Conjugate Heat Transfer Solver Research Articles

A 3D symmetry-preserving simulation of a concentrated photovoltaic thermal (CPVT) solar collector

In this work, a general collocated and unconditionally stable framework on unstructured meshes for solving Conjugate Heat Transfer (CHT) problems is presented by means of preserving the underlying symmetries of the continuous differential operators, thus not introducing uncontrolled artificial numerical dissipation to our system. Then, this framework is applied to solve a Concentrated PhotoVoltaic Thermal (CPVT) Solar Collector. Furthermore, a new boundary condition is implemented to consider the heat transfer between enclosed elements, including radiation. The model is validated using experimental data.

An open-source porous media modelling approach to investigate thermohydraulic features of compact printed circuit heat exchangers

An experimental air-foil printed circuit heat exchanger (PCHE) with CO2 as a working fluid is numerically modelled and developed within the OpenFOAM environment as a freely available package for more general PCHE designs. The conjugate heat transfer solver (chtMultiRegionFoam) is adapted to include both the hot and cold fluid streams of the PCHE, along with the solid recuperator body, within three uniquely specified overlapping mesh regions. The fluid stream momentum equation is adapted to incorporate porosity, with the additional streamwise air-foil drag (friction factor) accounted for by the Darcy–Forcheimer porous media model. A simple linear ad-hoc model for the transverse friction factor is evaluated to determine the dispersion of the momentum across the flow. Heat transfer between the fluid streams and the solid body is driven by a volumetric thermal resistance with a cell volume-weighted interpolation method (volume-to-volume coupling), with experimentally determined Nusselt number correlations applied. Temperature-dependent parameters based on isobaric NIST data for CO2 are tabulated as a user library and integrated within the coding package. The model predictions of the solid body temperature distributions are assessed and validated against experimental data with eight equidistant fibre optical measurements across the PCHE core and compared against finite-element-based MATLAB numerical results. Thermal stresses are evaluated and qualitatively evaluated against experimental data, demonstrating the capability of the model to highlight potential design features for improvement.

Numerical modelling of an electric motor cooling jacket

The automotive industry is amid a sweeping change of propulsion technology to meet the increasingly stringent limits on emissions and fuel consumption. Traditional combustion engines are gradually being replaced by electric motors or hybrid power trains. The efficiency and power density levels achievable by electric motors are entirely dependent on the effectiveness of the employed cooling solution. Therefore, extensive analyses are needed to determine and optimise the thermal performance of these systems. In this work a numerical model is developed to determine the friction losses and the heat transfer properties of an electric motor cooling jacket. The cooling channels, which coil along the circumferential direction within the motor casing, are studied by means of CFD analysis of a basic periodic module. Flow and temperature fields are determined by applying a 3D Finite Volume approach. Numerical solutions are obtained by means of a validated conjugate heat transfer solver. Integral flow field results are employed to derive the equivalent Darcy friction factor and side-wall specific Nusselt numbers for several flow regimes. A lumped parameter thermal model, based on the graph theory and aforementioned CFD results is also developed to determine the overall system performance. The equivalent thermal resistances are computed from geometric parameters and CFD results. Finally preliminary numerical results on friction losses and heat transfer are compared with available experimental data.

Investigation on thermo-hydraulic characteristic of lead–bismuth eutectic and supercritical carbon dioxide in a straight-channel printed circuit heat exchanger

The Printed Circuit Heat Exchanger (PCHE) is considered a promising heat exchanger for Lead-Bismuth Eutectic (LBE) cooled fast reactors due to its superior pressure-bearing capacity and heat transfer efficiency. This paper introduces a conjugate heat transfer solver to investigate the thermo-hydraulic performance of a straight channel PCHE incorporating LBE and Supercritical CO2 (S-CO2). A four-equation model is implemented in the solver to capture the low Prandtl number turbulent heat transfer characteristics of LBE. Comparisons with LBE circular tube experimental results demonstrate that the solver presented enhances the resolution of LBE heat transfer simulations. This improvement in numerical resolution is crucial for understanding and predicting the behaviors of LBE-S-CO2 conjugate heat transfer process. Building on this, the present work explores the impacts of inlet mass flow rate, inlet temperature, S-CO2 pressure, and geometric parameters on the thermo-hydraulic performance of the straight channel PCHE. In terms of inlet temperature, quantitative analyses emphasize the effectiveness of augmenting the mass flow rate on the S-CO2 side to enhance overall heat transfer performance of PCHE. Adjusting the inlet temperature of S-CO2 or LBE to increase the temperature difference between the two fluids improves the average heat transfer rate, but reducing the S-CO2 inlet temperature may decrease the overall heat transfer coefficient. Furthermore, increasing S-CO2 pressure positively affects the thermal conductivity and specific heat capacity of S-CO2, thereby improving the thermo-hydraulic performance of PCHE. Additionally, geometric parameter sensitivity analyses indicate that decreasing wall thickness or increasing ridge width improves heat transfer, but increasing ridge width may significantly increase PCHE’s volume. The increased channel length results in a higher pressure drop, simultaneously enhancing heat transfer. From the Performance Evaluation Criteria (PEC) perspective, lengthening the channel is advantageous for the S-CO2 side but unfavorable for the LBE side. Regarding channel width, reducing channel width yields a larger increase in PEC on the S-CO2 side compared to the LBE side. Therefore, narrower flow channels on the S-CO2 side seem more advantageous. The present work provides a numerical tool with higher numerical resolution for studying LBE-S-CO2 conjugate heat transfer process and offers valuable insights for straight channel PCHE design.

Study on continuous adjoint-based optimization method for internal cooling structures in turbine blades with conjugate heat transfer

A continuous adjoint-based shape optimization system is presented in this paper for conjugate heat transfer (CHT) problems and is applied to the optimization for internal cooling structures of gas turbine blades. With the consideration for the variation of heat conduction equation in the solid regions, the adjoint equations and adjoint boundary conditions in different regions are derived. The adjoint energy correction equation is also derived successfully based on the SIMPLE algorithm, and the adjoint CHT solver is implemented by imposing the values of adjoint energy at the interfaces. Two cases of full 3D optimization for the C3X hollow blade and cooling channel with pin fins are conducted by using the optimization system. In both cases, their flow and heat transfer characteristics are optimized and analyzed in detail. This study demonstrates the potential advantages and basic capabilities of the continuous adjoint method in dealing with CHT optimization problems.

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.

Coupling heat transfer study of liquid sodium and supercritical carbon dioxide in a PCHE straight channel based on a four-equation model

The Brayton cycle using supercritical carbon dioxide (S-CO2) as the working fluid is expected to be a thermo-power conversion technology for sodium-cooled fast reactors. Printed Circuit Heat Exchanger (PCHE) is the key heat transport structure to realize the above technology. The study of conjugate heat transfer characteristics of sodium (Na) with low Prandtl number turbulent heat transfer characteristics and S-CO2 with supercritical convective heat transfer behaviors in a PCHE channel are of great significance. However, the constant turbulent Prandtl number (Prt) model obtained by the general Reynolds analogy hypothesis may affect the conjugate heat transfer assessment between Na and S-CO2. Compared with the constant Prt model, the fluid’s Prt distribution can be obtained by four-equation models, introducing the transport of turbulent kinetic energy k, dissipation rate ε of k, temperature fluctuation kθ, and dissipation rate εθ of kθ. The four-equation model is expected to obtain more effective conjugate heat transfer characteristics between Na andS-CO2, while there are no available commercial codes. Therefore, in this paper, two kinds of four-equation model, which can effectively evaluate the heat transport performance of Na with low-Prandtl number and S-CO2 away from the pseudo-critical region, respectively, are first introduced into the conjugate heat transfer solver of OpenFOAM. Then the conjugate heat transfer experiment data of Na in a pipe and the simulation data of S-CO2 in a PCHE straight channel are used to verify the validity of the numerical model in this paper. The results show that the present calculation method can effectively reproduce the numerical conjugate heat transfer process of Na and S-CO2. Finally, based on four-equation models, the coupling heat exchange performance of Na/S-CO2 are studied to obtain the effects of mass rate and temperature on the conjugate heat transfer process between Na and S-CO2 in a PCHE straight channel.

Insulation behavior of foamed based geopolymer as a thermally efficient sustainable blocks

The importance of sustainability and energy efficiency in the construction and design of houses is crucial in today's environment. The material used as an insulation layer within the building envelope restricts heat transfer through it. However, heat transfer depends upon the characteristics of the insulating layers and their properties. Therefore, creating materials that possess low thermal conductivity while maintaining their mechanical, physical and durability properties is of utmost significance. The aim of this research is to explore the feasibility of utilizing foamed insulating geopolymer blocks as a means to address energy efficiency and environmental sustainability issues. The research involves utilizing copper slag and glass powder as the primary raw materials to produce the geopolymer. Additionally, the technique of foaming is applied to enhance the thermal resistance of the resulting product. The study results revealed that the foamed geopolymer material exhibited thermal conductivity in the range of 0.13 to 0.16 W/mK. Also, the developed product was subjected to conjugate thermal analysis to understand the heat transfer behavior of material. The heat transfer analysis is performed by in-house developed conjugate heat transfer solver in OpenFOAM. The variation of temperature through the solid geopolymer walls to internal room environment is reported, and Nusselt number at the solid–fluid interface is plotted to observe the insulation strength of developed geopolymer. The findings suggest the developed product can provide better thermal insulation than conventional material, in addition to this the foamed geopolymer can be treated as sustainable material as it utilizes waste and reduces the energy requirements of buildings.

Numerical study on conjugate heat transfer characteristics of liquid lead-bismuth eutectic and supercritical carbon dioxide in a PCHE straight channel

The Printed Circuit Heat Exchanger (PCHE) is the optimal heat transfer structure of the fourth-generation advanced Lead–Bismuth Eutectic (LBE) cooled fast reactor coupling with the supercritical carbon dioxide (S-CO2) Brayton cycle system. It is of great significance to study the conjugate heat transfer characteristics between LBE with low Prandtl number turbulent heat transfer characteristics and S-CO2 with supercritical convective heat transfer characteristics. However, the conventional Reynolds analogy assumption will affect the numerical heat transfer precision of LBE and, thus, the accuracy of the coupled heat transfer of LBE and S-CO2. In the present work, an advanced two-equation turbulent heat transfer model, which can effectively correct the numerical heat transfer process of LBE, is introduced into the conjugate heat transfer solver of the open-source Computational Fluid Dynamics (CFD) program OpenFOAM, where the Reynolds analogy assumption is retained to reproduced the heat transfer of S-CO2 flow away from the pseudo-critical region. The currently developed model and numerical method are compared with the experimental data of an LBE-cooled pipe and the simulation data of conjugated heat transfer of S-CO2 and S-CO2 in a PCHE straight channel. The results show that the calculation method in this study can improve the numerical conjugate heat transfer accuracy of LBE compared with the Reynolds analogy assumption model and can reproduce the flow and heat transfer process of S-CO2 in a PCHE straight channel. Then, the conjugate heat transfer characteristics between LBE and S-CO2 in a PCHE straight channel are studied. The effects of inlet Reynolds number and inlet temperature are focused on to study the conjugate heat transfer law of LBE coupling S-CO2.

XFEM level set-based topology optimization for turbulent conjugate heat transfer problems

Solving conjugate heat transfer design problems is relevant for various engineering applications requiring efficient thermal management. Heat exchange between fluid and solid can be enhanced by optimizing the system layout and the shape of the flow channels. As heat is transferred at fluid/solid interfaces, it is crucial to accurately resolve the geometry and the physics responses across these interfaces. To address this challenge, this work investigates for the first time the use of an eXtended Finite Element Method (XFEM) approach to predict the physical responses of conjugate heat transfer problems considering turbulent flow. This analysis approach is integrated into a level set-based optimization framework. The design domain is immersed into a background mesh and the geometry of fluid/solid interfaces is defined implicitly by one or multiple level set functions. The level set functions are discretized by higher-order B-splines. The flow is predicted by the Reynolds Averaged Navier–Stokes equations. Turbulence is described by the Spalart–Allmaras model and the thermal energy transport by an advection–diffusion model. Finite element approximations are augmented by a generalized Heaviside enrichment strategy with the state fields being approximated by linear basis functions. Boundary and interface conditions are enforced weakly with Nitsche’s method, and the face-oriented ghost stabilization is used to mitigate numerical instabilities associated with the emergence of small integration subdomains. The proposed XFEM approach for turbulent conjugate heat transfer is validated against benchmark problems. Optimization problems are solved by gradient-based algorithms and the required sensitivity analysis is performed by the adjoint method. The proposed framework is illustrated with the design of turbulent heat exchangers in two dimensions. The optimization results show that, by tuning the shape of the fluid/solid interface to generate turbulence within the heat exchanger, the transfer of thermal energy can be increased.

Transient Heat Transfer Analysis on Composite Solids for Hypersonic Flow Applications

Surface heating rates have the importance in high speed flow due to viscous or aerodynamic heating which leads to enormous rise in surface temperature. Prediction of exact heat transfer rates is essential for design of protection systems for aerodynamic bodies aimed. For the thermal protection system, the aerodynamic Surfaces are generally configured with multiple solids. Hence present study is planned to develop the conjugate heat transfer (CHT) solver for composite solids. A CHT solver is in hypersonic flow environment. Finite volume framework and explicit time stepping have been implemented for both the compressible Navier-Stokes solver and conduction solver. Loose coupling has been established between the above mentioned fluid and solid domain solvers. The following observations were made in the CHT simulations. In the case of hypersonic flows over finite thickness flat plate, considerable difference in surface heat transfer rate has been noticed along the stream wise direction at the solid-fluid interface and also the Effect of wall material on heat diffusion for hypersonic application has been analyzed using loosely coupled CHT solver. The CHT solver has also been implemented for hypersonic flow over composite cylinder. Necessity of insulating material in the region of stagnation point has been realized as the outcome of these studies.
 HIGHLIGHTS
 
 Accurate prediction of Convective heating rates is essential for the design of thermal protection system for hypersonic vehicles
 In The thermal protection system, the aerodynamic surfaces are generally configured with multiple solids. Hence the present study is planned to develop the conjugate heat transfer (CHT) solver for composite solids
 The CHT solver has been implemented for hypersonic flow over composite flat plate and cylinder. It has been observed flows over finite thickness flat plate, a considerable difference in surface heat transfer rate has been noticed along the stream wise direction at the solid-fluid interface and the necessity of insulating material in the region of stagnation point has been realized as the outcome of these studies
 
 GRAPHICAL ABSTRACT

Evaluation of thermal and energy consumption behavior of novel foamed copper slag based geopolymer masonry blocks

The building sector is focused on adopting passive design strategies to reduce the energy needs of the building envelope. Currently there has been lack of research related to the understanding of thermal and energy efficiency performance of foamed geopolymer based material. In this regard, this research provides a solution of thermally efficient wall material developed from copper industry by-product (copper slag). All the performance criteria (i.e. physical, mechanical and thermal) of the developed foamed copper slag geopolymer (FCSG) blocks as a building block was found to be in compliance with the performance of standard commercial product (i.e., autoclave aerated block). Further, the numerical analysis of the developed FCSG material is performed and the conjugate heat transfer through three different solid-wall zones to the fluid domain is perceived. The incompressible conjugate heat transfer solver is developed in the open-source computational fluid dynamics (CFD) tool OpenFOAM to perform the present numerical analysis. It is noted that the temperature in the fluid zone for the FCSG layer attained less than 300 (K) however, for the red clay bricks it reaches 302 (K). Hence, the thermal efficiency of the FCSG incorporated insulation layer reduces the heat transmission from outdoor to indoor, consequently improving the comfortable environment of occupants. Further, the developed blocks were subjected to simulation study using eQuest tool to understand the influence of its thermal characteristics on energy demands. The study found that the yearly energy savings was found to be 7.5% in comparison to commercially available clay bricks. Also, the cost savings can reach up to 8.94% during the peak summer month and 7.4% annually. Thus, the developed blocks emphasize waste utilization, providing better indoor thermal for occupant and energy efficiency benefits for end-users. Thus, achieving overall sustainability as a building envelope component.

Conjugate heat transfer study of hypersonic flow past a cylindrical leading edge composed of functionally graded materials

Aero-thermodynamic analysis of a cylindrical leading edge placed in a hypersonic stream is carried out using an in-house developed conjugate heat transfer (CHT) solver. Isotropic and functionally graded materials (FGM) are tested as heat shields to understand the effects of the material property on the flow structure and aerodynamic heating associated with the mutual coupling of fluid flow and heat transfer. A simplified partitioned approach is employed to couple the independently developed fluid flow and heat transfer solvers to perform conjugate heat transfer studies. This framework employs a cell-centred finite volume formulation with an edge-based algorithm. Both strong and loose coupling algorithms are implemented for the data transfer across the fluid–solid interface. A test case of hypersonic flow over a cylindrical leading edge composed of an isotropic material is considered to validate the accuracy and correctness of numerical formulation adopted in the in-house solver. The significance of solid domain materials on the conjugate heat transfer has been studied by considering both isotropic material and FGM. The loosely coupled CHT solver required 10 times less simulation time when compared with the strongly coupled CHT solver. The interface heat flux evolution over time showed a decreasing trend, whereas an increasing trend was for the interface temperature. The current study strongly recommends CHT analysis for the design of thermal protection system of space vehicles. The thermal performance of FGMs composed of various volume fractions of Zirconia and Titanium alloy (Ti6Al4V) is assessed. The temperature distributions obtained from the CHT analysis shows that FGM with a power index of unity is a good material choice for thermal protection systems.

Conjugate Heat Transfer Simulation and Entropy Generation Analysis of Gas Turbine Blades

Abstract Reynolds-averaged Navier–Stokes (RANS) model-based conjugate heat transfer (CHT) method is so far popularly used in simulations and designs of internally cooled gas turbine blades. One of the important factors influencing the RANS-based CHT method's prediction accuracy is the choice of turbulence models for different fluid regions because the blade passage flow and internal cooling have considerably different flow features. However, most studies in the open literature adopted the same turbulence models in the blade passage flow and internal cooling. Another important issue is the comprehensive evaluation of the losses caused by the flow and heat transfer for both fluid and solid regions. In this study, a RANS-based CHT solver suitable for subsonic/transonic flows was developed based on OpenFOAM and then validated and used to explore suitable RANS turbulence model combinations for internally cooled gas turbine blades. Entropy generation, being able to weigh the losses caused by both flow friction and heat transfer, was used in the analyses of two vanes with smooth and ribbed cooling ducts to reveal the loss mechanisms. Findings indicate that the combination of the k–ω SST–γ–Reθ transition model for passage flow and the standard k–ε model for internal cooling provided the best agreement with measurement data. The relative error of vane surface dimensionless temperature was less than 3%. The variations of entropy generation with different internal cooling inlet velocities and temperatures indicate that reducing entropy generation was contradictory with enhancing heat transfer performance. This study, which provides a reliable computing tool and a comprehensive performance parameter, has an important application value for the design of advanced internally cooled gas turbine blades.

$$\lambda $$-DNNs and their implementation in conjugate heat transfer shape optimization

A data-driven two-branch deep neural network (DNN), to be referred to as $$\lambda $$ -DNN, used to predict scalar fields is presented. The network architecture consists of two separate branches (input layers) connected to the main one towards its output. In multi-disciplinary shape optimization problems, such as those this paper is dealing with, the input to the $$\lambda $$ -DNN contains data relevant to the geometrical shape and the case itself. Herein, the $$\lambda $$ -DNN is used in conjugate heat transfer (CHT) analysis and shape optimization problems, synergistically with codes simulating flows over the fluid domain and solving the heat conduction equations over the solid one. It is used to optimize a duct and an internally cooled turbine blade-airfoil surrounded by hot gas. The $$\lambda $$ -DNNs, after being trained on fields computed using the CHT solver, are used as surrogates for either the heat conduction equation solver of the solid domain, replicating either one out of the two disciplines of the problem or the coupled CHT solver.

Investigation of the pressure vessel lower head potential failure under IVR-ERVC condition during a severe accident scenario in APR1400 reactors

In the event of a core meltdown in a high-power reactor, the integrity of the reactor pressure vessel is presumably protected by severe accident mitigation systems such as in-vessel retention external reactor vessel cooling (IVR-ERVC). However, in the late phase of the accident, two possible locations on the RPV are prone to failure: the location of the focusing effect and location of in-core instrument penetration. These two potential points of damage in the RPV are investigated in this study. A numerical model for the prediction of the natural convection, melting, and solidification processes for IVR-ERVC is presented. The model is based on the enthalpy-porosity approach with an extension for continuous liquid fraction function. The model is implemented in open-source field operation and manipulation (OpenFOAM) computational fluid dynamic code to produce a new solver which is based on the combination of conjugate heat transfer solver and buoyant-driven natural convection solver and the new solver is validated against the melting Gallium experimental test, in-core instrumentation failure experimental test, and BALI experimental test. This numerical model is applied for the investigation of the RPV rupture at the location of the focusing effect and in-core instrumentation penetrations. Severe ablations of the cladding and the weld materials are observed at a heat load of about ~1800 K which is expected to lead to the ejection of the penetration tubes if the force holding the penetration tube in place is lower than the force exerted by the system pressure. Subsequently, a two-layer IVR configuration is assessed and the integrity of the RPV is found not to be compromised under external reactor vessel cooling. However, in the case of a boiling crisis, the temperature of the ex-vessel wall is expected to rise quickly and this is simulated by increasing the ex-vessel wall temperature. The RPV is found to fail near the beltline due to a phenomenon known as focusing effect when the ex-vessel wall temperature rises above 1200 K.

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.

A computational fluid dynamics study by conjugate heat transfer in OpenFOAM: A liquid cooling concept for high power electronics

A conjugate heat transfer (CHT) study of a liquid cooling heat exchanger is carried out using the open source computational fluid dynamics (CFD) library OpenFOAM. The heat exchanger was 3D printed using aluminium and experimentally verified by temperature probing and thermal imaging. The functionality of the heat exchanger in cooling localized heat sources is demonstrated. Three different turbulence models were utilized including k-ω shear stress transport (SST) model, the standard k-ε model and large-eddy simulation (LES). The numerical results indicate that the k-ω SST and LES models produced similar results in terms of flow structures and temperature levels while the k-ε model deviated from the two other models. The scalability of the heat exchanger was numerically demonstrated by comparing the flow uniformity by varying the inlet Reynolds number between 4960 and 14880. The conclusions of the paper consists of the following main results. (1) The numerical results indicate that the flow uniformity in the channels is noted to be affected by the flow structures before and after the fin system. (2) The simulated hot-spot temperatures were noted to be relatively sensitive to the predicted flow laminarization inside the channels. (3) The heat exchanger was shown to be functional and to maintain cool surface temperatures in the simulations and the experiments. Additionally, the used CHT solver in OpenFOAM is tested and verified in different ways.

A high-order discontinuous Galerkin method for simulating incompressible fluid-thermal-structural interaction problems

This paper presents a framework for the application of the discontinuous Galerkin(DG) finite element method to the multi-physics simulation of the solid thermal deformation interacting with incompressible flow problems in two-dimensions. Recent applications of the DG method are primarily for thermoelastic problems in a solid domain or fluid-structure interaction problems without heat transfer. Based on a recently published conjugate heat transfer solver, the incompressible Navier-Stokes equation, the fluid advection-diffusion equation, the Boussinesq term, the solid heat equation and the solid linear elastic equation are solved using an explicit DG formulation. A Dirichlet-Neumann partitioning strategy has been implemented to achieve the data exchange process via the numerical flux computed at interface quadrature points in the fluid-solid interface. Formal hp convergence studies employing the method of manufactured solutions demonstrate that the expected order of accuracy is achieved for each solver. The algorithm is then further validated against several existing benchmark cases including the in-plane loaded square, the Timoshenko Beam, the laminated beam subject to thermal-loads and the lid-driven cavity with a flexible bottom wall. The computational effort demonstrates that for all cases the highest order accurate algorithm has several magnitudes lower error than the second-order schemes for a given computational effort. It is a strong justification for the development of such high order discretisations. The solver can be employed to predict thermal deformation of a structure due to convective and conductive heat transfer at low Mach, such as chip deformation on a printed circuit board, wave-guide structure optimization, thermoelectric cooler simulation, and optics mounting method verification.

A conjugate heat transfer model for unconstrained melting of macroencapsulated phase change materials subjected to external convection

A new conjugate heat transfer model for unconstrained melting of macroencapsulated phase change material subjected to external convection is presented. Flow and heat transfer processes are modeled for the phase change material, the capsule wall and the external heat transfer fluid. The solvers for each region operate in a segregated and sequential manner and are coupled by mixed thermal boundary conditions. For the description of the solid body motion in unconstrained melting, the enthalpy-porosity method is modified. The solid body surface is reconstructed from the liquid volume fraction field for every time step by a triangulated isosurface using a marching tetrahedra technique. Based on computation of the forces exerted on the solid, the motion of the solid is determined iteratively in a strong coupling between solid velocity and pressure. The new conjugate heat transfer solver is utilized to simulate the commonly experimentally and numerically investigated scenario of a spherically encapsulated phase change material immersed in a water bath. The coupled flow and heat transfer is investigated for a natural convection dominated mixed convection problem with a Richardson number of 50 · 103 and Stefan numbers of 0.075, 0.1, 0.15, 0.2 and 0.25. Contrary to the commonly made assumption, the resulting capsule wall temperature is transient and highly non-uniform. The differences in melting times range from 50.7 to 67.5% between the consideration of external heat transfer and the assumption of constant uniform wall temperatures.