Academic literature on the topic 'Bingham fluids'
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Journal articles on the topic "Bingham fluids"
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Frigaard, I. A., S. D. Howison, and I. J. Sobey. "On the stability of Poiseuille flow of a Bingham fluid." Journal of Fluid Mechanics 263 (March 25, 1994): 133–50. http://dx.doi.org/10.1017/s0022112094004052.
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The stability to linearized two-dimensional disturbances of plane Poiseuille flow of a Bingham fluid is considered. Bingham fluids exhibit a yield stress in addition to a plastic viscosity and this description is typically applied to drilling muds. A non-zero yield stress results in an additional parameter, a Bingham number, and it is found that the minimum Reynolds number for linear instability increases almost linearly with increasing Bingham number.
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Shelukhin, V. V., and M. Ružička. "On Cosserat-Bingham fluids." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 93, no. 1 (September 24, 2012): 57–72. http://dx.doi.org/10.1002/zamm.201200037.
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Yigit, Sahin, and Nilanjan Chakraborty. "Influences of aspect ratio and wall boundary condition on laminar Rayleigh–Bénard convection of Bingham fluids in rectangular enclosures." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 2 (February 6, 2017): 310–33. http://dx.doi.org/10.1108/hff-09-2015-0366.
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Purpose This paper aims to investigate the aspect ratio (AR; ratio of enclosure height:length) dependence of steady-state Rayleigh–Bénard convection of Bingham fluids within rectangular enclosures for both constant wall temperature and constant wall heat flux boundary conditions. A nominal Rayleigh number range 103 ≤ Ra ≤ 105 (Ra defined based on the height) for a single representative value of nominal Prandtl number (i.e. Pr = 500) has been considered for 1/4 ≤ AR ≤ 4. Design/methodology/approach The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in rectangular enclosures. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity. Findings It has been found that buoyancy-driven flow strengthens with increasing nominal Rayleigh number Ra, but the convective transport weakens with increasing Bingham number Bn, because of additional flow resistance arising from yield stress in Bingham fluids. The relative contribution of thermal conduction (advection) to the total thermal transport strengthens (diminishes) with increasing AR for a given set of values of Ra and Pr for both Newtonian and Bingham fluids for both boundary conditions, and the thermal transport takes place purely because of conduction for tall enclosures. Originality/value Correlations for the mean Nusselt number Nu ¯ have been proposed for both boundary conditions for both Newtonian and Bingham fluids using scaling arguments, and the correlations have been demonstrated to predict Nu ¯ obtained from simulation data for 1/4 ≤ AR ≤ 4, 103 ≤ Ra ≤ 105 and Pr = 500.
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Shelukhin, V. V., and V. V. Neverov. "Thermodynamics of micropolar Bingham fluids." Journal of Non-Newtonian Fluid Mechanics 236 (October 2016): 83–90. http://dx.doi.org/10.1016/j.jnnfm.2016.08.005.
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Shelukhin, V. V., and V. V. Neverov. "Thermodynamics of micropolar Bingham fluids." Journal of Non-Newtonian Fluid Mechanics 238 (December 2016): 16–23. http://dx.doi.org/10.1016/j.jnnfm.2016.11.006.
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Liu, Tong, Shiming Zhang, and Moran Wang. "Does Rheology of Bingham Fluid Influence Upscaling of Flow through Tight Porous Media?" Energies 14, no. 3 (January 28, 2021): 680. http://dx.doi.org/10.3390/en14030680.
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Non-Newtonian fluids may cause nonlinear seepage even for a single-phase flow. Through digital rock technologies, the upscaling of this non-Darcy flow can be studied; however, the requirements for scanning resolution and sample size need to be clarified very carefully. This work focuses on Bingham fluid flow in tight porous media by a pore-scale simulation on CT-scanned microstructures of tight sandstones. A bi-viscous model is used to depict the Bingham fluid. The results show that when the Bingham fluid flows through a rock sample, the flowrate increases at a parabolic rate when the pressure gradient is small and then increases linearly with the pressure gradient. As a result, an effective permeability and a start-up pressure gradient can be used to characterize this flow behavior. By conducting flow simulations at varying sample sizes, we obtain the representative element volume (REV) for effective permeability and start-up pressure gradient. It is found that the REV size for the effective permeability is almost the same as that for the absolute permeability of Newtonian fluid. The interesting result is that the REV size for the start-up pressure gradient is much smaller than that for the effective permeability. The results imply that the sample size, which is large enough to reach the REV size for Newtonian fluids, can be used to investigate the Bingham fluids flow through porous media as well.
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Lv, Yiyan, Wei Zhu, and Tingting Han. "Mechanism Underlying Bonding Water Film Effect on Rheological Parameters." Advances in Materials Science and Engineering 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/8451391.
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From experiments on bonding water of different slurries and the analysis of flow curves, the bilinear fluid model has been improved. The results showed that the rheological parameters correspond to physical processes at different stages of shear strain. As shear rate increases, slurries evolve from high-viscosity Bingham fluids to low-viscosity Bingham fluids. Specific surface area determines the number of edge-to-face arrangements; mineral composition influences the binding strength of each edge-to-face arrangement; and the volume fraction of particles regulates the distance between clay particles and number of edge-to-face arrangements.
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Safa Riyadh Ridha. "A Review Report of Present Trend in Peristaltic Activity of MHD NON-Newtonian and Newtonian Fluids." Jornual of AL-Farabi for Engineering Sciences 1, no. 2 (December 1, 2022): 9. http://dx.doi.org/10.59746/jfes.v1i2.40.
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This academic paper deals with reviewing theoretical studies on MHD peristaltic transport of the Non-Newtonian as well as Newtonian fluids such as Hyperbolic Tangent fluid, Carreau fluid and Bingham fluid. Here, a wide range of study subjects, concepts, points of view, and mathematical models are presented. All of these studies are focused on Non-Newtonian fluids peristaltic activity. Among numerous of the Non- Newtonian fluids flows in physiological system, blood pumping mechanics
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Cui, Jing Wen, Zhi Shang Liu, and Yu Chen Zhang. "Study on the Generalized Darcy's Law for Bingham and Herschel-Bulkley Fluids." Applied Mechanics and Materials 433-435 (October 2013): 1933–36. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.1933.
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Extra-heavy oil, polymer solution and some drilling fluids are typical non-Newtonian Herschel-Bulkley fluids, which behave as sheer-thinning with yield stress. In this paper, the Generalized Darcy's law for Herschel-Bulkley fluids flow in porous media was formulated, by the same way formulating the Generalized Darcy's Law for Bingham fluids. Then, the applications of the two type flow models were compared; Bingham type model was still widely applied due to its conciseness and relatively satisfied accuracy. In addition, the Generalized Darcys Law was revised to describe thixotropic non-Newtonian fluids conceptually.
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Jafargholinejad, Shapour, and Mohammad Najafi. "Inertia flows of Bingham fluids through a planar channel: Hydroelastic instability analysis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 13 (May 29, 2017): 2394–403. http://dx.doi.org/10.1177/0954406217711470.
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In this paper, the effect of inertial terms on hydroelastic stability of a pressure-driven flow of a viscoplastic fluid flowing through a channel lined with a highly compliant polymeric gel is investigated. It is assumed that the fluid obeys the Bingham constuitive equation and the polymeric gel follows a two-constant Mooney–Rivlin material, which is used for modeling a nonviscous hyperelastic polymeric coating. A base-state solution is obtained for the fluid motion and solid deformation, simultaneously. Next, some infinitesimally small two-dimensional disturbances are imposed on the base-state solution. Dropping out all nonlinear perturbation terms, the modal linear stability analysis of the channel flow is conducted. The effects of the Bingham number and material constants are then examined on the critical Reynolds number. It is found that the yield stress has a stabilizing effect while the Mooney–Rivlin parameters have destabilizing effects on the pressure-driven flow of Bingham fluids.
Dissertations / Theses on the topic "Bingham fluids"
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Zengeni, Brian Tonderai. "Bingham yield stress and Bingham plastic viscosity of homogeneous Non-Newtonian slurries." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2458.
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Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2016.This dissertation presents how material properties (solids densities, particle size distributions, particle shapes and concentration) of gold tailings slurries are related to their rheological parameters, which are yield stress and viscosity. In this particular case Bingham yield stresses and Bingham plastic viscosities. Predictive models were developed from analysing data in a slurry database to predict the Bingham yield stresses and Bingham plastic viscosities from their material properties. The overall goal of this study was to develop a validated set of mathematical models to predict Bingham yield stresses and Bingham plastic viscosities from their material properties. The interaction of the non-Newtonian material properties is very complex at varying mass solids concentrations. The evaluation of these interactions in terms of constitutive equations is almost impossible and the relationship between material properties, mass solids concentration and rheology can only be modelled in a statistical manner. The validity of each model is checked to ensure that predictions and interpretations are unbiased and efficient. This is done by comparing the resulting models to experimental data generated from test work. An in-depth analysis was conducted to see the interrelationship between the material properties and how they affect the yield stress and viscosity values.
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Nassar, Waad. "La rhéologie des fluides magnétiques au dessous du seuil de Bingham." Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00843471.
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Les fluides magnétorhéologiques sont des dispersions de micro-particules magnétiques dans un fluide porteur non magnétique. Leurs caractéristiques varient avec l'application d'un champ magnétique. Le modèle de Bingham décrit le comportement des FMR pour des grandes vitesses de cisaillement. En dessous du seuil de Bingham, le comportement des FMR a reçu moins d'attention, cependant sa compréhension est nécessaire dans les interfaces homme-machine où de faibles contraintes de cisaillement sont observées. Une analyse expérimentale du comportement des FMR au cisaillement linéaire par une plaque, à de faibles taux de cisaillement, montre une réponse gouvernée par deux régimes successifs limités par un phénomène d'interface. Dans le régime initial, le FMR se comporte comme un matériau pseudo-élastique, l'élasticité observée est indépendante du champ magnétique et de la fraction volumique des particules. Le revêtement extérieur des particules magnétiques par des polymères (révélé par microscopie) est à l'origine de cette cohésion non-magnétique. Ce régime est limité par un seuil proportionnel au carré du champ magnétique et à la fraction volumique de particules. Dans le régime suivant, la déformation en cisaillement est non uniforme dans le liquide. La moyenne de la contrainte de cisaillement augmente linéairement avec la moyenne du cisaillement. Le coefficient de variation est proportionnel au carré du champ magnétique et diminue avec la fraction volumique de particules. Ce régime est limité par une perte d'adhérence des agrégats magnétiques avec la plaque de cisaillement, en cas de cisaillement avec une plaque amagnétique, ou avec le pôle magnétique en cas de cisaillement avec une plaque magnétique. La perte d'adhérence se produit à un seuil proportionnel au carré du champ magnétique et à la fraction volumique des particules et dépend de la nature de la plaque de cisaillement. Ce seuil peut être localisé au-dessus du seuil de Bingham.
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Obando, Vallejos Benjamin. "Mathematical models for the study of granular fluids." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0274/document.
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Cette thèse vise à obtenir et à développer des modèles mathématiques pour comprendre certains aspects de la dynamique des fluides granulaires hétérogènes. Plus précisément, le résultat attendu consiste à développer trois modèles. Nous supposons dans un premier temps que la dynamique du matériau granulaire est modélisée à l’aide d’une approche fondée sur la théorie du mélange. D’autre part, pour les deux modèles restant, nous considérons que le fluide granulaire est modélisé à l’aide d’une approche multiphase associant des structures et des fluides rigides. Plus exactement : • Dans le premier modèle, nous avons obtenu un ensemble d’équations basées sur la théorie du mélange en utilisant des outils d’homogénéisation et une procédure thermodynamique. Ces équations reflètent deux propriétés essentielles des fluides granulaires : la nature visqueuse du fluide interstitiel et un comportement de type Coulomb de la composante granulaire. Avec nos équations, nous étudions le problème de Couette entre deux cylindres infinis d’un écoulement hétérogène granulaire dense, composé d’un fluide newtonien et d’une composante solide. • Dans le deuxième modèle, nous considérons le mouvement d’un corps rigide dans un matériau viscoplastique. Les équations 3D de Bingham modélisent ce matériau et les lois de Newton régissent le déplacement du corps rigide. Notre résultat principal est d’établir l’existence d’une solution faible pour le système correspondant. • Dans le troisième modèle, nous considérons le mouvement d’un corps rigide conducteur thermique parfait dans un fluide newtonien conducteur de la chaleur. Les équations 3D de Fourier-Navier-Stokes modélisent le fluide, tandis que les lois de Newton et l’équilibre de l’énergie interne modélisent le déplacement du corps rigide. Notre principal objectif dans cette partie est de prouver l’existence d’une solution faible pour le système correspondant. La formulation faible est composée de l’équilibre entre la quantité du mouvement et l’équation de l’énergie totale, qui inclut la pression du fluide, et implique une limite libre due au mouvement du corps rigide. Pour obtenir une pression intégrable, nous considérons une condition au limite de glissement de Navier pour la limite extérieure et l’interface mutuelleThis Ph.D. thesis aims to obtain and to develop some mathematical models to understand some aspects of the dynamics of heterogeneous granular fluids. More precisely, the expected result is to develop three models, one where the dynamics of the granular material is modeled using a mixture theory approach, and the other two, where we consider the granular fluid is modeled using a multiphase approach involving rigid structures and fluids. More precisely : • In the first model, we obtained a set of equations based on the mixture theory using homogenization tools and a thermodynamic procedure. These equations reflect two essential properties of granular fluids : the viscous nature of the interstitial fluid and a Coulomb-type of behavior of the granular component. With our equations, we study the problem of a dense granular heterogeneous flow, composed by a Newtonian fluid and a solid component in the setting of the Couette flow between two infinite cylinders. • In the second model, we consider the motion of a rigid body in a viscoplastic material. The 3D Bingham equations model this material, and the Newton laws govern the displacement of the rigid body. Our main result is the existence of a weak solution for the corresponding system. • In the third model, we consider the motion of a perfect heat conductor rigid body in a heat conducting Newtonian fluid. The 3D Fourier-Navier-Stokes equations model the fluid, and the Newton laws and the balance of internal energy model the rigid body. Our main result is the existence of a weak solution for the corresponding system. The weak formulation is composed by the balance of momentum and the balance of total energy equation which includes the pressure of the fluid, and it involves a free boundary (due to the motion of the rigid body). To obtain an integrable pressure, we consider a Navier slip boundary condition for the outer boundary and the mutual interface
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Massingill, Robert Derryl Jr. "Mixing energy analysis of Bingham plastic fluids for severe lost circulation prevention using similitude." Texas A&M University, 2005. http://hdl.handle.net/1969.1/3339.
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As the demand for oil and gas resources increases, the need to venture into more
hostile environments becomes a dynamic focus in the petroleum industry. One problem
associated with certain high risk formations is lost circulation. As a result, engineers
have concentrated research efforts on developing novel Lost Circulation Materials
(LCMÂs) that will effectively treat thief zones. The most pioneering LCMÂs require
mixing energy to activate a reaction involving two or more chemicals. However,
minimal research has been conducted to accurately predict downhole mixing
capabilities. Therefore, this research focuses on developing a correlation between
laboratory experiments and scaled model experiments for accurate prediction of
downhole mixing energies in terms of flow rate for adequate mixing of lost circulation
prevention fluids.
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Lavarda, Jairo Vinícius. "Convecção natural de fluidos de lei de potência e de Bingham em cavidade fechada preenchida com meio heterogêneo." Universidade Tecnológica Federal do Paraná, 2015. http://repositorio.utfpr.edu.br/jspui/handle/1/1306.
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CAPESVários estudos numéricos investigaram cavidades fechadas sob o efeito da convecção natural preenchidas com fluidos newtonianos generalizados (FNG) nos últimos anos pelas aplicações diretas em trocadores de calor compactos, no resfriamento de sistemas eletrônicos e na engenharia de polímeros. Neste trabalho é realizada a investigação numérica do processo de convecção natural de fluidos de lei de Potência e de Bingham em cavidades fechadas, aquecidas lateralmente e preenchidas com meios heterogêneos e bloco centrado. O meio heterogêneo é constituído de blocos sólidos, quadrados, desconectados e condutores de calor. Como parâmetros são utilizados a faixa de Rayleigh de 104 à 107, índice de potência n de 0, 6 à 1, 6, número de Bingham de 0, 5 até Bimax , sendo investigado da influência do número de Prandtl para cada modelo de fluido. Nas cavidades com meio heterogêneo são utilizadas as quantidades de blocos de 9, 16, 36 e 64, mantendo-se a razão entre a condutividade térmica do sólido e do fluido κ = 1. Para as cavidades com bloco centrado, são utilizados os tamanhos adimensionais de 0, 1 à 0, 9 com κ = 0, 1; 1 e 10. A modelagem matemática é realizada pelas equações de balanço de massa, de quantidade de movimento e de energia. As simulações são conduzidas no programa comercial ANSYS FLUENT R . Inicialmente são resolvidos problemas com fluidos newtonianos em cavidade limpa, seguida de cavidade preenchida com meio heterogêneo e posteriormente bloco centrado para validação da metodologia de solução. Na segunda etapa é realizada o estudo com os modelos de fluidos de lei de Potência e de Bingham seguindo a mesma sequência. Os resultados são apresentados na forma de linhas de corrente, isotermas e pelo número de Nusselt médio na parede quente. De maneira geral, a transferência de calor na cavidade é regida pelo número de Rayleigh, tamanho e condutividade térmica dos blocos, pelo índice de potência para o modelo de lei de Potência e do número de Bingham para o modelo de Bingham. O número de Prandtl tem grande influência nos dois modelos de fluidos. O meio heterogêneo reduz a transferência de calor na cavidade quando interfere na camada limite térmica para ambos os fluidos, sendo feita uma previsão analítica para o fluido de lei de Potência. Para bloco centrado, a interferência na camada limite com fluido de lei de Potência também foi prevista analiticamente. A transferência de calor aumentou com bloco de baixa condutividade térmica e pouca interferência e com bloco de alta condutividade térmica e grande interferência, para ambos os fluidos.
Many studies have been carried out in square enclosures with generalized Newtonian fluids with natural convection in past few years for directly applications in compact heat exchangers, cooling of electronics systems and polymeric engineering. The natural convection in square enclosures with differently heated sidewalls, filled with power-law and Bingham fluids in addition with heterogeneous medium and centered block are analyzed in this study. The heterogeneous medium are solid, square, disconnected and conducting blocks. The parameters used are the Rayleigh number in the range 104 - 107 , power index n range of 0, 6 - 1, 6, Bingham number range of 0, 5 - Bimax , being the influence of Prandtl number investigated for each fluid model. The number of blocks for heterogeneous medium are 9, 16, 36 and 64, keeping constant solid to fluid conductive ratio, κ = 1. For enclosures with centered block are used the nondimensional block size from 0, 1 to 0, 9, with solid to fluid conductive ratio in range κ = 0, 1; 1 and 10. Mathematical modeling is done by mass, momentum and energy balance equations. The solution of equations have been numerically solved in ANSYS FLUENT R software. Firstly, numerical solutions for validation with Newtonian fluids in clean enclosures are conducted, followed by enclosures with heterogeneous medium and centered block. Subsequently, numerical solutions of power-law and Bingham fluids with same enclosures configurations are conducted. The results are reported in the form of streamlines, isotherms and average Nusselt number at hot wall. In general, the heat transfer process in enclosure is governed by Rayleigh number, size and thermal conductivity of the blocks, power index n for power-law fluid and Bingham number for Bingham fluid. Both fluid models are very sensitive with Prandtl number changes. Heterogeneous medium decrease heat transfer in enclosure when affects thermal boundary layer for both fluid models. One analytical prediction was made for power-law fluid. An increase in heat transfer occurs with low thermal conductivity block and few interference and with high thermal conductivity block and great interference, for both fluids.
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Cascavita, Mellado Karol. "Méthodes de discrétisation hybrides pour les problèmes de contact de Signorini et les écoulements de Bingham." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC1158/document.
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Cette thèse s'intéresse à la conception et à l'analyse de méthodes de discrétisation hybrides pour les inégalités variationnelles non linéaires apparaissant en mécanique des fluides et des solides. Les principaux avantages de ces méthodes sont la conservation locale au niveau des mailles, la robustesse par rapport à différents régimes de paramètres et la possibilité d’utiliser des maillages polygonaux / polyédriques avec des nœuds non coïncidants, ce qui est très intéressant dans le contexte de l’adaptation de maillage. Les méthodes de discrétisation hybrides sont basées sur des inconnues discrètes attachées aux faces du maillage. Des inconnues discrètes attachées aux mailles sont également utilisées, mais elles peuvent être éliminées localement par condensation statique. Deux applications principales des discrétisations hybrides sont abordées dans cette thèse. La première est le traitement par la méthode de Nitsche du problème de contact de Signorini (dans le cas scalaire) avec une non-linéarité dans les conditions aux limites. Nous prouvons des estimations d'erreur optimales conduisant à des taux de convergence d'erreur d'énergie d'ordre (k + 1), si des polynômes de face de degré k >= 0 sont utilisés. La deuxième application principale concerne les fluides à seuil viscoplastiques. Nous concevons une méthode de Lagrangien augmenté discrète appliquée à la discrétisation hybride. Nous exploitons la capacité des méthodes hybrides d’utiliser des maillages polygonaux avec des nœuds non coïncidants afin d'effectuer l’adaptation de maillage local et mieux capturer la surface limite. La précision et la performance des schémas sont évaluées sur des cas tests bidimensionnels, y compris par des comparaisons avec la littératureThis thesis is concerned with the devising and the analysis of hybrid discretization methods for nonlinear variational inequalities arising in computational mechanics. Salient advantages of such methods are local conservation at the cell level, robustness in different regimes and the possibility to use polygonal/polyhedral meshes with hanging nodes, which is very attractive in the context of mesh adaptation. Hybrid discretizations methods are based on discrete unknowns attached to the mesh faces. Discrete unknowns attached to the mesh cells are also used, but they can be eliminated locally by static condensation. Two main applications of hybrid discretizations methods are addressed in this thesis. The first one is the treatment using Nitsche's method of Signorini's contact problem (in the scalar-valued case) with a nonlinearity in the boundary conditions. We prove optimal error estimates leading to energy-error convergence rates of order (k+1) if face polynomials of degree k >= 0 are used. The second main application is on viscoplastic yield flows. We devise a discrete augmented Lagrangian method applied to the present hybrid discretization. We exploit the capability of hybrid methods to use polygonal meshes with hanging nodes to perform local mesh adaptation and better capture the yield surface. The accuracy and performance of the present schemes is assessed on bi-dimensional test cases including comparisons with the literature
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Meira, Rodrigo Esperança da Cunha Pimentel de. "Estudo do escoamento de fluidos de lei de potência e de Bingham em canal parcialmente poroso utilizando o método Lattice Boltzmann." Universidade Tecnológica Federal do Paraná, 2016. http://repositorio.utfpr.edu.br/jspui/handle/1/2715.
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CERNNNeste trabalho, propõe-se o estudo numérico do escoamento de fluidos de lei de potência e Bingham junto à interface entre uma região livre e outra porosa (interface fluido-porosa) utilizando o método lattice Boltzmann. Para tanto, considera-se o escoamento entre placas planas e paralelas entre as quais se faz presente um meio poroso abordado de forma heterogênea (resolução espacial da ordem de grandeza dos poros), representado através de obstáculos sólidos quadrados uniformemente distribuídos na parte inferior do canal. As análises realizadas mostram o efeito dos diversos parâmetros adimensionais que descrevem o problema sobre o fator de atrito na região livre do canal. De um modo geral, constata-se que a discrepância entre os fatores de atrito na região livre do canal e para o escoamento entre placas planas e paralelas cresce com o aumento da porosidade e do número de Bingham e com as reduções do número de obstáculos que compõem o meio poroso, número de Reynolds e índice de lei de potência. Ademais, propõe-se a adaptação do modelo analítico para a representação da interface fluido- porosa para escoamento de fluido newtoniano proposto por Ochoa-Tapia e Whitaker (1995b) ao escoamento de fluido de lei de potência, verificando-se a possibilidade de incorporar o comportamento não newtoniano do fluido ao parâmetro empírico do modelo.
The goal of this work is to numerically investigate the flow of power law and Bingham fluids next to the interface between a free and a porous region (fluid-porous interface) using the lattice Boltzmann method. For this, the flow between parallel plates partially filled by a porous material is studied, with the porous medium being represented by a set of solid square obstacles uniformly distributed in lower half of the channel. Results show the influence of non-dimensional parameters in the free region friction factor. In geral, it is observed that the friction factor decreases when porosity or Bingham number are increased and number of obstacles, Reynolds number or power law index are lowered. Moreover, it is porposed the application of the fluid-porous interface model proposed by Ochoa-Tapia e Whitaker (1995b) to the flow of power law fluids by varying the stress jump coefficient with the power law index.
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Obando, Vallejos Benjamin. "Mathematical models for the study of granular fluids." Electronic Thesis or Diss., Université de Lorraine, 2018. http://www.theses.fr/2018LORR0274.
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Cette thèse vise à obtenir et à développer des modèles mathématiques pour comprendre certains aspects de la dynamique des fluides granulaires hétérogènes. Plus précisément, le résultat attendu consiste à développer trois modèles. Nous supposons dans un premier temps que la dynamique du matériau granulaire est modélisée à l’aide d’une approche fondée sur la théorie du mélange. D’autre part, pour les deux modèles restant, nous considérons que le fluide granulaire est modélisé à l’aide d’une approche multiphase associant des structures et des fluides rigides. Plus exactement : • Dans le premier modèle, nous avons obtenu un ensemble d’équations basées sur la théorie du mélange en utilisant des outils d’homogénéisation et une procédure thermodynamique. Ces équations reflètent deux propriétés essentielles des fluides granulaires : la nature visqueuse du fluide interstitiel et un comportement de type Coulomb de la composante granulaire. Avec nos équations, nous étudions le problème de Couette entre deux cylindres infinis d’un écoulement hétérogène granulaire dense, composé d’un fluide newtonien et d’une composante solide. • Dans le deuxième modèle, nous considérons le mouvement d’un corps rigide dans un matériau viscoplastique. Les équations 3D de Bingham modélisent ce matériau et les lois de Newton régissent le déplacement du corps rigide. Notre résultat principal est d’établir l’existence d’une solution faible pour le système correspondant. • Dans le troisième modèle, nous considérons le mouvement d’un corps rigide conducteur thermique parfait dans un fluide newtonien conducteur de la chaleur. Les équations 3D de Fourier-Navier-Stokes modélisent le fluide, tandis que les lois de Newton et l’équilibre de l’énergie interne modélisent le déplacement du corps rigide. Notre principal objectif dans cette partie est de prouver l’existence d’une solution faible pour le système correspondant. La formulation faible est composée de l’équilibre entre la quantité du mouvement et l’équation de l’énergie totale, qui inclut la pression du fluide, et implique une limite libre due au mouvement du corps rigide. Pour obtenir une pression intégrable, nous considérons une condition au limite de glissement de Navier pour la limite extérieure et l’interface mutuelleThis Ph.D. thesis aims to obtain and to develop some mathematical models to understand some aspects of the dynamics of heterogeneous granular fluids. More precisely, the expected result is to develop three models, one where the dynamics of the granular material is modeled using a mixture theory approach, and the other two, where we consider the granular fluid is modeled using a multiphase approach involving rigid structures and fluids. More precisely : • In the first model, we obtained a set of equations based on the mixture theory using homogenization tools and a thermodynamic procedure. These equations reflect two essential properties of granular fluids : the viscous nature of the interstitial fluid and a Coulomb-type of behavior of the granular component. With our equations, we study the problem of a dense granular heterogeneous flow, composed by a Newtonian fluid and a solid component in the setting of the Couette flow between two infinite cylinders. • In the second model, we consider the motion of a rigid body in a viscoplastic material. The 3D Bingham equations model this material, and the Newton laws govern the displacement of the rigid body. Our main result is the existence of a weak solution for the corresponding system. • In the third model, we consider the motion of a perfect heat conductor rigid body in a heat conducting Newtonian fluid. The 3D Fourier-Navier-Stokes equations model the fluid, and the Newton laws and the balance of internal energy model the rigid body. Our main result is the existence of a weak solution for the corresponding system. The weak formulation is composed by the balance of momentum and the balance of total energy equation which includes the pressure of the fluid, and it involves a free boundary (due to the motion of the rigid body). To obtain an integrable pressure, we consider a Navier slip boundary condition for the outer boundary and the mutual interface
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Goncalves, Fernando D. "Characterizing the Behavior of Magnetorheological Fluids at High Velocities and High Shear Rates." Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/26142.
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Magnetorheological (MR) fluids offer solutions to many engineering challenges. The success of MR fluid is apparent in many disciplines, ranging from the automotive and civil engineering communities to the biomedical engineering community. This well documented success of MR fluids continues to motivate current and future applications of MR fluid.
One such application that has been considered recently is MR fluid devices for use in impact and other high velocity applications. In such applications, the fluid environment within the device may be well beyond the scope of our understanding for these fluids. To date, little has been done to explore the suitability of MR fluids in such high velocity and high shear applications.
While future applications may expose the fluid to adverse flow conditions, we must also consider current and existing applications which expose the fluid to extreme flow environments. Consider, for example, an MR damper intended for automotive primary suspensions, in which shear rates may exceed 10^5 s^-1. Flow conditions within these dampers far exceed existing fluid behavior characterization.
The aim of the current study is to identify the behavior of the fluid under these extreme operating conditions. Specifically, this study intends to identify the behavior of MR fluid subject to high rates of shear and high flow velocities. A high shear rheometer is built which allows for the high velocity testing of MR fluids. The rheometer is capable of fluid velocities ranging from 1 m/s to 37 m/s, with corresponding shear rates ranging from 0.14x10^5 s^-1 to 2.5x10^5 s^-1. Fluid behavior is characterized in both the off-state and the on-state.
The off-state testing was conducted in order to identify the high shear viscosity of the fluid. Because the high shear behavior of MR fluid is largely governed by the behavior of the carrier fluid, the carrier fluid behavior was also identified at high shear. Experiments were conducted using the high shear rheometer and the MR fluid was shown to exhibit nearly Newtonian post-yield behavior. A slight thickening was observed for growing shear rates. This slight thickening can be attributed to the behavior of the carrier fluid, which exhibited considerable thickening at high shear.
The purpose of the on-state testing was to characterize the MR effect at high flow velocities. As such, the MR fluid was run through the rheometer at various flow velocities and a number of magnetic field strengths. The term â dwell timeâ is introduced and defined as the amount of time the fluid spends in the presence of a magnetic field. Two active valve lengths were considered, which when coupled to the fluid velocities, generated dwell times ranging from 12 ms to 0.18 ms. The yield stress was found from the experimental measurements and the results indicate that the magnitude of the yield stress is sensitive to fluid dwell time. As fluid dwell times decrease, the yield stress developed in the fluid decreases. The results from the on-state testing clearly demonstrate a need to consider fluid dwell times in high velocity applications. Should the dwell time fall below the response time of the fluid, the yield stress developed in the fluid may only achieve a fraction of the expected value. These results imply that high velocity applications may be subject to diminished controllability for falling dwell times.
Results from this study may serve to aid in the design of MR fluid devices intended for high velocity applications. Furthermore, the identified behavior may lead to further developments in MR fluid technology. In particular, the identified behavior may be used to develop or identify an MR fluid well suited for high velocity and high shear applications.Ph. D.
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Riber, Stéphanie. "Méthodes numériques pour la simulation des écoulements de matériaux granulaires par une approche continue." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEM020/document.
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Cette thèse traite de la modélisation et des méthodes numériques pour la simulation d'écoulements de fluides non-Newtoniens, et particulièrement, de matériaux granulaires. Une application de ce travail concerne les poudres de couverture utilisées pour protéger thermiquement le métal de l'air dans le procédé de coulée en source d'alliages métalliques. Ces poudres sont conditionnées dans des sacs disposés dans la lingotière, qui brûlent suite aux fortes chaleurs engendrées, et permettant son écoulement sur la surface du métal. Ainsi, la simulation numérique apparaît comme un puissant outil pour l'optimisation du procédé, et notamment, de l'étalement de ces poudres.Dans ce travail, une formulation éléments finis a été proposée pour modéliser l'écoulement multiphasique des matériaux granulaires dans un formalisme de la mécanique des milieux continus. Les équations associées sont résolues via des schémas numériques stabilisés, couplés avec la méthode Level-Set pour capturer et suivre le profil du matériau granulaire au cours de la simulation. Dans un premier temps, les outils numériques ont été testés sur des cas d'écoulements de fluides de Bingham, où les fortes non-linéarités sont traitées par une méthode de régularisation. Puis la formulation est étendue aux écoulements de granulaires secs, dont le comportement piezzo-dépendent est traduit par la loi mu(I). Le modèle a été validé sur des cas d'effondrement de colonnes de grains, et une étude de sensibilité aux conditions aux limites et constantes physiques du modèle est proposée.Enfin, des cas industriels de chutes de poudres sur substrats solide et métal fondu ont été menés, amenant à des premières pistes pour l'optimisation du procédé de coulée en lingotièreThis thesis is devoted to the modeling and numerical methods for the simulation of non-Newtonian flows, and focuses particularly on granular materials flows. This work is applied to molten powders aiming to ensure metal thermal protection from the air in ingot casting process of metallic alloys. These powders are conditionned into bags disposed into the mold, which burn due to high temperatures, and allowing the powder spreading onto the metal surface. Thus, numerical simulation appears as a powerful tool for the process optimization, and especially, for the powder spreading.In this work, a finite element formulation has been proposed for the modeling of granular multiphase flows, by a continuum approach. The associated equations are solved using stabilized numerical schemes, coupled with the Level-Set method to capture and follow the granular profile during the simulation. First, the numerical tools have been implemented for Bingham flows, by using regularization a method. Then, the formulation was extended to dry granular flows, by the use of the mu(I) rheology constitutive model for describing its pressure-dependent behavior. The model has been validated on granular collapses, and a sensitivity analysis to boundary conditions and physical constants has been proposed.Finally, industrial cases of powder chutes ontoboth solid and liquid metla substrates have been conducted, leading to preliminary solutions for the optimization of ingot casting process
Book chapters on the topic "Bingham fluids"
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Wittum, Gabriel, Volker Schulz, Bernd Maar, and Dmitriy Logashenko. "Numerical Methods for Parameter Estimation in Bingham-Fluids." In Mathematics — Key Technology for the Future, 204–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55753-8_17.
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Nokka, Marjaana, and Sergey Repin. "Error Estimates of Uzawa Iteration Method for a Class of Bingham Fluids." In Computational Methods in Applied Sciences, 31–42. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23564-6_3.
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Bulíček, Miroslav, and Josef Málek. "On Unsteady Internal Flows of Bingham Fluids Subject to Threshold Slip on the Impermeable Boundary." In Recent Developments of Mathematical Fluid Mechanics, 135–56. Basel: Springer Basel, 2016. http://dx.doi.org/10.1007/978-3-0348-0939-9_8.
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Pavan Kumar, Singeetham, and Kadaba Puttanna Vishwanath. "Squeezing of Bingham Fluid Between Two Plane Annuli." In Lecture Notes in Mechanical Engineering, 385–96. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5329-0_28.
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Bunoiu, R., G. Cardone, and C. Perugia. "Unfolding Method for the Homogenization of Bingham Flow." In Modelling and Simulation in Fluid Dynamics in Porous Media, 109–23. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5055-9_7.
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Saravana, R., P. Hariprabakaran, R. Hemadri Reddy, and S. Sreenadh. "Peristaltic Flow of a Bingham Fluid in Contact with a Jeffrey Fluid." In Lecture Notes in Mechanical Engineering, 505–13. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5329-0_37.
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Singeetham, Pavan Kumar, and Vishwanath Kadaba Puttanna. "Inertia Effects in the Planar Squeeze Flow of a Bingham Fluid: A Matched Asymptotics Analysis." In Advances in Fluid Dynamics, 839–49. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-4308-1_64.
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Mullai Venthan, S., and I. Jayakaran Amalraj. "Numerical Investigation of Bingham Fluid Flow in the Entrance Region of Rotating Annuli." In Lecture Notes in Mechanical Engineering, 499–518. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-4488-0_42.
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Wang, Jiangshuai, Jun Li, Yanfeng He, Gonghui Liu, and Song Deng. "A Novel Model to Calculate the Fluctuating Pressure in Eccentric Annulus for Bingham Fluid." In Computational and Experimental Simulations in Engineering, 151–63. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-02097-1_12.
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Muthuraj, R., S. Srinivas, and D. Lourdu Immaculate. "Impacts of Variable Viscosity on Hydromagnetic Peristaltic Flow of a Bingham Fluid in a Vertical Channel." In Lecture Notes in Mechanical Engineering, 1–14. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1929-9_1.
Full textConference papers on the topic "Bingham fluids"
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Fellouah, H., C. Castelain, A. Ould El Moctar, and H. Peerhossaini. "Dean Instability in Non-Newtonian Fluids." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60095.
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We present a numerical study of Dean instability in non-Newtonian fluids in a laminar 180° curved-channel flow of rectangular cross section. A methodology based on the Papanastasiou model [1] was developed to take into account Bingham-type rheological behavior. After validation of the numerical methodology, simulations were carried out (using Fluent CFD code) for Newtonian and non-Newtonian fluids in curved channels of square and rectangular cross section and of large aspect and curvature ratios. A criterion based on the axial velocity gradient was defined to detect the instability threshold. This criterion is used to optimize the grid geometry. The effects of curvature and aspect ratios on the instability are studied for all fluids, Newtonian and non-Newtonian. In particular, we show that the critical value of the Dean number decreases with increasing duct curvature ratio. The variation of the critical Dean number with duct aspect ratio is less regular. The results are compared with those for Newtonian fluids to emphasize the effect of the power-law index and the Bingham number. The onset of Dean instability is delayed with increasing power-law index. The same delay is observed in Bingham fluids when the Bingham number is increased.
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Pease, Leonard F., Arich J. Fuher, Judith A. Bamberger, Carolyn A. Burns, Richard C. Daniel, and Michael J. Minette. "Is Radioactive Tank Waste a Bingham Fluid?" In ASME-JSME-KSME 2019 8th Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/ajkfluids2019-5216.
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Abstract Slurries and sludges across the United States Department of Energy (DOE) complex rank among the most rheologically interesting. Their composition is heterogeneous, spanning a very broad range of particle sizes, densities, and interparticle forces. All exhibit shear thinning, some have yield stresses, and many are thixotropic. Despite the variety, these complex fluids are often represented using the historic Bingham fluid model, which fits higher shear rate data to a simple straight line. The intercept provides a yield stress, which has been a key design parameter in construction of large-scale waste processing facilities. However, many radioactive wastes are simply not Bingham fluids, and this representation extrapolates poorly across low to intermediate shear rates that are characteristic of typical processing conditions. Indeed, processing shear rates as high as 200 1/s, which has been a typical minimum shear rate used in fitting the Bingham fluid model, are seldom encountered in nuclear waste processing. Therefore, more realistic rheological models are necessary to accurately predict waste processing performance. Pacific Northwest National Laboratory (PNNL) recently re-evaluated the rheology of reconstituted Hanford REDOX (reduction-oxidation) process sludge waste against a wide variety of rheological models including the Bingham, Cross, Cross with yield stress, Carreau, biviscous, Herschel-Bulkley (which includes a power law dependence), Casson, and Gay models. They found that all of the models provided a closer fit than the Bingham model and that the biviscous model and Cross with yield stress model were convincing. However, reconstituted Hanford REDOX sludge waste is but one type of DOE waste and a direct contrast, and comparison of these three models against undiluted, unmixed tank waste (actual not simulant) has not been performed previously. Therefore, the purpose of this paper is to evaluate the rheology of actual tank waste with these more accurate rheological models. In this paper, we evaluate select rheological data for slurry samples from Hanford’s AZ-101, AZ-102, and SY-101 waste tanks. In each of these cases, we find that Cross’ model with yield stress and the biviscous model significantly outperform the Bingham fluid model. Furthermore, the AZ-101 data also shows that the shear stress peak at startup significantly exceeds the Bingham yield stress, which is commonly observed in the initial moments of rheological measurements on simulants. Remarkably, Cross’ model may empirically accommodate an initial spike in shear stress at modest shear rates. These are important observations because computational and analytical fluid dynamics simulations rely on rheological constitutive models for accurately and conservatively predicting waste processing performance. These findings suggest the need for better rheological modeling of and validation against radioactive waste.
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Patel, S. A., A. H. Raja, and R. P. Chhabra. "Natural Convection in Yield Stress Fluids From a Confined Horizontal Plate." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-11258.
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Abstract The heat transfer characteristics from an isothermal heated plate in a quiescent yield stress fluid in a cavity was investigated over a wide range of parameters (Rayleigh number, 102 ≤ Ra ≤ 105, Prandtl number, 10 ≤ Pr ≤ 100, and Bingham number, Bn ≥ 0) where the flow is known to be laminar and steady. The coupled momentum and energy equations have solved here numerically within the framework of Boussinesq approximation to capture the temperature-dependent fluid density. The results demonstrate that for a given value of the Rayleigh number, there exists a critical value of the Bingham number, above which the fluid is completely unyielded and heat transfer occurs solely by conduction. In order to delineate the effect of domain geometry on the conduction limit, the study was extended over a range of geometrical aspects by varying the aspect ratio (λ = diameter of the cavity/ a length of the plate), 2 ≤ λ ≤ 5. This work shows that the critical value of the Bingham number can be described as a function of geometry of domain, Ra and Pr. The value of critical Bingham number increases with the increasing aspect ratio and Rayleigh number in order to approach the conduction limit. The yield surfaces show that the increasing values of Rayleigh number induce fluid-like behaviour whereas Bingham number opposes this propensity. The average Nusselt number decreases with the increasing Bingham number due to the suppression of the advective component of heat transfer.
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KARAZEEVA, N. A. "APPROXIMATIONS OF THE EQUATIONS DESCRIBING MOTIONS OF BINGHAM FLUIDS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0191.
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Letelier, Mario F., Dennis A. Siginer, Diego Contreras, Patricio Jacobs, and Cristian Barrera. "Heat Transfer in Laminar Flow With Elastoviscoplastic Fluids in Non-Circular Ducts." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71001.
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The interplay of yield stress and elasticity on the temperature field and heat transfer rates in tube flow of elastoviscoplastic (EVP) fluids is investigated in this paper. The constitutive structure of the EVP fluid obeys a linear combination of the Phan-Thien-Tanner model for viscoelastic fluids and the Bingham model for viscoplastic fluids. The momentum and energy equations are solved asymptotically under constant wall heat flux. The fluid behavior is governed by the Weissenberg Wi and the Bingham N numbers.
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Wereley, Norman M. "Nondimensional Analysis of Electrorheological and Magnetorheological Dampers Using a Herschel-Bulkley Constitutive Model." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45046.
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Quasisteady modeling of linear stroke flow mode magnetorheological (MR) and electrorheological (ER) dampers has focused primarily on the utilization of the Bingham-plastic constitutive model to assess performance metrics such as damping capacity. In such Bingham-plastic MR (or ER) flows, the yield stress of the fluid, τy, is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a preyield condition where the local shear stress is less than the yield stress, τ < τy, or (2) a postyield condition, where the local shear stress is greater than the yield stress, τ > τy, so that the material flows with a constant postyield viscosity. The objective of this paper is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits postyield shear thinning or thickening behavior, that is, the postyield viscosity is a function of shear rate. A Herschel-Bulkley model with a field dependent yield stress is proposed, and the impact of shear rate dependent viscosity on damping capacity is assessed. Key analysis results — velocity profile, shear stress profile, and damping coefficient — are presented in a nondimensional formulation that is consistent with prior results for the Bingham-plastic analysis. The nondimensional analysis formulated here clearly establishes the Bingham number as the independent variable for assessing flow mode damper performance.
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Vradis, George C. "Heat Transfer and Fluid Mechanics of Herschel-Bulkley Fluids." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0452.
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Abstract A comprehensive review of the heat transfer phenomena related to the flow of purely viscous non-Newtonian fluids exhibiting a yield stress in some simple and complex geometries is presented. Both attached and separated flows of Bingham and Herschel-Bulkley fluids are discussed. The presence of a yield-stress is shown to significantly impact the heat transfer and flow characteristics, as compared to those in the case of a Newtonian fluid, in particular in the cases where separation of the flow would be expected.
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Hammad, Khaled J. "The Confined Flow Behavior of a Bingham Non-Newtonian Jet." In ASME/JSME/KSME 2015 Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/ajkfluids2015-15232.
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The flow behavior of a confined viscoplastic non-Newtonian jet is investigated numerically within the steady laminar flow regime. The Bingham constitutive equation is used to model the rheology of interest. A parametric study is implemented to investigate the influence of confinement ratio and rheology over the following range of parameters: Confinement ratio, CR = {5, 10, 20}, and Yield number, Y = {0, 0.5, 2}. A large corner recirculation region typically characterizes the flow of a confined Newtonian jet. However, in the case of a Bingham viscoplastic jet, once a critical yield number is exceeded, flow recirculation is eliminated and a stagnant corner region is formed. The confinement ratio has a dramatic impact on the recirculation intensity and the evolution characteristics of the jet only in the case of Newtonian flows, i.e. Y = 0. In general, a more intense recirculation is associated with higher confinement ratios. The extent and the strength of flow recirculation are found to significantly diminish with the yield number. The axial penetration of the confined jet substantially increases with the confinement ratio for Newtonian fluids only and decreases with the yield numbers for all confinement ratios.
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Saasen, Arild, and Jan David Ytrehus. "Viscosity Models for Drilling Fluids: Viscosity Parameters and Their Use." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-96595.
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Abstract The most common viscosity models used in the drilling industry are the Bingham, the Power-Law and the Herschel-Bulkley models. The scope of the present paper is to outline how to select the individual models, and how the models need to be re-formulated to be able to have parameters with a physical meaning. In principle, the Bingham model itself have physical parameters being the yield point and the plastic viscosity. However, the Bingham model very often only very poorly describe the viscosity in complex fluids. This yield stress can be described within a reasonable accuracy by application of the low-shear yield point. A similar problem exists with the Power-Law model resulting from the model’s absence of a yield stress. The compromise model is the Herschel-Bulkley model which contains a yield stress and a power-law term. This model describes the drilling fluid viscosity with reasonable accuracy and includes both the Bingham and Power-Law models as limit formulations. It is not possible to select fluids based on the Herschel-Bulkley traditional parameters alone. The reason is that the Herschel-Bulkley power-law term’s viscosity parameter has a unit dependent on its power-law exponent. In the present approach the fluid is described using a yield stress, a surplus stress at a characteristic shear rate of the fluid flow and finally a power-law exponent making the fluid applicable in the practical shear rate ranges. The surplus stress is no-longer dependent on other parameters. Hence, we have re-arranged the viscosity model to have independent measurable quantities.
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NISHIYAMA, H., S. FUSHIMI, and M. NAKANO. "NUMERICAL SIMULATION OF MR FLUIDS DAMPING CHARACTERISTICS USING MODIFIED BINGHAM MODEL." In Proceedings of the Eighth International Conference. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777546_0039.
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