Problem Of Convective Flow Research Articles

Grid convergence of variable-density flow simulations in discretely-fractured porous media

Grid convergence in space and time of variable-density flow in fractured-porous rock is systematically assessed. Convergence of the flow simulation is attained using both uniform and adaptive time-stepping. This contrasts to variable-density flow in unfractured porous media where grid convergence variable-density flow problems is almost never achieved. At high discretization levels, the number of fingers in fractured-porous rock is no longer influenced by spatial–temporal grid discretization, which is not the case in unfractured porous media. However, similar to unfractured porous media, the number of fingers in fractured-porous media varies at low discretization levels. Simulated convective pattern and penetration depth of the dense plume in fractured rock depend more on spatial discretization than on temporal discretization. The appropriate spatial–temporal grid is then used to examine some aspects of mixed convection in fractured-porous rock, characterized by the mixed convection number M. The critical mixed convection number M c = 46 represents the transition between forced and free convection in fractured porous media, which is much higher than M c = 1 in unfractured porous media. Thus, for mixed convective flow problems, the value of M c is not a sufficient indicator to predict the convective mode (free convection–forced convection), and the presence of vertical fractures must be included in the prediction of convective flow modes.

THE EFFECT OF BUOYANCY ON VORTEX SHEDDING AND ENTROPY GENERATION OF A HEATED SQUARE CYLINDER

The effect of buoyancy on vortex shedding and entropy generation phenomena of a heated square cylinder has been studied numerically for assisting and opposing mixed convection flows. The present analysis is valid when the buoyancy force effects are small compared to forced convection effects. The mixed convection flow problem is formulated by two-dimensional incompressible flow, with the buoyancy term represented by Boussinesq approximation. The hyperbolic grid generation method is applied to provide an efficient mesh system for the flow. The governing equations are transformed into an orthogonal transformed plane and are solved in stream function and vorticity form using high-accuracy finite difference schemes. Results show that the strength of the vortex shedding is increased with increasing Reynolds number. The effect of buoyancy reduces or stops the vortex shedding phenomena for assisting mixed convection flows with the combination of Reynolds and Richardson numbers. The effect of buoyancy increases the strength of the vortex shedding as the Richardson number increases for opposing mixed convection flows. Heat transfer characteristics and entropy generation are reported for various combinations of Reynolds and Richardson numbers. The effect of buoyancy increases the average Nusselt number and entropy generation for assisting mixed convection flows, and we see the opposite trend for opposing mixed convection flows. The reported average Nusselt number values match very well with the numerical and experimental values available from the literature. © 2010 by Begell House, Inc.

Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption

The problem of magneto-hydrodynamic mixed convective flow and heat transfer of an electrically conducting, power-law fluid past a stretching surface in the presence of heat generation/absorption and thermal radiation has been analyzed. After transforming the governing equations with suitable dimensionless variables, numerical solutions are generated by an implicit finite-difference technique for the non-similar, coupled flow. The solution is found to be dependent on the governing parameters including the power-law fluid index, the magnetic field parameter, the modified Richardson number, the radiation parameter, the heat generation parameter, and the generalized Prandtl number. To reveal the tendency of the solutions, typical results for the velocity and temperature profiles, the skin-friction coefficient, and the local Nusselt number are presented for different values of these controlling parameters.

Numerical investigation of the first transition in the three-dimensional problem of convective flow in a porous medium

The branching off of steady-state regimes from mechanical equilibrium is studied for the problem of filtration convection in a parallelepiped. The conditions for the geometric parameters under which stable continuous families of steady-state regimes develop are found. The stability of equilibria of the family with respect to three-dimensional perturbations is analyzed in a numerical experiment using a finite-difference method.

Comparison of Whole-Domain and Sequential Algorithms for Function Specification Method in the Inverse Heat Transfer Problem of Laminar Convective Pipe Flow

This article compares the application of the whole-domain function specification method (WDFSM) and the sequential function specification method (SFSM) to the inverse problem of transient conjugate heat transfer of laminar forced convection in a circular pipe. The two inverse methods are used to estimate the time-varying inlet temperature and the outer-wall heat flux simultaneously on the basis of temperature measurements taken at two different locations within the pipe flow. The numerical results reveal that the estimations obtained from the WDFSM method are marginally better than those obtained from the SFSM approach.

Scenarios of the onset of unsteady regimes in the problem of plane convective flow through a porous medium

The problem of plane convective flow through a porous medium in a rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. The onset of unsteady regimes is investigated numerically. It is shown that their onset scenarios depend on the vessel dimensions and the seepage Rayleigh number and may be as follows: the generation of stable and unstable periodic regimes as a result of a one-sided bifurcation, the generation of a stable periodic regime as a result of an Andronov-Hopf cosymmetric bifurcation, the formation of a chaotic attractor, the branching-out of a stable quasi-periodic regime from a point of a single-parameter family of steady-state regimes, and the generation of unstable periodic regimes as a result of disintegration of homoclinic trajectories. The specifics of most of the bifurcations mentioned above are attributable to the cosymmetry of the problem considered.

Effect of Permeability on Steady Flow in a Dendrite Layer

We consider the problem of nonlinear steady convective flow in a horizontal dendrite layer during alloy solidification. We analyze the effect of permeability of the layer on the stationary modes of convection in the form of two-dimensional rolls and threedimensional patterns. Under a near-eutectic approximation and the limit of large far-field temperature, we determine the twoand three-dimensional solutions to the weakly nonlinear problem by using a perturbation technique, and the stability of these solutions are investigated with respect to arbitrary three-dimensional disturbances. An inverse form of the permeability function introduces two non-negative non-dimensional parameters K1 and K2 that are significant in the present problem. The results of the analyses in particular range of values of the magnitude |e| of the amplitude of convection indicate, in particular, that the effects of K1 and K2 on the flow pattern are destabilizing and stabilizing, respectively, and different types of flow pattern can be stable for particular values of these parameters. For sufficiently small and non-zero values of |e| and K1, the steady flow pattern in the form of subcritical hexagons can stable. For |e| beyond some value and depending on the values of the parameters of the problem, supercritical rolls, squares or rectangles can be stable. For K1=0.0, the only stable flow pattern is that due to steady rolls.

Investigation of difference schemes on method of lines

A second-order high-resolution Total Variation Diminishing (TVD) scheme based on Lagrange interpolation polynomial was proposed for the spatial discretisation of convective terms in strongly convected problems with non-uniform grid topologies. Performances of classical and TVD-based Finite Difference (FD) schemes, higher-order Lagrange interpolation polynomial-based schemes and the proposed scheme were investigated on the Method of Lines (MOL) solution of two test problems, a simple one-dimensional convective flow and a two-dimensional unsteady laminar diffusion flame. The proposed scheme produced accurate results without spurious oscillations and numerical diffusion encountered in the classical schemes, and hence, was found to be a successful scheme applicable to strongly convective flow problems with non-uniform grid resolution. The proposed algorithm can be readily incorporated into existing codes based not only on MOL but also on other numerical solution techniques.

Problem of Critical Convective Flows in Horizontal-Cylindrical Cavities

The results of an analysis of the linear perturbations of equilibrium of a viscous heat-conducting fluid or gas in cavities with simple geometric cross-sections are given. Both plane motions and motions periodic in the direction of the horizontal generator of the boundary surface are considered. Variants in which the acceleration of the mass force field can be both constant and periodically modulated are calculated. The solutions of the problem for the stream function (or the vertical velocity component) and the temperature are represented in the form of double or triple Fourier series. For the coefficients in the expansions an infinite system of equations which admits reduction is obtained. The results are found to be in good agreement with the known data.

Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε .

Numerical Investigation of the Second Transition in the Problem of Plane Convective Flow through a Porous Medium

The problem of convective flow through a porous medium in a plane rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. Single-parameter families of steady-state regimes resulting from the existence of cosymmetry of the corresponding differential equations are investigated using the Galerkin method. The onset and development of instability on these families and the characteristics of convective regimes as functions of the seepage Rayleigh number and the rectangle side ratio are studied. It is shown that the number of regimes which lose stability, the instability type, the number of convective rollers developed, and the heat transfer depend significantly on the vessel geometry. Several bifurcations of single-parameter families of steady-state regimes are identified and investigated.

Inclusion of Hydrodynamic Dispersion in Fluid Flow Computations Using the Complex Variable Boundary Element Method

The complex variable boundary element method (CVBEM) has been successfully applied to convective flow problems. This study aims at extending the applicability of the CVBEM to convective-dispersive flow problems. In order to utilize the analytical solutions obtained for one-dimensional (1D) problems, two-dimensional (2D) transport is decomposed into transport along multiple 1D streamlines. Varying velocity along the streamlines can be taken into account with a set of coordinate transformations τ and ω. The CVBEM is suitable for streamline tracking and yields accurate evaluations of τ and ω. Along each streamline, 1D transport is analytically modeled, and the complete 2D solution is recovered by combining the individual 1D solutions. The developed method is verified against a diverging radial flow problem and applied to some example problems. Tracer concentration profiles and effluent concentration curves, which can directly be constructed from the analytical solutions, are of use for evaluating hydrodynamic characteristics.

Hydromagnetic double-diffusive convection in a rectangular enclosure with uniform side heat and mass fluxes and opposing temperature and concentration gradients

The problem of hydromagnetic double-diffusive convective flow of a binary gas mixture in a rectangular enclosure with the upper and lower walls being insulated is solved numerically by the finite-difference methodology. Constant heat and mass fluxes conditions are imposed along the left and right walls of the enclosure and a uniform magnetic field is applied in the direction normal to the left and right walls. In this study, the thermal and the compositional buoyancy forces are assumed to be opposite and internal heat generation or absorption effects are assumed to exist. Numerical results illustrating the effects of the heat generation or absorption coefficient and the Hartmann number on the contours of streamline, temperature and concentration are presented graphically. In addition, results for the velocity, temperature and concentration profiles at mid-section of the enclosure as well as the average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions.

Computations of laminar and turbulent mixed convection in a driven cavity using pseudo-compressibility approach

A driven cavity, for two different thermal boundary conditions, has been chosen as a test case to establish the suitability of pseudo-compressibility algorithm for mixed convection flow problems for both laminar and turbulent flow situations. Here shear stress transport eddy viscosity model has been modified to include the buoyancy effects. The flow is computed inside the cavity under the influence of varying buoyancy and inertia forces. The computed results demonstrate the ability of the pseudo-compressibility approach and shear stress transport model to solve complex heat transfer problems.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

Comparison of low Mach number models for natural convection problems

We investigate in this paper two numerical methods for solving low Mach number compressible flows and their application to single-phase natural convection flow problems. The first method is based on an asymptotic model of the Navier–Stokes equations valid for small Mach numbers, whereas the second is based on the full compressible Navier–Stokes equations with particular care given to the discretization at low Mach numbers. These models are more general than the Boussinesq incompressible flow model, in the sense that they are valid even for cases in which the fluid is subjected to large temperature differences, that is when the compressibility of the fluid manifests itself through low Mach number effects. Numerical solutions are computed for a series of test problems with fixed Rayleigh number and increasing temperature differences, as well as for varying Rayleigh number for a given temperature difference. Numerical difficulties associated with low Mach number effects are discussed, as well as the accuracy of the approximations.

The DRM sub-domain decomposition approach for two-dimensional thermal convection flow problems

This work presents a domain decomposition boundary integral equation method for the solution of the coupling of the momentum and energy equations governing the motion of a viscous fluid due to natural convection. The domain integrals in the proposed integral representation formula of both equations are transformed into surface integrals at the contour of each sub-region via the dual reciprocity method (DRM). Finally, some examples showing the accuracy, the efficiency and the flexibility of the proposed method are presented.

Natural Convection Heat Transfer in an Asymmetrically Heated Vertical Channel Controlled by Through Flows.

The effort to solve the fundamental problem of convective flows and heat transfer in a vertical channel is continued in this work, considering a new control parameter for the thermal flow regime. A numerical investigation of the developing heat convection in the channel is presented, while considering the effects of a vertical forced flow on the Nusselt number at the cold wall for a wide range of related parameters. By the analysis of these results, it is possible to predict heat transfer behavior especially in cases when the Nusselt number at the cold wall becomes practically zero. The main results obtained from this study are the critical Reynolds number variation obtained for different geometrical aspect ratios (A=H/L=2 ; 4 ; 8; 16) and the natural convection parameter, Ra=10 4 -10 7 . Based on the scaling analysis it is determined that the critical Reynolds number is independent of Ra and scaled as R ect HT A 2 , where A is the aspect ratio

Development of BEM for convective viscous flow problems

Three kinds of boundary element approaches for an unsteady flow problem of incompressible viscous fluid are presented. The first approach which is the so-called boundary-domaintype is based on the use of fundamental solution for the only linear differential operator and the Newton-Raphson iterative procedure. The second one is based on the time splitting technique of the governing equations in which the fundamental equations are split into the convection equation and the Stokes equations. The third one is based on the well-known fractional step (FS) method which is one of the time splitting techniques. In order to show the applicability and effectiveness of our approaches, numerical results of the driven cavity flow example are demonstrated through a comparison with other numerical results.

Convection in multiple layers of immiscible liquids in a shallow cavity—I. Steady natural convection

The problem of convective flow in multiple immiscible liquid layers in a differentially heated shallow rectangular cavity with rigid and insulated upper and lower boundaries is considered. As a model for multiple layers, a three-layer system featuring two non-deformable interfaces is investigated. The method of matched asymptotic expansions is used to determine the flow in the two distinct regions: the core region characterized by parallel flow; and the end-wall regions where flow turns around. The driving mechanism for convection is buoyancy. To study mechanical coupling across interfaces between immiscible liquids, the influence of varying encapsulant viscosity is investigated.