Showing papers on "Fluid dynamics published in 2011"
TL;DR: In this article, the decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet.
Abstract: The decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet. The algorithm relies on the reconstruction of a low-dimensional inter-snapshot map from the available flow field data. The spectral decomposition of this map results in an eigenvalue and eigenvector representation (referred to as dynamic modes) of the underlying fluid behavior contained in the processed flow fields. This dynamic mode decomposition allows the breakdown of a fluid process into dynamically revelant and coherent structures and thus aids in the characterization and quantification of physical mechanisms in fluid flow.
505 citations
TL;DR: This paper summarized the current state of knowledge of fluid flow and pore pressure in subduction forearcs, and focus on recent advances that have quantified permeability architecture, fluxes, the nature and timing of transience, and pressure distribution, thus providing new insights into the connections between fluid, metamorphic, mechanical, and fault slip proc...
Abstract: At subduction zones, fluid flow, pore pressure, and tectonic processes are tightly interconnected. Excess pore pressure is driven by tectonic loading and fluids released by mineral dehydration, and it has profound effects on fault and earthquake mechanics through its control on effective stress. The egress of these overpressured fluids, which is in part governed by the presence of permeable fault zones, is a primary mechanism of volatile and solute transport to the oceans. Recent field measurements, new constraints gained from laboratory studies, and numerical modeling efforts have led to a greatly improved understanding of these coupled processes. Here, we summarize the current state of knowledge of fluid flow and pore pressure in subduction forearcs, and focus on recent advances that have quantified permeability architecture, fluxes, the nature and timing of transience, and pressure distribution, thus providing new insights into the connections between fluid, metamorphic, mechanical, and fault slip proc...
413 citations
TL;DR: The transition from ballistic to diffusive Brownian motion has been measured for the first time in this article, where the transition from long-lived to short-lived Brownian motions has been explored.
Abstract: That Brownian particles in a liquid move diffusively at long times but ballistically at very short times has been understood for more than a century. However, the full details of the transition between these regimes are yet to be explored. Now, the transition from ballistic to diffusive Brownian motion has been measured for the first time.
393 citations
TL;DR: In this paper, energy transport and chemistry are modeled in an extension of the Eulerian-Lagrangian computational particle fluid dynamics (CPFD) methodology, where an enthalpy equation describes energy transport for fluid, and provides for transfer of sensible and chemical energy between phases and within the fluid mixture.
320 citations
TL;DR: In this paper, the dusty-gas model for flow was used to model flow in shale gas systems, which couples diffusion to advective flow and showed that for very small average pore throat diameters, lighter gases preferentially produced at concentrations significantly higher than in situ conditions.
Abstract: Various attempts have been made to model flow in shale gas systems. However, there is currently little consensus regarding the impact of molecular and Knudsen diffusion on flow behavior over time in such systems. Direct measurement or model-based estimation of matrix permeability for these “ultra-tight” reservoirs has proven unreliable. The composition of gas produced from tight gas and shale gas reservoirs varies with time for a variety of reasons. The cause of flowing gas compositional change typically cited is selective desorption of gases from the surface of the kerogen in the case of shale. However, other drivers for gas fractionation are important when pore throat dimensions are small enough. Pore throat diameters on the order of molecular mean free path lengths will create non-Darcy flow conditions, where permeability becomes a strong function of pressure. At the low permeabilities found in shale gas systems, the dusty-gas model for flow should be used, which couples diffusion to advective flow. In this study we implement the dusty-gas model into a fluid flow modeling tool based on the TOUGH+ family of codes. We examine the effects of Knudsen diffusion on gas composition in ultra-tight rock. We show that for very small average pore throat diameters, lighter gases are preferentially produced at concentrations significantly higher than in situ conditions. Furthermore, we illustrate a methodology which uses measurements of gas composition to more uniquely determine the permeability of tight reservoirs. We also describe how gas composition measurement could be used to identify flow boundaries in these reservoir systems. We discuss how new measurement techniques and data collection practices should be implemented in order to take advantage of this method. Our contributions include a new, fit-for-purpose numerical model based on the TOUGH+ code capable of characterizing transport effects including permeability adjustment and diffusion in micro- and nano-scale porous media.
295 citations
TL;DR: In this paper, the authors present a harmonic decomposition of the initial fluctuations in shape and orientation of the fireball and perform event-by-event (2 + 1)-dimensional ideal fluid dynamical simulations to extract the resulting fluctuations in the magnitude and direction of the corresponding harmonic components of the final anisotropic flow at midrapidity.
Abstract: Heavy-ion collisions create deformed quark-gluon plasma (QGP) fireballs which explode anisotropically. The viscosity of the fireball matter determines its ability to convert the initial spatial deformation into momentum anisotropies that can be measured in the final hadron spectra. A quantitatively precise empirical extraction of the QGP viscosity thus requires a good understanding of the initial fireball deformation. This deformation fluctuates from event to event, and so does the finally observed momentum anisotropy. We present a harmonic decomposition of the initial fluctuations in shape and orientation of the fireball and perform event-by-event (2 + 1)-dimensional ideal fluid dynamical simulations to extract the resulting fluctuations in the magnitude and direction of the corresponding harmonic components of the final anisotropic flow at midrapidity. The final harmonic flow coefficients are found to depend nonlinearly on the initial harmonic eccentricity coefficients. We show that, on average, initial density fluctuations suppress the buildup of elliptic flow relative to what one obtains from a smooth initial profile of the same eccentricity and discuss implications for the phenomenological extraction of the QGP shear viscosity from experimental elliptic flow data.
253 citations
Book•
05 Sep 2011
TL;DR: In this article, a finite difference method for solving the Navier-Stokes equations for an incompressible fluid has been developed, which is equally applicable to problems in two and three space dimensions.
Abstract: A finite difference method for solving the Navier-Stokes equations for an incompressible fluid has been developed. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Essentially it constitutes an extension to time dependent problems of the artificial compressibility method introduced in [ l ] for steady flow problems. The equations to be solved can be written in the dimensionless form
235 citations
TL;DR: In this paper, the authors discussed the unsteady flow and heat transfer of a Casson fluid over a moving flat plate with a parallel free stream, and the analytic solutions of the system of nonlinear partial differential equations valid for all times in the whole spatial domain are constructed in the series form by a homotopic approach.
Abstract: This paper discusses the unsteady flow and heat transfer of a Casson fluid over a moving flat plate with a parallel free stream. The analytic solutions of the system of nonlinear partial differential equations valid for all times in the whole spatial domain are constructed in the series form by a homotopic approach. The influences of the governing parameters on the velocity, temperature, skin friction coefficient, and local Nusselt number are thoroughly investigated. It is revealed that an increase in the dimensionless time decreases the velocity and enhances the temperature. The surface shear stress and surface heat transfer are enhanced by increasing the Casson fluid parameter (β) and Eckert number (Ec), respectively. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20358
231 citations
TL;DR: In this article, a direct numerical simulation (DNS) study of dilute turbulent particulate flow in a vertical plane channel was conducted, considering thousands of finite-size rigid particles with resolved phase interfaces.
Abstract: We have conducted a direct numerical simulation (DNS) study of dilute turbulent particulate flow in a vertical plane channel, considering thousands of finite-size rigid particles with resolved phase interfaces. The particle diameter corresponds to approximately 11 wall units and their terminal Reynolds number is set to 136. The fluid flow with bulk Reynolds number 2700 is directed upward, which maintains the particles suspended upon average. Two density ratios were simulated, differing by a factor of 4.5. The corresponding Stokes numbers of the two flow cases were O(10) in the near-wall region and O(1) in the outer flow. We have observed the formation of large-scale elongated streak-like structures with streamwise dimensions of the order of 8 channel half-widths and cross-stream dimensions of the order of one half-width. At the same time, we have found no evidence of significant formation of particle clusters, which suggests that the large structures are due to an intrinsic instability of the flow, triggered by the presence of the particles. It was found that the mean fluid velocity profile tends towards a concave shape, and the turbulence intensity as well as the normal stress anisotropy are strongly increased. The effect of varying the Stokes number while maintaining the buoyancy, particle size and volume fraction constant was relatively weak.
221 citations
TL;DR: In this paper, the experimental data are analyzed in terms of friction factor, laminar-to-turbulent transition, and the effect of roughness on fluid hydrodynamics for different cross-sectional geometries.
214 citations
Book•
18 Jan 2011
TL;DR: In this article, the authors present a detailed analysis of flow properties in a pipe with respect to the Euler's Equation and the Bernoulli Equation along a streamline.
Abstract: CHAPTER 1 INTRODUCTION. 1.1 Note to Students. 1.2 Scope of Fluid Mechanics. 1.3 Definition of a Fluid. 1.4 Basic Equations. 1.5 Methods of Analysis. 1.6 Dimensions and Units. 1.7 Analysis of Experimental Error. 1.8 Summary. Problems. CHAPTER 2 FUNDAMENTAL CONCEPTS. 2.1 Fluid as a Continuum. 2.2 Velocity Field. 2.3 Stress Field. 2.4 Viscosity. 2.5 Surface Tension. 2.6 Description and Classification of Fluid Motions. 2.7 Summary and Useful Equations. References. Problems. CHAPTER 3 FLUID STATICS. 3.1 The Basic Equation of Fluid Statics. 3.2 The Standard Atmosphere. 3.3 Pressure Variation in a Static Fluid. 3.4 Hydraulic Systems. 3.5 Hydrostatic Force on Submerged Surfaces. 3.6 Buoyancy and Stability. 3.7 Fluids in Rigid-Body Motion (on the Web). 3.8 Summary and Useful Equations. References. Problems. CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME. 4.1 Basic Laws for a System. 4.2 Relation of System Derivatives to the Control Volume Formulation. 4.3 Conservation of Mass. 4.4 Momentum Equation for Inertial Control Volume. 4.5 Momentum Equation for Control Volume with Rectilinear Acceleration. 4.6 Momentum Equation for Control Volume with Arbitrary Acceleration (on the Web). 4.7 The Angular-Momentum Principle. 4.8 The First Law of Thermodynamics. 4.9 The Second Law of Thermodynamics. 4.10 Summary and Useful Equations. Problems. CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION. 5.1 Conservation of Mass. 5.2 Stream Function for Two-Dimensional Incompressible Flow. 5.3 Motion of a Fluid Particle (Kinematics). 5.4 Momentum Equation. 5.5 Introduction to Computational Fluid Dynamics. 5.6 Summary and Useful Equations. References. Problems. CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW. 6.1 Momentum Equation for Frictionless Flow: Euler's Equation. 6.2 Euler's Equations in Streamline Coordinates. 6.3 Bernoulli Equation-Integration of Euler's Equation Along a Streamline for Steady Flow. 6.4 The Bernoulli Equation Interpreted as an Energy Equation. 6.5 Energy Grade Line and Hydraulic Grade Line. 6.6 Unsteady Bernoulli Equation: Integration of Euler's Equation Along a Streamline (on the Web). 6.7 Irrotational Flow. 6.8 Summary and Useful Equations. References. Problems. CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE. 7.1 Nondimensionalizing the Basic Differential Equations. 7.2 Nature of Dimensional Analysis. 7.3 Buckingham Pi Theorem . 7.4 Determining the PI Groups. 7.5 Significant Dimensionless Groups in Fluid Mechanics. 7.6 Flow Similarity and Model Studies. 7.7 Summary and Useful Equations. References. Problems. CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW. 8.1 Introduction. PART A. FULLY DEVELOPED LAMINAR FLOW. 8.2 Fully Developed Laminar Flow between Infinite Parallel Plates. 8.3 Fully Developed Laminar Flow in a Pipe. PART B. FLOW IN PIPES AND DUCTS. 8.4 Shear Stress Distribution in Fully Developed Pipe Flow. 8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow. 8.6 Energy Considerations in Pipe Flow. 8.7 Calculation of Head Loss. 8.8 Solution of Pipe Flow Problems. PART C. FLOW MEASUREMENT. 8.9 Direct Methods. 8.10 Restriction Flow Meters for Internal Flows. 8.11 Linear Flow Meters. 8.12 Traversing Methods. 8.13 Summary and Useful Equations. References. Problems. CHAPTER 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW. PART A. BOUNDARY LAYERS. 9.1 The Boundary-Layer Concept. 9.2 Boundary-Layer Thicknesses. 9.3 Laminar Flat-Plate Boundary Layer: Exact Solution (on the Web). 9.4 Momentum Integral Equation. 9.5 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient. 9.6 Pressure Gradients in Boundary-Layer Flow. PART B. FLUID FLOW ABOUT IMMERSED BODIES. 9.7 Drag. 9.8 Lift. 9.9 Summary and Useful Equations. References. Problems. CHAPTER 10 FLUID MACHINERY. 10.1 Introduction and Classification of Fluid Machines. 10.2 Turbomachinery Analysis. 10.3 Pumps, Fans, and Blowers. 10.4 Positive Displacement Pumps. 10.5 Hydraulic Turbines. 10.6 Propellers and Wind-Power Machines. 10.7 Compressible Flow Turbomachines. 10.8 Summary and Useful Equations. References. Problems. CHAPTER 11 FLOW IN OPEN CHANNELS. 11.1 Basic Concepts and Definitions. 11.2 Energy Equation for Open-Channel Flows. 11.3 Localized Effect of Area Change (Frictionless Flow). 11.4 The Hydraulic Jump. 11.5 Steady Uniform Flow. 11.6 Flow with Gradually Varying Depth. 11.7 Discharge Measurement Using Weirs. 11.8 Summary and Useful Equations. References. Problems. CHAPTER 12 INTRODUCTION TO COMPRESSIBLE FLOW. 12.1 Review of Thermodynamics. 12.2 Propagation of Sound Waves. 12.3 Reference State: Local Isentropic Stagnation Properties. 12.4 Critical Conditions. 12.5 Summary and Useful Equations. References. Problems. CHAPTER 13 COMPRESSIBLE FLOW. 13.1 Basic Equations for One-Dimensional Compressible Flow. 13.2 Isentropic Flow of an Ideal Gas: Area Variation. 13.3 Normal Shocks. 13.4 Supersonic Channel Flow with Shocks. 13.5 Flow in a Constant-Area Duct with Friction. 13.6 Frictionless Flow in a Constant-Area Duct with Heat Exchange. 13.7 Oblique Shocks and Expansion Waves. 13.8 Summary and Useful Equations. References. Problems. APPENDIX A FLUID PROPERTY DATA. APPENDIX B EQUATIONS OF MOTION IN CYLINDRICAL COORDINATES. APPENDIX C VIDEOS FOR FLUID MECHANICS. APPENDIX D SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS. APPENDIX E FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW. APPENDIX F ANALYSIS OF EXPERIMENTAL UNCERTAINTY. APPENDIX G SI UNITS, PREFIXES, AND CONVERSION FACTORS. APPENDIX H A BRIEF REVIEW OF MICROSOFT EXCEL (ON THE WEB). Answers to Selected Problems. Index.
TL;DR: In this article, the steady two-dimensional boundary layer flow past a static or a moving wedge immersed in nanofluids is investigated numerically using an implicit finite difference scheme known as the Keller-box method and the NAG routine DO2HAF.
Book•
28 Aug 2011TL;DR: In this article, the front tracking method is applied to the Euler equations describing compressible gas dynamics, and the results on a series of test problems for which comparison answers can be obtained by independent methods.
Abstract: Front tracking is an adaptive computational method in which a lower dimensional moving grid is fitted to and follows the dynamical evolution of distinguished waves in a fluid flow. The method takes advantage of known analytic solutions, derived from the Rankine-Hugoniot relations, for idealized discontinuities. In this paper the method is applied to the Euler equations describing compressible gas dynamics. The main thrust here is validation of the front tracking method: we present results on a series of test problems for which comparison answers can be obtained by independent methods.
TL;DR: In this paper, a polariton fluid flowing past an obstacle and the observation of nucleation of quantized vortex pairs in the wake of the obstacle is reported. But the experimental results are successfully reproduced by numerical simulations based on the resolution of the Gross-Pitaevskii equation.
Abstract: Quantized vortices appear in quantum gases at the breakdown of superfluidity. In liquid helium and cold atomic gases, they have been indentified as the quantum counterpart of turbulence in classical fluids. In the solid state, composite light‐matter bosons known as exciton polaritons have enabled studies of non-equilibrium quantum gases and superfluidity. However, there has been no experimental evidence of hydrodynamic nucleation of polariton vortices so far. Here we report the experimental study of a polariton fluid flowing past an obstacle and the observation of nucleation of quantized vortex pairs in the wake of the obstacle. We image the nucleation mechanism and track the motion of the vortices along the flow. The nucleation conditions are established in terms of local fluid density and velocity measured on the obstacle perimeter. The experimental results are successfully reproduced by numerical simulations based on the resolution of the Gross‐Pitaevskii equation. H ydrodynamic instabilities in classical fluids were studied in the pioneering experiments of BOnard in the 1910’s. Convective BOnardRayleigh flows and BOnardVon KAErmAEn streets are now well known examples in nonlinear and chaos sciences 1 . In conventional fluids, the flow around an obstacle is characterized by the dimensionless Reynolds number ReD vR= , withv and the fluid velocity and dynamical viscosity, respectively, and R the diameter of the obstacle. When increasing the Reynolds number, laminar flow, stationary vortices, BOnardVon KAErmAEn streets of moving vortices and fully turbulent regimes are successively observed in the wake of the obstacle 1 .
TL;DR: In this article, the role of heat transfer between the rock matrix and circulating fluid on economic hot water production from fractured geothermal systems is investigated and a numerical procedure is developed by coupling fluid flow with heat transfer.
TL;DR: In this article, the authors investigated changes in fluid permeability and associated changes in P-wave and S-wave velocities, at elevated effective pressure for intact, macro-fractured and micro-fracted samples of Seljadur basalt.
Book•
24 May 2011
TL;DR: This chapter discusses the development of fast solvers for transonic potential equations using the Cauchy-Riemann equations, as well as applications to Fluid Dynamics.
Abstract: List of figures List of tables Preface to the Classics Edition Preface Introduction 1. Elementary acquaintance with multigrid Part I. Stages in Developing Fast Solvers: 2. Stable discretization 3. Interior relaxation and smoothing factors 4. Interior two-level cycles 5. Boundary conditions and two-level cycling 6. Many-level cycles 7. Full multi-grid (FMG) algorithms Part II. Advanced Techniques and Insights: 8. Full approximation scheme (FAS) and applications 9. Local refinements and grid adaptation 10. Higher-order techniques 11. Coarsening guided by discretization 12. True role of relaxation 13. Dealgebraization of multigrid 14. Practical role of rigorous analysis and quantitative predictions 15. Chains of problems: frozen tau 16. Time dependent problems Part III. Applications to Fluid Dynamics: 17. Cauchy-Riemann equations 18. Steady-state Stokes equations 19. Steady-state incompressible Navier-Stokes equations 20. Compressible Navier-Stokes and Euler equations 21. Remarks on solvers for transonic potential equations Appendix: test cycle: MATLAB code Bibliography Index.
TL;DR: The microfluidic-based hydrodynamic trap facilitates particle trapping using the sole action of fluid flow and provides a viable alternative to existing confinement and manipulation techniques based on electric, optical, magnetic or acoustic force fields.
Abstract: We report an integrated microfluidic device for fine-scale manipulation and confinement of micro- and nanoscale particles in free-solution. Using this device, single particles are trapped in a stagnation point flow at the junction of two intersecting microchannels. The hydrodynamic trap is based on active flow control at a fluid stagnation point using an integrated on-chip valve in a monolithic PDMS-based microfluidic device. In this work, we characterize device design parameters enabling precise control of stagnation point position for efficient trap performance. The microfluidic-based hydrodynamic trap facilitates particle trapping using the sole action of fluid flow and provides a viable alternative to existing confinement and manipulation techniques based on electric, optical, magnetic or acoustic force fields. Overall, the hydrodynamic trap enables non-contact confinement of fluorescent and non-fluorescent particles for extended times and provides a new platform for fundamental studies in biology, biotechnology and materials science.
TL;DR: In this paper, a mathematical equation is proposed to describe the relation between hydraulic aperture and mechanical aperture by means of the ratio of the standard deviation of local mechanical aperture to its mean value.
TL;DR: In this article, a large-scale 2D vortex and small-scale 3D turbulence are combined to form an upscale energy cascade that powers intermediate and large scale flows, respectively.
Abstract: When a thick fluid, such as the Earth’s atmosphere, is driven simultaneously by a large-scale two-dimensional vortex and small-scale three-dimensional turbulence, experiments show that the large-scale flow dominates. Turbulence is thus confined to two dimensions, giving rise to an upscale energy cascade that powers the intermediate and large-scale flows.
TL;DR: In this article, a quasi-static creep test with mesoscopic-scale heterogeneities is proposed to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations.
Abstract: [1] The finite element method is used to solve Biot's equations of consolidation in the displacement-pressure (u − p) formulation. We compute one-dimensional (1-D) and two-dimensional (2-D) numerical quasi-static creep tests with poroelastic media exhibiting mesoscopic-scale heterogeneities to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations. The P wave modulus is used to calculate the frequency-dependent attenuation (i.e., inverse of quality factor) and phase velocity of the medium. Attenuation and velocity dispersion are due to fluid flow induced by pressure differences between regions of different compressibilities, e.g., regions (or patches) saturated with different fluids (i.e., so-called patchy saturation). Comparison of our numerical results with analytical solutions demonstrates the accuracy and stability of the algorithm for a wide range of frequencies (six orders of magnitude). The algorithm employs variable time stepping and an unstructured mesh which make it efficient and accurate for 2-D simulations in media with heterogeneities of arbitrary geometries (e.g., curved shapes). We further numerically calculate the quality factor and phase velocity for 1-D layered patchy saturated porous media exhibiting random distributions of patch sizes. We show that the numerical results for the random distributions can be approximated using a volume average of White's analytical solution and the proposed averaging method is, therefore, suitable for a fast and transparent prediction of both quality factor and phase velocity. Application of our results to frequency-dependent reflection coefficients of hydrocarbon reservoirs indicates that attenuation due to wave-induced flow can increase the reflection coefficient at low frequencies, as is observed at some reservoirs.
TL;DR: In this paper, a three-dimensional transient numerical model is developed and used to simulate fluid injection into geothermal reservoirs, which couples fracture flow and heat transport to thermo-poroelastic deformation of the rock matrix via the displacement discontinuity (DD) method.
TL;DR: The results obtained in this work partially revise this last statement and demonstrate that firm conclusions on the limits of RANS simulations can be drawn only after careful verification of numerical uncertainties.
TL;DR: In this paper, a review of the literature on convective heat transfer on internal separated flows has been extensively conducted in the past decades, and the influence of several parameters such as the geometrical specifications, boundary conditions, type of fluids, and inclination angle on the hydrodynamic and thermal characteristics using (BFS).
Abstract: Research in convective heat transfer on internal separated flows has been extensively conducted in the past decades. This review summarizes numerous researches on two topics. The first section focuses on studying the fluid flow and heat transfer behavior of different types of single-phase fluid flows over backward facing step (BFS) at different orientations. The second section concentrates on everything related to nanofluids; its preparation, properties, behavior, applications, and many others. The purpose of this article is to get a clear view and detailed summary of the influence of several parameters such as the geometrical specifications, boundary conditions, type of fluids, and inclination angle on the hydrodynamic and thermal characteristics using (BFS). The reattachment length and maximum Nusselt number are the main target of such research where correlation equations were developed and reported in experimental and numerical studies. The heat transfer enhancement of nanofluids along with the nanofluids preparation technique, types and shapes of nanoparticles, base fluids and additives, transport mechanisms, and stability of the suspension are also discussed.
TL;DR: In this paper, the authors extended the Darcy's law to two-component nonisothermal flow with two phases inside the porous medium and one phase in the free-flow region, and the phenomenological explanations leading to a simple, solvable model, which accounts for the physics at the interface, are laid out in detail.
Abstract: [1] Domains composed of a porous part and an adjacent free-flow region are of special interest in many fields of application. So far, the coupling of free flow with porous-media flow has been considered only for single-phase systems. Here we extend this classical concept to two-component nonisothermal flow with two phases inside the porous medium and one phase in the free-flow region. The mathematical modeling of flow and transport phenomena in porous media is often based on Darcy's law, whereas in free-flow regions the (Navier-) -Stokes equations are used. In this paper, we give a detailed description of the employed subdomain models. The main contribution is the developed coupling concept, which is able to deal with compositional (miscible) flow and a two-phase system in the porous medium. It is based on the continuity of fluxes and the assumption of thermodynamic equilibrium, and uses the Beavers-Joseph-Saffman condition. The phenomenological explanations leading to a simple, solvable model, which accounts for the physics at the interface, are laid out in detail. Our model can account for evaporation and condensation processes at the interface and is used to model evaporation from soil influenced by a wind field in a first numerical example.
TL;DR: In this article, the equations of motion of a double-porosity medium were derived based on Biot's theory of poroelasticity and on a generalization of the theory of fluid collapse to the porous case.
Abstract: [1] We derive the equations of motion of a double‐porosity medium based on Biot’s theory of poroelasticity and on a generalization of Rayleigh’s theory of fluid collapse to the porous case. Spherical inclusions are imbedded in an unbounded host medium having different porosity, permeability, and compressibility. Wave propagation induces local fluid flow between the inclusions and the host medium because of their dissimilar compressibilities. Following Biot’s approach, Lagrange’s equations are obtained on the basis of the strain and kinetic energies. In particular, the kinetic energy and the dissipation function associated with the local fluid flow motion are described by a generalization of Rayleigh’s theory of liquid collapse of a spherical cavity. We obtain explicit expressions of the six stiffnesses and five density coefficients involved in the equations of motion by performing “gedanken” experiments. A plane wave analysis yields four wave modes, namely, the fast P and S waves and two slow P waves. As an example, we consider a sandstone and compute the phase velocity and quality factor as a function of frequency, which illustrate the effects of the mesoscopic loss mechanism due to wave‐induced fluid flow.
TL;DR: In this paper, the effect of temperature differences on the fluid flow and heat transfer in the energy storage/release system is analyzed using a commercial computational fluid dynamics (CFD) package based on the finite volume method.
TL;DR: This work determines a feedback boundary control law, robust with respect to boundary perturbations, by solving a max-min linear quadratic control problem and shows that this feedback law locally stabilizes the Navier-Stokes system.
Abstract: We study the robust or $H^\infty$ exponential stabilization of the linearized Navier-Stokes equations around an unstable stationary solution in a two-dimensional domain $\Omega$. The disturbance is an unknown perturbation in the boundary condition of the fluid flow. We determine a feedback boundary control law, robust with respect to boundary perturbations, by solving a max-min linear quadratic control problem. Next we show that this feedback law locally stabilizes the Navier-Stokes system. Similar problems have been studied in the literature in the case of distributed controls and disturbances. To the authors' knowledge, it is the first time that the robust stabilization of the Navier-Stokes equations is studied for boundary controls and boundary disturbances.