Conjugate Heat Transfer Problem Research Articles

About Calculation of Combined Cooling Systems for Propulsion Engines

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

Development of a food temperature prediction model for real time food quality assessment

Multilayer food temperature models considering the spatial temperature distribution in the food were developed to predict temporal temperature changes experienced by food during distribution considering the surrounding temperature, initial food temperature, and the predetermined surface heat transfer coefficient. Parameters used in the models were determined using the results of unsteady three-dimensional computational fluid dynamics simulations for the conjugated heat transfer problem between the food and surroundings. Models were validated by comparing model predictions with the food temperature experimentally measured under fluctuating temperature conditions with a mean absolute deviation of less than 1 °C.The developed food temperature model was integrated with a freshness monitoring model to complete the real-time food quality monitoring system. Food quality prediction using the integrated food quality monitoring system was validated for eggs and milk. Quality predictions using the food temperature model showed better accuracy than when using a single point measurement of food temperature.

A CFD-supported dynamic system-level model of a sodium-cooled billboard-type receiver for central tower CSP applications

This work focusses on the dynamic modeling of a sodium-cooled billboard-type receiver, as adopted in the reference plant of this study, the Jemalong Solar Thermal Station, in Australia. A detailed system-level thermal-fluid-dynamic model is developed in the OpenModelica framework, with the aim to predict the receiver behavior during transients, as well as its performance upon reaching steady-state conditions. The model solves the conjugate heat transfer problem relating conduction in the receiver pipes to the internal flow of sodium. The convective losses from the irradiated face of the receiver, due to the external flow of air, are calculated using empirical correlation available in literature for flat-plates and then carefully evaluated using 3D Computational Fluid Dynamics (CFD), which allows taking into account the actual geometry of the receiver. The CFD results, considering different wind speeds and highlighting the cavity-like effects of the receiver geometry under consideration, are first compared with those obtained from empirical correlations available in the literature for vertical plates in the case of uniform temperature distribution on the absorber pipes, showing significant differences. Then an iterative coupling procedure with the system-level model of the same receiver is proposed, which facilitates handling of the more realistic case of a non-uniform temperature distribution. Finally, we present and discuss the successful benchmark in a simple case of the system-level model against another model from the literature, its preliminary validation against experimental data, and first applications to a fast start-up/passing cloud/shut-down transient and to a whole-day simulation with controls.

An immersed boundary method to conjugate heat transfer problems in complex geometries. Application to an automotive antenna

Considering that the most common reason for electronic component failure is the excessive temperature level, an efficient thermal management design can prolong the operating life of the equipment, while also increasing its performance. Computational Fluid Dynamics and Heat Transfer (CFD&HT) have proved valuable in the study of these problems, since they can produce reliable fields of fluid flow, temperature and heat fluxes. Moreover, thanks to the recent advances in high-performance computers, CFD&HT numerical simulations are becoming viable tools to study real problems. The conventional approach, which consists of employing body-conformal meshes to the solids and fluids regions, often results costly and ineffective in applications with very complex geometries and large deformation. For these cases, an alternative approach, the Immersed Boundary Method (IBM), which employs a non-body conformal mesh and discretizes the entire domain using a special treatment in the vicinity of the solid-fluid interfaces, has proven more effective. In this work, an IBM was extended to simulate problems with conjugate heat transfer (CHT) boundary conditions taking into account the radiative exchange between surfaces. It was designed to work with any type of mesh (domain discretization) and to handle any body geometry. The implementation was validated and verified by several simulations of benchmark cases. Moreover, the IBM was applied in an industrial application which consists of the simulation of a Smart Antenna Module (SAM). All in all, the carried out studies resulted in a monolithic methodology for the simulation of realistic situations, where all three heat transfer mechanisms can be considered in complex geometries.

Manufacturability evaluation: a CFD approach for Jominy hardenability test

ABSTRACTHeat treatment is an essential process in the manufacture of high-performance steel and other alloy components. Jominy end quench test is used to study the hardenability and microstructure growth in metal alloys when subjected to heat treatment. This is of significance to the manufacturing industry as it provides useful information, allowing selection of appropriate heat treatment procedures. An austenized cylinder is cooled with a fluid jet from one end, causing differential cooling, and resulting in varying properties along the length. This paper presents a manufacturability assessment tool for determination of hardenability of metal alloy components. Jominy test is simulated using a CFD approach as a conjugate heat transfer problem instead of conventional approaches that utilize estimations of the heat transfer rate. The model captures the problem physics by evaluating the temperature and velocity behavior. Cooling rate was found to be highly sensitive to jet velocity, increasing with increase in velocity. Oil was tried as a quenchant in the study and showed slower cooling rates as expected. This approach can be extended to achieve accurate results for cooling rates for complex parts and novel quenching procedures. This was demonstrated by studying the effect of inlet velocity and quenchant type on the cooling behavior.

On the Thermal Performance of a Microparallel Channels Heat Exchanger

Abstract This paper presents the experimental and theoretical analysis of a micro heat exchanger designed for the waste heat recovery from a high concentration photovoltaic (HCPV) system. A test bench was built to analyze the thermal behavior of a heat exchanger targeted to work in a similar condition of an existing HCPV panel. A high power heater was encapsulated inside a copper cartridge, covered by thermal insulation, leading to dissipated heat fluxes around 0.6 MW/m2, representative of the heat flux over the solar cell within the HCPV module. The experimental campaign employed water as the coolant fluid and was performed for three different mass flow rates. An infrared camera was used to nonintrusively measure the temperature field over the micro heat exchanger external surface, while thermocouples were placed at the contact between the heat exchanger and the heater, and at the water inlet and outlet ports. In the theoretical analysis, a hybrid numerical–analytical treatment is implemented, combining the numerical simulation through the comsolmultiphysics finite elements code for the micro heat exchanger, and the analytical solution of a lumped-differential formulation for the electrical heater cartridge, offering a substantial computational cost reduction. Such computational simulations of the three-dimensional conjugated heat transfer problem were critically compared to the experimental results and also permitted to inspect the adequacy of a theoretical correlation based on a simplified prescribed heat flux model without conjugation effects. It has been concluded that the conjugated heat transfer problem modeling should be adopted in future design and optimization tasks. The analysis demonstrates the enhanced heat transfer achieved by the microthermal system and confirms the potential in reusing the recovered heat from HCPV systems in a secondary process.

Concurrent shape and topology optimization for steady conjugate heat transfer

This work explores topology optimization under unsteady conditions on a fundamental design problem to gain design insights between steady and unsteady regimes. A previously studied steady conjugate heat transfer problem at a Reynolds number of 20 is extended to unsteady conditions at a Reynolds number of 100 exhibiting vortex shedding. Interesting non-intuitive optimized shapes and internal topologies for a heated body are computed that do not qualitatively match optimized designs generated with a Reynolds number of 20. Shape optimization under unsteady conditions with a solid interior relies on vortex shedding to improve heat transfer while shape optimization under steady conditions increased the exposed surface area near cool fluid. Concurrent shape and topology optimization with two shape parameter spaces are considered and show that the higher parameter space leverages a higher frequency of vortex shedding to improve cooling. The internal optimized topologies with concurrent shape and topology optimization prioritize heat transfer near the flow separation point biased towards the leading or trailing edge of the body, dependent on the location of most efficient convection. Computing reasonably converged time-averaged objectives and constraints for the presented unsteady case requires 4000 time steps while the steady case requires one time step, leading to a large marginal computational cost increase.

Three-dimensional fluid topology optimization for heat transfer

In this work, an in house topology optimization (TO) solver is developed to optimize a conjugate heat transfer problem: realizing more complex and efficient coolant systems by minimizing pressure losses and maximizing the heat transfer. The TO method consists in an idealized sedimentation process in which a design variable, in this case impermeability, is iteratively updated across the domain. The optimal solution is the solidified region uniquely defined by the final distribution of impermeability. Due to the geometrical complexity of the optimal solutions obtained, this design method is not always suitable for classic manufacturing methods (molding, stamping....) On the contrary, it can be thought as an approach to better and fully exploit the flexibility offered by additive manufacturing (AM), still often used on old and less efficient design techniques. In the present article, the proposed method is developed using a Lagrangian optimization approach to minimize stagnation pressure dissipation while maximizing heat transfer between fluid and solid region. An impermeability dependent thermal conductivity is included and a smoother operator is adopted to bound thermal diffusivity gradients across solid and fluid. Simulations are performed on a straight squared duct domain. The variability of the results is shown on the basis of different weights of the objective functions. The solver builds automatically three-dimensional structures enhancing the heat transfer level between the walls and the flow through the generation of pairs of counter rotating vortices. This is consistent to solution proposed in literature like v-shaped ribs, even if the geometry generated is more complex and more efficient. It is possible to define the desired level of heat transfer and losses and obtain the closest optimal solution. It is the first time that a conjugate heat transfer optimization problem, with these constraints, has been tackled with this approach for three-dimensional geometries.

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

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

Numerical Modeling of the Influence of Thermal Protection Materials on Characteristics of Conjugate Heat and Mass Transfer with Spatial Flow around Blunted Bodies

The three-dimensional problem of conjugate heat and mass transfer upon the motion of a spherically blunted cone at various angles of attack along a set trajectory is theoretically explored. Thermal protection materials, including carbon materials with high heat-conducting properties, conventional carbon fiber-reinforced plastic coatings, and promising nondestructible ceramic materials, are analyzed. It is shown that the application of the latter makes it possible to preserve the initial geometry of the body and to attain a considerable temperature decrease in the coating surface upon the development of new materials with high thermal conductivity.

Investment casting and experimental testing of heat sinks designed by topology optimization

Topology optimization (TO) is an attractive numerical tool to obtain optimized engineering designs, which has been originally developed for mechanical optimization and extended to the area of conjugate heat transfer. With rapid developments in topology optimization models, promising designs have been proposed and presented recently for conjugate heat transfer problems. However, only a very small number of experimental validations of TO heat transfer devices have been reported. In this paper, investment casting (IC) using 3D stereolithography (SLA) printed patterns is proposed to fabricate 3D metal heat transfer devices designed by TO. Three heat sinks for natural convection are designed by a previously reported topology optimization model and five reference pin-fin heat sinks are devised for comparison. From those designs six heat sinks are cast in Britannia metal, fully reproducing the complex 3D optimized designs. It shows that SLA-assisted IC is a very promising technology with low cost and high accuracy for fabricating TO metal parts, which is not limited to heat transfer devices and can be extended to other areas such as structural optimization. A natural convection experimental setup is used to experimentally study the performance of the fabricated heat sinks. The results show that the tested TO heat sinks can always realize the best heat dissipation performance compared to pin-fin heat sinks, when operating under the conditions used for the optimization. Moreover, validation simulations have been conducted to investigate the temperature distribution, fluid flow pattern and local heat transfer coefficient for the TO and pin-fin designs, further evidencing that TO designs always perform better under the design conditions. In addition, the impact of heat sink orientation and radiation are presented.

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

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

Chaotic Rayleigh-Bénard convection with finite sidewalls.

We explore the role of finite sidewalls on chaotic Rayleigh-Bénard convection. We use large-scale parallel spectral-element numerical simulations for the precise conditions of experiment for cylindrical convection domains. We solve the Boussinesq equations for thermal convection and the conjugate heat transfer problem for the energy transfer at the solid sidewalls of the cylindrical domain. The solid sidewall of the convection domain has finite values of thickness, thermal conductivity, and thermal diffusivity. We compute the Lyapunov vectors and exponents for the entire fluid-solid coupled problem. We quantify the chaotic dynamics of convection over a range of thermal sidewall boundary conditions. We find that the dynamics become less chaotic as the thermal conductivity of the sidewalls increases as measured by the value of the fractal dimension of the dynamics. The thermal conductivity of the sidewall is a stabilizing influence; the heat transfer between the fluid and solid regions is always in the direction to reduce the fluid motion near the sidewalls. Although the heat interaction for strongly conducting sidewalls is only about 1% of the heat transfer through the fluid layer, it is sufficient to reduce the fractal dimension of the dynamics by approximately 25% in our computations.

Conjugate heat transfer problem with cold injection from the ground surface

Conjugate heat transfer problem with cold injection from the ground surface

A unified thermal lattice Boltzmann equation for conjugate heat transfer problem

In the present paper, an optimal two-relaxation-time (OTRT) thermal lattice Boltzmann equation (TLBE) is proposed to simulate conjugate heat transfer. The derivation process is based on a developed idea of virtual heat capacity correction method. Finally, it is found that a unified TLBE can be achieved. The derivation process shows how the modified equilibrium distribution function works in simulating conjugate heat transfer. It also reveals the relation between the virtual heat capacity correction method and the method of reconstructing the equilibrium distribution function. By using Chapman-Enskog expansion, the proposed OTRT TLBE can recover the standard energy equation up to second-order accuracy. For validation, six test cases including both steady and transient conjugate heat transfer with flat or curved interfaces are calculated. The results show that the OTRT TLBE performs well in simulating conjugate heat transfer problems with both flat and curved interfaces, at both transient and steady states, and the OTRT TLBE could have better numerical accuracy than the single-relaxation-time (SRT) TLBE.

Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO2/LCH4 cryogenic flame

High-fidelity numerical simulations are used to study flame root stabilization mechanisms of cryogenic flames, where both reactants (O2 and CH4) are injected in transcritical conditions in the geometry of the laboratory scale test rig Mascotte operated by ONERA (France). Simulations provide a detailed insight into flame root stabilization mechanisms for these diffusion flames: they show that the large wall heat losses at the lips of the coaxial injector are of primary importance, and require to solve for the fully coupled conjugate heat transfer problem. In order to account for flame–wall interaction (FWI) at the injector lip, detailed chemistry effects are also prevalent and a detailed kinetic mechanism for CH4 oxycombustion at high pressure is derived and validated. This kinetic scheme is used in a real-gas fluid solver, coupled with a solid thermal solver in the splitter plate to calculate the unsteady temperature field in the lip. A simulation with adiabatic boundary conditions, an hypothesis that is often used in real-gas combustion, is also performed for comparison. It is found that adiabatic walls simulations lead to enhanced cryogenic reactants vaporization and mixing, and to a quasi-steady flame, which anchors within the oxidizer stream. On the other hand, FWI simulations produce self-sustained oscillations of both lip temperature and flame root location at similar frequencies: the flame root moves from the CH4 to the O2 streams at approximately 450 Hz, affecting the whole flame structure.

An adaptive approach for prediction of propellant feedline dynamics in fluid network

PurposeThis paper aims to propose an adaptive unstructured finite volume procedure for efficient prediction of propellant feedline dynamics in fluid network.Design/methodology/approachThe adaptive strategy is based on feedback control of errors defined by changes in key variables in two subsequent time steps.FindingsAs an evaluation of the proposed approach, two feedline dynamics problems are formulated and solved. First problem involves prediction of pressure surges in a pipeline that has entrapped air and the second is a conjugate heat transfer problem involving prediction of chill down of cryogenic transfer line. Numerical predictions with the adaptive strategy are compared with available experimental data and are found to be in good agreement. The adaptive strategy is found to be efficient and robust for predicting feedline dynamics in flow network at reduced CPU time.Originality/valueThis study uses an adaptive reduced-order network modeling approach for fluid network.

Prediction of the maximum temperature inside container with spent nuclear fuel

The definition of the thermal state of containers with spent nuclear fuel is important part of the ensuring of its safe storage during all period of storage facility operation. The this work all investigations are carried out for the storage containers of spent nuclear fuel of WWER-1000 reactors, which are operated in the Dry Spent Nuclear Fuel Storage Facility in Zaporizhska NPP. The analysis of existing investigations in the world nuclear engineering science concerning to the prediction of maximum temperatures in spent nuclear fuel storage container is carried out. The absence of studies in this field is detected and the necessity of the dependence for the maximum temperature in the storage container and temperature of cooling air on the exit of ventilation duct from variated temperatures of atmospheric air and decay heat formulation is pointed out. With usage of numerical simulation by solving of the conjugate heat transfer problems, the dependence of maximum temperatures in storage container with spent nuclear fuel from atmospheric temperature and decay heat is detected. The verification of used calculation method by comparison of measured air temperature on exit of ventilation channels and calculated temperature of cooling air was carried out. By regression analysis of numerical results of studies the dependence of ventilation air temperature from the temperature of atmospheric air and the decay heat of spent nuclear fuel was formulated. For the obtained dependence the statistical analysis was carried out and confidence interval with 95% of confidence is calculated. The obtained dependences are expediently to use under maximum temperature level estimation at specified operation conditions of spent nuclear fuel storage containers and for the control of correctness of thermal monitoring system work.

The continuous adjoint method for shape optimization in Conjugate Heat Transfer problems with turbulent incompressible flows

In this paper, the development of the continuous adjoint method for shape optimization in Conjugate Heat Transfer (CHT) problems with incompressible flows is presented. The main focus of this study is to develop a continuous adjoint method which computes accurate sensitivity derivatives by (a) extending the adjoint to the Spalart-Allmaras turbulence model, by taking into consideration additional contributions arising from the differentiation of the heat transfer equation valid in the flow domain and (b) extending the Enhanced-Surface Integral adjoint formulation, recently introduced by the authors’ group for single-disciplinary problems, to CHT ones. The so-computed sensitivities are compared to the outcome of finite differences and alternative adjoint formulations in 2D turbulent flows. The proposed method is firstly validated in two simple cases and, then, used to perform the CHT optimization of a 2D internally cooled turbine blade and a 3D car piston-engine cylinder head.

Conjugated heat transfer and entropy generation of Al2O3–water nanofluid flows over a heated wall-mounted obstacle

The present study reports numerical simulations of water-based Al2O3 nanofluid flowing in a 2D channel with a heated wall-mounted obstacle. The conjugated heat transfer problem including forced convection within the fluid and conduction inside the obstacle is numerically solved using the mixture model with temperature-dependent properties. The model has been first carefully validated against published data. Then, the fluid flow and heat transfer have been investigated for six nanoparticle volume fractions $$\varphi$$ up to $$1.8\%$$ and bulk Reynolds numbers within the range $$100 \le Re \le 1600$$ . The results show that only the Reynolds number has an influence on the hydrodynamic field, especially on the reattachment length behind the obstacle. The heat transfer rate increases with increasing nanoparticle concentrations and/or Reynolds number. The second law analysis is employed to study the heat transfer and fluid friction irreversibilities. The average entropy generation increases linearly with the Reynolds number. Increasing the nanoparticle volume fraction reduces the thermal entropy generation while the frictional one increases. Finally, the benefit of using this nanofluid is discussed regarding five merit criteria.