Transient Conjugate Heat Transfer Research Articles

Accelerating Transient Aerothermal Simulations of the BOLT II Flight Experiment

Aircraft with short flight durations may not reach thermal steady state due to limited time for aeroheating to conduct throughout their internal structure. Consequently, predictions of the solid temperature field require time-accurate simulation of the transient heat conduction. In this work, the use of an explicit super-time-stepping scheme to accelerate the time-accurate solution of the heat equation has been explored. The experience with this technique is documented here because, to the authors’ knowledge, it is not widely used in the hypersonics simulation community. The performance of the super-time-stepping scheme was investigated by comparison to a standard explicit scheme and an implicit time-differencing scheme. Both the super-time-stepping scheme and the implicit time-differencing scheme demonstrate significant speedup over the standard explicit scheme, with comparable wall-clock performance. The solid solver has been coupled with an existing open-source fluid solver to perform conjugate heat transfer simulations. The efficacy of the developed solver in simulating hypersonic aerothermal problems is demonstrated through verification and validation studies. By applying the coupled solver to the aerothermal analysis of the BOLT II flight experiment, the effectiveness of the super-time-stepping scheme in mitigating the computational expense associated with transient conjugate heat transfer simulations is demonstrated.

Determination of Local Heat Transfer Coefficients and Friction Factors at Variable Temperature and Velocity Boundary Conditions for Complex Flows

Transient conjugate heat transfer measurements under varying temperature and velocity inlet boundary conditions at incompressible flow conditions were performed for flat plate and ribbed channel geometries. Therefrom, local adiabatic wall temperatures and heat transfer coefficients were determined. The data were analyzed using typical heat transfer correlations, e.g., Nu=CRemPrn, determining the local distributions of C and m. It is shown that they are closely linked. A relationship lnC=A−mB is observed, with A and B as modeling parameters. They could be related to parameters in log-law or power-law representations for turbulent boundary layer flows. The parameter m is shown to have a close link to local pressure gradients and, therewith, near wall streamlines as well as friction factor distributions. A normalization of the C parameter allows one to derive a Reynolds analogy factor and, therefrom, local wall shear stresses.

Conjugate heat transfer analysis of the transient thermal discharge of a metallic latent heat storage system

Thermal energy storage systems utilizing metallic phase change materials exhibit great potential as a technology for mobile applications, offering high storage densities and high thermal discharge rates. First experimental investigations show the functionality and performance characteristics of this system. For a deeper understanding of the thermal discharge, this paper presents a numerical model and analysis of the transient conjugate heat transfer. For validation of the numerical model, the results of the simulations are compared to the available experimental data. The investigated storage is based on an aluminum silicon alloy and a box-shaped graphite container design. In this system, heat extraction is achieved by forced convection of ambient air. The transient thermal discharge was simulated from 650 °C to 100 °C, and the solidification of the storage material at around 577 °C was simulated using an enthalpy-porosity approach. The discharge time and total heat flow show good agreement with the experimental data, indicating the model’s successful validation. An empirical study was carried out to determine the thermal contact resistance at the interface between the storage material and the graphite container. The present study contributes new physical insights regarding the thermal discharge of a novel metallic latent heat thermal energy storage system.

Transient simulation of conjugate heat transfer of kerosene with thermal oxidative and surface coking reactions at a supercritical pressure

The regenerative cooling technology in aerospace applications often involves supercritical-pressure heat transfer of a hydrocarbon fuel, in which thermal oxidative reactions of the fuel would lead to surface coke accumulation on the cooling channel wall. In this paper, the long-term transient conjugate heat transfer of kerosene has been numerically investigated in a circular mini tube at a supercritical pressure of 3 MPa. The modified chemical mechanism and kinetics of thermal oxidative and surface coking reactions of kerosene are proposed, which, with an additional surface reaction, are capable of treating large coke deposition in regions with sharp temperature gradients. Transient surface coke accumulation and its effect on heat transfer are handled by a dynamic mesh technique. A series of numerical studies are conducted to elucidate the influences of surface heat flux, dissolved oxygen mass fraction, inlet fuel mass flow rate, and coke layer thermal conductivity on the supercritical-pressure heat transfer and thermal oxidative reactions. The effects of different reaction pathways on surface coke accumulation are analyzed comprehensively, and it is revealed that the oxygen-consuming surface coke deposition is initiated only at the high fuel temperature at around 590 K. The present numerical results would enhance fundamental understanding of the long-term transient heat transfer process of a hydrocarbon fuel at supercritical pressures in the regenerative cooling applications.

Reduced-order modeling of conjugate heat transfer in lithium-ion batteries

Reduced-order modeling (ROM) techniques involving physics are gaining importance due to their ability to generate physically meaningful results swiftly and accurately. They are finding applications in design and optimization and in digital twins where real-time results are required. The proper orthogonal decomposition (POD)-Galerkin ROM based on finite volume discretization methodology is utilized here for solving a high-dimensional system in a reduced dimensional space in which the reduced basis is spanned by the POD modes. The reduced-order equations are obtained by projecting the discretized form of the full-order model (FOM) equations onto the reduced basis which eliminates the need for boundary control techniques. The proposed methodology is demonstrated for transient conjugate heat transfer (CHT) in an electric vehicle battery. The POD modes are computed using simulation data for three Reynolds numbers and the ROM is evaluated for transient analysis of temperature from initial state to steady state for seven Reynolds numbers. The ROM predictions are fairly accurate both in the interpolated and the extrapolated regions with significant computational speed-up. Five modes are sufficient for constructing the fluid and battery temperature ROM solution. The ROM computational speed-up obtained with 5 modes is approximately 4–7.4 times compared to the FOM. The proposed methodology is generic and can be readily applied for any engineering system involving CHT.

Topography optimisation using a reduced-dimensional model for transient conjugate heat transfer between fluid channels and solid plates with volumetric heat source

Consideration of transient effects is important for industrial applications of heat transfer structure optimisation studies; however, the huge computational cost associated with transient problems is a pressing concern. This paper proposes an extension of a previous reduced-dimensional model to transient conjugate heat transfer between a fluid flow and solid-heated plates in a plate heat exchanger. The extended reduced-dimensional model introduces the temperature field of the plate governed by the heat conduction equation, which is coupled to the temperature field of the fluid, governed by the convection-diffusion equation, through the heat flux balance equation at the contact surface. The model is based on assumptions of fully developed flow and constant temperature profile, reducing the three-dimensional problem to a planar problem and significantly reducing computational costs. The accuracy of the model for the simulation of transient heat transfer is verified by comparison with a three-dimensional model. In this paper, the topography of the heat exchanger plate is optimised for both steady-state and transient conditions by applying the reduced-dimensional model. The effectiveness of the optimised design was demonstrated by the cross-check of both the reduced-dimensional and full three-dimensional models. Furthermore, this work considers the effect of time-independent boundary conditions and time-dependent boundary conditions on transient optimisation. The transient and steady-state optimised designs are analysed and compared for both conditions, and the necessity of transient optimisation is discussed.

Experimental Validation of a Numerical Coupling Environment Applying FEM and CFD

Experimental results for the transient heat transfer characteristics over a flat plate and over a plate with V-shaped ribs were compared to numerical results from a coupling environment applying FEM and CFD. In order to simulate transient effects in the cooling process of engine components during typical flight missions, the temperature and the velocity at the inlet of the channel were varied over time. The transient temperature distribution at the plate was measured using infrared thermography. Five different plate materials (perspex, PEEK, quartz, aluminum, and steel) were considered to investigate the influence of thermal conduction on the heat transfer between solid and fluid depending on the Biot number. The experimental results represent a reference database for a Python-based coupling environment applying CalculiX (FEM) and ANSYS CFX (CFD). The results were additionally compared to numerical results simulating the complete transient conjugated heat transfer with CFD. A good agreement between the numerical and the experimental results was achieved using different coupling sizes at different Biot numbers for the flat plate and the plate with V-shaped ribs.

Film Boiling around a Finite Size Cylindrical Specimen—A Transient Conjugate Heat Transfer Approach

The DNS of film boiling requires strong computational resources that are difficult to obtain for daily CFD use by expert practitioners of industrial R&D. On the other hand, film boiling experiments are associated with the usage of expensive and highly sophisticated apparatus, and research to this end is relatively difficult due to high heat flow rates that are present in the process itself. When combined with transient heat conduction in a solid, the problem becomes significantly difficult. Therefore, a novel method in computation of conjugate heat transfer during film boiling in a quiescent liquid is proposed in this paper. The method relies on the solution of mass, momentum and energy conservation equations in a two-fluid framework, supplemented with the appropriate closures. Furthermore, turbulent flow was determined as an important parameter in obtaining an accurate solution to temperature field evolution in a solid specimen, via the proper modeling of the turbulent kinetic energy (TKE) value, that was imposed as a constant value, i.e., the frozen turbulence approach. It was found, in addition, that the appropriate TKE value can be obtained by use of Kelvin–Helmholtz instability theory in conjunction with boundary layer theory. The obtained results show excellent agreement with the experimental data within the first 15 s of the experiment, i.e., the first ca. 10% of the total duration of the film boiling mode of heat transfer. Furthermore, the heat transfer coefficient matched the error bands prescribed by the authors of this paper, which presented the correlations, whilst the averaged values are far beyond this band, i.e., are slightly more than 30% higher. Further inspection revealed a measure of similarity between the computational result of the volume fraction field distribution and the experiment, thus confirming the capability of the method to obtain realistic interface evolution in time. The method shows full capability for further pursuing industrial-scale film boiling problems that involve turbulent flow and the conjugate heat transfer approach.

Research on transient heat transfer of ball valves in high-pressure liquid hydrogen receiving stations

As one of the most important fluid control devices in the liquid hydrogen receiving station, the liquid hydrogen ball valve's performance directly affects the system's stability. Aiming at the problem of insufficient cold shrinkage compensation ability of ball valve under high-temperature difference and excessive flow rate during the working process, a high-pressure liquid hydrogen hollow ball valve with elastic compensation ability is designed. Based on the conjugate heat transfer method, the transient conjugate heat transfer and transient thermal stress analysis were carried out on the high-pressure hollow ball valve of the liquid hydrogen receiving station. The results show that the transient temperature of each part of the ball valve decreases under different flow rates, and the closer to the flow part of the medium, the faster the cooling. In the initial stage, the larger the flow rate of liquid hydrogen, the greater the heat flux density of the fluid-solid interface, but after a certain period, the large flow rate is cooled to a greater extent, the heat transfer is weakened, and the heat flux density is smaller. Under different flow rates, the transient thermal stress of the key components of the ball valve first increases sharply and then decreases. At large flow rates, the temperature change is more obvious, and the maximum stress of each component increases. The research results have guiding significance for designing and applying ball valves in high-pressure liquid hydrogen receiving stations.

Transient Conjugate Heat Transfer Analysis of a Cylindrical Pin Fin Made by Functionally Graded Material Embedded in the Turbulent Flow

Transient Conjugate Heat Transfer Analysis of a Cylindrical Pin Fin Made by Functionally Graded Material Embedded in the Turbulent Flow

Numerical and experimental study of the transient conjugate heat transfer and fluid flow of passive residual heat removal heat exchanger

The transient heat transfer performance of passive residual heat removal heat exchanger (PRHR HX) with C-tube bundle directly influences nuclear reactor safety under accident condition. This paper presents an investigation of transient conjugate heat transfer and fluid flow phenomena and characteristics of scaled-down single C-tube submerged in water tank under atmospheric pressure at the initial period before saturation pool boiling occurs. Empirical calculation model, experimental setup and numerical model were established separately, and both numerical and experimental studies were carried out. The distributions of tube outlet temperature and water temperatures at horizontal and vertical monitoring points in tank were obtained. Detailed comparisons of the results show good agreements. Also, the change tendencies of heat flux, heat transfer coefficients and heat load were analyzed. The fluctuation of heat flux along normalized length from tube inlet firstly increases but finally tends to keep stable with the change of temperature difference and transformation of heat transfer mechanism. The heat transfer coefficient inside tube shows a slight downtrend along normalized length from tube inlet, but the heat transfer coefficient outside tube shows obvious change in the transient process. The total heat load continuously decreases with time. Furthermore, the volume fraction of vapor is relatively low during the subcooled boiling period. The two-phase flow enhances the agitation in water tank and the fluid velocity near tube outside wall is much larger.

Experimental investigation of unsteady convective heat transfer under airflow velocity and temperature variations

An experimental approach to study unsteady local heat transfer characteristics due to airflow velocity and/or airflow temperature variations is presented. It uses controlled electrical heaters and rotating vanes to independently vary the flow and thermal boundary conditions. Time-resolved surface temperatures are measured using an in situ calibrated infrared thermography camera. Those surface temperatures are analyzed by modeling the transient conjugate heat transfer process in the wall to obtain locally resolved surface heat flux distributions. The applicability is illustrated for a flow and heat transfer behind a tetrahedral vortex generator on a flat plate.

Bi-Fo time scaling method in the numerical simulation of transient conjugate heat transfer

Reliable transient thermal analysis plays a very important role in the engine safety analysis. Transient conjugate heat transfer simulation is an important way of temperature analysis. But there exists a great disparity in the time scales between solid conduction and fluid convection. The calculation cost of transient conjugate heat transfer analysis is very huge because of the tiny time step of computational fluid dynamics. The Bi-Fo time scaling method is proposed to improve the computational efficiency of transient conjugate heat transfer. On the one hand, this method carries out a similar transformation on solid heat conduction, scaling the calculation time with the product of density and specific heat capacity to maintain the consistency of Fourier number. On the other hand, it takes very short time for the fluid domain to recover stability after a boundary disturbance. Based on the above characteristic, the flow time is directly compressed to the same as that of the solid domain. It is verified by Mark Ⅱ vane that increasing the solid thermal diffusivity can reduce the time scale of heat conduction. In the situation of rapidly stable flow field, scaling flow time does not affect the solid thermal boundary under corresponding dimensionless time. Within the application scope, the Bi-Fo time scaling method can greatly reduce the time cost of transient conjugate heat transfer simulation while maintaining the accuracy of transient temperature analysis.

Thermal-striping analysis methodology for sodium-cooled reactor design

Computational fluid dynamics simulations have been performed to study the applicability of engineering CFD methods for thermals striping analysis. Thermal striping is the fluctuating temperature profile in a solid caused by fluctuating fluid temperature, and the resulting thermal stresses cause high cycle fatigue and eventual material failure. This study presents the methodology for thermal striping analysis, including a transient conjugate heat transfer RANS simulation benchmarked against a sodium triple jet experiment. Multiphysics calculations are implemented to analyze the thermal stresses in the solid domain caused by the coupled heat transfer between the fluid and solid domains. Validation data from a liquid sodium triple jet experiment include time-averaged temperature measurements and power spectra of the temperature signal. The numerical results agree well with these experimental measures, demonstrating key features such as the dominant frequency of temperature fluctuations. The applicability of a low-cost wall treatment method is demonstrated, enabling key computational savings. Finally, the performance of two finite element stress analysis software packages is compared, and the validity of the lower-cost method is confirmed. These results demonstrate the applicability of engineering methods for computational thermal striping calculations, enabling thermal striping estimations in large fluid systems such as the core of a liquid metal-cooled nuclear reactor.

Effects of non-isothermal oxidation on transient conjugate heat transfer of the cryo-supersonic air-quenching

In this paper, the effects of non-isothermal oxidation on transient conjugate heat transfer of the cryo-supersonic air-quenching are investigated based on a double-layered oxidation kinetics model, while a unified conjugate heat transfer formula is developed to synthetically consider the near-wall turbulence, non-isothermal oxidation, and surface radiation. The comparison between numerical and experimental results are also presented to check the validity of the developed model. The results indicate that the film growth has some degree of inhibition to the conjugate heat transfer, in particular, the stagnation temperature increases linearly by about 5 K per 100 ?m increase in film thickness, and the effective conjugate heat transfer coefficient in the stagnation region decreases linearly by about 55 Wm?2K?1 per 100 ?m increase in film thickness. Moreover, the oxide film would have little impact on transient conjugate heat transfer when the near-wall velocity is higher due to the effect of viscous dissipation.

Steady-State Fluid-Solid Mixing Plane to Replace Transient Conjugate Heat Transfer Computations during Design Phase

The demand for increased turbomachinery performance, both, towards higher pressures and temperatures, leads to high thermal-loads of specific components and can critically affect mechanical integrity. In the particular case of rotating-disk configurations, like the back-side of wheels or in cavities, a very efficient way for cooling is jet impingement. An example for this situation are high pressure-ratio turbochargers, where cooling of the impeller disk (back wall) is introduced to achieve tolerable thermal loads. From the physical point of view, jet impingement on a rotating wall generates an unsteady heat transfer situation. On the other end, accurate values of time-averaged temperatures would be sufficient for design purposes. In general, obtaining circumferentially time-averaged solutions requires transient analysis of the conjugate heat transfer (CHT) process to account for the mean effect of jet cooling on solids. Such analysis is computationally expensive, due to the difference in information propagation time-scale for the solid and the fluid. In this paper, a new approach to directly compute circumferentially time-averaged (i.e., steady-state) temperature distributions for rotating-disk CHT problems is presented based on an adaption of the well known fluid-fluid mixing plane approach.

Study of oscillating flows through a novel constructal bifurcation Stirling regenerator

High flow resistance in conventional porous regenerators has been an important factor for limiting the overall performance of Stirling engines. Herein, a novel constructal bifurcation regenerator based on constructal concept was developed to reduce the flow resistance in the Stirling regenerator. First, the pressure drop and transient conjugate heat transfer characteristics of oscillating flows through the constructal bifurcation regenerator with various geometrical parameters were investigated by the CFD approach. The results showed that the fluid flow and heat transfer between the acceleration and deceleration phases, as well as the discharge and suction phases, were varied significantly. These differences should be resulted from the local acceleration effect, the formation of eddies in the acceleration phase, and different windward surfaces generated by the regenerator matrix to the fluid in the discharge and suction phases. Additionally, the flow characteristics between the oscillating and steady flows were compared and the local acceleration effect was proven to be the main cause of the difference between them. Then the three-parameters correlation equations of friction factor and Nusselt number for each structure and four master correlation equations with geometrical parameter dependence were built to predict the regenerator performance. Thereafter, the constructal bifurcation regenerators were converted to equivalent porous media, and thus the main porous parameters were obtained for the full Stirling engine simulation in the next studies. Finally, the friction factor and Nusselt number of the constructal bifurcation regenerator were compared with those of other commonly used regenerators. It showed that the constructal bifurcation regenerator had a low flow resistance and moderate heat transfer, thus obtaining a high comprehensive performance. The superior comprehensive performance of the regenerator makes it possible to improve the performance of Stirling engines.

Tomography-based investigation of flow and heat transfer inside reticulated porous ceramics

This study investigates the flow and heat transfer within reticulated porous ceramics, with the aim of enhancing the understanding of phenomena occurring at the pore scale in order to extract useful information for the optimisation of heat sinks or other reticulated porous devices in engineering applications. In this study, X-ray computed tomography is used to reconstruct the reticulated porous ceramic. From the voxel mesh, the real geometry of the foam sample can be obtained, and an unstructured mesh is generated using ICEM. Then, a fully coupled heat transfer model is established. Based on this model, the transient conjugate heat transfer between the airstream and the porous matrix is solved using FLUENT software. The numerical results show that the pressure drop vs. the superficial velocity follows the Darcy–Forchheimer equation, and the border-affected region is only 1–2 times the mean cell size. Moreover, a local thermal equilibrium lasting for 7–10 s is found in the transient coupled flow and heat transfer process in this study. Additionally, the local convective heat transfer coefficient, which mainly depends on the velocity, is constant along the flow direction, and the instantaneous volumetric heat transfer coefficient increases monotonically with time. The obtained results are important theoretical supplements for understanding the flow and heat transfer in porous materials, and are crucial for enhancing the heat transfer in applications of reticulated porous ceramic materials.

Numerical and experimental study of transient conjugate heat transfer in helical closed‐loop geothermal heat exchangers for application of thermal energy storage in backfilled mine stopes

The geothermal potential available from deep underground mines has yet to be utilized. However, stope-coupled heat exchangers (SCHE) are aiming to take advantage of the unused low-grade geothermal energy. Backfilled stopes provide a unique opportunity to install nonlinear heat exchangers, as the geometry is not limited to the shape of a borehole. Helical pipes deliver superior fluid mixing and heat exchange compared to straight pipes, due to the effect of the secondary flow within the helical pipe. The helical closed-loop geothermal heat exchanger enables the backfilled stopes of the mine to be repurposed as thermal energy storage units. This article delves into the experimental results from a unique state-of-the-art laboratory scale helical closed-loop heat exchanger with varying thermophysical parameters. Additionally, a novel conjugate numerical model is developed and its results are validated against the base case of the experimental studies. Additionally, the numerical model is validated in a spatial-temporal sense with thermocouple data from the experimental rig. The numerical model is also applied to a helical SCHE situated within a backfilled stope for the first time. The results of the numerical model suggest that the pumping rate through the SCHE has a significant effect on the heat exchange rate and the overall energy transfer between the SCHE and the backfill. Additionally, the temperature contours from the numerical model suggest that a decreased pitch/helical diameter will increase the storage capacity of the helical SCHE. Overall, an average of 2.5 MW can be stored over the first 4 days of geothermal charging with the investigated full-scale SCHE, boasting a pseudo-steady-state storage rate of 1.7 MW.

On the Validity of Scaling Transient Conjugate Heat Transfer Characteristics

Abstract Accurate prediction of unsteady thermal loads is of paramount importance in several engineering disciplines and applications. Performing time-accurate unsteady conjugate heat transfer (CHT) simulations presents considerable challenges due to the markedly different time scales between the solid and fluid domains. Two methods have been recently proposed, aimed at addressing this issue: multiscale modeling (MSM) and equalized time-scales (ET). The former is based on the separation of the disparate short and long temporal scales of the solution and subsequent averaging of the flow/energy equations. In the latter, the equalization of the time scales is achieved through manipulation of the solid's thermal properties. Both methods are very appealing due to the possibility of being easily implemented on an existing solver. It becomes, thus, relevant to assess their performance and/or limitations. This paper work presents a comparative study of the two methods for the prediction of transient thermal load, first using a simplified case of a solid body with uniform temperature, then through the investigation of the prewarming phase of a steam turbine. Both methods are then compared against a reference baseline fully coupled (FC) CHT solution. The results show how the MSM allows greater accuracy and robustness with considerable saving in computational cost with respect to the baseline solution.