when a critical shear stress is reached. With a more complete rheological model (non-Newtonian rheology) it should be possible to perform simulations at even higher contact pressures. Paper B presents the results of isothermal simulations comparing the N-S and Reynolds equation approaches. The result show that there may be some discrepancies between the two approaches; although only small discrepancies have been observed in the smooth line contact simulations made. The characteristics of the EHL-contact with a wide range of scales and large gradients in pressure, viscosity and temperature make developing accurate numerical simulations to a difficult task. The computational cost is high due to the small under-relaxations factors that must be used in order to obtain converged numerical solutions. The work to date has shown that is possible to use the extended approach in conjunction with a commercial software, CFX 4.3 [1]. This approach makes it possible to extend the computational domain in future in EHL-simulations, where the Reynolds approach is not valid. Paper C presents the results of simulations of a lubricated pivoted thrust bearing. The objective of this study was to verify a thermo-hydrodynamic (THD) model for this type of bearing. The model developed handles three-dimensional temperature distribution in the oil film and pad, as well as two-dimensional temperature variation in the runner. The viscosity and density are treated as functions of both temperature and pressure. Experiments have been performed in a test rig consisting of two identical equalising pivoted pad thrust bearings. Experimentally measured power loss, runner temperature and pressure profiles as a function of load and rotational speed were compared with the theoretical investigations. The results showed fairly good agreement when the oil inlet temperature and heat transfer coefficients were modified in order to obtain the same runner temperature in both theory and experiment.Godkänd; 2001; 20070314 (ysko)
13
Balupari, Raja Shekar. "VALIDATION OF FINITE ELEMENT PROGRAM FOR JOURNAL BEARINGS -- STATIC AND DYNAMIC PROPERTIES." UKnowledge, 2004. http://uknowledge.uky.edu/gradschool_theses/325.
Повний текст джерелаАнотація:
The analysis of bearing systems involves the prediction of their static and dynamic characteristics. The capability to compute the dynamic characteristics for hydrodynamic bearings has been added to Bearing Design System (BRGDS), a finite element program developed by Dr. R.W. Stephenson, and the results obtained were validated. In this software, a standard finite element implementation of the Reynolds equation is used to model the land region of the bearing with pressure degrees of freedom. The assumptions of incompressible flow, constant viscosity, and no fluid inertia terms are made. The pressure solution is integrated to give the bearing load, and the stiffness and damping characteristics were calculated by a perturbation method. The static and dynamic characteristics of 60, 120 and 180 partial bearings were verified and compared for a length to diameter (L/D) ratio of 0.5. A comparison has also been obtained for the 120 bearing with L/D ratios of 0.5, 0.75 and 1.0. A 360-journal bearing was verified for an L/D ratio of 0.5 and also compared to an L/D ratio of 1.0. The results are in good agreement with other verified results. The effect of providing lubricant to the recesses has been shown for a 120 hybrid hydrostatic bearing with a single and double recess.
14
Hannon, William M. "THE GENERALIZED UNIVERSAL REYNOLDS EQUATION FOR VARIABLE PROPERTY FLUID-FILM LUBRICATION AND VARIABLE GEOMETRY SELF-ACTING BEARINGS." University of Akron / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1156347717.
Повний текст джерела
15
Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds-averaged Navier-Stokes equations." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-35199.
Повний текст джерела
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Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds averaged Navier-Stokes equations." München Verl. Dr. Hut, 2007. http://d-nb.info/988422433/04.
Повний текст джерела
17
Wang, Chao. "Static, dynamic and levitation characteristics of squeeze film air journal bearing : designing, modelling, simulation and fluid solid interaction." Thesis, Brunel University, 2011. http://bura.brunel.ac.uk/handle/2438/5832.
Повний текст джерелаАнотація:
Bearings today need to be able to run at very high speed, providing high positional accuracy for the structure that it supports, and requiring very little or no maintenance. For this to happen, bearings must have tight tolerances and very low or zero friction during operation. This pushes many traditional contact-type bearings to their limits as they often fail due to friction, generating heat and causing wear. By comparison, existing non-contact bearings fare better because of their very low or zero friction. But some have their own problem too. For example, the fact that aerostatic bearings require an air supply means having to use a separate air compressor and connecting hoses. This makes the installation bulky. Aerodynamic and hydrodynamic bearings cannot support loads at zero speed. Both hydrodynamic and hydrostatic bearings may cause contamination to the work-pieces and the work environment because of the use of lubricating fluid. A potential solution to the above-mentioned problems is the new squeeze film air bearing. It works on the rapid squeeze action of an air film to produce separation between two metal surfaces. This has the benefit of being compact with a very simple configuration because it does not require an external pressurized air supply, can support loads at zero speed and is free of contamination. For this research, two squeeze film air journal bearings, made from material of Al 2024 - T3 and Cu - C101 with the same geometry, were designed. The bearing is in the shape of a round tube with three fins on the outer surface and the journal, a round rod. When excited at a certain normal mode, the bearing shell flexes with a desirable modal shape for the squeeze film action. The various modes of vibration of Al bearing were obtained from a finite-element model implemented in ANSYS. Two Modes, the 13th and 23rd, at the respective frequencies of 16.320 kHz and 25.322 kHz, were identified for further investigation by experiments with respect to the squeeze film thickness and its load-carrying capacity. For Cu bearing, the two Modes are also 13th and 23rd at the respective frequencies of 12.184 kHz and 18.459 kHz. In order to produce dynamic deformation of the bearings at their modes, a single layer piezoelectric actuator was used as a driver. The maximum stroke length and the maximum blocking force of the single layer piezoelectric actuator were determined using manual calculation and ANSYS simulation. In the coupled-field analysis, the single layer piezoelectric actuator was mounted on the outside surface of the bearing shell and loaded with an AC and a DC voltage in order to produce the static and dynamic deformation. For the static analysis, the maximum deformation of Al bearing shell is 0.124 μm when the actuators are driven at the DC of 75 V. For the dynamic analysis, the actuators are driven at three levels of AC, namely 55, 65 and 75V with a constant DC offset of 75V and the driving frequency coincided with the modal frequency of the bearing. The maximum dynamic deformation of Al bearing shell is 3.22μm at Mode 13 and 2.08μm at Mode 23 when the actuators were driven at the AC of 75 V and the DC of 75 V. Similarly, the FEA simulation was used for analyzing Cu bearing. Furthermore, the dynamic deformation of both Al and Cu bearing at Mode 13 and 23 are validated by experiments. This research developed two theoretical models that explain the existence of a net pressure in a squeeze film for the levitation. The first model uses the ideal gas law as first approximation whilst the second uses the CFX simulation to provide a more exact explanation. In terms of the load-carrying capacity, Mode 13 was identified to be better than Mode 23 for both bearings. However, at Mode 13, Al bearing has a higher load-carrying capacity than Cu bearing. This is due to Al bearing having a higher modal frequency and amplitude. Finally, the coupled-field analysis for fluid solid interaction (FSI) was studied at both Mode 13 and 23 for Al bearing. The findings are that: a) the fluid force in the squeeze film can affect the dynamic deformation of the bearing shell, especially at high oscillation frequency, more at Mode 13 than at Mode 23 due to the relatively high pressure end-leakage in the latter; b) the dynamic deformation of the bearing shell increases with the gap clearance in a logarithmic manner at Mode 13; and c) the micron levels of gap clearance provide a damping effect on the dynamic deformation of the bearing shell at Mode 13 and at Mode 23, though much less dominant.
18
Snyder, Troy Alan. "On Hydrodynamic Lubrication using Perturbed Reynolds equation and CFD-FSI: Static and Dynamic Characteristics of Compliant Marine Bearings." University of Akron / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=akron157552061871739.
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19
Dupuy, Florence. "Etude tribologique d'une butée aérodynamique en régime supersonique." Thesis, Lyon, INSA, 2015. http://www.theses.fr/2015ISAL0124.
Повний текст джерелаАнотація:
L’amélioration des turbomachines passe par l’augmentation de leurs vitesses de rotation et peut conduire leurs composants à se trouver en présence d’un régime d’écoulement supersonique, en particulier leurs systèmes de pivoterie à air. L’étude d’une butée aérodynamique en régime supersonique est traitée dans ce manuscrit et s’inscrit dans la continuité de la recherche sur les butées hautes vitesses mais qui n’a que très peu été abordée dans la littérature. Ce problème se trouve à la frontière entre deux domaines scientifiques : la lubrification et l’aérodynamique. L’enjeu ici est développer un modèle réaliste traduit par un code de calcul écrit en FORTRAN, capable de capturer les phénomènes liés au régime supersonique (choc, détente) et d’être adapté à la géométrie des films minces. Pour cela, deux modèles ont été développés et codés à l’aide de la méthode numérique des différences finies : les équations de Reynolds Modifiées et les équations de Navier-Stokes adaptées aux films minces. Ce premier modèle est une extension de l’équation de Reynolds généralisée, prenant en compte l’inertie et déjà utilisé dans des études de la lubrification. Le second modèle a été établi à partir des équations de Navier-Stokes et conserve leur forme. Ce système possède l’avantage de pouvoir utiliser les outils numériques adaptés à la capture de choc (WENO). La comparaison des deux modèles montre que les équations de Reynolds Modifiées ne sont pas suffisantes pour l’étude d’un écoulement film mince en régime supersonique. Les résultats des simulations menées montrent la présence d’une détente sur le changement d’inclinaison du double profil qui dépend de la vitesse, de la température et de l’angle de la géométrie. Cette détente, même dans des conditions sévères de fonctionnement (grandes vitesses ou fort convergent), n’a pas beaucoup d’influence sur le comportement global statique de la butée. Les résultats montrent également que contrairement à la théorie des écoulements supersoniques, aucun choc n’est observé en film mince supersonique. Une transition géométrique obtenue par homothétie, entre un écoulement contenant un choc et un autre n’en contenant pas, a été observée à une certaine valeur du rapport des longueurs d’adimensionnement pour une vitesse et une géométrie donnée. L’extrapolation de ces résultats pour un cas réaliste montre qu’un choc ne peut se produire qu’à partir de 5500 m/s pour une épaisseur de film de 40 μm avec epsilon = 0.001. Il est donc peu probable qu’un choc ne se produise dans une butée en conditions supersoniques dans le cadre industrielThe improvement of turbomachines requires to increase their rotational speeds and can leads components to be in presence of a supersonic regime, particularly their air bearing systems. This manuscript deals with a study of an aerodynamic thrust bearing in a supersonic regime. This work belongs to the research field on the high-speed thrust bearings, but very few studies are focused on this subject. This problem is at the boundary between two scientific fields: lubrication and aerodynamic. The aim of this study is to develop models transcribed as a FORTRAN code, able to capture phenomenon related to the supersonic regime (shock, expansion wave) and adapted to the thin film geometry. For this, two models have been developed as well as computer codes related to these models using the finite difference method: the Modified Reynolds equations and the Navier-Stokes equations adapted to thin films. The first model is an extension of the generalized Reynolds equation, taking into account inertia effects. It is a model already used in lubrication studies. The second model was developed from the Navier-Stokes and has their shape. This system has the advantage of using numerical schemes for shock capturing (WENO). The comparison of the two models shows that the Modified Reynolds equations are not appropriate to the study of a supersonic air thin film. Numerical results show the presence of an expansion wave at the end of the sloping region of the tapper flat geometry which depends on speed, on temperature and on the angle of the geometry. This expansion wave, under severe conditions, does not have much influence on the overall static behavior of the thrust bearing. The results also show that, contrary to the supersonic flow theory, a shock is not observed in a supersonic thin film. A geometrical transition obtained by homothetic, between a flow containing a shock and another with no shock, is observed at a given value of the characteristic length ratio for a given speed and geometry. Extrapolation of these results for a realistic case shows that a shock occurs from 5500 m/s for a film thickness of 40 μm with epsilon = 0.001. It is therefore unlikely that a shock occurs in a supersonic thrust bearing in industrial settings
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Tsandzana, Afonso Fernando. "Homogenization of some new mathematical models in lubrication theory." Doctoral thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-59629.
Повний текст джерелаАнотація:
We consider mathematical modeling of thin film flow between two rough surfaces which are in relative motion. For example such flows take place in different kinds of bearings and gears when a lubricant is used to reduce friction and wear between the surfaces. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation, which describes the motion of viscous fluids. In thin domains several approximations are possible which lead to the so called Reynolds equation. This equation is crucial to describe the pressure in the lubricant film. When the pressure is found it is possible to predict vorous important physical quantities such as friction (stresses on the bounding surfaces), load carrying capacity and velocity field. In hydrodynamic lubrication the effect of surface roughness is not negligible, because in practical situations the amplitude of the surface roughness are of the same order as the film thickness. Moreover, a perfectly smooth surface does not exist in reality due to imperfections in the manufacturing process. Therefore, any realistic lubrication model should account for the effects of surface roughness. This implies that the mathematical modeling leads to partial differential equations with coefficients that will oscillate rapidly in space and time. A direct numerical computation is therefore very difficult, since an extremely dense mesh is needed to resolve the oscillations due to the surface roughness. A natural approach is to do some type of averaging. In this PhD thesis we use and develop modern homogenization theory to be able to handle the questions above. Especially, we use, develop and apply the method based on the multiple scale expansions and two-scale convergence. The thesis is based on five papers (A-E), with an appendix to paper A, and an extensive introduction, which puts these publications in a larger context. In Paper A the connection between the Stokes equation and the Reynolds equation is investigated. More precisely, the asymptotic behavior as both the film thickness
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Noutary, Marie-Pierre. "A robust Reynolds solver for textured surfaces in the piston ring cylinder liner contact." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEI105/document.
Повний текст джерелаАнотація:
Le contact Segment-Piston-Chemise (SPC) est essentiel pour la réduction des émissions de CO2 et de polluants dans les moteurs automobile. Pour optimiser ces deux contraintes antagonistes, il est nécessaire d’étudier l’influence de la microgéométrie afin de trouver de nouvelles architectures de ce contact. L’étude expérimentale étant très coûteuse, il est impératif de pouvoir modéliser les performances du contact SPC. Les méthodes multigrilles permettent de réduire considérablement les temps de calcul. Pour le contact SPC, les méthodes multigrilles classiques perdent leur efficacité en présence de texture. Un nouvel algorithme, basé sur des idées développées par Alcouffe et al. a été conçu qui permet l’étude du contact hydrodynamique en présence de texturation importante. Il a été validé par comparaison avec un modèle analytique 1D, ses performances ont été étudiées et une première étude de l’influence des paramètres sur la portance pour une surface striée a été faite. L’algorithme a ensuite été modifié pour imposer la conservation des flux. Un processus de relaxation plus proche de la physique du phénomène est utilisé. Le code obtenu n’atteint pas l’efficacité multigrille optimale. Cependant sa convergence est suffisamment rapide pour étudier l’influence de pores pour le segment plat et montrer l’importance d’une texturation partielle. Pour finir, le terme transitoire de l’équation de Reynolds est pris en compte. Pour un segment parabolique et une chemise striée, l’influence des paramètres des stries (profondeur, largeur, distance et angle des stries) sur la variation moyenne de la hauteur de film par rapport à une surface lisse est analyséeThe piston ring cylinder liner (PRCL) contact is essential in the CO2 and pollutant emission reduction in internal combustion engine. These two constraints being antagonistic, a compromise has to be found and it is necessary to study the microgeometry influence in order to find new PRCL contact architectures. As experimental study can be very expensive, modeling PRCL contact performance becomes crucial. Multigrid methods allow a huge reduction of the computational time. Unfortunately, in presence of texture, classical multigrid efficiency decays significantly and are not usable. A new algorithm based on an approach developed by Alcouffe et al. was designed that allows the study of the hydrodynamic lubrication of this contact even in the case of a highly varying geometry due to the texture. The obtained code was validated by comparison with a 1D analytical model, its performance was evaluated and a first study of an analytic cross hatched geometry parameter influence on the load carrying capacity was completed. The code was modified to include flow conservation. A relaxation process based closer to the physics phenomenon is used. The code efficiency is not the one that is expected from multigrid technics. However it convergence is sufficiently fast to study the dimple influence for the oil control ring and show the importance of partial texturing. Finally the transient term of the Reynolds equation is accounted for. In the case of a parabolic ring and for a cross hatched liner, the influence of the groove parameters ( depth, width, distance and groove angle) on the average minimum film thickness with respect to the smooth case is analyzed
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Oliver, Todd A. "A High-Order, Adaptive, Discontinuous Galerkin Finite Element Method for the Reynolds-Averaged Navier-Stokes Equations." Ft. Belvoir : Defense Technical Information Center, 2008. http://handle.dtic.mil/100.2/ADA488912.
Повний текст джерела
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Oliver, Todd A. 1980. "A high-order, adaptive, discontinuous Galerkin finite element method for the Reynolds-Averaged Navier-Stokes equations." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/46818.
Повний текст джерелаАнотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 175-182).
This thesis presents high-order, discontinuous Galerkin (DG) discretizations of the Reynolds-Averaged Navier-Stokes (RANS) equations and an output-based error estimation and mesh adaptation algorithm for these discretizations. In particular, DG discretizations of the RANS equations with the Spalart-Allmaras (SA) turbulence model are examined. The dual consistency of multiple DG discretizations of the RANS-SA system is analyzed. The approach of simply weighting gradient dependent source terms by a test function and integrating is shown to be dual inconsistent. A dual consistency correction for this discretization is derived. The analysis also demonstrates that discretizations based on the popular mixed formulation, where dependence on the state gradient is handled by introducing additional state variables, are generally asymptotically dual consistent. Numerical results are presented to confirm the results of the analysis. The output error estimation and output-based adaptation algorithms used here are extensions of methods previously developed in the finite volume and finite element communities. In particular, the methods are extended for application on the curved, highly anisotropic meshes required for boundary conforming, high-order RANS simulations. Two methods for generating such curved meshes are demonstrated. One relies on a user-defined global mapping of the physical domain to a straight meshing domain. The other uses a linear elasticity node movement scheme to add curvature to an initially linear mesh. Finally, to improve the robustness of the adaptation process, an "unsteady" algorithm, where the mesh is adapted at each time step, is presented. The goal of the unsteady procedure is to allow mesh adaptation prior to converging a steady state solution, not to obtain a time-accurate solution of an unsteady problem. Thus, an estimate of the error due to spatial discretization in the output of interest averaged over the current time step is developed. This error estimate is then used to drive an h-adaptation algorithm. Adaptation results demonstrate that the high-order discretizations are more efficient than the second-order method in terms of degrees of freedom required to achieve a desired error tolerance. Furthermore, using the unsteady adaptation process, adaptive RANS simulations may be started from extremely coarse meshes, significantly decreasing the mesh generation burden to the user.
by Todd A. Oliver.
Ph.D.
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Fabricius, John. "Homogenization of some problems in hydrodynamic lubrication involving rough boundaries." Doctoral thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25734.
Повний текст джерелаАнотація:
This thesis is devoted to the study of some homogenization problems with applications in lubrication theory. It consists of an introduction, five research papers (I–V) and a complementary appendix.Homogenization is a mathematical theory for studying differential equations with rapidly oscillating coefficients. Many important problems in physics with one or several microscopic scales give rise to this kind of equations, whence the need for methods that enable an efficient treatment of such problems. To this end several mathematical techniques have been devised. The main homogenization method used in this thesis is called multiscale convergence. It is a notion of weak convergence in Lp spaces which is designed to take oscillations into account. In paper II we extend some previously obtained results in multiscale convergence that enable us to homogenize a nonlinear problem with a finite number of microscopic scales. The main idea in the proof is closely related to a decomposition of vector fields due to Hermann Weyl. The Weyl decomposition is further explored in paper III.Lubrication theory is devoted to the study of fluid flows in thin domains. More generally, tribology is the science of bodies in relative motion interacting through a mechanical contact. An important aspect of tribology is to explain the principles of friction, lubrication and wear. The mathematical foundations of lubrication theory are given by the Navier–Stokes equation which describes the motion of a viscous fluid. In thin domains several simplifications are possible, as shown in the introduction of this thesis. The resulting equation is named after Osborne Reynolds and is much simpler to analyze than the Navier--Stokes equation.The Reynolds equation is widely used by engineers today. For extremely thin films, it is well-known that the surface micro-topography is an important factor in hydrodynamic performance. Hence it is important to understand the influence of surface roughness with small characteristic wavelengths upon the solution of the Reynolds equation. Since the 1980s such problems have been increasingly studied by homogenization theory. The idea is to replace the original equation with a homogenized equation where the roughness effects are “averaged out”. One problem consists of finding an algorithm for computing the solution of the homogenized equation. Another problem consists of showing, on introducing the appropriate mathematical definitions, that the homogenized equation is the correct method of averaging. Papers I, II, IV and V investigate the effects of surface roughness by homogenization techniques in various situations of hydrodynamic lubrication. To compare the homogenized solution with the solution of the deterministic Reynolds equation, some numerical examples are also included.Godkänd; 2011; 20110408 (johfab); DISPUTATION Ämnesområde: Matematik/Mathematics Opponent: Professor Guy Bayada, Institut National des Sciences Appliquées de Lyon (INSA-LYON), Lyon, France, Ordförande: Professor Lars-Erik Persson, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Tid: Tisdag den 7 juni 2011, kl 10.00 Plats: D2214/15, Luleå tekniska universitet
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Valivarthi, Mohan Varma, and Hema Chandra Babu Muthyala. "A Finite Element Time Relaxation Method." Thesis, Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-17728.
Повний текст джерелаАнотація:
In our project we discuss a finite element time-relaxation method for high Reynolds number flows. The key idea consists of using local projections on polynomials defined on macro element of each pair of two elements sharing a face. We give the formulation for the scalar convection–diffusion equation and a numerical illustration.
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Garcia, Gonzalez Jesus. "Numerical analysis of fluid motion at low Reynolds numbers." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/numerical-analysis-of-fluid-motion-at-low-reynolds-numbers(4cf30194-0155-439d-879a-c49787549e8c).html.
Повний текст джерелаАнотація:
At low Reynolds number flows, the effect of inertia becomes negligible and the fluid motion is dominated by the effect of viscous forces. Understanding of the behaviour of low Reynolds number flows underpins the prediction of the motion of microorganisms and particle sedimentation as well as the development of micro-robots that could potentially swim inside the human body to perform targeted drug/cell delivery and non-invasive microsurgery. The work in this thesis focuses on developing an understanding in the mathematical analysis of objects moving at low Reynolds numbers. A boundary element implementation of the Method of regularized Stokeslets (MRS) is applied to analyse the low Reynolds number flow field around an object of simple shape (sphere and cube). It also showed that the results obtained by a boundary element implementation for an unbounded cube, where singularities are presented in the corners of the cube, agrees with more complex solutions methods such as a GBEM and FEM.A methodology for analysing the effect of walls by locating collocation points on the surface of the walls and the object is presented. First at all, this methodology is validated with a boundary element implementation of the method of images for a sphere at different locations. Then, the method is extended when more than one wall is presented. This methodology is applied to predict the velocity filed of a cube moving in a tow tank at low Reynolds numbers for two different cases with a supporting rod similar to an experimental set-up, and without the supporting rod as in the CFD simulations based on the FVM. The results indicate a good match between CFD and the MRS, and an excellent approximation between the MRS and experimental data from PIV measurements. The drag, thrust and torque generated by helices moving at low Reynolds numbers in an unbounded medium is analysed by the resistive force theory, a slender body theory, and a boundary element method of the MRS. The results show that the resistive force theory predict accurately the drag, thrust and torque of moving helices when the resistive force coefficients are calculated from a slender body theory approximation by calculating independently the resistive force coefficients for translation and rotation, because it is observed that the resistive force coefficients depend also of the nature of motion. Moreover, the thrust generated by helices of different pitch angles is analysed calculated by a CFD numerical simulation based on the FVM and a boundary element implementation, an compared with experimental data. The results also show an excellent prediction between the boundary element implementation, the CFD results and the experimental data. Finally, a boundary element implementation of the MRS is applied to predict swimming of a biomimetic swimmer that mimics the motion of E.coli bacteria in an unbounded medium. The results are compared with the propulsive velocity and induced angular velocity measurement by recording the motion of the biomimetic swimmer in a square tank. It is observed that special care needs to be taken when the biomimetic swimmer is modelled inside the tank, as there is an apparent increment in the calculate thrust propulsion which does not represent a real situation of the biometic swimmer which propels by a power supply. However, this increment does not represent the condition of the biomimetic swimmer and a suggested methodology based on the solution from an unbounded case and when the swimmer is moving inside the tank is presented. In addition, the prediction of the free-swimming velocity for the biomimetic swimmer agrees with the results obtained by the MRS when the resistive force coefficients are calculated from a SBT implementation. The results obtained in this work have showed that a boundary element implementation of the MRS produces results comparable with more complex numerical implementations such as GBEM, FEM, FVM, and also an excellent agreement with results obtained from experimentation. Therefore, it is a suitable and easy to apply methodology to analyse the motion of swimmers at low Reynolds numbers, such as the biomimetic swimmer modelled in this work.
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Guilmineau, Emmanuel. "Contribution a la prediction du decrochage sur des ailes en incidence au moyen des equations de navier-stokes-reynolds." Nantes, 1995. http://www.theses.fr/1995NANT2097.
Повний текст джерелаАнотація:
Ce travail concerne la resolution numerique des equations de navier-stokes, ecrites sous forme conservative, pour un ecoulement de fluide incompressible. La reconstruction des flux est realisee par la methode cpi (consistent physical interpolation) qui s'applique aussi bien aux flux de masse qu'a ceux de quantite de mouvement. Des comparaisons avec des donnees experimentales sont systematiquement realisees. Les premieres applications sont la mise en impulsion d'un ecoulement laminaire autour d'un cylindre de section circulaire et d'un profil d'aile naca 0012. De tels problemes sont souvent utilises comme cas tests numeriques pour des etudes d'ecoulement instationnaire produisant une separation massive. Ensuite, on s'interesse a la prediction d'un ecoulement laminaire autour d'un profil d'aile naca 0012 en oscillations de tangage. Une autre application envisagee est la prediction d'ecoulements turbulents pour etudier les caracteristiques du decrochage de profils bidimensionnels a incidence fixe. Trois modeles de turbulence sont utilises: le modele baldwin-lomax, le modele baldwin-barth et le modele k-sst. Les profils d'aile etudies sont: le profil naca 4412 a son incidence de portance maximale, 13. 87, le profil as 240 ou profil b pour deux incidences: 8 et 19 et le profil ga(w)-1 pour les incidences suivantes: 4. 17, 14. 4 et 20. 05. Pour achever cette etude, l'ecoulement turbulent autour d'un profil naca 0012 en mouvement de tangage est considere avec plusieurs modeles de turbulence. Dans tous les cas, le modele k-sst donne de meilleurs resultats de portance et moment. Ce travail se termine par l'etude d'un ecoulement tridimensionnel turbulent autour d'une aile, en incidence, de section naca 0015 et d'envergure finie
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Lahjomri, Jawad. "Caractérisation de la structure des sillages M. H. D. Amont et aval d'un cylindre à petit nombre de Reynolds magnétique." Grenoble 1, 1988. http://www.theses.fr/1988GRE10046.
Повний текст джерелаАнотація:
Etude theorique et experimentale. Mesures locales des fluctuations de vitesse avec des sondes a film chaud et du champ magnetique induit avec des magnetodiodes. Analyse du sillage aval en detectant la perturbation magnetique associee a l'allee de von karman
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Mane, Laure. "Parallelisation sur un systeme multiprocesseur d'une methode de resolution des equations de navier-stokes instationnaires a grands nombres de reynolds." Paris 6, 1987. http://www.theses.fr/1987PA066507.
Повний текст джерелаАнотація:
Simulation numerique d'ecoulements instationnaires decolles autour d'un profil a grands nombres de reynolds sur un systeme multiprocesseur a memoire partagee. Resolution des equations de navier stokes en formulation fonction de courant-vorticite par une methode combinant schemas aux difference finies et techniques de direction alternees implicites. Presentation des performances du code parallele
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Jarray, Mohamed. "Étude numérique et expérimentale du comportement d'étanchéité des joints sans contact à rainures hélicoïdales." Thesis, Poitiers, 2018. http://www.theses.fr/2018POIT2299/document.
Повний текст джерелаАнотація:
Les joints sans contact sont des solutions d’étanchéité optimales pour les systèmes mécaniques fonctionnant à des vitesses relativement élevées. Ils ont une durée de vie importante et ont été proposés pour une utilisation dans les moteurs spatiaux. Une type de joints d'étanchéité sans contact, le joint visqueux, est étudié en détail dans ce travail de thèse au moyen d'une analyse numérique et expérimentale. Ce travail présente un modèle numérique développé pour prédire le comportement du joint visqueux en régime laminaire et turbulent. L’interface liquide-air dans le joint est également étudiée en utilisant une approche CFD basée sur la méthode VOF. La conception et la réalisation d’un dispositif expérimental a permis de confronter les résultats numériques et expérimentaux, l’écart entre les deux approches n’excède pas 10% dans 95% des cas étudiésContactless seals are optimal sealing solution for mechanical systems operating with relatively high speeds. They have an important operation life time, and they were proposed for use in space engines. One sub-category of non-contact seals, the viscoseal, is studied in detail in this work through a numerical and experimental analysis. This work presents a numerical model developed to predict the viscoseal performance in laminar and turbulent regime. Furthermore the sealing performance of the viscoseal is investigated for different geometrical characteristics of the seal. The interface liquid-air in the seal is also studied using a CFD approach based on VOF method. The design and installation of an experimental device allowed the comparison of the numerical and experimental results, the difference between the two does not exceed 10% for 95% of studied cases
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Diop, Khadim. "Estimation de la fiabilité d'un palier fluide." Thesis, Angers, 2015. http://www.theses.fr/2015ANGE0029/document.
Повний текст джерелаАнотація:
Les travaux de recherche constituent une contribution au développement de la théorie de la fiabilité en mécanique des fluides. Pour la conception de machines et de systèmes mécatroniques complexes, de nombreux composants fluides, difficiles à dimensionner, sont utilisés. Ces derniers ont des caractéristiques intrinsèques statiques et dynamiques sensibles et ont donc une grande importance sur la fiabilité et la durée de vie de la plupart des machines et des systèmes.Le développement effectué se concentre spécialement sur l'évaluation de la fiabilité d’un palier fluide grâce à un couplage « mécanique des fluides - fiabilité ». Ce couplage exige une définition propre de la fonction d’état limite permettant d’estimer la probabilité de défaillance d’un palier fluide. La modélisation par l'équation de Reynolds modifiée permet de déterminer la capacité de charge d’un palier fluide en fonction des conditions de fonctionnement. Plusieurs formes simples de paliers fluides ont été modélisées analytiquement et leurs probabilités de défaillance ont été estimées grâce à des méthodes d'approximation FORM/SORM (First Order Reliability, Second Order Reliability) et de simulation Monte CarloThese research is a contribution to the development of reliability theory in fluid mechanics. For the machines design and complex mechatronic systems, many fluid components are used. These components have static and dynamic sensitive characteristics and thus have a great significance on the reliabilityand lifetime of the machines and systems. Development performed focuses specifically on the reliability evaluation of a fluid bearing using a"fluid mechanics - reliability" interaction approach. This coupling requires a specific definition of the limit state function for estimating the failure probability of a fluid bearing. The Reynolds equation permits to determine the fluid bearing load capacity according to the operating conditions. Several simple geometries of fluid bearings were modeled analytically and their failure probabilities were estimated using the approximation methods FORM / SORM (First Order Reliability Method,Second Order Reliability Method) and Monte Carlo simulation
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Palma, Alfredo Del Carmen Jaramillo. "Modelação matemática de contatos lubrificados micro-texturizados." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-15092015-152346/.
Повний текст джерелаАнотація:
No desenho de mecanismos lubrificados, tais como Mancais hidrodinâmicos ou anéis de pistões de Motores a Combustão, atrito e desgaste são efeitos não desejados. Por exemplo, é sabido que aproximadamente 5% da energia perdida em um motor a combustão esta associada ao atrito presente no sistema de anéis/cilindro do pistão. Após vários trabalhos experimentais e teóricos, as superfícies texturizadas hão mostrado serem capazes de reduzir o atrito em algumas condições de funcionamento. O estudo da relação entre o atrito e os parâmetros de texturização é um problema difícil e de interesse tanto industrial como acadêmico. O contexto matemático e computacional destes trabalhos apresentam desafios por si mesmos, como o estudo da boa colocação dos modelos matemáticos, a consideração adequada das descontinuidades das superfícies. Este trabalho enfoca-se no contexto matemático, apresentando e estudando a equação de Reynolds junto com diferentes modelos de cavitação que podem encontrar-se na literatura. Começamos estudando a matemática da equação de Reynolds. Depois disso, modelos de cavitação são inclusos, aumentando a complexidade da matemática envolvida. Seguidamente, como aplicação da teoria apresentada, um rolamento deslizante será estudado junto com uma texturização da superfície móvel. Os resultados deste estudo revelam mecanismos básicos de redução de atrito e propriedades gerais que não haviam sido reportadas anteriormente. Possíveis trabalhos futuros são apresentados, tal como o uso de Métodos Descontínuos de Galerkin em vez dos Métodos de Volumes Finitos. O último em procura de uma melhor acomodação da formulação matemática, tentando melhorar a flexibilidade da malha e a precisão.In the design of lubricated mechanisms, such as Journal Bearings or Piston Rings of Combustion Engines, friction and wear are undesirable effects. It is known, for instance, that about 5% of the energy loss in a Combustion Engine is associated to friction taking place in the Piston Rings/Cylinder system. Textured surfaces, after a significant number of experimental and theoretical studies, have shown to reduce friction in some operating conditions. The study of the relation between the friction and the texture parameters is a challenging problem with both industrial and academic interest. The mathematical and computational frameworks involved present challenges by themselves, such as establishing the well-posedness of the mathematical models with suitable consideration of discontinuous surfaces. In this work we focus on the mathematical framework, presenting and studying the Reynolds equation along with different state-of-the-art cavitation models. We begin by studying the Reynolds equation and then incorporate two different cavitation models of increasing mathematical complexity. Next, as an application of the theory already presented, a slider bearing is numerically studied considering a sinusoidal texture on the runner. The results of this study unveil basic mechanisms of friction reduction and global quantitative trends that had not been previously reported. In this way, the applicability of numerical tools for texture selection is established. Future research directions are also identified, such as using Discontinuous Galerkin methods instead of Finite Volume Methods, aiming at improving the mesh exibility and thus the accuracy of the discrete formulation.
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Hackl, Jason F. "Fixed-scale statistics and the geometry of turbulent dispersion at high reynolds number via numerical simulation." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41100.
Повний текст джерелаАнотація:
The relative dispersion of one fluid particle with respect to another is
fundamentally related to the transport and mixing of contaminant species in
turbulent flows. The most basic consequence of Kolmogorov's 1941 similarity
hypotheses for relative dispersion, the Richardson-Obukhov law that mean-square
pair separation distance grows with the cube of time
at intermediate times in the inertial subrange, is notoriously difficult to
observe in the environment, laboratory, and direct numerical simulations (DNS).
Inertial subrange scaling in size parameters like the mean-square pair separation requires
careful adjustment for the initial conditions of the dispersion process as well
as a very wide range of scales (high Reynolds number) in the flow being studied.
However, the statistical evolution of the shapes of clusters of more than two
particles has already exhibited statistical invariance at intermediate times in
existing DNS. This invariance is identified with inertial-subrange scaling and
is more readily observed than inertial-subrange scaling for seemingly simpler quantities such as the mean-square pair separation
Results from dispersion of clusters of four particles (called tetrads) in
large-scale DNS at grid resolutions up to 4096 points in each of three directions and Taylor-scale Reynolds
numbers from 140 to 1000 are used to explore the question of
statistical universality in measures of the size and shape of tetrahedra in
homogeneous isotropic turbulence in distinct scaling regimes at very small times
(ballistic), intermediate times (inertial) and very late times (diffusive).
Derivatives of fractional powers of the mean-square pair separation with respect to time normalized by the
characteristic time scale at the initial tetrad size constitute a powerful
technique in isolating cubic time scaling in the mean-square pair separation. This technique
is applied to the eigenvalues of a moment-of-inertia-like tensor formed from the
separation vectors between particles in the tetrad. Estimates of the
proportionality constant "g" in the Richardson-Obukhov law from DNS at a
Taylor-scale Reynolds number of 1000 converge towards the value g=0.56 reported in
previous studies. The exit time taken by a particle pair to first reach
successively larger thresholds of fixed separation distance is also briefly
discussed and found to have unexplained dependence on initial separation
distance for negative moments, but good inertial range scaling for positive
moments. The use of diffusion models of relative dispersion in the inertial
subrange to connect mean exit time to "g" is also tested and briefly discussed
in these simulations.
Mean values and probability density functions of shape
parameters including the triangle aspect ratio "w," tetrahedron
volume-to-gyration radius ratio, and normalized moment-of-inertia
eigenvalues are all found to approach invariant forms in the inertial subrange
for a wider range of initial separations than size parameters such as
mean-square gyration radius. These results constitute the
clearest evidence to date that turbulence has a
tendency to distort and elongate multiparticle configurations more severely in
the inertial subrange than it does in the diffusive regime at asymptotically
late time. Triangle statistics are found to be independent of
initial shape for all time beyond the ballistic regime.
The development and testing of different schemes for parallelizing the cubic
spline interpolation procedure for particle velocities needed to track particles in DNS is also covered. A "pipeline" method of moving batches of particles
from processor to processor is adopted due to its low memory overhead, but there are challenges in achieving good performance scaling.
34
Wakrim, Mohamed. "Analyse numérique des équations de Navier-Stokes incompressibles et simulations dans des domaines axisymétriques." Saint-Etienne, 1993. http://www.theses.fr/1993STET4015.
Повний текст джерелаАнотація:
Dans cette thèse, on a développé une méthode numérique pour la simulation des écoulements de fluides à nombre de Reynolds élevé, utilisant deux types d'éléments finis. On a établi la convergence de l'algorithme d'Uzawa en formulation de Petrov-Galerkin et on a étudié l'élément fini de Crouzeix-Raviart en formulation de Petrov-Galerkin. Pour finir, on a construit un préconditionneur du CGS pour une formulation couplée
35
Gao, Wenjun. "Modelling of windage and churning losses in high speed rolling element bearings." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEI048/document.
Повний текст джерелаАнотація:
Dans un système de machines rotatives comme un moteur à turbine, les paliers d'éléments roulants à grande vitesse jouent un rôle important dans le support de l'arbre ou du rotor rotatif, et ont besoin d'une lubrification pour assurer leur fonction. Sauf qu'une petite quantité d'huile est nécessaire pour former le film lubrifiant élastohydrodynamique dans la zone de contact, la plus grande partie du lubrifiant reste en suspension dans l'air, formant un mélange huile/air. Ce phénomène entraîne des pertes hydrauliques parasitaires excessives lorsque les éléments roulants se translatent et tournent dans l'environnement fluide, ce qui peut constituer une partie relativement importante de la perte de puissance totale du roulement, appelée traînée d'enroulement et pertes de barattage. Pour une vitesse de rotation jusqu'à 3× 106 Ndm, la contribution de la traînée/dérive au total peut atteindre 50%. Cependant, jusqu'à présent, il existe peu d'approches utilisées directement pour l'estimation des pertes par traînage, qui ne pouvait fournir qu'une approximation plutôt grossière. Dans cette thèse, la méthode CFD est utilisée pour analyser d'abord l'écoulement autour d'un cylindre circulaire de longueur finie avec deux extrémités libres dans un espace ouvert. Ensuite, le modèle est remplacé par plusieurs cylindres circulaires en ligne pris en sandwich par deux parois plates, ce qui représente une approche simplifiée. Le fluide est ici considéré comme incompressible, représentant un fluide monophasé équivalent pour l'écoulement diphasique huile/air à l'intérieur de la cavité de palier avec des propriétés de fluide spécifiées. Les résultats indiquent que l'écoulement autour de l'élément de rouleau de longueur finie est perturbé par ses deux extrémités libres, les anneaux environnants, la cage et d'autres éléments roulants. Il est proposé une relation entre le coefficient de traînée et le nombre de Reynolds approprié pour un cylindre circulaire dans les roulements à rouleaux (1In a rotating machinery system like turbine engine, high speed rolling element bearings play an important role in supporting the rotating shaft or rotor, and need lubrication to insure their function. Except a small quantity of oil is needed to form the elastohydrodynamic lubricant film in the contact zone, most of lubricant remains in suspension in air, forming an oil/air mixture. This phenomenon leads to excessive parasitic hydraulic losses when rolling elements translate and rotate into the fluid environment, which may constitute a relatively large portion of the bearing's total power loss, named windage drag and churning losses. For high speed applications, i.e. for rotational speed up to 3× 10^6 Ndm, the contribution of drag/windage loss to the total one may reach up to 50%. However, so far there are few approaches used directly for drag and churning losses estimation, which could only provide a rather gross approximation. In this thesis, the Computational Fluid Dynamics (CFD) method is employed to analyze first the flow around one finite-length circular cylinder with two free ends in an open space. Then the model is changed to several in-line circular cylinders sandwiched by two flat walls, which represents a simplified approach. The fluid here is regarded as incompressible, representing an equivalent one-phase fluid for the oil/air two-phase flow inside the bearing cavity with specified fluid properties. The results indicate that the flow around the finite length roller element is perturbed by its two free ends, the surrounding rings, the cage and other rolling elements. A relationship between the drag coefficient and the Reynolds number suitable for circular cylinder in roller bearings (1
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Bouchehit, Bachir. "Etude dynamique d’un palier compliant lubrifié à l’aide de fluide réfrigérant." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEI013/document.
Повний текст джерелаАнотація:
Depuis plusieurs années à nos jours, les paliers à gaz sont utilisés avec succès sur une large gamme de turbo-machines. Certains de ces systèmes sont utilisés dans des environnements de contrôle de l’environnement par gaz réfrigérant. Dans ce travail, nous présentons un modèle théorique et numérique qui tient compte de la transition du lubrifiant vapeur / liquide, la transition de l’écoulement laminaire / turbulent et les variations 3D de la viscosité et de la température dans le fluide et les solides pour les deux situations statiques et dynamiques. Ce modèle comporte : la résolution de l'équation de Reynolds généralisée pour les fluides compressibles à viscosité variable en 3D, la description des effets de la turbulence en utilisant l'approche phénoménologique de Elrod, en utilisant un champ de viscosité turbulente 3D, la résolution de l’équation d’état non linéaire du lubrifiant, capable de décrire la transition vapeur / liquide et une approche thermique local afin d'obtenir une estimation 3D de la température du fluide, grâce à l'équation d'énergie pour film mince. La prise en compte également des effets thermiques dans les solides. Dans cette étude, nous avons montré l'importance d'une description précise des paramètres du film fluide, dont les variations influencent largement le comportement du palier. Parmi les principales théories, il y a: lubrifiant compressible, avec un comportement non-linéaire près de la transition vapeur / liquide, la transition vapeur / liquide et le calcul des paramètres équivalents du mélange, un écoulement turbulent du fluide pour le palier GFB à grande vitesse en utilisant un modèle 3D de la viscosité turbulente, un comportement 3D pour la viscosité, en particulier les variations inter-films (dépendant de la température), et un comportement 3D pour la température, en particulier dans le sens transversal du film afin d'être compatible avec la viscosité, mais également dans la direction axiale afin de tenir en compte du gradient de température potentiel qui modifie considérablement le profil 3D de la température du palier. Ces deux comportements statiques et dynamiques du palier compliant GFB sont analysésFor years now, gas bearings are successfully used over a large panel of turbo-machineries. Some of these systems are bound to be run in controlled environments such as refrigerating gas. In this work we present a theoretical and numerical model which takes into account the vapor/liquid lubricant transition, the laminar/turbulent flow transition and both temperature and viscosity 3D variations in the fluid and the solids for both static and dynamic situations. This model involves: the resolution of the generalized Reynolds equation for compressible fluids with 3D variable viscosity, the description of the turbulence effects by the phenomenological approach of Elrod, using a 3D eddy viscosity field, the resolution of a non-linear equation of state for the lubricant, able to describe the vapor/liquid transition and a local thermal approach to obtain a 3D estimation of the fluid temperature, thanks to the thin-film energy equation. The thermal effects in solids are also taken into account. In this study, we showed the importance of an accurate description of the film parameters, which variations largely influence the bearing behaviour. Among the principal theories, there are: compressible lubricant, with an appropriate non-linear behaviour when close to the vapor/liquid transition, vapor/liquid transition and calculation of the mixture equivalent parameters, turbulent flow for high-speed GFBs with a 3D eddy viscosity mode, a 3D behaviour for viscosity, particularly the cross-film variations, (temperature dependent)and a 3D behaviour for temperature, particularly in cross-film direction in order to be consistent with viscosity, but also in the axial direction in order to account for potential temperature gradient which considerably modifies the bearing 3D temperature profile. Both static and dynamic behaviours of GFBs are analysed
37
Rocke, Ann H. "Elastohydrodynamic Analysis of a Rotary Lip Seal Using Flow Factors." Thesis, Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/4771.
Повний текст джерелаАнотація:
An elastohydrodynamic analysis of a rotary lip seal is performed numerically, incorporating both the fluid mechanics of the lubricating film and the elastic deformation of the lip, by solving the Reynolds equation with flow factors. Asperities on the lip surface dominate the behavior of the flow field in the lubricating film and the elastic deformation of the lip. Since previous analyses treated those asperities deterministically, they required very large computation times. The present approach is much less computationally intensive because the asperities are treated statistically.
Since cavitation and asperity orientation play important roles, these are taken into account in the computation of the flow factors. An asperity distortion analysis is introduced to obtain a more realistic model of the complex variations in the asperity distribution on the surface of the seal.
Results of the analysis show how the operating parameters of the seal and the characteristics of the asperities affect such seal characteristics as the thickness of the lubricating film, reverse pumping rate, power dissipation and load carrying capacity.
38
Kline, Sara E. "An Investigation of the Performance of Compliant Finger Seals for use in Gas Turbine Engines using Navier-Stokes and Reynolds Equation Based Numerical Models and Experimental Evaluation." University of Akron / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=akron1478984223281402.
Повний текст джерела
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Lambrechtsen, Frans Joseph. "Second-Order Perturbation Analysis of the St. Venant Equations in Relation to Bed-Load Transport and Equilibrium Scour Hole Development." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/4274.
Повний текст джерелаАнотація:
This analysis is an expansion of research done by Rollin Hotchkiss during his Ph.D work. The research uses fluid flow, sediment transport, and perturbation theory to predict where scour will occur in a variable-width channel. The resulting equations also determine equilibrium scour depth based upon the stream bed elevation derived from a dimensionless bed slope equation. Hotchkiss perturbed the width of the channel using a second order Taylor Series perturbation but neglected second order terms. The present work follows the same procedures as Hotchkiss but maintains the second order terms. The primary purpose is to examine how the additional terms impact the final equilibrium scour depth and location results. The results of this research show a slight variation from the previous work. With respect to a hypothetical case, there was not a significant amount of change, thereby verifying that scour migrates downstream with an increase in discharge. Interestingly, the comparison shows a slight increase in sediment discharge through the test reach analyzed. Supplementary to previous research, values of scour depth and location in terms of distance from the start of channel-width perturbation are provided; at the lowest discharge maximum scour occurs 4% of a wavelength upstream of the narrowest portion, and at the highest discharge maximum scour occurs at the narrowest point. Additionally, a one-dimensional HEC-RAS sediment transport model and a two- dimensional SRH flow model were compared to the analytical results. Results show that the model output of the HEC-RAS model and the SRH model adequately approximate the analytical model studied. Specifically, the results verify that maximum scour depth transitions downstream as discharge increases.
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Sawadkosin, Paranee. "Optimalizace tvaru strojních součástí s vlivem variabililty vstupních údajů." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401572.
Повний текст джерелаАнотація:
The objective of this Master’s thesis is to find shape optimal design based on min- imizing friction force of thrust bearing by using genetic algorithm(GA) which is one of an optimization toolbox in Matlab. Reducing the friction force of thrust bearing is one way of making shaft to decreasing friction losses. With four parameters of thrust bearing geometry number of segments(m), angle of running surface(), segment inner radius(R0), and segment outer radius(R1) substitute in Reynolds’ equation. In order to know friction force, it is necessary to generate a connecting variable, oil film thickness(h0) from loading capacity(W ) and revolution per minute(rpm). Friction power loss, as well as weight func- tion conclude the final shape optimization of thrust bearing: m = 7, = 0.1, R0 = 15 mm, and R1 = 20 mm.
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Bakhshi, Shashwat. "Numerical Analysis to Study the Effect of Sag and Non-circular Whirl Orbits on the Damping Performance of a Squeeze Film Damper." University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1522420027908978.
Повний текст джерела
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William, James Pringle. "Two-way Coupled Multiscale Tsunami Modelling from Generation to Coastal Zone Hydrodynamics." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215503.
Повний текст джерела
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Reid, Francis John Edward School of Mathematics UNSW. "The weakly nonlinear stability of an oscillatory fluid flow." Awarded by:University of New South Wales. School of Mathematics, 2006. http://handle.unsw.edu.au/1959.4/33364.
Повний текст джерелаАнотація:
A weakly nonlinear stability analysis was conducted for the flow induced in an incompressible, Newtonian, viscous fluid lying between two infinite parallel plates which form a channel. The plates are oscillating synchronously in simple harmonic motion. The disturbed velocity of the flow was written in the form of a series in powers of a parameter which is a measure of the distance away from the linear theory neutral conditions. The individual terms of this series were decomposed using Floquet theory and Fourier series in time. The equations at second order and third order in were derived, and solutions for the Fourier coefficients were found using pseudospectral methods for the spatial variables. Various alternative methods of computation were applied to check the validity of the results obtained. The Landau equation for the amplitude of the disturbance was obtained, and the existence of equilibrium amplitude solutions inferred. The values of the coefficients in the Landau equation were calculated for the nondimensional channel half-widths h for the cases h = 5, 8, 10, 12, 14 and 16. It was found that equilibrium amplitude solutions exist for points in wavenumber Reynolds number space above the smooth portion of the previously determined linear stability neutral curve in all the cases examined. Similarly, Landau coefficients were calculated on a special feature of the neutral curve (called a ???finger???) for the case h = 12. Equilibrium amplitude solutions were found to exist at points inside the finger, and in a particular region outside near the top of the finger. Traces of the x-components of the disturbance velocities have been presented for a range of positions across the channel, together with the size of the equilibrium amplitude at these positions. As well, traces of the x-component of the velocity of the disturbed flow and traces of the velocity of the basic flow have been given for comparison at a particular position in the channel.
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BENHABOUCHA, Nadia. "Quelques problèmes mathématiques relatifs à la modélisation des conditions aux limites fluide-solide pour des écoulements de faible épaisseur." Phd thesis, Université Claude Bernard - Lyon I, 2003. http://tel.archives-ouvertes.fr/tel-00005482.
Повний текст джерелаАнотація:
Ce travail de thèse est consacré à l'étude asymptotique d'écoulements de faible épaisseur et à la modélisation des conditions aux limites à imposer à l'interface fluide-solide dans différentes situations. Le chapitre 1 est consacré à l'etude asymptotique d'un écoulement fluide constitué d'une couche poreuse mince adjacente à un milieu fluide mince. On met en évidence l'existence d'un rapport critique entre la taille de la microstructure du milieu poreux et les deux épaisseurs, rapport pour lequel une équation de Reynolds modifiée est obtenue. De plus il est montré qu'on peut toujours pour une géométrie réelle se placer dans ce cas critique. Enfin, on présente des simulations numériques qui mettent en évidence les différences entre le modèle présenté ici et deux autres modèles utilisés en mécanique. Dans le chapitre 2, on s'intéresse à l'étude d'un écoulement de faible épaisseur quand une des surfaces est rugueuse. Ceci peut etre relié à l'étude du chapitre précédent en considérant un milieu poreux qui ne comporterait qu'une seule couche. On utilise la technique de la double échelle en homogénéisation pour obtenir rigoureusement les résultats de convergences. En outre, la convergence des contraintes normales et tangentielles sur les surfaces lisses et rugueuses est étudiée. Dans le chapitre 3, on étudie un écoulement d'un fluide non newtonien de type micropolaire avec de nouvelles conditions à l'interface fluide solide couplant la vitesse et la microrotation par l'introduction d'une viscosité de surface. On démontre l'existence et l'unicité de la solution et des estimations a priori qui conduisent, via l'étude asymptotique, à une équation de Reynolds micropolaire généralisée. Une étude numérique montre l'influence des conditions aux limites sur la charge et le coefficient de frottement. Les résultats sont comparés avec ceux d'autres modèles retenant une condition d'adhérence à la paroi.
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Noakes, Caroline. "The dynamics of liquid films on rotating surfaces." Thesis, University of Nottingham, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368933.
Повний текст джерела
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Elzaabalawy, Hashim ibrahim mohamed. "Towards High-Order Compact Discretization of Unsteady Navier-Stokes Equations for Incompressible Flows on Unstructured Grids." Thesis, Ecole centrale de Nantes, 2020. https://tel.archives-ouvertes.fr/tel-03274249.
Повний текст джерелаАнотація:
Une méthode haut ordre de résolution des équations de Navier-Stokes pour un écoulement incompressible basée sur une discrétisation éléments finis Galerkin discontinu hybride est présentée pour laquelle la stabilité énergétique est assurée et la masse et la quantité de mouvement sont conservées. La formulation calcule exactement des champs de vitesse solénoïdaux pour des types d'élément standard sans avoir recours à des opérateurs de post-traitement ou à des espaces fonctionnels \textit{H}(div) conformes. Ceci est réalisé en proposant une définition simple et nouvelle de l'espace fonctionnel pour la pression, de sorte qu'il contienne la divergence de la vitesse discrétisée. Une attention particulière est accordée à l'application de cette méthode à différentes formes d'éléments en introduisant le concept d'éléments d'ordre réduit pour toutes les formes standard en 2D et 3D. En outre, la contrainte d'incompressibilité est gérée via la condensation statique pour résoudre le problème du point selle. De plus, dans le but de simuler des écoulements à nombres de Reynolds élevés, la signification de la stabilisation de la diffusion dans le cadre discontinue de Galerkin hybride est analysée. Alors que dans la littérature, le terme de stabilisation de la diffusion est directement proportionnel à la diffusivité ou à la viscosité pour les équations de Navier-Stokes, la présente étude dérive mathématiquement une nouvelle expression pour le terme de stabilisation de diffusion où le terme est inversement proportionnel à la diffusivité ou à la viscosité. Son importance pour les écoulements dominés par la convection est soulignée et étayée par de nombreux exemples numériques. De plus, la formulation proposée pour les équations de Navier-Stokes en régime incompressible est étendue pour résoudre ces équations en moyenne de Reynolds (RANSE) pour les modèles de turbulence TNT, BSL et SST $ k- \omega $ pour des nombres de Reynolds jusqu'à $ 10 ^ 9 $. La résolution des équations en formulation RANSE est une tâche difficile pour les méthodes d'ordre élevé, en raison de profils non réguliers des quantités caractérisant la turbulence. Dans le cadre de la formulation Galerkin discontinu, l'approximation polynomiale de ces quantités conduit à de grandes oscillations qui impactent le solveur non linéaire. Compte tenu de la complexité des méthodes d'ordre élevé et des erreurs de modélisation assez importantes de la modélisation RANS, les méthodes d'ordre inférieur sont par conséquent, souvent considérées dans la littérature comme plus pragmatiques. Cependant, cette thèse montre que la résolution des équations RANSE avec la méthode d'ordre élevé proposée est robuste et conduit à des amplitudes d'erreur significativement plus faibles par rapport aux solveurs basés sur les volumes finis du second ordre. De plus, on observe une réduction remarquable du nombre d'itérations pour obtenir une solution convergée. Une attention particulière est portée au traitement du taux spécifique de dissipation de la turbulence $\omega$ dans le cadre des approximations d’ordre élevé. Les possibilités et les limites de la simulation d'écoulements incompressibles industriels à l'aide de cette formulation haut-ordre sont évaluées afin de tirer des conclusions générales pour les applications industriellesA high-order energy-stable method for solving the incompressible Navier-Stokes equations based on hybrid discontinuous Galerkin method is presented for which the mass and momentum are conserved. The formulation computes exactly pointwise divergence-free velocity fields for standard element types without post-processing operators nor using \textit{H}(div)-conforming spaces. This is achieved by proposing a simple and novel definition to the functional space of the pressure, such that it contains the divergence of the approximate velocity. Specific focus is given on applying this method on different element shapes by introducing the concept of reduced-order elements for all standard shapes in 2D and 3D. Further, the incompressibility constraint is handled via the static condensation to solve the saddle point problem. Furthermore, with the aim to simulate high Reynolds numbers flows, the significance of the diffusion stabilization in the hybridizable discontinuous Galerkin framework is analyzed. Referring to literature, the diffusion stabilization term is directly proportional to the diffusivity or the viscosity for the Navier-Stokes equations. In this work, a new expression for the diffusion stabilization term is mathematically derived, where the term is inversely proportional to the diffusivity or viscosity. Its importance for convection dominated flows is emphasized and supported by numerical examples.Moreover, the proposed formulation for the incompressible Navier-Stokes is extended to solve the RANSE for the TNT, BSL, and SST $k-\omega$ models for Reynolds numbers up to $10^9$.Solving RANSE is a resilient task for high-order methods, due to the non-smooth profiles of the turbulence quantities. In the discontinuous Galerkin framework, the polynomial approximation for these quantities leads to large oscillations that obstruct the non-linear solver. Taking into account the complexity with high-order methods and the fairly large modeling errors of the RANS modeling, low-order methods are believed to be more pragmatic. However, it is illustrated that solving RANSE with high-order methods leads to significantly smaller error magnitudes compared with second-order finite volume based solvers. Additionally, there is a remarkable improvement regarding the number of iterations to obtain a converged solution. Attention is given to the treatment of the specific rate of turbulence dissipation $\omega$ in the high-order framework. The possibilities and limitations of simulating industrial incompressible flows using discontinuous Galerkin based methods are assessed in order to draw some general conclusions for industrial applications
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Cordova, Hinojosa Rogers Bill. "Modélisation de la rupture d'un milieu fragile soumis à l'injection d'un fluide visqueux : Analyse de la singularité en pression et du décollement en pointe de fissure." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLY016/document.
Повний текст джерелаАнотація:
La propagation d'une fissure chargée par un écoulement de fluide visqueux est un phénomène complexe où la compréhension des phénomènes mécaniques mis en jeu en pointe de fissures reste encore partielle. C'est le cas de la zone de décollement entre le solide et le fluide qui apparaît pour un certain choix de débit d'injection, de viscosité du fluide et de ténacité du matériau. Cette thèse propose une modélisation simplifiée de ce problème d'interaction fortement couplé. Dans un premier chapitre, on étudie un modèle simplifié unidimensionnel de film élastique collé sur un substrat rigide et on considère une injection de fluide visqueux entre le film et le substrat. On suppose que la propagation de la fissure est régie par la loi de Griffith. On néglige l'existence du retard possible entre le fluide et le solide et on choisit une loi de comportement non-linéaire pour le fluide visqueux. A partir d'une analyse asymptotique pour une faible viscosité, on établit une solution approchée du problème. On montre que le champ pression est singulier en pointe de fissure et on montre l'influence du débit d'injection sur la cinétique du trajet de fissuration. Dans le deuxième chapitre on propose de prendre en compte l'existence de la zone de décollement en modifiant la formulation du modèle et en le réécrivant sous la forme d'un problème d'optimisation en temps discret où les zones de décollement font partie des inconnues du problème. On valide la formulation proposée sur l'exemple analytique de l'écrasement d'une goutte par une barre rigide. On montre ensuite que cette formulation et l'algorithme lié à son implémentation sont capables de gérer l'évolution de l'écrasement de plusieurs gouttes de forme quelconque en capturant correctement les phase d'étalement des gouttes ainsi que de leur coalescence. On étend ensuite cette formulation au cas de l'écrasement d'une goutte par un film élastique. Dans le dernier chapitre, on examine la validité de l'hypothèse de lubrification utilisée en fracturation hydraulique. A l'aide de la méthode de développement asymptotique, on construit une équation de Reynolds régularisée avec des termes de gradient supérieur tenant compte de la variation spatiale de la hauteur des parois. On compare alors le comportement des champs de pression donnés par les équations de Reynolds classique et régularisée sur des exemples d'écoulement entre des conduits de formes multiplesThe crack evolution under a viscous fluid action is a complex phenomenon where the understanding of the mechanical phenomena near the crack tip is still largely limited. This is the case for the lag between the solid and the fluid front propagation which appears for some configurations of injection rate, fluid viscosity and material toughness. This thesis proposes a simplified model for this strongly coupled interaction problem.The first chapter studies a simplified one-dimensional model of a elastic film bonded to a rigid substrate. We consider a viscous fluid injection between the film and the substrate. The crack propagation is assumed to follow the Griffith's law. The existence of the lag is neglected and a non-linear behavior law is chosen for the viscous fluid. Using an asymptotic analysis, an approximate solution is established for the low viscosity case. It is shown that the pressure field diverges at the crack tip and that the kinetics of the crack is influenced by the injection rate. The second chapter proposes to take into account the existence of the lag by modifying the model formulation and rewriting it as a discrete time optimisation problem where the delamination zones are part of the unknowns of the problem. This formulation is validated for the analytical example of a drop crushed by a rigid bar. It is shown that this formulation and its implementation can manage the evolution of several drops of any shape and correctly captures the drops spreading and coalescence. This formulation is then extended to the case of a drop crushed by an elastic film. In the last chapter, the validity of the lubrication hypothesis is examinated. Using an asymptotic analysis, a regularized Reynolds equation is constructed with higher gradient terms taking into account the spatial variation of the walls height. A comparison between the pressure fields behaviour given by the classical and the regularized Reynolds equation is shown for different conducts
48
Grec, Bérénice. "Fluides complexes en films minces." Phd thesis, Ecole Centrale de Lyon, 2008. http://tel.archives-ouvertes.fr/tel-00351462.
Повний текст джерелаАнотація:
Cette thèse est consacrée à la modélisation, à l'analyse mathématique et à la simulation numérique d'écoulements de divers fluides complexes dans des domaines de faible épaisseur. En effet, les modèles de fluides newtoniens ne sont pas toujours suffisants pour décrire de manière réaliste les écoulements considérés. Plusieurs phénomènes peuvent être pris en compte :* le caractère complexe des fluides eux-mêmes, comme pour des fluides non-newtoniens ;
* l'hétérogénéité de l'écoulement, dans le cas de mélanges de fluides par exemple.
Il est important d'analyser comment ces modèles peuvent être simplifiés dans le cas de domaines minces, et d'étudier rigoureusement les modèles approchés.
Dans une première partie, des écoulements de fluides non newtoniens visco-élastiques représentés par une loi de comportement de type Oldroyd-B couplée aux équations de Navier-Stokes sont étudiés. Dans le cas de géométries minces, un modèle approché a été proposé. On justifie la validité de cette approximation ; la démonstration repose sur des estimations et des résultats de régularité fins.
Dans une deuxième partie, on considère un modèle d'écoulement piezovisqueux utilisé en lubrification hydrodynamique. Ce modèle fait aussi intervenir la déformation élastohydrodynamique du domaine (déformation du type Hertz), et l'aspect diphasique de la cavitation, qui est décrit par le modèle d'Elrod-Adams (en pression-saturation). On montre l'existence d'une solution à ce problème pour des lois pression-viscosité réalistes.
Dans une troisième partie, on introduit un modèle diphasique à interface diffuse, permettant de rendre compte de phénomènes plus fins tels que les gouttes. Pour cela, un paramètre d'ordre est introduit (fraction volumique d'une phase dans le mélange), gouverné par le modèle de Cahn-Hilliard. Un système approché est obtenu de manière heuristique pour un domaine de faible épaisseur. On étudie les propriétés mathématiques de ce système, et on montre un résultat d'existence, avec prise en compte ou non de la tension de surface.
Dans la dernière partie, un schéma numérique est mis en place pour simuler le modèle décrit précédemment d'écoulements diphasiques en domaines minces. Il permet de prendre en compte différents phénomènes physiques, comme de grandes variations de la viscosité ou la présence de recirculations à l'intérieur d'une goutte, ainsi que de simuler des mélanges dans le cadre d'écoulements lubrifiés.
49
Kaya, Mustafa. "Computation Of Viscous Flows Over Flapping Airfoils And Parallel Optimization Of Flapping Parameters." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/12612286/index.pdf.
Повний текст джерелаАнотація:
Airfoils °apping in pitch and plunge are studied, and the °
apping motion parameters are op- timized to maximize thrust generation and the e±
ciency of the thrust generation. Unsteady viscous °
ow¯
elds over °
apping airfoils are computed on overset grids using a Navier-Stokes solver. Computations are performed in parallel using Parallel Virtual Machine library routines in a computer cluster. A single °
apping airfoil and dual airfoils °
apping in a biplane con- ¯
guration are considered. A gradient based optimization algorithm is employed. The thrust production and the e±
ciency of the thrust production are optimized with respect to °
apping parameters
the plunging and pitching amplitudes, the °
apping frequency, and the phase shift between the pitch and plunge motions. It is observed that thrust generation of °
apping airfoils strongly depends on the phase shift and high thrust values may be obtained at the expense of reduced e±
ciency. For a high e±
ciency in thrust generation, the e®
ective angle of attack of the airfoil is reduced and large scale vortex formations at the leading edge are prevented. At a ¯
xed reduced °
apping frequency of 1, a single °
apping airfoil in pitch and plunge motion produces the maximum average thrust coe±
cient of 1:41 at the plunge amplitude of 1:60, the pitch amplitude of 23:5o, and the phase shift of 103:4o whereas the maximum e±
ciency of 67:5% is obtained at the plunge amplitude of 0:83, the pitch amplitude of 35:5o and the phase shift of 86:5o.
50
Lohéac, Jérôme. "Contrôle en temps optimal et nage à bas nombre de Reynolds." Phd thesis, Université de Lorraine, 2012. http://tel.archives-ouvertes.fr/tel-00801240.
Повний текст джерелаАнотація:
Cette thèse est divisée en deux parties, le fil directeur étant la contrôlabilité en temps optimal. Dans la première partie, après un rappel du principe du maximum de Pontryagin dans le cas des systèmes de dimension finie, nous mettrons en œuvre ce principe sur le cas d'un intégrateur non-holonome connu sous le nom de système de Brockett pour lequel nous imposons des contraintes sur l'état. La difficulté de cette étude provient du fait que l'on considère un problème de contrôle avec des contraintes sur l'état. Après cet exemple, nous nous intéressons à une extension du principe du maximum de Pontryagin au cas des systèmes de dimension infinie. Plus précisément, l'extension que nous considérons s'applique au cas de systèmes exactement contrôlables en tout temps. Typiquement, ce résultat s'applique à l'équation de Schrödinger avec contrôle interne. Pour de tels systèmes, sous une condition de contrôlabilité approchée, depuis un ensemble de temps non négligeable, nous montrons l'existence d'un contrôle bang-bang. Dans la seconde partie, nous étudions le problème de la nage à bas nombre de Reynolds. Une modélisation physique convenable nous permet de le formaliser comme un problème de contrôle. Nous obtenons alors un résultat de contrôlabilité sur ce problème. Plus précisément, nous montrons que quelque soit la forme du nageur, celui-ci peut se déformer légèrement pour suivre une trajectoire imposée. Nous étudions ensuite le cas d'un nageur à symétrie axiale. Les résultats de la première partie permettent alors la recherche d'un contrôle en temps optimal.