Academic literature on the topic 'Finite volume methods applied to problems in fluid mechanic'
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Journal articles on the topic "Finite volume methods applied to problems in fluid mechanic"
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GUSTAFSSON, BERTIL. "Analysis and Methods in Fluid Mechanics." International Journal of Modern Physics C 02, no. 01 (March 1991): 75–85. http://dx.doi.org/10.1142/s0129183191000093.
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When constructing numerical methods for partial differential equations, it is important to have a thorough understanding of the continuous model and the characteristic properties of its solutions. We shall present methods of analysis for determining well-posedness of hyperbolic and mixed hyperbolic-parabolic équations which are applicable to the time-dependent Euler and Navier-Stokes equations. We shall then discuss difference- and finite volume methods and the construction of grids. The geometry of realistic problems is usually such that it is almost impossible to construct one structured grid. One way to overcome this difficulty is to use overlapping grids, where each domain has a structured grid. We discuss stability and accuracy of difference methods applied on such grids. Many problems in physics and engineering are defined in boundary domains, and artificial boundaries are introduced for computational reasons. In some cases one can construct accurate boundary conditions at these open boundaries. We shall indicate how this can be achieved, but we will also point out certain cases where accurate solutions are impossible to be obtained on limited domains. Finally some comments will be given on the difficulties arising when almost incompressible flow is computed. This corresponds to small Mach-numbers, and extra care must be taken when designing numerical methods. The theory will be complemented by numerical experiments for various flow problems in two space dimensions.
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Ramírez-Espinoza, Germán I., and Matthias Ehrhardt. "Conservative and Finite Volume Methods for the Convection-Dominated Pricing Problem." Advances in Applied Mathematics and Mechanics 5, no. 06 (December 2013): 759–90. http://dx.doi.org/10.4208/aamm.12-m1216.
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AbstractThis work presents a comparison study of different numerical methods to solve Black-Scholes-type partial differential equations (PDE) in the convection-dominated case, i.e., for European options, if the ratio of the risk-free interest rate and the squared volatility-known in fluid dynamics as Péclet number-is high. For Asian options, additional similar problems arise when the “spatial” variable, the stock price, is close to zero.Here we focus on three methods: the exponentially fitted scheme, a modification of Wang’s finite volume method specially designed for the Black-Scholes equation, and the Kurganov-Tadmor scheme for a general convection-diffusion equation, that is applied for the first time to option pricing problems. Special emphasis is put in the Kurganov-Tadmor because its flexibility allows the simulation of a great variety of types of options and it exhibits quadratic convergence. For the reduction technique proposed by Wilmott, a put-call parity is presented based on the similarity reduction and the put-call parity expression for Asian options. Finally, we present experiments and comparisons with different (non)linear Black-Scholes PDEs.
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Rakhsha, Milad, Christopher E. Kees, and Dan Negrut. "Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems." Fluids 6, no. 12 (December 16, 2021): 460. http://dx.doi.org/10.3390/fluids6120460.
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As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain.
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Issakhov, Alibek, and Medina Imanberdiyeva. "Numerical Study of the Movement of Water Surface of Dam Break Flow by VOF Methods for Various Obstacles." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 5 (July 28, 2020): 475–500. http://dx.doi.org/10.1515/ijnsns-2018-0278.
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AbstractIn this paper, the movement of the water surface is numerically simulated when a dam is broken by the volume of fluid (VOF) method. The mathematical model is based on the Navier–Stokes equations and uses the large eddy simulation turbulent model, describing the flow of an incompressible viscous fluid and the equation for the phase. These equations are discretized by the finite-volume method. Numerical PISO (Pressure-Implicit with Splitting of Operators) algorithm was chosen for numerical solution of this equation system. The movement of the water surface is captured by using the VOF method, which leads to a strict mass conservation law. The accuracy of the three-dimensional model and the chosen numerical algorithm were tested using several laboratory experiments on dam break problem. In each of the problems, the obtained results were compared with the experimental data and several calculations by other authors and in each of the test problems, the developed model showed results close to the experimental data. Comparison of simulation results with experimental data for various turbulent models was also performed. And also two combined problems were performed which are more close to real conditions; with the help of these problems, flooding zones and flooding time were identified that would help in evacuating people from dangerous zones.
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Baliga, Bantwal R. (Rabi), and Iurii Yuri Lokhmanets. "Generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (May 3, 2016): 1121–44. http://dx.doi.org/10.1108/hff-10-2015-0445.
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Purpose – The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical predictions of multidimensional, steady and unsteady, fluid flow and heat transfer phenomena in regular and irregular calculation domains. Design/methodology/approach – Pattern-preserving grid-refinement strategies are proposed for mathematically rigorous generalizations of the Richardson extrapolation procedure for numerical predictions of steady fluid flow and heat transfer, using finite volume methods and structured multidimensional Cartesian grids; and control-volume finite element methods and unstructured two-dimensional planar grids, consisting of three-node triangular elements. Mathematically sound extrapolation procedures are also proposed for numerical solutions of unsteady and boundary-layer-type problems. The applicability of such procedures to numerical solutions of problems with curved boundaries and internal interfaces, and also those based on unstructured grids of general quadrilateral, tetrahedral, or hexahedral elements, is discussed. Findings – Applications to three demonstration problems, with discretizations in the asymptotic regime, showed the following: the apparent orders of accuracy were the same as those of the numerical methods used; and the extrapolated results, measures of error, and a grid convergence index, could be obtained in a smooth and non-oscillatory manner. Originality/value – Strict or approximate pattern-preserving grid-refinement strategies are used to propose generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions. Such extrapolation procedures play an indispensable role in the verification and validation techniques that are employed to assess the accuracy of numerical predictions which are used for designing, optimizing, virtual prototyping, and certification of thermofluid systems.
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de Boer, Gregory Nicholas, Adam Johns, Nicolas Delbosc, Daniel Burdett, Morgan Tatchell-Evans, Jonathan Summers, and Remi Baudot. "Three computational methods for analysing thermal airflow distributions in the cooling of data centres." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 2 (February 5, 2018): 271–88. http://dx.doi.org/10.1108/hff-10-2016-0431.
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Purpose This aim of this work is to investigate different modelling approaches for air-cooled data centres. The study employs three computational methods, which are based on finite element, finite volume and lattice Boltzmann methods and which are respectively implemented via commercial Multiphysics software, open-source computational fluid dynamics code and graphical processing unit-based code developed by the authors. The results focus on comparison of the three methods, all of which include models for turbulence, when applied to two rows of datacom racks with cool air supplied via an underfloor plenum. Design/methodology/approach This paper studies thermal airflows in a data centre by applying different numerical simulation techniques that are able to analyse the thermal airflow distribution for a simplified layout of datacom racks in the presence of a computer room air conditioner. Findings Good quantitative agreement between the three methods is seen in terms of the inlet temperatures to the datacom equipment. The computational methods are contrasted in terms of application to thermal management of data centres. Originality/value The work demonstrates how the different simulation techniques applied to thermal management of airflow in a data centre can provide valuable design and operational understanding. Basing the analysis on three very different computational approaches is new and would offer an informed understanding of their potential for a class of problems.
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Mustafa, Mustafa Abdulsalam, Atheer Raheem Abdullah, Wajeeh Kamal Hasan, Laith J. Habeeb, and Maadh Fawzi Nassar. "Two-way fluid-structure interaction study of twisted tape insert in a circular tube having integral fins with nanofluid." Eastern-European Journal of Enterprise Technologies 3, no. 8(111) (June 30, 2021): 25–34. http://dx.doi.org/10.15587/1729-4061.2021.234125.
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This work deals with fluid-structure interaction (FSI), one of the emerging areas of numerical simulation and calculation. This research shows a numerical study investigating heat transfer enhancement and fluid-structure interaction in a circular finned tube by using alumina nanofluid as a working fluid with a typical twisted tape that has a twisting ratio of 1.85. The studied nanofluid volumes of fraction are φ=0, 3, 5 % under conditions of laminar and turbulent flow. The solution for such problems is based on the relations of continuum mechanics and is mostly done with numerical methods. FSI occurs when the flow of fluid influences the properties of a structure or vice versa. It is a computational challenge to deal with such problems due to complexity in defining the geometries, nature of the interaction between a fluid and solid, intricate physics of fluids and requirements of computational resources. CFD investigations were made based on the numerical finite volume techniques to solve the governing three-dimensional partial differential equations to get the influence of inserted twisted tape and concentration of nanofluid on heat transfer enhancement, friction loss, average Nusselt number, velocity profile, thermal performance factor characteristics, and two-way interaction in a circular tube at laminar and turbulent flow. The governing continuity, momentum and energy transfer equations are solved using Ansys Fluent and Transient Structural. The simulation results show that the deformations of two-way coupling fluctuate from side to side, with 0.004 mm, as maximum amplitude, located at the typical twisted tape center. Heat transfer dissipation improved by adding fins and as Reynolds numbers increase the heat transfer behavior increases.
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Rajapakse, R. K. N. D., and T. Senjuntichai. "Fundamental Solutions for a Poroelastic Half-Space With Compressible Constituents." Journal of Applied Mechanics 60, no. 4 (December 1, 1993): 847–56. http://dx.doi.org/10.1115/1.2900993.
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This paper presents a comprehensive analytical treatment of the three-dimensional response of a poroelastic half-space with compressible constituents. General solutions for equations of equilibrium expressed in terms of displacements and variation of fluid volume are derived by applying Fourier expansion, Hankel transforms, and Laplace transforms with respect to the circumferential, radial, and time coordinates, respectively. The general solutions are used to derive a set of fundamental solutions corresponding to circular ring loads and to a fluid source applied at a finite depth below the free surface of a poroelastic half-space. The circumferential variation of the ring loads and the fluid source is described by appropriate trigonometric terms. Fundamental solutions presented in this paper can be used to model arbitrarily distributed loadings and a fluid source as well as a number of other problems encountered in geomechanics and energy resource explorations. In addition, these fundamental solutions can be used as the kernel functions in the development of boundary integral equation methods for a poroelastic half-space. Solutions for buried circular patch loads/fluid sink and concentrated loads/fluid sink are also deduced. Numerical evaluation of the fundamental solutions is also discussed. Comparisons are presented for time domain solutions obtained by using the Stehfest’s and Schapery’s schemes for Laplace inversion. A selected set of numerical solutions are presented to portray the features of consolidation process in six different poroelastic materials under buried patch loads and a sink.
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Ghassemi, H., M. Mansouri, and S. Zaferanlouei. "Interceptor hydrodynamic analysis for handling trim control problems in the high-speed crafts." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 11 (September 14, 2011): 2597–618. http://dx.doi.org/10.1177/0954406211406650.
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In this study, the effects of hydrodynamic interceptors on fast crafts are investigated to find their optimum geometrical characteristics based on numerical methods. Interceptors are vertical blades installed symmetrically at the aft of the craft. They are designed either fixed or variable. In variable mode, interceptors’ heights are adjusted by various mechanisms. They also cause changes in pressure disruption around the craft and especially at the end of the hull. The pressure variations have an effect on draft height and lifting forces which directly results in a better control of trim. Using the computational fluid dynamics, the pressure distribution around the hull and its effects on trim are computed and then discussed. The Reynolds Average Navier–Stokes equations are also applied to model the flow around the fixed flat and wedge craft with an interceptor at different heights. The model is analysed based on finite volume method and SIMPLE algorithm using dynamic mesh. The results show that the interceptor causes an intense pressure rate in its contact point. It also decreases the wet surface of the craft and drag forces coefficient. At last, they lead to a better control of trim. The height of interceptor has an important effect on its efficiency and it should be selected according to the speed of the craft.
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Okano, T., and M. Koishi. "A New Computational Procedure to Predict Transient Hydroplaning Performance of a Tire." Tire Science and Technology 29, no. 1 (January 1, 2001): 2–22. http://dx.doi.org/10.2346/1.2135228.
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Abstract “Hydroplaning characteristics” is one of the key functions for safe driving on wet roads. Since hydroplaning depends on vehicle velocity as well as the tire construction and tread pattern, a predictive simulation tool, which reflects all these effects, is required for effective and precise tire development. A numerical analysis procedure predicting the onset of hydroplaning of a tire, including the effect of vehicle velocity, is proposed in this paper. A commercial explicit-type FEM (finite element method)/FVM (finite volume method) package is used to solve the coupled problems of tire deformation and flow of the surrounding fluid. Tire deformations and fluid flows are solved, using FEM and FVM, respectively. To simulate transient phenomena effectively, vehicle-body-fixed reference-frame is used in the analysis. The proposed analysis can accommodate 1) complex geometry of the tread pattern and 2) rotational effect of tires, which are both important functions of hydroplaning simulation, and also 3) velocity dependency. In the present study, water is assumed to be compressible and also a laminar flow, indeed the fluid viscosity, is not included. To verify the effectiveness of the method, predicted hydroplaning velocities for four different simplified tread patterns are compared with experimental results measured at the proving ground. It is concluded that the proposed numerical method is effective for hydroplaning simulation. Numerical examples are also presented in which the present simulation methods are applied to newly developed prototype tires.
Dissertations / Theses on the topic "Finite volume methods applied to problems in fluid mechanic"
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PHAN, THI MY DUYEN. "Finite volume method for one-dimensional Euler equations and application to multi-fluid problem." Doctoral thesis, Gran Sasso Science Institute, 2021. http://hdl.handle.net/20.500.12571/23332.
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This thesis is about studying the finite volume method for hyperbolic conservation laws system. Starting from the one dimensional Euler equations, we rewrite them from the form in Eulerian coordinates into the form in the Lagrangian coordinates. This technique transforms a moving grid in Eulerian co- ordinates into a fixed grid in Lagrangian coordinates, thus allowing easier imple- mentation of boundary conditions.
The thesis consists of three parts:
• piston problem,
• multi-fluid models,
• asymptotic behavior of Euler equations.
In the first part, we consider the piston problem in the paper where the authors Yoshinori Inoue and Takeru Yano study the nonlinear propagation of plane waves radiated into a semi-infinite space filled with a perfect gas, by the sinusoidal motion of an infinite plate. They use the Euler equations in Eulerian coordinates describing the conservation of mass, momentum, and energy then approximate the solution. From this idea, we consider the waves propagating into a semi- infinite tube, which is filled with a perfect gas, closed by a piston on one end and extending along the x-axis at infinity. We use the mass Lagrangian coordinates to obtain the Euler equations rewritten in Lagrangian coordinates and reproduce the results following the piston problem in Yano's paper. The goal is to perform the computation in a finite computational domain, and to develop non-reflecting boundary conditions to impose on the right boundary. In order to reduce the impact of the reflected wave, we propose to combine the Burgers equation in few additional cells of the computational domain. The numerical error caused by the reflected wave is reduced by an order of magnitude by using this approach.
In the second part, we consider the tube filled periodically by a large number of pairs of two immiscible fluids. We use Roe’s solver, which is described in Munz's paper, in Lagrangian coordinates, to study the motion of multi-fluid problem and then compare this detailed numerical solution with two isentropic homogeneous models. The first one is a 2 × 2 isentropic system and the second model is a 3 × 3 system which takes into account some turbulent effects. The goal is to check which homogenized model gives better prediction. We study two cases according to the ratio of densities of the two fluids: moderate ratio and large ratio. For each case, we perform the test with smooth and discontinuous initial condition in pressure and velocity. For the problem with smooth initial conditions before the shock formation, the detailed numerical solutions and the numerical results of the two isentropic homogeneous models are in very good agreement. After the shock formation, the detailed numerical solution is strongly oscillatory and we have to use the average values, namely smoothed numerical solution, for the comparison with the two models. We observe the difference between the predictions of the two models. For moderate density ratio the 2×2 model gives a better prediction of the shock position, while for large density ratio, the turbulent 3×3 model is in better agreement with a smoothed out version of the detailed numerical solution compared with the simple 2 × 2 model.
In the third part, we study long time behavior of the solutions to the Euler equations by using two different numerical methods: the second order finite volume method in Lagrangian coordinates adopted in the previous chapters, and a high order finite volume method in Eulerian coordinate. In particular, the latter is based on WENO (Weighted Essentially Non-Oscillatory) reconstruction. Then we perform the comparison of the numerical solutions obtained at a final time, when pressure and velocity profiles are almost flat.
Conference papers on the topic "Finite volume methods applied to problems in fluid mechanic"
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Fowler, Bryce L., and Raymond K. Yee. "Application of Finite Volume Method for Solid Mechanics." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-55297.
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Polymers constitute a large class of nearly incompressible solid materials (i.e., Poisson’s Ratio near 0.5). These materials are often used as passive vibration isolators. Accurately modeling vibration isolators made of nearly incompressible materials has been extremely difficult with standard finite element analysis. This paper provides an alternative to the specialized finite element formulations currently used to model incompressible materials. The finite volume methodology of computational fluid dynamics is employed in this paper to solve the Hooke’s Law equations in solid mechanics. Test cases have been performed to evaluate the performance of finite volume method applied to solid mechanics problems. The formulation has been coded in Matlab for practical use. Based on the preliminary test case results, the finite volume formulation compares favorably to finite element method.
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Zhang, Sheguang, Daniel Liut, Kenneth Weems, and Woei-Min Lin. "A 3-D Finite Volume Method for Green Water Calculations." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67318.
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A 3-D Finite Volume method (FV3D) is developed and applied to green water problems. The Navier-Stokes (N-S) equations are discretized with the 3-D finite volume method on collocated Cartesian grids. The free surface motion is captured with the Volume of Fluid (VOF) method. The velocity and pressure fields are solved by the SIMPLER scheme with an alternating direction implicit solver. FV3D is validated against existing experimental and numerical results for tank sloshing and ship green-water-on-deck cases. This method is applicable to calculation of the green water effect on advanced wave-piercing hull forms.
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Ouchi, Hisanao, Amit Katiyar, John T. Foster, and Mukul M. Sharma. "A Peridynamics Model for the Propagation of Hydraulic Fractures in Heterogeneous, Naturally Fractured Reservoirs." In SPE Hydraulic Fracturing Technology Conference. SPE, 2015. http://dx.doi.org/10.2118/spe-173361-ms.
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Abstract A novel fully coupled hydraulic fracturing model based on a nonlocal continuum theory of peridynamics is presented and applied to the fracture propagation problem. It is shown that this modeling approach provides an alternative to finite element and finite volume methods for solving poroelastic and fracture propagation problems and offers some clear advantages. In this paper we specifically investigate the interaction between a hydraulic fracture and natural fractures. Current hydraulic fracturing models remain limited in their ability to simulate the formation of non-planar, complex fracture networks. The peridynamics model presented here overcomes most of the limitations of existing models and provides a novel approach to simulate and understand the interaction between hydraulic fractures and natural fractures. The model predictions in two-dimensions have been validated by reproducing published experimental results where the interaction between a hydraulic fracture and a natural fracture is controlled by the principal stress contrast and the approach angle. A detailed parametric study involving poroelasticity and mechanical properties of the rock is performed to understand why a hydraulic fracture gets arrested or crosses a natural fracture. This analysis reveals that the poroelasticity, resulting from high fracture fluid leak-off, has a dominant influence on the interaction between a hydraulic fracture and a natural fracture. In addition, the fracture toughness of the rock, the toughness of the natural fracture, and the shear strength of the natural fracture also affect the interaction between a hydraulic fracture and a natural fracture. Finally, we investigate the interaction of multiple completing fractures with natural fractures in two-dimensions and demonstrate the applicability of the approach to simulate complex fracture networks on a field scale.
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Varanasi, Chandrashekhar, Jayathi Y. Murthy, and Sanjay Mathur. "A Meshless Finite Difference Method for Conjugate Heat Conduction Problems." In ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/ht2009-88098.
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In recent years, there has been a great deal of interest in developing meshless methods for computational fluid dynamics (CFD) applications. In this paper, a meshless finite difference method is developed for solving conjugate heat transfer problems in complex geometries. Traditional finite difference methods (FDMs) have been restricted to an orthogonal or a body-fitted distribution of points. However, the Taylor series upon which the FDM is based is valid at any location in the neighborhood of the point about which the expansion is carried out. Exploiting this fact, and starting with an unstructured distribution of mesh points, derivatives are evaluated using a weighted least squares procedure. The system of equations that results from this discretization can be represented by a sparse matrix. This system is solved with an algebraic multigrid (AMG) solver. The implementation of Neumann, Dirichlet and mixed boundary conditions within this framework is described, as well as the handling of conjugate heat transfer. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. Metrics for accuracy are provided and future extensions are discussed.
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Subramanian, Rajkumar, and Milind A. Jog. "Droplet Heating in a Direct-Contact Heat Exchanger: Effect of Electric Field." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79787.
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Heat transfer between two immiscible fluids in a direct contact heat exchanger can be enhanced by the application of an electric field. In this paper, we have numerically modeled heat transfer to a spherical droplet translating in an immiscible medium with an applied electric field. The electric field induces circulatory motion inside and outside the droplet that results in increase in the rate of heat transport. The governing equations for both phases are solved simultaneously by a finite volume method. The external heat transfer problem is considered where the bulk of the resistance is assumed to be in the continuous phase. Effects of electric field strength and translational Reynolds number are investigated.
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Liu, Lijun, Yongzan Liu, Xiaoguang Wang, and Jun Yao. "A Coupled Hydro-Mechanical Model for Simulation of Two-Phase Flow and Geomechanical Deformation in Naturally Fractured Porous Media." In 56th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2022. http://dx.doi.org/10.56952/arma-2022-2097.
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ABSTRACT: This paper presents a coupled fluid flow and geomechanics model for analysis of two-phase flow and deformation behaviors in naturally fractured porous media. The discrete fracture model (DFM) is used to model two-phase fluid flow. The zero-thickness interface element method coupled with a modified Barton-Bandis’s constitutive model is applied to model the mechanical behavior of natural fractures. The finite volume (FVM) and finite element (FEM) methods are used for the discretization of flow and geomechanical equations, respectively. The coupled problem is iteratively solved using the fixed-stress splitting algorithm. Then the proposed model is applied to investigate the two-phase fluid flow in fractured porous media under various in-situ stress conditions. The results show that fracture aperture significantly increases as the differential stress increases due to shear dilation, which accordingly enhances the equivalent permeability of the fractured medium. Channelized flow is formed through the dilated fractures, which results in early water breakthrough and reduces the water sweep efficiency. This study illustrates the importance of shear dilation on two-phase flow behaviors in fractured porous media and highlights the necessity of considering shear dilation for accurate prediction of saturation distributions. The simulations also demonstrate the capacity of our model to capture the complex coupled behavior induced by the interaction between pore pressure and in-situ stress loadings. 1. INTRODUCTION Hydro-mechanical coupling in fractured media is an important issue in various engineering applications, such as oil and gas recovery (Moinfar et al. 2013; Yan et al. 2018), geothermal reservoirs (Pandey et al. 2017; Li et al. 2019), CO2 sequestration (Rutqvist et al. 2007; Cappa and Rutqvist 2011), and nuclear waste disposal (Nguyen and Selvadurai 1995; Yow and Hunt 2002). As the high-conductive flow channels and weak surfaces, fractures are often characterized by the rough surfaces, which could deform under the joint influence of normal closure and shear dilation. In particular, shear dilation may play a dominant role when rough fractures suffer certain shear displacement, which is believed to be able to significantly enhance the fracture permeability (Zhang et al. 2008).
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Narayanan, Venkat R. T., Jianbo Li, Jeffrey D. Zahn, and Hao Lin. "Numerical Modeling of Microfluidic Two-Phase Electrohydrodynamic Instability." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67757.
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Organic-aqueous liquid (phenol) extraction is one of many standard techniques to efficiently purify DNA directly from cells. Effective dispersion of one fluid phase in the other increases the surface area over which biological component partitioning may occur, and hence enhances DNA extraction efficiency. Electrohydrodynamic (EHD) instability can be harnessed to achieve this goal and has been experimentally demonstrated by one of the co-authors (JDZ). In this work, analysis and simulation are combined to study two-phase EHD instability. In the problem configuration, the organic (phenol) phase flows into the microchannel in parallel with and sandwiched between two aqueous streams, creating a three-layer planar geometry; the two liquid phases are immiscible. An electric field is applied to induce instability and to break the organic stream into droplets. The Taylor-Melcher leaky-dielectric model is employed to investigate this phenomenon. A linear analysis is carried out with a Chebyshev pseudo-spectral method, whereas a fully nonlinear numerical simulation is implemented using a finite volume, immersed boundary method (IBM). The results from both models compare favorably with each other. The linear analysis reveals basic instability characteristics such as kink and sausage modes. On the other hand, the nonlinear simulation predicts surface deformation in the strongly nonlinear regime pertinent to droplet formation. These numerical tools will be used to investigate the effects of the applied electric field, geometry, and convective flow rate on mixing and dispersion. The eventual objective is to maximize surface area of the organic phase under given experimental conditions for optimized DNA extraction.
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Hasbestan, Jaber J., James C. Newman, and Abdollah Arabshahi. "A New Approach to Mesh Adaptation Procedure Using Linear Elasticity for Geometries Undergoing Large Displacements." In ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fedsm2014-22010.
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The equations of linear elasticity have been extensively used in computational fluid dynamics to deform meshes for moving boundary simulations, shape design optimization, solution adaptive refinement, and for the construction of higher-order discetizations in finite-element schemes. Inherently this method does not have any mechanism to control the quality of the mesh, since it represents the structural response to prescribed surface deflections. Unfortunately, this method does not prevent the possibility of generating negative volumes in the mesh when large deformations take place. In the current work, two approaches are examined in an attempt to mitigate this shortcoming. In the first approach, a source term is added to each node in the mesh. These source terms are chosen as design variables, and an optimization strategy is utilized to improve mesh quality. The second approach represents a modification to an existing method whereby each element in the mesh may be considered as a different material. Entries in the constitutive relations are then selected as the design variables. In this approach the number of design variables is extremely large and, thus, very computationally expense. To alleviate some of this computational burden, the design variables are selected from a subset of the elements in the mesh. In both approaches presented, the cost function is defined as a function of the mesh quality, and a limited memory BFGS optimization scheme used to minimize this function. Results for two dimensional test cases are presented; however, the concept can be easily applied to three dimensional meshes and practical problems.
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Ouazzani, Jalil, and Yves Garrabos. "A Novel Numerical Approach for Low Mach Number: Application to Supercritical Fluids." In ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/ht2013-17732.
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A new numerical algorithm has been developed to compute low Mach number fluids using the cV-formulation of the energy equation. cV is the specific heat at constant volume. It has been applied to both supercritical fluid flows (using a nonlinear equation of state like the van der Waals cubic equation of state) and gas flows (using an ideal gas law). The algorithm is introduced successfully in a finite volume code using the SIMPLE and SIMPLER methods. Its main advantage lies in the decoupling of the energy equation and equation of state from the momentum and continuity equations, leading to decrease significantly the CPU time in the case of supercritical fluids simulations. Moreover it allows for supercritical fluid flow simulations the use of other discretization methods (such as spectral methods and/or finite differences) and any other nonlinear form of the equation of state. The new algorithm is presented after a brief description of the previously existing algorithm to solve supercritical fluid flows. Then three published Benchmark problems for steady and unsteady ideal gas flows are treated, as well as the side heated cavity problem for a near critical carbon dioxide filling. The results are then compared to those obtained from the previous algorithm as well as to those obtained from a spectral code using the new algorithm. This comparative investigation is extended to the Rayleigh-Bénard problem for a near critical carbon dioxide filled square cavity with the use of the Van der Waals and the Peng-Robinson equations of state.
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Amiroudine, S., A. Ambari, and K. Boutrouft. "Acoustic Filtering Procedure in Supercritical Fluids: Application to Thermal Instabilities." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72420.
Full textAbstract:
An acoustic filtering procedure [1] has been applied to fluids above their critical point in order to decrease computational costs. The Navier-Stokes equations coupled with the energy and linearized state equations have been considered in order to solve problems related to thermal instabilities in such fluids. In the vicinity of the critical point, we showed that the Schwartchild criterion dominates over the classical one in the Rayleigh-Be´nard configuration. The numerical calculation by finite volume methods considered here, in comparison with the experiments of Meyer & Kogan [2], has given an interpretation of the unexpected oscillations at the convection onset. We have also studied the stability of two layers (hot and cold) of the same supercritical fluid (SCF) in an unstable configuration. The analogy with the stability of two miscible fluids has been clearly identified and stabilisation has been observed by reducing the height of the lower layer in this Rayleigh-Taylor like configuration.