Conjugate Heat Transfer Problem Research Articles

Numerical investigation on a novel milli-sized heat sink equipped by twisted elliptical tubes

Thermal management in some small chemical reactors is essential to achieve a final high-quality product and heat sinks can play a remarkable role in dissipating heat from such systems. In this regard, this study attends to evaluate the conjugate heat transfer problem in a heat sink equipped by twisted elliptical tubes (TETs). The effects of significant parameters such as Reynolds number (Re = 250, 350, 500, 700 and 950) and twist ratio (TR = 2.5, 5 and 10) on hydrothermal and thermodynamics performance of the novel heat sink are investigated. The swirling flow is the main reason of fluid particles migration from hot surface to cold one and vice versa, leading a better heat transfer occurs at the expense of not significant pressure loss augmentation. The results revealed that the TETs are responsible of more wall temperature uniformity and avoids generating hot spots. Compared with plain elliptical tubes, the presence of TETs inside heat sink improves the heat transfer rate and enlarges the pressure drop by 1.08–2.03 times and by 1.02–1.92 times, respectively. In addition, the TETs decrease the entropy generation rate inside heat sink and the best value of second law efficiency is about 35 %, detected at TR = 2.5 and Re = 250.

Hydrogen peroxide droplet gasification and decomposition: Classic evaporation model vs. conjugate model

The purpose of the present study is to investigate the evaporation of hydrogen peroxide droplet and the impacts of gas phase thermal decomposition on this process. Two different flow solvers are developed for analysis where one uses the classic evaporation model, and the other solves the conjugate heat transfer problem considering temperature distribution within both gas and liquid phases accurately. The finite volume method is utilized to solve the governing equations of the reacting two-phase flow. Single droplet evaporation in the hot open surrounding is analyzed first to illustrate the effect of gas phase decomposition on droplet regression rate. It is shown that the decomposition changes the temperature distribution around droplet that leads to higher regression rate by increasing the heat transfer from the gas phase into the liquid phase. This cannot be captured using the classic model and must be studied by conjugate model. In addition, the effects of droplet radius, ambient pressure, and ambient temperature on the regression rate augmentation due to decomposition are investigated for single droplet. Finally, evaporation and decomposition of hydrogen peroxide droplet cloud in a closed vessel is simulated and it is demonstrated that conjugate model has more accurate prediction than the classic model and must be used in practical studies especially when the transient processes are drastic.

An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques

In this study, an inverse conjugate heat transfer problem is examined to estimate temporally and spatially the dependent unknown surface heat flux using thermography techniques with a thermal camera in a three-dimensional domain. Thermography techniques encompass a broad set of methods and procedures used for capturing and analyzing thermal data, while thermal cameras are specific tools used within those techniques to capture thermal images. In the present study, the interface conditions of the plate and air domains are obtained using perfect thermal contact conditions, and therefore we define the problem studied as an inverse conjugate heat transfer problem. Achieving the simultaneous solution of the continuity, Navier–Stokes, and energy equations within the air domain, alongside the heat conduction equation in the plate domain, presents a more intricate challenge compared to conventional inverse heat conduction problems. The validity of our inverse solutions was verified through numerical simulations, considering various inlet air velocities and plate thicknesses. Notably, it was found that due to the singularity of the gradient of the cost function at the final time point, the estimated results near the final time must be discarded, and exact measurements consistently produce accurate boundary heat fluxes under thin-plate conditions, with air velocity exhibiting no significant impact on the estimates. Additionally, an analysis of measurement errors and their influence on the inverse solutions was conducted. The numerical results conclusively demonstrated that the maximum error when estimating heat flux consistently remained below 3% and higher measurement noise resulted in the accuracy of the heat flux estimation decreasing. This underscores the inherent challenges associated with inverse problems and highlights the importance of obtaining accurate measurement data in the problem domain.

A Modified Enthalpic Lattice Boltzmann Method for Simulating Conjugate Heat Transfer Problems in Non-Homogeneous Media

A Modified Enthalpic Lattice Boltzmann Method for Simulating Conjugate Heat Transfer Problems in Non-Homogeneous Media

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.

A novel thermal turbulence reconstruction method using proper orthogonal decomposition and compressed sensing coupled based on improved particle swarm optimization for sensor arrangement

With the development of offshore wind turbine single power toward levels beyond 10 MW, the increase in heat loss of components in the nacelle leads to a high local temperature in the nacelle, which seriously affects the performance of the components. Accurate reconstruction and control of thermal turbulence in the nacelle can alleviate this problem. However, the physical environment of thermal turbulence in the nacelle is very complex. Due to the intermittent and fluctuating nature of turbulence, the turbulent thermal environment is highly nonlinear when coupled with the temperature field. This leads to large reconstruction errors in existing reconstruction methods. Therefore, we improve the sparse reconstruction method for compressed sensing (CS) based on the concept of virtual time using proper orthogonal decomposition (POD). The POD-CS method links the turbulent thermal environment reconstruction with matrix decomposition to ensure computational accuracy and computational efficiency. The improved particle swarm optimization (PSO) is used to optimize the sensor arrangement to ensure stability of the reconstruction and to save sensor resources. We apply this novel and improved PSO-POD-CS coupled reconstruction method to the thermal turbulence reconstruction in the nacelle. The effects of different basis vector dimensions and different sensor location arrangements (boundary and interior) on the reconstruction errors are also evaluated separately, and finally, the desired reconstruction accuracy is obtained. The method is of research value for the reconstruction of conjugate heat transfer problems with high turbulence intensity.

A fast fluid–solid coupled heat transfer algorithm based on dividing the development stages of the flow field

In this study, a fast numerical method for solving the forced convection conjugate heat transfer problem was developed. The method first proposes a new dimensionless number (Fs) that represents the degree of influence of convection on the temperature field in the flow field. It delineates the stage of development of the flow field by monitoring the change in Fs to determine the moment when the flow field suspends updating and improve the computational efficiency of the transient temperature field. The accuracy of the algorithm is verified by taking the fluid–solid conjugate heat transfer under forced convection conditions as an example, which can accurately capture the changes of the flow field for a given monitoring step number of 100, and classify the flow field into E3, E4 and E5 development stages according to the judgment criteria. The results show that the higher development stages correspond to smaller levels of root mean square error (RMSE) of monitoring point temperatures within 3600 s of physical simulation time, and stages E3, E4, and E5 can reach the levels of E-2, E-3, and E-4, which are 3.4, 3.3, and 3.1 times faster than the traditional coupled calculations, respectively. The algorithm is still applicable at variable time steps, but it will require a higher number of determinations compared to a fixed step. The initial error of the quasi-steady algorithm can be reduced from the E-1 level to E-4 by choosing a higher stage of development. Finally the algorithm is tested under a variety of conditions by varying the inlet temperature and flow rate and is found to be robust to both device warming and cooling.

The Cut-Cell Method for the Conjugate Heat Transfer Topology Optimization of Turbulent Flows Using the “Think Discrete–Do Continuous” Adjoint

This paper presents a topology optimization (TopO) method for conjugate heat transfer (CHT), with turbulent flows. Topological changes are controlled by an artificial material distribution field (design variables), defined at the cells of a background grid and used to distinguish a fluid from a solid material. To effectively solve the CHT problem, it is crucial to impose exact boundary conditions at the computed fluid–solid interface (FSI); this is the purpose of introducing the cut-cell method. On the grid, including also cut cells, the incompressible Navier–Stokes equations, coupled with the Spalart–Allmaras turbulence model with wall functions, and the temperature equation are solved. The continuous adjoint method computes the derivatives of the objective function(s) and constraints with respect to the material distribution field, starting from the computation of derivatives with respect to the positions of nodes on the FSI and then applying the chain rule of differentiation. In this work, the continuous adjoint PDEs are discretized using schemes that are consistent with the primal discretization, and this will be referred to as the “Think Discrete–Do Continuous” (TDDC) adjoint. The accuracy of the gradient computed by the TDDC adjoint is verified and the proposed method is assessed in the optimization of two 2D cases, both in turbulent flow conditions. The performance of the TopO designs is investigated in terms of the number of required refinement steps per optimization cycle, the Reynolds number of the flow, and the maximum allowed power dissipation. To illustrate the benefits of the proposed method, the first case is also optimized using a density-based TopO that imposes Brinkman penalization terms in solid areas, and comparisons are made.

Studies on acceleration algorithms for numerical simulations of hypersonic conjugate heat transfer problems

This research proposes acceleration algorithms for the coupled numerical simulation of the long-time hypersonic conjugate heat transfer problem from two perspectives. First, the newly developed disturbance region update method (DRUM) is introduced to enhance the convergence speed of the steady flow field. The numerical investigations reveal that, in the context of hypersonic CHT issues, the disturbance prompted by variations in wall temperature remains confined post the detached shock wave. The implementation of DRUM has been shown to substantially diminish the computational demand per iteration and the total iterations required for convergence. DRUM could reduce the time needed to calculate the flow field by over 60 % for a typical CHT case. Second, a new aerodynamic heat flux estimate method is introduced based on the local wall temperature within a coupled time step to increase the coupled time step. Combining this method with the adaptive coupled time step method, a long-time CHT problem with a total time of 1100s requires only 25 coupled time steps, much less than the 220 steps needed for the existing method. Meanwhile, the average error of the obtained solid temperature field, when compared to the temperature obtained from an accurate simulation with a fixed small coupled time step, is maintained below 0.22 %.

Direct numerical simulation of a pressurized thermal shock scenario at higher reynolds number

Direct Numerical Simulation (DNS) is performed for a pressurized thermal shock scenario in a reactor downcomer geometry. In the present work, a simplified representative geometry is adopted where cold fluid injected from a square duct is injected in a planar downcomer. A secondary hot inlet at the top of the downcomer is employed to enforce a downward flow of the injected emergency core cooling water, to mimic the effect of density driven flow. The Reynolds number of the impinging flow, based on bulk velocity and duct height, equals 12,500, while a unity Prandtl number fluid is used. The simulation is performed for two thermal boundary conditions, namely an isotemperature condition and an adiabatic condition, representing the two extreme scenarios of a conjugate heat transfer problem. The instantaneous and mean fields are first analysed in order to study the flow pattern and formation of vortical structures within the downcomer. The impinging flow is deflected radially outwards in the vicinity of the barrel wall, which then interacts with the surrounding hot fluid forming large vortical structures and bringing the cold fluid back to the vessel wall. The mixing of flow and penetration of colder temperatures in the downcomer is observed to be greatly influenced by interaction of these vortical structures. The descending cold plume in the downcomer is observed to form three branches separated by low-speed regions. The maximum values of turbulent kinetic energy are observed only in the vicinity of flow impingement, while high values of its production and dissipation are also observed within the shear layers of the descending plume. The maximum values of temperature fluctuations are found at the interface of the descending cold plume and surrounding hot fluid, while relatively high values are also seen at the locations of large vortical strucutres. Anisotropy in turbulence is also analysed using the componentality contour approach and a modified barycentric colour mapping scheme. Also reported herein is a comparison of mean and statistical profiles with those at lower Reynolds number reported in the literature. At higher Reynolds number, the cold impinging jet is deflected farther outwards in the downcomer. The locations of peak fluctuations in velocity and temperature are also farther away from the impingement. The magnitudes of fluctuating temperature and turbulent kinetic energy are observed to be higher for the present higher Reynolds number case. The peak Nusselt number at the barrel wall is observed to scale with a factor of Re1/2 in the present configuration.

A numerical study on the effects of inclination angle and container material on thermal energy storage by phase change material in a thick-walled disc

PurposeThe purpose of this study is to examine the effects of inclination angle on the thermal energy storage capability of a phase change material (PCM) within a disc-shaped container. Different container materials are also tested such as plexiglass and aluminium. This study aims to assess the energy storage capacity, melting behaviour and temperature distributions of PCM with a specific melting range (22°C–26°C) for various governing parameters such as inclination angles, aspect ratios (AR) and temperature differences (ΔT) and compare the melting behaviour and energy storage performance of PCM in aluminium containers to those in plexiglass containers.Design/methodology/approachA finite volume approach was adopted to evaluate the thermal energy storage capability of PCMs. Five inclination angles ranging from 0° to 180° were considered and the energy storage capacity. Also, the melting behaviour of the PCM and temperature distributions of the container with different materials were tested. Two different AR and ΔT values were chosen as parameters to analyse for their effects on the melting performance of the PCM. Conjugate heat transfer problem is solved to see the effects of conduction mode of heat transfer.FindingsThe results of the study indicate that as AR decreases, the effect of the inclination angles on the energy storage capacity of the PCM decreases. For lower ΔT, the difference between the maximum and minimum stored energies was 20.88% for AR = 0.20, whereas it was 6.85% for AR = 0.15. Furthermore, under the same conditions, the PCM stored 8.02% more energy in plexiglass containers than in aluminium containers.Originality/valueThis study contributes to the understanding of the influence of inclination angle, container material, AR and ΔT on the thermal energy storage capabilities of PCM in a novel designed container. The findings highlight the importance of AR in mitigating the effect of the inclination angle on energy storage capacity. Additionally, comparing aluminium and plexiglass containers provides insights into the effect of container material on the melting behaviour and energy storage properties of PCM.

Topology Optimization for Conjugate Heat Transfer Problems Based on the k-omega Turbulence Model

Topology Optimization for Conjugate Heat Transfer Problems Based on the k-omega Turbulence Model

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.

A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface

A diffuse interface-lattice Boltzmann model is proposed for modeling conjugate heat transfer problems with imperfect interfaces. According to the continuity condition of heat flux and jump condition of temperature across the imperfect interface, a unified sharp interface equation of the temperature field with a singular source term in the composite media domain is established. Then a diffuse interface equation is obtained by making a smoothed approximation of the unified sharp interface equation. The novel diffuse interface equation is restructured into a second-order heat diffusion equation with an anisotropic diffusion coefficient tensor. To numerically solve the second-order anisotropic diffusion equation, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme is employed. Several numerical simulations of benchmark test examples with analytical solutions are carried out to demonstrate the accuracy of the present model, including the steady-state heat diffusion in a two-layer medium with a flat interface, steady heat diffusion in a square domain with a curved interface and unsteady-state temperature diffusion with two-layer media. The numerical results show that the phenomenon of temperature jump across the imperfect interface can be successfully and correctly captured. Moreover, as an example of practical application, the new proposed diffuse interface model is utilized to predict the effective thermal conductivity of porous media with thermal contact resistance at pore scale. The variation law of the effective thermal conductivity is obtained for each parameter by studying the effects of thermal conductivity ratios of the dual-component material, the shape and volume fraction of blocks in the material, the interfacial thermal conductance coefficient, and the number of blocks on the effective thermal conductivity. Both uniform and random pore structures are considered. The previous theoretical equations strongly support the validity of the present model.

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.

Experimental and numerical study of inverse natural convection-conduction problem in a fully partitioned cavity

The inverse three-dimensional (3D) computational fluid dynamics method combined with the least squares method and overdetermined temperature measurements on the partition is used to study the natural convection-conduction conjugate heat transfer problem in a fully partitioned cavity. An unknown heat transfer rate, an appropriate flow model, heat transfer coefficients on all solid surfaces, and heat transfer characteristics are predicted. The conditions for verifying the accuracy of the obtained estimates are as follows. The root mean square error (RMSE) obtained by an appropriate flow model needs to be smaller than that obtained by other flow models. The obtained Nusselt number (Nuh ) on the hot wall must also line up with current correlations. The results show that the zero-equation model and the RNG k–ε model are suitable for problems with a horizontal partition and a vertical partition, respectively. This implies that choosing a suitable flow model may be influenced by the partition site. The partition-induced obstruction and buoyancy-driven flow may interact to create a complicated flow field and temperature distribution. The RMSE value and the maximum error of Nuh obtained by the appropriate flow model are about 0.45 and 4% for the horizontal partition and about 0.8 and 14.5% for the vertical partition, respectively. The obtained estimate of Nuh is closer to the proposed correlation. The Q values for horizontal and vertical partitions in this study are predicted to be 4.05, 5.06, and 4.64 W, respectively. The heat loss can be as high as 43 and 33% for horizontal and vertical partitions, respectively. Few researchers have used this inverse CFD method to predict the present problem. A literature review found that these findings have not yet appeared in the open literature. Thus, this study is novel and original.

Hyperreduced-order modeling of thermally coupled flows

This article presents a full and reduced-order methodology based on the finite element method that allows the characterization of convective-dominant conjugate heat transfer flows. Reduced-order modeling (ROM) allows the description of several degrees of freedom problems, referred to as full-order modeling (FOM), through a reduced-order surrogate representation based on a Petrov-Galerkin projection onto a reduced subspace. The FOM and ROM problems are stabilized through the Variational Multi-Scale (VMS) method, which ensures stability in dominant convective problems and allows equal interpolation spaces for the pressure, velocity, and temperature. The proposed methodology is validated solving natural heat convection in a differentially heated square cavity, considering air as the working fluid and Rayleigh numbers in the interval 104≤Ra≤108. In this problem, the benefit of using a ROM approximation for the three unknown fields, i.e., velocity, pressure, and temperature, is compared against ROM approximation only in the velocity and pressure fields and a FOM type approximation for temperature. The benefit of using mesh-based hyperreduction and its computational performance and precision are also analyzed. Subsequently, the method simulates a conjugate heat transfer problem that includes natural heat convection, allowing the inclusion of different rheologies between the working fluids. The results verify the precision and speed up of the calculations by more than three hundred times with respect to the time necessary to solve a full-order formulation, emerging it as a great potential tool in the resolution of thermally coupled flows.

A multi region adjoint-based solver for topology optimization in conjugate heat transfer problems

This work presents an exploration of fluid region optimization within coupled fluid–thermal problems of industrial significance, namely the design of a cooling plate for the thermal management of Printed Circuit Boards (PCB) of electrical propulsion systems. The Topology Optimization technique has been employed through a in-house developed multi-region adjoint solver and a set of customized boundary conditions, allowing the sensitivity computation independently on the problem size. The technique involves the integration of solid material into the computational domain to induce modifications in flow dynamics. This alteration aims to minimize a multi-objective function that considers both the skin temperature and the mechanical power dissipation caused by fluid movement across the domain. The obtained sensitivity values were then employed in optimizing material distribution through the Method of Moving Asymptotes. The derived material distribution was further post-processed to extract the newly optimized configuration of the system. This enabled a thorough evaluation of the optimization methodology’s performance and its effectiveness in enhancing the system’s overall efficiency.

Numerical Investigation of Conjugate Heat Transfer Problems

Conjugate heat transfer (CHT) analysis has been carried out for laminar flow past flat plate and turbulent flow between parallel plates using a commercial CFD software CFX-TASCFlow. Navier-Stokes equations along with k-e turbulence model in the fluid and conduction equation in the solid have been solved simultaneously to obtain the flow features. The computed temperature distribution of the flow past flat plat matches very welL with analytical and other numerical results. For the turbulent flow between parallel plates, nondimensional temperature distribution and Nusselt number distribution matches very well with the analytical and experimental results for different values of Reynolds number and thickness of the heat transfer plate.

Numerical investigation of melting process for phase change material (PCM) embedded in metal foam structures with Kelvin cells at pore scale level

The present numerical study analyzes the melting process of phase change material (PCM) embedded in a metallic foam structure at pore scale level. The computational domain consists of two different sizes of 3D cubic boxes. The analyzed domain is filled with Kelvin cell-structures with different Cell Per Length (CPL) and constant porosity of 0.956. A constant temperature, higher than the melting temperature of PCM, is assigned to one external surface of the enclosure, while the other surfaces are adiabatic. The conjugate problem for the heat transfer between the PCM and the solid structure with Kelvin cells is developed. Enthalpy-porosity method is used to describe the PCM melting process. The finite volume method is used to solve the conjugate heat transfer problem at pore scale level by Ansys-Fluent code. A comparison of different CPL values is reported in terms of liquid fraction, average temperature of the PCM, and energy storage. The comparison is also considered between the two different volumes of the cubic boxes. The presence of the metallic structured Kelvin cells increases the overall heat transfer rate and decreases the melting time. Results for smaller cavity indicates that as the CPL number increases, the time required for the PCM melting process decreases. Furthermore, the total heat accumulation process takes a shorter time to reach the maximum value. The melting time and the duration of heat accumulation are worsened for the large cubic box (L = 4 inch) at CLP>6. This is due to the dominant viscous effect, which decreases the velocity induced by the buoyancy forces because of higher contact surface area. In these cases, heat transfer between liquid and solid phases of the PCM decreases substantially.