Solving Conjugate Heat Transfer Problems Research Articles

Numerical Simulation of the Conjugate Heat Transfer of a “Fluid–Solid Body” System on an Unmatched Grid Interface

Recently, when modeling transient problems of conjugate heat transfer, the independent construction of grid models for fluid and solid subdomains is increasingly being used. Such grid models, as a rule, are unmatched and require the development of special grid interfaces that match the heat fluxes at the interface. Currently, the most common sequential approach to modeling problems of conjugate heat transfer requires the iterative matching of boundary conditions, which can significantly slow down the process of the convergence of the solution in the case of modeling transient problems with fast processes. The present study is devoted to the development of a direct method for solving conjugate heat transfer problems on grid models consisting of inconsistent grid fragments on adjacent boundaries in which, in the general case, the number and location of nodes do not coincide. A conservative method for the discretization of the heat transfer equation by the direct method in the region of inconsistent interface boundaries between liquid and solid bodies is proposed. The proposed method for matching heat fluxes at mismatched boundaries is based on the principle of forming matched virtual boundaries, proposed in the GGI (General Grid Interface) method. A description of a numerical scheme is presented, which takes into account the different scales of cells and the sharply different thermophysical properties at the interface between liquid and solid media. An algorithm for constructing a conjugate matrix, the form of matrix coefficients responsible for conjugate heat transfer, and methods for calculating them are described. The operability of the presented method is demonstrated by the example of calculating conjugate heat transfer problems, the grid models of which consist of inconsistent grid fragments. The use of the direct conjugation method makes it possible to effectively solve both stationary and non-stationary problems using inconsistent meshes, without the need to modify them in the conjugation region within a single CFD solver.

Development and validation of a one-dimensional solver in a CFD platform for boiling flows in bubbly regimes

This paper presents a new one-dimensional solver for two-phase flow simulations where boiling is involved. The solver has been implemented within the OpenFOAM® platform. The basic formulation follows the Eulerian description of the Navier–Stokes equations. Different closure equations for one-dimensional simulations are also included, as well as a subcooled boiling model in order to perform accurate computations of the mass and heat transfer between phases. In addition to the fluid, a domain is included in order to represent the solid structure, so the solver is able to solve conjugate heat transfer problems. Two different test cases are presented in this work, first a single-phase test case in order to verify the conjugate heat transfer, and then a case based on the Bartolomej international benchmark, which consists of a vertical pipe where the fluid runs upwards while it is heated. Transient calculation were performed, and the results were compared to the TRACE system code, and to the experimental data in the corresponding case. With this calculations, the capability of this new solver to simulate one-dimensional single-phase and two-phase flows including boiling is demonstrated. This work is a first step of a final objective, which consists in allowing a 1D–3D coupling within the CFD platform, avoiding external links.

Very high-order accurate polygonal mesh finite volume scheme for conjugate heat transfer problems with curved interfaces and imperfect contacts

The conjugate heat transfer problem is found in non-isothermal physical systems that involve thermodynamic processes between materials that are thermally coupled through non-adiabatic contacts. A very high-order accurate finite volume scheme in general polygonal meshes is proposed to solve conjugate heat transfer problems with arbitrary curved interfaces and imperfect thermal contacts. Besides the discontinuous thermal properties, imperfect thermal contacts are challenging to address since the obtained temperature is also discontinuous on the interface as a consequence of the interfacial thermal resistance. Moreover, the arbitrary curved interfaces are discretized with polygonal meshes to avoid the shortcomings of classical curved mesh approaches, but a specific treatment is required to overcome the geometrical mismatch and properly fulfill the prescribed interface conditions. The proposed method is based on a partitioned formulation of the conjugate heat transfer problem with the appropriate thermal coupling. A generic polynomial reconstruction method is used to provide local approximations of the temperature complemented with the reconstruction for off-site data method to properly fulfill the prescribed interface conditions. A comprehensive numerical benchmark is provided to verify the proposed method and assess its capability in terms of accuracy, convergence order, stability, and robustness. The results provide the optimal very high-order of convergence and prove the capability of the method to handle arbitrary curved interfaces and imperfect thermal contacts. This contribution represents a significant step towards more efficient and versatile numerical methods for complex conjugate heat transfer problems in engineering applications.

About Calculation of Combined Cooling Systems for Propulsion Engines

A numerical method is proposed for solving conjugate heat transfer problems as applied for calculation of combined cooling systems for combustion chambers of propulsion systems. A procedure is presented for joint calculation of temperature conditions of gaseous cooling film and cooling system elements in the entire cross-section of a combustion chamber, including the inner wall material. The numerical results and their verification are presented.

Challenges for radiative transfer 1: Towards the effective solution of conjugate heat transfer problems

This paper lists crucial challenges in radiative transfer with the objective of gathering information on improving and choosing methods for solving conjugate heat transfer problems. Developments in computational and experimental techniques allow much deeper analysis of the complex problems that industry faces. Accurate and efficient solution of such multi-dimensional problems is important to reduce energy consumption in industry, with long-term positive impacts on climate change. In this paper, four challenging conjugate heat transfer problems are defined. These problems are presented with the hope of attracting researchers to solve them and provide information on the methods used and difficulties encountered. This ‘challenge’ is to be an on-going effort as the new solutions to these problems and the detailed comparisons are to be posted as they become available. In addition, new challenge problems will be added as needed.

Coupling of Continuous and Hybridizable Discontinuous Galerkin Methods: Application to Conjugate Heat Transfer Problem

A coupling strategy between hybridizable discontinuous Galerkin (HDG) and continuous Galerkin (CG) methods is proposed in the framework of second-order elliptic operators. The coupled formulation is implemented and its convergence properties are established numerically by using manufactured solutions. Afterwards, the solution of the coupled Navier–Stokes/convection–diffusion problem, using Boussinesq approximation, is formulated within the HDG framework and analysed using numerical experiments. Results of Rayleigh–Benard convection flow are also presented and validated with literature data. Finally, the proposed coupled formulation between HDG and CG for heat equation is combined with the coupled Navier–Stokes/convection diffusion equations to formulate a new CG–HDG model for solving conjugate heat transfer problems. Benchmark examples are solved using the proposed model and validated with literature values. The proposed CG–HDG model is also compared with a CG–CG model, where all the equations are discretized using the CG method, and it is concluded that CG–HDG model can have a superior computational efficiency when compared to CG–CG model.

An iterative, analytical method for solving conjugate heat transfer problems

Conjugate heat transfer involving convection and conduction in a fluid flow and a solid body in contact with each other occurs commonly in engineering applications. While analytical solutions for individual convection and conduction problems are relatively easier, it is a lot more challenging to solve the combined conjugate heat transfer problem. In this paper, an iterative method is developed for analytically solving conjugate heat transfer problems. Based on an initial assumption of the temperature field at the solid–fluid interface, the temperature distributions in the fluid and solid body are determined by separately solving the governing energy conservation equations in the two domains. These solutions are used to improve the initial assumption of the interface temperature until convergence. It is found that only a few iterations of this process are needed for convergence. Temperature fields computed from this analytical approach are found to be in good agreement with finite element simulation results. The iterative analytical approach is used to solve two technologically relevant problems related to internal and external flows. Given the general nature of the iterative approach, results from this paper may be helpful in solving a variety of conjugate heat transfer problems.

An efficient hybrid BEM–RBIE method for solving conjugate heat transfer problems

In this paper, a hybrid boundary element method (BEM) — radial basis integral equation (RBIE) method is derived to solve conjugate heat transfer (CHT) problems. The BEM is used to solve the heat transfer in the solid region, while the fluid region is solved by using the RBIE. The capability of the RBIE to calculate the potential and the spatial gradients, while advantageous when knowledge of the spatial gradients is of primary importance, can lead to unnecessary increases in the computational cost when solving CHT problems due to the additional equations imposed per node. By using the BEM to solve the heat transfer in the solids, a significant reduction in the size of the system matrix compared to the case of using the RBIE for both the heat transfer in the solid and fluid regions can be achieved. A case study that examines the CHT inside the human eye is solved using the derived hybrid BEM–RBIE method.

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

A meshless finite difference method is developed for solving conjugate heat transfer problems. Starting with an arbitrary distribution of mesh points, derivatives are evaluated using a weighted least-squares procedure. The resulting system of algebraic equations is sparse and is solved using an algebraic multigrid method. The implementation of the Neumann, Dirichlet, and mixed boundary conditions within this framework is described. For conjugate heat transfer problems, continuity of the heat flux and temperature are imposed on mesh points at multimaterial interfaces. 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. The method improves on existing meshless methods for conjugate heat conduction by eliminating spurious oscillations previously observed. Metrics for accuracy are provided and future extensions are discussed.

Combined Streamline Upwind Petrov Galerkin method and segregated finite element algorithm for conjugate heat transfer problems

A combined Streamline Upwind Petrov-Galerkin method (SUPG) and segregated finite element algorithm for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow is presented. The Streamline Upwind Petrov-Galerkin method is used for the analysis of viscous thermal flow in the fluid region, while the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the presented method is to consistently couple heat transfer along the fluid-solid interface. Four test cases, which are the conjugate Couette flow problem in parallel plate channel, the counter-flow in heat exchanger, the conjugate natural convection in a square cavity with a conducting wall, and the conjugate natural convection and conduction from heated cylinder in square cavity, are selected to evaluate efficiency of the presented method.

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.

Numerical Study of Conjugate Heat Transfer in a System Consisting of Porous Media and Bounding Walls.

A numerical scheme based on the control volume method to solve conjugate heat transfer problems in a system consisting of porous media and bounding walls has been developed using a two-energy equation model for porous insert. Appropriate wall heat flux expressions for the fluid phase and solid phase were obtained from the proposed heat transfer model at the interface between porous media and solid wall. The heat transfer model clarifies physics of the known thermal boundary condition at the interface. Predicted interface temperature distribution and Nusselt number show very good agreement with the available experimental data for the case of using metal foams as the porous insert. Effect of wall thickness on heat transfer to the porous media has been investigated and the importance of considering heat conduction in the wall as well as heat transfer in porous media was demonstrated.

A simplified approach to solving conjugate heat transfer problems in annular and dissimilar parallel plate ducts

A simple perturbation technique is used to reformulate the energy equations which describe the treatment thermal behaviour of a radially lumped conjugate that transfer problem is annular and dissimilar parallel plate ducts of finite wall thickness. The simplified perturbation tecnique is used to eliminate the coupling between the fluid and the solid-wall energy equations when the temperature difference between the fluid and the solid-wall is a small perturbed quantity, which is true when the interface convective heat transfer coefficient between the fluid and the solid-wall is high. A mathematical criterion is derived to determine the conditions under which the fluid and the solid-wall are in thermal equilibrium. It is found that seven dimensionless parameters control the state of the thermal equilibrium between the fluid and the solid domains. © 1998 John Wiley & Sons, Ltd.

ADAPTIVE FINITE ELEMENT METHOD FOR CONJUGATE HEATTRANSFER

This article presents an adaptive finite element method to solve conjugate heat transfer problems. Solutions are obtained in primitive variables using a high-order finite element approximation on unstructured grids. Two general estimators are developed for analyzing finite element solutions to conjugate heat transfer problems. The adaptive methodology is demonstrated on problems for which experimental measurements are available. The methodology is then applied to heat transfer predictions for two cases of practical interest.

A Method to Solve Conjugate Heat Transfer Problems: The Case of Fully Developed Laminar Flow in a Pipe

A simple, fast, and rather general procedure combining the superposition principle with a finite element method is proposed to deal with conjugate heat transfer problems. The method is employed to consider the wall conduction effect on heat transfer to fully developed laminar flow through a pipe whose exterior boundary is uniformly heated along a finite length. Results are given for two values of each of the four parameters determining the relative importance of axial conduction: the Peclet number of the fluid, the wall to fluid conductivity ratio, and the dimensionless thickness and length of the heated section of the pipe.