Convection Problem Research Articles

Numerical investigations of free and forced convection with various features using mesoscopic Lattice Boltzmann method

This paper is concerned with the free and forced convection of heat transfer characteristics by Lattice Boltzmann method (LBM). The LBM is used as the alternative method for the prediction of fluid flow and heat transfer characteristics for the past few years. The fluid flow equation was combined with energy equation in order to get the temperature field in the flow. In natural convection problem, the motion of the fluid inside a cavity domain is considered. The motion takes place because of change in density and due to the gravitational force. The problem of natural convection and forced convection is solved using internal energy density distribution function model for Rayleigh number ranging from 103 to 106. And for the forced convection problem the Reynolds number is varied. In all the problems streamline patterns are plotted, where the intricate details of the flow such as primary and secondary vortices are captured. Thus, it is shown that Lattice Boltzmann Method can be used to solve fluid flow and heat transfer characteristics.

A Pod/Galerkin Model from Eigenfunctions of Non-Converged Newton Iterations in a Convection Problem

A Pod/Galerkin Model from Eigenfunctions of Non-Converged Newton Iterations in a Convection Problem

On spectral/hp simulations of heat-exchange effects in low-Mach non-stationary fluid flow

Non-stationary flow of fluid, whose material properties change as influenced by heating, is the subject of this study. Model of coupled Navier-Stokes-Fourier system with temperature dependent material properties is introduced together with construction of appropriate numerical scheme. Spectral/hp element method is used as the discrete approximation of the functions in the spatial coordinates. Performance of the code implemented using Nektar++ library [1] is presented on problems of forced and natural convection around the heated cylinder.

The role of boundary conditions in scaling laws for turbulent heat transport

<abstract><p>In most results concerning bounds on the heat transport in the Rayleigh-Bénard convection problem no-slip boundary conditions for the velocity field are assumed. Nevertheless it is debatable, whether these boundary conditions reflect the behavior of the fluid at the boundary. This problem is important in theoretical fluid mechanics as well as in industrial applications, as the choice of boundary conditions has effects in the description of the boundary layers and its properties. In this review we want to explore the relation between boundary conditions and heat transport properties in turbulent convection. For this purpose, we present a selection of contributions in the theory of rigorous bounds on the Nusselt number, distinguishing and comparing results for no-slip, free-slip and Navier-slip boundary conditions.</p></abstract>

Mmc-Based Heat Sink Topology Optimization Design for Natural Convection Problems

Mmc-Based Heat Sink Topology Optimization Design for Natural Convection Problems

A fast method for solving time-dependent nonlinear convection diffusion problems

<abstract><p>In this paper, a fast scheme for solving unsteady nonlinear convection diffusion problems is proposed and analyzed. At each step, we firstly isolate a nonlinear convection subproblem and a linear diffusion subproblem from the original problem by utilizing operator splitting. By Taylor expansion, we explicitly transform the nonlinear convection one into a linear problem with artificial inflow boundary conditions associated with the nonlinear flux. Then a multistep technique is provided to relax the possible stability requirement, which is due to the explicit processing of the convection problem. Since the self-adjointness and coerciveness of diffusion subproblems, there are so many preconditioned iterative solvers to get them solved with high efficiency at each time step. When using the finite element method to discretize all the resulting subproblems, the major stiffness matrices are same at each step, that is the reason why the unsteady nonlinear systems can be computed extremely fast with the present method. Finally, in order to validate the effectiveness of the present scheme, several numerical examples including the Burgers type and Buckley-Leverett type equations, are chosen as the numerical study.</p></abstract>

A Numerical Approach for Natural Convection With Curved Obstacles in an Enclosure Using Lattice Boltzmann Method

Abstract The impact of placing curved obstacles on natural convection in enclosures with differentially heated side walls is analyzed in the current study using the lattice Boltzmann method (LBM). A method to choose characteristic velocity based on Knudsen number is implemented which eradicates the need of arbitrarily guessing characteristic velocities to proceed with simulations. In addition, a less computationally intensive probability distribution function for equilibrium temperature is used. For validation, a standard natural convection problem with left wall at high temperature, right wall at low temperature, and top and bottom adiabatic walls is considered. A grid independence test is conducted and the code is validated with existing results for various Rayleigh numbers, which shows a good agreement. The problem is then modified by including circular and elliptical obstacles of adiabatic, hot, and cold nature. A boundary interpolation technique is used to implement the velocity and temperature boundary conditions at the inner boundaries. The streamline patterns and temperature contours show interesting observations such as dependence of location of vortices on the type of obstacle boundary used, and formation of low or high temperature zones around obstacle at high Rayleigh numbers. Results show that the change in the shape of the obstacle contributes to the Nusselt number variations at the high temperature boundary and low Rayleigh numbers.

A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface

In this paper, we extend the discontinuous Galerkin (DG) isogeometric analysis (IgA) methods to solve nonlinear convection (Burgers) problems on implicitly defined surfaces or manifold. We establish an a priori error estimate for space semidiscretization with the sub-optimal convergence order in the L2. We prove that the resulting methods can be implemented as efficiently as they are for the case of flat space or Euclidean space. The theoretical results are illustrated by two numerical experiments.

Characteristic methods for thermal convection problems with infinite Prandtl number on nonuniform staggered grids

In this paper, two characteristic methods are introduced to solve the thermal convection problems with infinite Prandtl number on nonuniform staggered grids. We obtain spatial second order superconvergence in the discrete L2 norm for the temperature, velocity and pressure. Besides, second order superconvergence in the discrete H1 norm for both the temperature and some terms of the velocity on nonuniform grids is established. First and second order time discretizations of the thermal balance equation are provided. Numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis.

Natural convection of a binary liquid in cylindrical porous annuli/rectangular porous enclosures with cross-diffusion effects under local thermal non-equilibrium state

The present article reports an analytical study of the double diffusive natural convection (DDNC) in cylindrical porous annuli (CPA) and rectangular porous enclosures (RPE), which are handled in a unified way using the curvature parameter, saturated by a binary liquid under the assumption of local thermal non-equilibrium (LTNE) state. The buoyancy forces (thermal and solutal) driving the flow are assumed to be induced by the maintenance of constant and uniform heat and mass fluxes applied along the vertical (radial) walls and insulation of both horizontal walls of the annuli/rectangular enclosures. The Darcy-Boussinesq equations with LTNE assumption between the fluid and solid phases are employed to model the problem of DDNC in a binary liquid-saturated porous medium with cross-diffusion effects. The analytical results are obtained by employing the Oseen-linearization transformation technique in the study. The influence of various dimensionless parameters on heat and mass transports of the system are depicted using the Nusselt and Sherwood numbers and isotherms plots, and the obtained results are analysed with the physical explanation. Special attention is given to understand the effect of LTNE parameter and cross-diffusion parameters on heat and mass transports of the system. Different aspect ratio values are chosen to obtain the results of three types of CPA/RPE (shallow, square and tall). Among these CPA/RPE, maximum and minimum heat and mass transports are achieved in the cases of shallow and tall CPA/RPE, respectively. The results of the pure thermal convection problem is obtained at the zero value of buoyancy ratio and solute Rayleigh number. The increasing value of N magnifies the heat and mass transports in the system due to the augmented buoyancy effect resulted from the thermal and solutal gradients. The increase of solid inner cylinder radius, by fixing its volume, makes the annulus slender which yields to decrease the heat and mass transports in the system. The effects of LTNE parameter and cross-diffusion parameters on heat and mass transports of the system are clearly brought out. The results of LTE model are obtained at the infinite value of ratio of porosity modified thermal conductivities, γ, as a particular case of the present model. From the study, we conclude that the shallow porous annulus and tall rectangular enclosure are best suited in the design of heat removal and heat storage systems, respectively.

Numerical simulation of the dynamics of a locally heated bilayer system under weak evaporation

The problem of thermocapillary convection under the conditions of weak evaporation in a plane confined volume is studied. The mathematical model to investigate the processes of heat- and mass transfer and phase transition parameters in a bilayer system subjected to local heating is suggested. A two-sided model based on the Boussinesq approximation of the Navier–Stokes equations is formulated in the “stream function–vorticity” terms. It includes governing equations and boundary conditions on the interface which are the consequences of the conservation laws and conditions on the outer boundaries of a cuvette. Special attention is given to the study of the effects of evaporation at the thermocapillary interface. The conditions of the heat and mass balance at the deformable interface with respect to the diffusive-type evaporation are assumed to be fulfilled. The temperature relations on the solid walls of a cell take into account the presence of thermal elements of finite size. The Dufour and Soret effects are considered in the interface conditions and in the governing equations describing the fluid motion in a gas-vapor mixture. A numerical algorithm is developed to calculate the basic characteristics of the liquid–gas system and interface location at any time. The results of the numerical study of the interface evolution and non-stationary flows in a cavity being under normal gravity conditions are presented. The possibility of intensifying the evaporation due to the arrangement of additional thermal elements is discussed. The proposed approach allows one to reliably feature the basic characteristics of convective regimes, to evaluate amplitude of the interface deformations and to forecast parameters of vapor content in a gas phase.

An Interpolated Bounce Back Thermable Method for Simulating Solid Particles Dynamics in a Viscous Medium

In this paper we discuss the mathematical and computer modeling of non-isothermal two-phase flows with suspended particles. Natural convection between an outer cubical cavity and an inner hot sphere is investigated. To simulate heat fluxes loaded with particles, a thermal model of the lattice Boltzmann equation in combination with the interpolated bounce back method (TLBM-IBB) has been developed. In TLBM-IBB, IBB is used to process liquid-solid interfaces, and TLBM is used to simulate the heat flow of a fluid. The momentum exchange method is used to calculate the hydrodynamic force on the particle surface. Simulation performed for a range of Rayleigh numbers . The accuracy and efficiency of the existing method is demonstrated by the example of solving the test problem of natural convection around a stationary particle and three-dimensional compressible natural convection in a square cavity filled with air, which has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The results obtained are in good agreement with the experimental and numerical results of other authors.

Multiple-relaxation-time lattice Boltzmann simulation of free convection and irreversibility of nanofluid with variable thermophysical properties

This numerical study demonstrates heat transfer and irreversibility or entropy generation of non-Newtonian power-law Al2O3-H2O (aluminum oxide-water) nanofluids in a square enclosure using multiple-relaxation-time lattice Boltzmann method accelerated by graphics processing unit computing. In this investigation, the effective thermal conductivity and viscosity are variables, and they depend on the fluid temperature and rate of strain, respectively. The enclosure’s left and right walls are uniformly heated with different temperatures, and the upper and lower walls are thermally adiabatic. There is no valid study and results on non-Newtonian fluid using multiple-relaxation-time lattice Boltzmann method for this configuration and hence the novelty of the present results have been ensured. This paper has formulated and appropriately validated the Newtonian and non-Newtonian natural convection problem with the available numerical results. This study includes a set of comprehensive simulations, showing the effects of these fluids’ natural convection by varying three key parameters: the Rayleigh number, the volume fraction of nanoparticles, and the power-law index on the streamlines, isotherms, local and average Nusselt number as well as the local and total entropy generation. The results show that increasing the volume fraction of the nanoparticles from 0% to 2%, the average rate of heat transfer and the total entropy generation increase 6.5% and 7.4%, respectively, while the Rayleigh number, Ra = 105 and the power-law index n = 0.6.

Data-Driven Modeling of Geometry-Adaptive Steady Heat Convection Based on Convolutional Neural Networks

Heat convection is one of the main mechanisms of heat transfer, and it involves both heat conduction and heat transportation by fluid flow; as a result, it usually requires numerical simulation for solving heat convection problems. Although the derivation of governing equations is not difficult, the solution process can be complicated and usually requires numerical discretization and iteration of differential equations. In this paper, based on neural networks, we developed a data-driven model for an extremely fast prediction of steady-state heat convection of a hot object with an arbitrary complex geometry in a two-dimensional space. According to the governing equations, the steady-state heat convection is dominated by convection and thermal diffusion terms; thus the distribution of the physical fields would exhibit stronger correlations between adjacent points. Therefore, the proposed neural network model uses convolutional neural network (CNN) layers as the encoder and deconvolutional neural network (DCNN) layers as the decoder. Compared with a fully connected (FC) network model, the CNN-based model is good for capturing and reconstructing the spatial relationships of low-rank feature spaces, such as edge intersections, parallelism, and symmetry. Furthermore, we applied the signed distance function (SDF) as the network input for representing the problem geometry, which contains more information compared with a binary image. For displaying the strong learning and generalization ability of the proposed network model, the training dataset only contains hot objects with simple geometries: triangles, quadrilaterals, pentagons, hexagons, and dodecagons, while the testing cases use arbitrary and complex geometries. According to the study, the trained network model can accurately predict the velocity and temperature field of the problems with complex geometries, which has never been seen by the network model during the model training; and the prediction speed is two orders faster than the CFD. The ability of accurate and extremely fast prediction of the network model suggests the potential of applying reduced-order network models to the applications of real-time control and fast optimization in the future.

Studying the Accuracy and Applicability of the Finite Difference Scheme for Solving the Diffusion–Convection Problem at Large Grid Péclet Numbers

Studying the Accuracy and Applicability of the Finite Difference Scheme for Solving the Diffusion–Convection Problem at Large Grid Péclet Numbers

Efficient Simulations of Large Scale Convective Heat Transfer Problems

We describe an approach for efficient solution of large scale convective heat transfer problems, formulated as coupled unsteady heat conduction and incompressible fluid flow equations. The original problem is discretized in time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid flow problem uses Picard's iterations to solve the arising nonlinear equations. Both problems, heat transfer and Navier-Stokes quations, give rise to large sparse systems of linear equations. The systems are solved using iterative GMRES solver with suitable preconditioning. For the incompressible flow equations we employ a special preconditioner based on algebraic multigrid (AMG) technique. The paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned, especially for ill conditioned systems arising from discretizations of incompressible Navier-Stokes equations. We describe parallel implementation of the solver using MPI and elements of PETSC library. The scalability of the solver is favourably compared with other methods such as direct solvers and standard GMRES method with ILU preconditioning.

TURBULENCE MODELS APPLIED TO CLASSICAL FLUID MECHANICS AND HEAT TRANSFER PROBLEMS - THE PERFORMANCE EVALUATION OF THE OPEN SOURCE CFD PACKAGE OPENFOAM

Topics related to the modeling of turbulent flow feature significant relevance in several areas, especially in engineering, since the vast majority of flows present in the design of devices and systems are characterized to be turbulent. A vastly applied tool for the analysis of such flows is the use of numerical simulations based on turbulence models. Thus, this work aims to evaluate the performance of several turbulence models when applied to classic problems of fluid mechanics and heat transfer, already extensively validated by empirical procedures. The OpenFOAM open source software was used, being highly suitable for obtaining numerical solutions to problems of fluid mechanics involving complex geometries. The problems for the evaluation of turbulence models selected were: two-dimensional cavity, Pitz-Daily, air flow over an airfoil, air flow over the Ahmed blunt body and the problem of natural convection between parallel plates. The solution to such problems was achieved by utilizing several Reynolds Averaged Equations (RANS) turbulence models, namely: k-ε, k-ω, Lam-Bremhorst k-ε, k-ω SST, Lien-Leschziner k-ε, Spalart-Allmaras, Launder-Sharma k-ε, renormalization group (RNG) k-ε. The results obtained were compared to those found in the literature which were empirically obtained, thus allowing the assessment of the strengths and weaknesses of the turbulence modeling applied in each problem.

On the Objective Function for Topology Optimization of Heat Sinks

In topology optimization, the optimal layout of the structure is obtained through an iterative update of the geometry. Since this update procedure utilizes the gradient of the objective function, it is important to select an appropriate objective function in order to obtain a meaningful geometry. From this point of view, the mathematical definition and physical meaning of the objective functions for topology optimization of heat sinks are reviewed in this article. For this, studies from conductive heat transfer problems to recent computational fluid dynamics (CFD)-based conjugate heat transfer problems are covered. In most of the studies, the objective functions are defined in order to minimize the thermal resistance of the heat sink or to minimize the maximum temperature of the heat source. In place of thermal resistance, thermal compliance is commonly used as the objective function. However, it is worth noting that minimization of the thermal compliance may lead to considerable deviation of the design from that based on the minimum thermal resistance. This is because the thermal compliance is linearly proportional to the average temperature of the heat source in the computational domain, and the average temperature of the heat source is usually different from the maximum temperature of the heat source. In heat conduction problems, the difference between the maximum temperature and the average temperature becomes large when the thermal conductivity of the solid material becomes low. In convection problems, the difference becomes large when the streamwise fluid temperature variation becomes large due to the low heat capacity rate of the fluid.

Acceleration of nonlinear solvers for natural convection problems

Abstract This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing the fixed point operator associated with the nonlinear iteration to prove that certain stability and regularity properties hold, we apply the authors’ recently constructed theory for Anderson acceleration, which yields a convergence result for the Anderson accelerated Picard iteration for the Boussinesq system. The result shows that the leading term in the residual is improved by the gain in the optimization problem, but at the cost of additional higher order terms that can be significant when the residual is large. We perform numerical tests that illustrate the theory, and show that a 2-stage choice of Anderson depth can be advantageous. We also consider Anderson acceleration applied to the Newton iteration for the Boussinesq equations, and observe that the acceleration allows the Newton iteration to converge for significantly higher Rayleigh numbers that it could without acceleration, even with a standard line search.

Application of artificial neural network for mixed convection in a square lid-driven cavity with double vertical or horizontal oriented rectangular blocks

The practicability of using Artificial Neural Network (ANN) to predict the thermal behaviour due to mixed convection is established. Numerical simulations are conducted first for a laminar mixed convection problem in a lid-driven square cavity with two internal rectangular blocks, oriented vertically or horizontally. CFD results are used for training and testing the ANN to predict new cases; thus, saving effort and computation time and validate the obtained numerical results of Nusselt number. A wide range of Reynolds (100 ≤ Re ≤ 1500), Grashof numbers (1.5 × 104 ≤ Gr ≤ 105), Richardson number (0.00667 ≤ Ri ≤ 10) and the distance between the two blocks (0.2 ≤ W/L ≤ 0.8) are considered. Results indicated that varying the distance W/L has an important influence on the Nusselt number. It was observed that increasing Re and Gr numbers magnitudes leads to an increased Nusselt number and that Nusselt number obtained for the case of vertical blocks is higher than the case of horizontal blocks. Furthermore, the maximum Nu number obtained for the vertical blocks was at W/L = 0.5 and Ri = 0.044 and for the horizontal blocks case was at W/L = 0.2 and Ri = 0.044. Finally, new correlations of Nu number versus Re, Gr and the spacing ratio between the two blocks W/L are derived for possible utilization in engineering design.