Unsteady Conjugate Research Articles

Unsteady conjugate heat transfer simulation around the throat insert in a high enthalpy shock tunnel

High enthalpy shock tunnel is a critical ground testing facility for evaluating the aerodynamic performance of hypersonic vehicles by simulating high-enthalpy, hypersonic flows. However, as the total temperature or pressure of the stagnant gas rises, the throat insert may be subjected to melting or oxidation, leading to a degradation in flow quality or a reduction in effective test time. This study investigates the unsteady heat transfer between the gas flow and the throat insert using a conjugate heat transfer model. The effects of test time, total temperature, and total pressure on the throat temperature are presented. An increase in any of these factors will raise the throat temperature. Moreover, oxidation will cause the copper throat insert to melt more quickly under the same conditions, which should be considered when addressing throat melting issues.

Numerical Analysis of an Efficient Time Integration Scheme for Unsteady Conjugate Heat Transfer

Numerical Analysis of an Efficient Time Integration Scheme for Unsteady Conjugate Heat Transfer

Unsteady conjugate heat transfer simulation of wall heat loads for rotating detonation combustor

Rotating detonation engines (RDEs) are the most promising pressure-gain combustion devices, but their long-duration operations are hindered by the harsh thermal environment inside the chamber. This study analyzes the instantaneous and average heat loads on chamber walls of RDEs based on the newly developed unsteady conjugate heat transfer (CHT) OpenFOAM solver named multiRegionBYRFoam. To enhance accuracy in predicting heat transfer characteristics compared to decoupled simulations focusing solely on fluid or solid behavior, three-dimensional CHT simulations are conducted for a premixed H2/air annular RDE coupling the detonation simulation with heat conduction in both inner and outer chamber walls. The transient time evolutions of wall heat flux in RDEs are numerically captured for the first time and agree well with experiments. The calculated peak wall heat flux is 1.98 MW/m2 at the inner wall and 2.63 MW/m2 at the outer wall when a single detonation wave propagates with a mass flow rate of 0.227 kg/s. By investigating the influence of inlet flow conditions and detonation modes, valuable guidelines on designing efficient thermal management systems for RDEs are obtained: larger mass flow rates and multi-wave modes result in higher average wall heat flux; the heat flux at the outer wall exceeds that at the inner wall while both walls require effective cooling for gas turbine engines with a rotating detonation combustor. Furthermore, a novel heat transfer model for RDEs is proposed based on a thermal operation map depicting total heat transfer rates to describe the nonlinear impact of mass flow rate and number of detonation waves, which can be employed to predict total wall heat loads under specific operation conditions of RDE.

Conjugate Heat Transfer Evaluation of Turbine Blade Leading-Edge Swirl and Jet Impingement Cooling With Particulate Deposition

Abstract Internal cooling structures for gas turbine engines are becoming more complicated to push the hot gas temperature as high as possible, which, however, allows particulates drawn into the coolant air to be more readily to deposit within these passages and thus greatly affect their flow loss and thermal performance. In this study, internal swirl cooling and jet impingement cooling subjected to particulate deposition were evaluated and compared using a conjugate heat transfer method, with an emphasis on the thermal effects of the insulative deposits. To accomplish the goal, an unsteady conjugate mesh morphing simulation framework was developed and validated, which involved particle tracking in an unsteady fluid flow, particle–wall interaction modeling, conjugate mesh morphing of both fluid and solid domains, and a deposit identification method. The swirl and the jet impingement cooling configurations modeled the internal cooling passage for the leading-edge region of a turbine blade and were investigated in a dust-laden coolant environment at real engine conditions. Coupling effects between the dynamic deposition process and the unsteady flow inside the two cooling channels were examined and the insulative effects of the deposits were quantified by comparing the temperatures on the external and internal surfaces of the metal channel walls, as well as on the deposit layers. Results demonstrated the ability of the newly developed, unsteady conjugate simulation framework to identify the deposits from the original bare wall surface and to predict the insulation effects of the deposits in the dynamic deposition process. The dust almost covered the entire impingement channel, while deposits were only seen in the vicinity of the jets in the swirl channel. Despite this, a dramatical decrease of convection heat transfer was found in the swirl channel because the swirling flow was sensitive to the interruption of the deposits. In contrast, the deposits improved the heat transfer rate in the impingement channel. When the thermal effects of the deposit layer were taken into account, the wall temperatures of both two cooling geometries were substantially elevated, exceeding the allowable temperature of the metal material. Due to the denser deposit coverage, the impingement channel wall had a greater temperature increase than the swirl channel. In terms of flow loss, the presence of the deposits inhibited the swirl intensity by interrupting the swirling flow and thus reduced the friction loss, whereas the pressure loss was improved by the deposits in the impingement cooling.

Investigation of unsteady conjugate heat transfer for a radial turbine with impingement cooling

For radial flow turbines, raising the temperature before the volute is also an important means of improving their thermal efficiency. As with axial flow turbines, excessive thermal load requires the application of cooling technology. In the study, impingement cooling technology was applied to a radial turbine, and the cooling effect of the turbine was investigated using conjugated heat transfer (CHT) simulations and experiments. The results showed that some of the coolant moved down into the back-disc heat shield cavity and impinged onto the back-disc. Most of the coolant eventually flowed into the rotor flow passage and stayed close to the blade suction side. The blade leading-edge shroud was the worst cooled area, but some temperature reduction was achieved. An experimental investigation was conducted with a high-speed infrared camera at much-reduced turbine speeds of 5000 and 10,000 rpm. The experimental results confirmed the numerical findings, and it was also found that cooling becomes more effective with the increase of turbine speed and of coolant relative mass flow. A 30°C reduction of blade leading-edge temperature was achieved with 3% relative coolant mass flow at 10,000 rpm.

A multiscale framework for unsteady conjugate heat transfer with turbulence resolving methods — With application to rotating cavities

Carrying out unsteady conjugate heat transfer (CHT) with turbulence resolving methods is challenging due to the significant disparity in both time and length-scales that appear in the problem. The solid domain initial transient needs to be accelerated to a steady state, but time-accuracy for the solid domain temperatures fluctuations must be maintained. Many current state-of-the-art methods aim to do this by accelerating the solid domain timescale until the simulation is temporally converged, before switching to a non-accelerated solid solution that is assumed to be correct. However, this paper demonstrates that these current time domain CHT methods still introduce a long-lasting error in the solid domain temperature.To meet this challenge, we present a new multiscale framework that enables the interaction of all timescales in the fluid and solid domains to be consistently captured, without corruption by mesh resolution effects or the solid initial transient. Monochromatic low frequency temperature fluctuations from large coherent structures in the fluid domain are coupled to a time-spectral solid domain solution with a harmonic balance interface condition. Broadband higher frequency temperature fluctuations from turbulence are captured locally on the wall using a wall transfer function approach, reformulated using recursive convolution to simplify its application.The framework is applied to the simulation of rotating cavities with various disk materials and heating configurations. Various aspects of the framework and unsteady conjugate heat transfer in general are illustrated — in particular that starting from a roughly correct time-average solution can still lead to a large initial transient once an unsteady wall temperature is introduced. Comparison of the simulations yields new insight into the effect that different industrially relevant choices for the cavity material can have, even at the same non-dimensional operating conditions.

A time adaptive multirate Dirichlet–Neumann waveform relaxation method for heterogeneous coupled heat equations

AbstractWe consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time‐adaptive Dirichlet‐Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler time integration, we analytically determine optimal relaxation parameters for the fully discrete scheme.We test the robustness of the relaxation parameters on the second order multirate method in 2D. DNWR is shown to be very robust and consistently yielding fast convergence rates, whereas the closely related Neumann‐Neumann Waveform relaxtion (NNWR) method is slower or even diverges.The waveform approach naturally allows for different timesteps in the subproblems. In a performance comparison for DNWR, the time‐adaptive method dominates the multirate method due to automatically finding suitable stepsize ratios. Overall, we obtain a fast, robust, multirate and time adaptive partitioned solver for unsteady conjugate heat transfer.

Effects of Reynolds number on thermal wake in conjugate heat transfer between a sphere and its surrounding fluid

Unsteady conjugate heat transfer between an aluminum sphere and its surrounding water was investigated. The mass, momentum and energy equations were solved, and for Reynolds number greater than 400, the large eddy simulation with the Smagorinsky–Lilly model was used. 3D transient simulations were carried out for the sphere Reynolds numbers ranging from 1 to 10,000 (6.99 ≤Pe ≤ 69,900). This study particularly focuses on the effect of Reynolds numbers on the thermal wake phenomenon. The simulation results showed that under the condition of the conductivity ratio of 337.33 and the heat capacity ratio of 0.567, thermal wake exists when 1≤ Re <8000 (6.99 ≤ Pe < 55,920). The Reynolds number of 8000 (Pe = 55,920) was determined as the turning point that thermal wake disappears. Two modes of reverse heat transfer, laminar and vortical were identified. For laminar thermal wake, the thermal inversion point starts from the rear stagnation, while for vortical thermal wake, it occurs near the separation point.

О прямом методе решения задачи сопряженного теплообмена газовой смеси и твердого тела

A novel methodology of numerical solving is developed for applications of unsteady conjugate heat transfer. It is based on a parallel integration strategy of governing equations in fluid and solid domains. The 3D numerical model takes into account an unsteady thermal interaction of viscous multicomponent flow and a solid body. The fluid dynamic model is based on an extended system of the compressible Navier–Stokes equations with the multicomponent diffusion. In a solid, the unsteady heat conduction equation is stated. In a fluid–solid system the heat transfer is fully coupled. Normal heat flux and temperature are continuous across an interface. The method is based on direct coupling heat transfer due to the time integration of the heat equation in fluid and in solid with an automatic approximation of the interfacial condition. This approach is especially effective for unsteady computations, since it does not require the use of an iterative method at each time step. The proposed method is generalized for multiblock conformal unstructured grids. This approach is especially effective for non-stationary calculations, since it does not require the use of an iterative method at each time step. The results of comparison with a model problem analytical solution confirm an efficiency of the proposed method.

Unsteady conjugate heat transfer characteristics in hexagonal cavity equipped with a multi-blade dynamic modulator

PurposeThe transient analysis of the thermal response and frictional loss characteristics for flow-modulated conjugate heat transfer phenomena has been investigated in the present study. The flow domain is a partitioned cavity of a hexagonal structure equipped with a multi-blade flow modulator. The clockwise rotating blade is adiabatic and stirrers the internal flow along with the natural convection caused by the bottom heated floor of uniform heat flux. The conjugate behavior is introduced through the solid subdomains consisting of two brick-made partitions and one glass partition of uniform thickness. The material of the partition wall reflects the physical aspects of industrial applications. ApproachThe two-dimensional unsteady continuity, momentum, and energy equations are expressed in a non-dimensional form where the buoyant force is modeled through the Boussinesq approximation. The Arbitrary Lagrangian Euler (ALE) finite element is adopted to solve the moving mesh problem by formulating a free triangular discretization scheme. Parametric computational investigations are carried out for air as the working fluid (Pr = 0.71) and 3 different configurations of the rotating modulator while varying the other parameters, i.e., Reynolds number (Re) and Rayleigh number (Ra) for a fixed Biot number (Bi = 104). This dynamic mesh problem encompasses a wide range of parameters, i.e., (100 ≤Re≤ 103), and (104≤Ra≤ 106) for Bi = 104 to evaluate the thermodynamic response of the present thermo-fluid system. Various thermo-fluid system responses are visualized through the spatially average Nusselt number evaluated on the heated surface, system effectiveness, average thermal storage capacity, and frictional power loss of the flow domain. The thermal response is fragmented into individual responses in terms of component signal frequency by the Fast Fourier Transform (FFT) analysis. FindingsAccording to the current analysis, increasing the number of blades increases the rate of heat transfer by a negligible amount. On the other hand, among three different types of modulators, the three-blade modulator shows the lowest power loss coefficient and the lowest power instability. Thus, a three-blade modulator qualifies as the optimum design to impart external motion to the working fluid to introduce forced convection. LimitationsThis research has some scope for improvement. Future studies can be conducted on the improvement of blade designs, thickness, and size of the blades. Practical ImplicationsThe present study can shed light on the modeling of a better storage system where heat transfer and moisture control are integrated for the proper functioning of the storage, such as food storage, cold storage, garment inventory, etc. OriginalityThis study is original, and no previous research has been conducted considering the hexagonal domain and variation of the number of blades. ConclusionThe present study reveals that a modulator best serves its purpose at low Rayleigh and high Reynolds numbers. Moreover, the three-blade modulator has the lowest power loss coefficient and lowest power instability, making it the most suitable modulator to impart external excitation to the working fluid.

Heat exchange structure design and overall performance analysis of double-concentrator solar thermal thruster

In this paper, the platelet heat exchanger in the thermal propulsion system of micro satellite with liquefied gas as propellant was designed, the complete gasification and stabilization scheme of propellant was proposed. The unsteady conjugate heat transfer (CHT) characteristics between the heat exchanger and gaseous propellant were analyzed, and the cumulative data of error estimation in the numerical simulation process was provided to ensure the credibility of the results. The CHT computational fluid dynamics (CFD) simulation of the platelet 3D model under steady-state conditions was carried out to find the empirical correlation between the average Nusselt number and the average Reynolds number. A simplified unsteady 1D model of heat exchanger was established by using the loose coupling method based on quasi steady flow field. The results show that the platelet structure could heat the working medium to more than 2379 K with the heat transfer efficiency of 86%, the outlet temperature and heat transfer efficiency of the heat exchanger were maintained at 1871 K and 69% in steady state when the mass flow rate was 1.14e-6 kg/s. The 1D model could accurately reflect the real heat transfer situation to a certain extent, the simulation error was less than 8.5% compared with the 3D model, and the calculation time was greatly shortened, making the adjustment of heat transfer strategy more convenient. Intermittent heat transfer method could keep the outlet gas temperature, thrust and specific impulse of the thruster at a high level to improve the performance of the system. Taking the nanosatellite with a total mass of 7.55 kg and a propellant mass of 0.25 kg as an example, when the duration of valve open time was 1.5s, the velocity increment of the satellite reached 72.21 m/s with the specific impulse of over 2400 m/s, which was twice than that of nanosatellites without heat exchange structure.

Unsteady conjugate model of fluid mechanics and mass transfer for butanol pervaporation process by non-porous membrane

A diffusion-convective mass transfer mathematical conjugated model of butanol recovery from a re-circulating aqueous solution by pervaporation using a polydimethylsiloxane (PDMS) membrane was developed based on computational fluid dynamics. Discretized continuity, linear momentum, and convective-diffusion mass transfer equations were solved by an in-house code based on the finite volume method for a laminar flow with a flat attached non-porous membrane. In addition, a novel numerical procedure to determine the butanol diffusivity in the PDMS membrane was developed based on the solution of the conjugate unsteady convection-diffusion model that included five coupled partial differential equations. The evolution of the distribution of the velocity profile in the fluid flow and the transient variation of butanol concentration in the feed solution and inside the PDMS membrane were determined. Variations in time and space of the dimensionless mass flux along the length of the pervaporation module were calculated from the conjugate convection-diffusion mass transfer model. The numerical predictions of the butanol mass flux in the feed solution exhibited good agreement with the experimental results with an error smaller than 3%. Understanding the mechanisms of mass and fluid transport phenomena by computational modeling can be helpful for improving the design of pervaporation processes.

Unsteady conjugate heat transfer with combined effects of MHD and moving conductive elliptic object in CNT-water nanofluid with ventilation ports

PurposeThe purpose of this paper is to analyze the unsteady conjugate mixed convective heat transfer characteristics in a vented porous cavity under the combined effects of moving conductive elliptic object and magnetic field.Design/methodology/approachThe finite element method and arbitrary Lagrangian-Eulerian (ALE), impacts of Reynolds number, Hartmann number, aspect ratio of the conductive ellipse and moving speed of the object on the hydro-thermal performance are analyzed.FindingsIt was observed that the dynamic characteristics of the local and average Nu number of each hot wall are different. Magnetic field strength increment resulted in the enhancement of average Nu number for bot steady and transient case while the optimum case for best hydro-thermal performance is achieved for highest Ha number and non-dimensional time of 10. Higher value of average Nu and lower pressure coefficient are achieved for aspect ratio of 4 and non-dimensional time of 10. When the moving velocity of the conductive ellipse is considered, 42% enhancement in the average Nu is obtained at non-dimensional time of 20 and object velocity equals to 0.012 times entering fluid velocity in the negative y direction while the pressure coefficient is higher. The moving object is used as a useful tool to control the dynamic features of heat transfer in a vented cavity.Originality/valueThe present method of convective heat transfer control inside a vented cavity with a moving elliptic object is novel and can be used as an effective tool with magnetic field effects owing to diverse use of convection in cavities with vented ports in many practical thermal engineering systems.

Improved water freezing with baffles attached to a freezing tunnel: Mathematical modeling and numerical simulation by a conjugate finite volume model

• Addition of baffles to tunnel walls originated major improvements in water freezing. • A CFD conjugate model describes convective processes in a refrigeration tunnel. • Control of vortex shedding behind foods is a key issue in enhanced cooling process. • Water freezing front and Nusselt number validated with experimental results. Unsteady conjugate mathematical model for natural heat convection with change phase of pure water inside of a square container caused by external mixed heat convection of cool air and the effect of baffles attached to a freezing tunnel has been studied numerically. The coupled equations were solved by Finite Volume method with the SIMPLE algorithm. Effect of the baffles on freezing time, evolution of local dimensionless heat flux and surface temperature distribution at the container with water were studied. The results showed that the hydrodynamic and thermal boundary layer were reduced due to the baffles, this effect reduced the freezing time and homogenized the superficial temperature of the container. Additionally, the effect of the length of baffles on the heat flux and vortex shedding frequency behind the water container were assessed.

Thermo-Structural Analysis of Steam Turbine Startup With and Without Integrated Prewarming System Using Hot Air

Abstract Motivated by the urgent need for flexibility and startup capability improvements of conventional power plants in addition to extending their life cycle, General Electric provides its customers with a product to prewarm steam turbines using hot air. In this paper, the transient thermal and structural analyses of a 19-stage intermediate pressure (IP) steam turbine in various startup operating modes are discussed in detail. The presented research is based on previous investigations and utilizes a hybrid finite element method (HFEM—numerical FEM and analytical) approach to efficiently determine the time-dependent temperature distribution in the components of the steam turbine. The simulation strategy of the HFEM model applies various analytical correlations to describe heat transfer in the turbine channel. These are developed by means of extensive unsteady multistage conjugate heat transfer (CHT) simulations for both startup turbine operation with steam and prewarming operation with hot air. Moreover, the complex numerical setup of the HFEM model also considers the thermal contact resistance (TCR) on the surfaces between vane and casing as well as blades and rotor. Prior to the analysis of other turbine startup operating modes, the typical startup turbine process is calculated and validated against an experimental data as a benchmark for subsequent analysis. In addition to heat transfer correlations, the simulation of a turbine startup from cold state uses an innovative analytic pressure model to allow for a consideration of condensation effects during first phase of startup procedure. Finally, the presented thermal investigation focuses on the comparison of transient temperature fields in the turbine for different startup scenarios after prewarming with hot air and provides the subsequent structural investigation with required boundary conditions. As a result, the values of the highest stress are numerically determined and compared to the values obtained by means of cold startup simulation. The final evaluation clearly displays the technical potential and the benefits of the prewarming concept.

The Brick Thermal Performance Improvement using Phase Change Materials

The problems of heat and mass transfer in phase change materials are of great engineering interest. The absorption and storage of energy in the form of latent heat makes it possible to use them in the construction industry to smooth out the effects of temperature transitions in the environment. This work is devoted to the study of heat transfer in a building block with paraffin inserts under unsteady external conditions. The influence of the geometric dimensions of the block and the volume fraction of the phase change material on the effect of restraining external temperature fluctuations was studied. The unsteady conjugate melting problem was solved in a closed rectangular region with two cavities filled with PCM. The temperature of the environment on the left boundary changes in harmonic law. Thermal distributions were obtained at various points in time.

Unsteady conjugate convective heat transfer in a vertical channel at a sudden heating of the bottom

The processes of unsteady heat transfer in the mode of thermogravitational convection in a vertical channel with solid walls of finite thermal conductivity after a sudden heating from bottom was studied numerically by the finite element method in three-dimensional problem statement. The system of thermogravitational convection equations was solved in the Boussinesq approximation in the variables of vortex–vector potential of the velocity field and temperature. The calculations were performed with the Prandtl number of 10, the Grashof number of 5000, and the ratio of the thermal conductivity of solid walls to the thermal conductivity of the liquid equal to 6.29. Distributions of the unsteady temperature field into the liquid and solid walls, temperature gradient fields, and velocity fields in the liquid were obtained. The process of formation, loss of axial symmetry and subsequent development of the rising stream was shown.

Concurrent shape and topology optimization for unsteady conjugate heat transfer

Concurrent shape and topology optimization for unsteady conjugate heat transfer

Effect of the time-dependent volumetric heat flux on heat transfer performance inside a heat sink based on the phase change materials

The issue of thermal control plays an important role in the development of technical systems of computing and radio equipment. Temperature conditions are an important factor in the performance and durability of devices. New models of heat sink containing materials with phase transitions “solid body–liquid” are appeared. In the present paper, the numerical study of natural convection melting/solidification of phase change material inside a finned heat sink with a local heater having time-dependent volumetric heat flux has been carried out. An unsteady conjugate phase change problem has been solved taking into account natural convection in the melt, in the presence of a heat-dissipating copper profile. The energy equation has been formulated using a special smoothing function of temperature. The equations of hydrodynamics have been formulated using non-primitive variables, namely the stream function and vorticity. The system of transient differential equations of natural convection, taking into account the melting process and the heat-generating and heat-conducting element, has been solved using the finite-difference method. Analysis has been performed for different values of the volumetric heat generation within the heater and the periodic volumetric heat generation frequency. Obtained results have shown that a rise of the volumetric heat generation frequency leads to an increase in the amplitude of the average temperature within the heater that can have a negative effect on the system operation.

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.