Conjugate Heat Transfer Problem Research Articles

Adaptive interface treatment for aerothermal coupling using a Discontinuous Galerkin method

This paper presents the application of a discontinuous Galerkin method to conjugate heat transfer problems using a Dirichlet-Robin interface treatment. The use of optimal coefficients derived from a Godunov-Ryabenkii stability analysis is adapted to the discontinuous Galerkin discretization. The stability and convergence of different coupling coefficients are explored for fluid-structure interactions of varying strength. The effects of increasing the order of the polynomial approximation are examined. It was found that for weak fluid-structure interactions, the optimal coefficients provide stable and quickly converged results. However, for moderate and strong interactions, relaxation coefficients that are larger than optimal must be used to stabilize the process. Because the coupling coefficient was adapted to the polynomial order of approximation, increasing the order of the polynomial was not found to destabilize conjugate heat transfer processes using adaptive coefficients. Finally, at the end of the paper, a validation vs empirical correlations is presented.

A loosely-coupled gas-kinetic BGK scheme for conjugate heat transfer in hypersonic flows

The gas-kinetic BGK scheme has shown to be a promising method in hypersonic flow simulation from many previous studies. In this paper, a loosely-coupled BGK scheme is developed for solving conjugate heat transfer (CHT) problems in hypersonic flows. For more accurate evaluation of heat flux and better numerical stability, some modifications to the original BGK scheme are suggested, including using an improved way to calculate slopes of distribution functions and applying a non-simplified Prandtl number fix. Different from most CHT solvers that adopt different methods in fluid and solid domains, the BGK scheme can also be extended to simulate the heat transfer in structures, as long as an appropriate BGK model for the heat conduction equation is constructed. The dual-time steeping approach and a recently-developed implicit JFNK–BGK method are used to obtain the time-accurate solutions in individual domains. To achieve the fluid-thermal coupling, two loosely-coupled algorithms are employed, which are based on quasi-steady and unsteady flow computations, respectively. For comprehensive validation of the developed method, several cases of standalone hypersonic flows, standalone structural heat transfers and a typical CHT problem are investigated, and its performances are shown by comparisons with other numerical and experimental results.

A localized meshless approach using radial basis functions for conjugate heat transfer problems in a heat exchanger

An understanding of conjugate heat transfer is important for enhancing the thermal performance of heat transfer devices. This study discusses the numerical solutions of the conjugate natural convective heat transfer problem using a local radial basis function meshless method. The temperature difference is assumed to be small enough to ensure the validity of the Boussinesq approximation. An artificial compressibility method is used to couple pressure to the continuity equation. The meshless method requires only one set of nodes, which are distributed in the spatial domain. The semi-algebraic equations are integrated using the second-order Runge–Kutta method. Three benchmark problems of conjugate natural convection with one vertical wall, conjugate natural convection with centrally vertical partition, and natural convection with a conducting solid in the middle of the square cavity are analyzed. The numerical results are compared with three benchmark solutions and experimental results; it was observed that the experimental and predicted results showed good agreement with each other. This numerical study is to contribute to understanding the knowledge of heat and fluid flow mechanisms for conjugate heat transfer in a heat exchanger acquired through experiments.

Effect of the wall properties on the shock wave / laminar boundary layer interaction

The CFD calculations have been performed based on RANS approach with the Menter transition model [1]. The boundary layer developing on a flat plate was considered. To generate the incident shock wave, a wedge was installed over the plate. The wall was represented by one cm thick solid flat plate made from aluminum and polyacetal. Flow parameters were M∞=1.41, P0=0.7 bar, T0=293K. As a result of solving the conjugate heat transfer problem, the SWBLI flow was studied. The temperature and pressure distributions on the wall for different surface materials were obtained. It was found that the streamwise heat fluxes inside the wall can lead to a change of the separation zone length.

Inexpensive Computations Using Computational Fluid Dynamics Combined With Asymptotics Applied to Laminar Mixed Convection in a Vertical Channel

Abstract In this work, a solution technique is proposed by synergistically combining asymptotics and computational fluid dynamics to ascertain a problem of laminar mixed convection heat transfer in a vertical channel. First, numerical simulation is carried out on a vertical channel that consists of an aluminum heater plate assembly at the center of the channel. The numerical model is treated as a conjugate heat transfer problem, and the concept of perturbation and blending is incorporated wherein the limiting solution of natural and forced convection is obtained in terms of average Nusselt number. These correlations are then blended to find a unified composite correlation that work very well for extreme limits of mixed convection. The Richardson number is chosen as an independent variable in the present analysis; as a result, the Nusselt number correlation is cogent for the mixed convection region. Upon performing the numerical simulations, the results of the mixed convection are then compared with experimental results available in the literature for the purpose of validation of the numerical solution. The results of the present work emphasize that, with minimum computational fluid dynamics (CFD) solutions, one can obtain a reasonably good composite correlation for the Nusselt number for mixed convection and also a substantial reduction of computations is possible ensuing an asymptotically flawless solution.

Multiphysics Study of Forced Convection Conjugate Heat Transfer (CHT) Problem

This paper presents a problem undergoing conjugate heat transfer (CHT). Conjugate heat transfer problems are common domestic heating/cooling, industrial heat exchangers, cooling of electronics (e.g. PC fans). It is to be noted that in conjugate heat transfer problems, the convection part of the heat transfer is dominated. In the given study, a hypothetical case is built where a heat source (a burning candle) is placed under a thin aluminium sheet. The aluminium sheet is exposed to wind velocity using a fan (velocity of ~1.75 m/s). The aluminium sheet is coated with acrylic paint to increase the infrared emissivity of the surface. FLIR® T1030sc camera is used to visualise the developed infrared signature. Precautions are taken to ensure the correctness of results. The given problem is simulated using ANSYS® Multiphysics, where fluid mechanics equations; continuity, momentum and energy are coupled with the heat equation. This Multiphysics problem is solved using a finite volume method. Mesh sensitivity analysis is performed to ensure the correctness of results. The results from infrared thermography and the Multiphysics model are compared and found to be in reasonable accuracy.

Temperature identification of a heat source in conjugate heat transfer problems via an inverse analysis

PurposeThe present study aims to perform inverse analysis of a conjugate heat transfer problem including conduction and forced convection via the quasi-Newton method. The inverse analysis is defined for a heat source that is surrounded by a solid medium which is exposed to a free stream in external flow.Design/methodology/approachThe objective of the inverse design problem is finding temperature distribution of the heat source as thermal boundary condition to establish a prescribed temperature along the interface of solid body and fluid. This problem is a simplified version of thermal-based ice protection systems in which the formation of ice is avoided by maintaining the interface of fluid and solid at a specified temperature.FindingsThe effects of the different pertinent parameters such as Reynolds number, interface temperature and thermal conductivity ratio of fluid and solid mediums are analyzed.Originality/valueThis paper fulfils the analysis to study how thermal based anti-icing system can be used with different heat source shapes.

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.

Nonstationary Conjugate Problem of Heat Transfer in Supersonic Flow Past Bodies in a Wide Range of Reynolds Numbers

In one of our earlier papers, we considered supersonic, laminar boundary-layer flows past bodies made of different materials and examined the possibility of controlling the temperature regime of a body immersed in flow. In the present work, for the conditions corresponding to aerodynamic experiments and to long flight times, we analyzed such values of deceleration parameters when regions of laminar, transitional, and turbulent regimes of flow are realized simultaneously in a boundary layer. The possibility of decreasing the level of maximal temperatures depending on the determining criteria of the problem has been evaluated for bodies made of different materials. The expediency of using simplified approaches is shown, including those for nonstationary conditions based on stationary solutions and on well-studied limiting cases of isothermal and adiabatic surface temperatures and allowing the determination of the temperature regimes in the entire range of thermophysical characteristics.

Transient numerical simulation of multiple pane windows filling with radiating gas

This work deals with parametric study of transient fluid flow and heat transfer characteristics in double and triple pane windows, while the filling gas in considered as a participating medium. The momentum and energy equations in the filling gas combined with conduction equation in the glass sheets are solved simultaneously as a conjugate heat transfer problem. The mechanism of heat transfer in the gas phase is combined natural convection and radiation. The gas radiation is calculated by solving the radiative transfer equation (RTE) using the discrete ordinates method (DOM). The computations are validated against the experimental and numerical data in literature and excellent consistency is found. The main contributions of this study are twofold. First, the effect of gas optical thickness on flow and thermal characteristics of double and triple pane windows is investigated. Second, the performances of these windows in transient condition are compared. The numerical results show that in large values of optical thickness, multicellular flow forms inside the gas layers which leads to periodic heat flux on the window surface.

Influence of thermal boundary conditions on local convective heat transfer in coiled tubes

Helical coil heat exchangers are commonly used in a wide variety of engineering applications because, due to curvature of the tube that generates secondary flows, this kind of geometry can generate an enhancement of the convective heat transfer coefficient. Since the distributions of the fluid velocity and temperature in coiled pipes are strongly asymmetrical over the cross-section of the tube, particularly in laminar flow conditions, it is important to monitor the local heat transfer phenomena, mainly with regard to the applications where the local behaviour plays a leading role, such as in food industry. Indeed, due to the high viscosity of fluid foods or to the low velocity in which they may operate, the flow regime is often laminar in this kind of devices. In laminar flow regime, the thermal boundary conditions considerably affect the convective heat transfer performance. In the present paper, a numerical investigation focused on the evaluation of the effect of the choice of the thermal boundary condition on the local heat transfer phenomena in coiled-tubes, within the laminar regime, is presented. To cover realistic configurations in which the helical coil heat exchangers are commonly used, the conjugate heat transfer problem in the tube was also considered. The momentum and energy equations were solved by means of the open-source CFD software OpenFOAM®, with second-order accurate finite-volume schemes. The here adopted numerical model was validated by comparing the results with local experimental data. The numerical outcomes, obtained for several values of the Prandtl number, revealed that the thermal boundary conditions could significantly change the local distribution of the convective heat transfer coefficient. Finally, the influence of the thermal boundary condition on the average convective heat transfer coefficient were evaluated by considering the two definitions of the circumferentially averaged Nusselt number commonly used in literature.

Simulation of Conjugate Heat Transfer in Thermal Processes with Open Source CFD

A verification and validation study was performed using the open source computational fluid dynamics software package OpenFOAM version 6-dev for conjugate heat transfer problems. The test cases had a growing complexity starting from a simple steady state problem over unsteady heat transfer to more realistic engineering applications. First, a fin effectiveness study was performed. Then, the external convection at pipes and internal pipe heat transfer were investigated. The validity of the techniques was shown for each test case by comparing the simulation results with experimental and analytic data available in the literature. Finally, a simplified shell-and-tube heat exchanger was simulated to demonstrate how these methods can be applied to plant scale engineering problems.

A single stable scheme for steady conjugate heat transfer problems

The goal of this paper is to propose a single interface treatment, based on the Dirichlet-Robin interface condition to deal with all steady CHT scenarios. These scenarios depend on the so-called numerical Biot number that controls the stability process and the optimal coefficient that ensures, in theory, unconditional stability. It is shown that this coefficient is closely related to fundamental thermal quantities. For very large thermal fluid-solid interactions, the Dirichlet-Robin condition may result in profound stability issues. A thorough examination of the stability behavior has highlighted a narrow and slow-varying stable zone located around the optimal coefficient. This allows us to determine coupling coefficients valid in any case and the reasonable value of these coefficients avoids significantly impairing the accuracy of CHT solutions. A flat plate, partially protected by a thermal barrier coating, is presented as a test case.

Conjugate natural heat transfer scrutiny in differentially heated cavity partitioned with a conducting solid using the lattice Boltzmann method

In the present paper, we numerically investigated the two-dimensional conjugate heat transfer problems in a unitary computational domain containing both the solid and fluid regions. The physical problem configuration consists of two adiabatic horizontal walls of finite thickness and two vertical walls; the left one is maintained at hot temperature Th and the right one is maintained at cold temperature Tc. The lattice Boltzmann method (LBM) based on the BGK model has been used to simulate laminar natural convection in the partitioned air-filled cavity with a heat-conducting solid. In the interface boundaries of the heat-conducting solid, the continuity of temperature and heat transfer is considered. A series of numerical simulation is carried out over a wide range of the Rayleigh number (Ra = 103–106), the thermal conductivity ratio kr and the solid partition thickness (δ = 1–95℅) and its horizontal position. The results show that the partition reduces the heat transfer rate in the cavity. For a centered partition (Xs = 0.5), the average Nusselt number decreases almost linearly with partition thickness for δ ≤ 0.45; however, it increases for δ ≥ 0.45 due to the confinement in the thin fluid regions. For Ra = 105, the heat transfer rate decreases with the partition position until a critical value close to 0.325 and rises slightly until Xs = 0.5. The critical position value decreases with the Ra number increase and it is close to 0.2 for Ra = 106 where Nu = 3.766. The heat transfer rate is enhanced with the increase in thermal conductivity. Correlations of the average Nusselt numbers are obtained as a function of Rayleigh number.

Diffuse-interface immersed-boundary framework for conjugate-heat-transfer problems.

A monolithic solver based on a diffuse-interface immersed-boundary (IB) approach for conjugate-heat-transfer (CHT) problems is presented. The IB strategy assumes that the solid which is "immersed" into the computational grid is occupied by a "virtual" fluid to facilitate construction of "unified" governing equations that are solved everywhere in the domain. A unified momentum equation is devised using the solid volume fraction that reduces to the Navier-Stokes equation outside of the solid and to the no-slip boundary condition inside of it. The "unified" energy equation is constructed in an analogous fashion reducing to a convective-diffusive equation in the fluid domain and a fully diffusive equation in the solid domain with different thermal conductivities (or diffusivities) for both domains. The resulting equations are solved in both domains simultaneously using a hybrid staggered and nonstaggered finite-volume (FV) framework for incompressible flows. The second-order accurate IB-FV solver is employed to carry out investigations for CHT problems in natural and forced convective regimes. Numerical studies for different fluid-to-solid conductivity ratios show that the monolithic IB-CHT solver is a fast, simple, and accurate framework for simulations of CHT problems for Boussinesq flows.

Simulation of conjugate heat transfer problems by lattice Boltzmann flux solver

In this work, a lattice Boltzmann flux solver (LBFS) is presented for simulation of conjugate heat transfer problems. Specifically, the mass and momentum equations used in the flow domain and the energy equation applied in both the flow and solid domains are discretized by finite volume method (FVM) and the numerical fluxes at the cell interface are reconstructed by the local solution of lattice Boltzmann equation (LBE) truncated to the Navier-Stokes level. To calculate the numerical fluxes, the Chapman-Enskog analysis is carried out first to reveal the connection between the macroscopic fluxes and the solution of LBE. With this relationship, the macroscopic fluxes can then be calculated locally and independently at each cell interface by the solution of LBE, which makes the developed scheme be very easy for application on non-uniform mesh and curved boundary as compared with lattice Boltzmann method (LBM). Overall, the present method well combines the advantages of simplicity and kinetic nature of LBM and geometric flexibility of Navier-Stokes solver discretized by FVM. In addition, in the calculation of numerical flux of energy equation, the concept of thermal resistance is innovatively introduced to evaluate the thermal conductivity at the cell interface. As compared with simple average technique, the introduced strategy can provide a more accurate prediction for temperature field. Numerical results showed that the solid-solid and fluid-solid conjugate heat transfer problems can be well simulated by the developed scheme and the second-order accuracy is achieved in space.

Direct numerical simulation of flow and heat transfer in a simplified pressurized thermal shock scenario

Direct numerical simulation (DNS) is carried out using a high order spectral element method in order to analyse the flow and thermal fields in a Pressurized Thermal Shock (PTS) scenario. The adopted configuration is representative of a simplified reactor pressure vessel. It consists of a square duct that intersects perpendicularly with a rectangular vessel (downcomer). Cold water is injected from the square duct. It impinges against the wall of the downcomer that contains water at higher temperature, and a mixing between the cold and hot water occurs in the downcomer. The fluid properties are assumed to be constant; hence the temperature is treated as a passive scalar. A secondary flow inlet in the upper part of the downcomer is used to mimic the effect of density driven flow. The friction Reynolds number in the duct equals to 180, and a unitary Prandtl number of the fluid is used. The thermal field is solved with two types of boundary conditions, i.e., iso-thermal and adiabatic conditions, which encompass the two extreme scenarios of a conjugate heat transfer problem. A careful meshing strategy is adopted and the mesh resolution is verified a posteriori in order to meet DNS quality. The mean flow and turbulent statistics are analysed first, and a particular attention is devoted to the analysis of the vortical structures at the edges of the duct flow. The instantaneous flow field is then analysed in order to study the turbulent structure and the vorticity field within the impingement region. The mean temperature and the turbulent statistics of the thermal fields are subsequently analysed for both thermal boundary conditions. The case with iso-thermal boundary condition corresponds to the initial phase of the thermal mixing during a PTS scenario. It is characterized by the presence of cold fluid near the impinging wall and pockets of fluid at higher temperature near the exit of the duct. Regions with large temperature fluctuations are observed near the edges of the duct and at the interface between the deflected impinging fluid and the descending fluid in the downcomer. The case with adiabatic boundary condition corresponds to the later stage of the thermal mixing during a PTS scenario in which a thermal equilibrium is reached. For this case, a region with lower temperature is observed in the downcomer within the impinging jet region and in the region below, whereas the fluid at higher temperature remains confined in the remaining part of the downcomer.

Problem of conjugate heat transfer between main gas pipeline and frozen ground

Mathematical model of non-isothermal gas flow within the framework of tube hydraulics including change of tube cross-section due to hydrate formation and the dependence of coefficient of heat transfer between gas and hydrate layer on varying flow area is proposed. The corresponding conjugate problem of heat exchange between imperfect gas in the pipeline and the environment is reduced to the solution of differential equations describing non-isothermal flow of gas in pipes and heat transfer equations in ground with the corresponding conjugation conditions. In the quasi-stationary mathematical model of hydrate formation (dissociation), the dependence of gas-hydrate transition temperature on gas pressure is taken into account. Some decisions taken in the design of the first section of the main gas pipeline «Power of Siberia» have been analyzed. It has been shown that if gas is not sufficiently dried, outlet pressure may drop below the technological limit in about 6-7 hours. At the same time, for completely dry gas ,it is possible to reduce the cost of thermal insulation of the pipeline at least two fold.

Heat transfer performance of film condensation created by forced flow

In this work, condensate film on a vertical wall cooled on the external side by forced flow is analysed as a conjugate heat transfer problem. The treated case is that the condensate film and forced flow boundary-layer are in a parallel-flow arrangement. The mass, momentum and energy boundary-layer equations of the condensate film and forced flow are set in a dimensionless form to generalize the model. The parameters affecting the thermal communication between the condensate film and the forced flow are defined from the analysis. These parameters explain the relative impact of the three involved thermal resistances of solid wall, forced convection and film condensation on the local and mean Nusselt number. The study shows that the Nusselt number predicted by the present conjugate model is different from that predicted by a Nusselt-type model.

Definition of mutual thermal influence of containers with spent nuclear fuel at the open storage site

The problem of spent nuclear fuel handling in Ukraine is a key issue. A half of spent nuclear fuel is currently stored in Ukraine at the open-site dry storage facility at Zaporizhzhya NPP. Thermal safety analysis should be performed as a part of the storage facility safety assessment. Thermal analysis of a container group is a poorly investigated area. As literature review shows, current results do not clearly identify mutual influence of the containers and influence of weather conditions on the thermal condition of stored spent nuclear fuel. This type of analysis could be performed using the multi-stage methodology proposed by the authors. Thus, mutual thermal influence of the containers and boundary conditions at the inlets to the ventilation duct of each storage container should be identified. Thermal processes in the container group where spent nuclear fuel is stored that are described in this paper are analyzed by solving the conjugate heat transfer problems. A row of containers under wind influence is simulated and the structure of ventilation airflow inside the containers is identified. The mutual thermal influence of the containers is absent under calm conditions, and heated air does not come from one container to another. Resulting from the simulation, boundary conditions at the inlet of the ventilation duct are specified and can be used in the iterative modelling methodology for spent fuel thermal condition. The dependence of the velocity of the inlet ventilation air in the ventilation duct of each container in the row was defined. The container placement methodology with the purpose of decreasing the wind influence on the thermal condition of spent fuel storage was proposed. Thermal studies are carried out for the containers and storage conditions of the dry spent nuclear storage facility at Zaporizhzhya NPP.