Conjugate Heat Transfer Analysis of an Ultrasonic Molten Metal Treatment System

In piezoceramic ultrasonic devices,the piezoceramic stacks may fail permanently or function improperly if their working temperatures overstep the Curie temperature of the piezoceramic material.While the end of the horn usually serves near the melting point of the molten metal and is enclosed in an airtight chamber,so that it is difficult to experimentally measure the temperature of the transducer and its variation with time,which bring heavy difficulty to the design of the ultrasonic molten metal treatment system.To find a way out,conjugate heat transfer analysis of an ultrasonic molten metal treatment system is performed with coupled fluid and heat transfer finite element method.In modeling of the system,the RNG model and the SIMPLE algorithm are adopted for turbulence and nonlinear coupling between the momentum equation and the energy equation.Forced air cooling as well as natural air cooling is analyzed to compare the difference of temperature evolution.Numerical results show that,after about 350 s of working time,temperatures in the surface of the ceramic stacks in forced air cooling drop about 7 K compared with that in natural cooling.At 240 s,The molten metal surface emits heat radiation with a maximum rate of about 19 036 W/m2,while the heat insulation disc absorbs heat radiation at a maximum rate of about 7922 W/m2,which indicates the effectiveness of heat insulation of the asbestos pad.Transient heat transfer film coefficient and its distribution,which are difficult to be measured experimentally are also obtained through numerical simulation.At 240 s,the heat transfer film coefficient in the surface of the transducer ranges from–17.86 to 20.17 W/（m2？K）.Compared with the trial and error method based on the test,the proposed research provides a more effective way in the design and analysis of the temperature control of the molten metal treatment system.

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.

Investigation of convection cooling guide vane with conjugate heat transfer method

This paper studied a certain blade with ten radial cooling holes which employed conjugate heat transfer method. The cooling air entered the cooling channel from the bottom of the blade and went out from the top, it was not ejected into the main flow. This paper used different numerical conditions including different turbulence models,turbulence intensities,thermal conduction coefficients and the influence on fluid property via temperature variation. The temperature distribution and pressure distribution of the blade were compared with experimental data. The results show that the numerical results using different turbulence models are almost identical to experimental data even little deviation occurs at shock wave location. The trends of temperature distribution under different numerical conditions are coincident to experimental data,especially Reynolds stress turbulence model. It can be concluded that anisotropic turbulence models can simulate the transition from laminar to turbulence,and the influence of turbulence intensity on laminar region and transition region is more than that on developed turbulent region.

A new algorithm of global tightly-coupled transient heat transfer based on quasi-steady flow to the conjugate heat transfer problem

Concerning the specific demand on solving the long-term conjugate heat transfer （CHT） problem, a new algorithm of the global tightly-coupled transient heat transfer based on the quasi-steady flow field is further put forward. Compared to the traditional loosely-coupled algorithm, the computational efficiency is further improved with the greatly reduced update frequency of the flow field, and moreover the update step of the flow field can be reasonably determined by using the engineering empirical formula of the Nusselt number based on the changes of the inlet and outlet boundary conditions. Taking a duct heated by inner forced air flow heating process as an example, the comparing results to the tightly-coupled transient calculation by Fluent software shows that the new algorithm can significantly improve the computational efficiency with a reasonable accuracy on the transient temperature distribution, such as the computing time is reduced to 22,8% and 40% while the duct wall temperature deviation are 7% and 5% respectively using two flow update time step of 100 s and 50 s on the variable inlet-flow rate conditions.

Numerical Study of Conjugate Heat Transfer for Cooling the Circuit Board

In this paper, a 3D model of a flat circuit board with a heat generating electronic chip mounted on it has been studied numerically. The conjugate heat transfer including the conduction in the chip and convection with the surrounding fluid has been investigated numerically. Computational fluid dynamics using the finite volume method has been used for modeling the conjugate heat transfer through the chip and the circuit board. Conjugate heat transfer has broad applications in engineering and industrial applications in design of cooling off electronic components. Effects of various inlet velocities have been studied on the heat transfer variation and temperature of the circuit board. Numerical results show that the temperature of the chip reduces as the velocity of the inlet fluid flow increases.

A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions

In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.

Lattice Boltzmann simulation of the effects of cavity structures and heater thermal conductivity on nucleate boiling heat transfer

The boiling heat transfer technology with cavity surfaces can provide higher heat flux under lower wall superheat,which is of great significance for the cooling of electronic chips and microelectromechanical devices.In this paper,the boiling characteristics of the cavity surfaces are investigated based on the lattice Boltzmann(LB)method,focusing on the effects of cavity shapes,sizes,and heater thermal conductivity on the heat transfer performance.The results show that the triangular cavity has the best boiling performance since it has less residual vapor and higher bubble departure frequency than those of the trapezoidal and rectangular cavities.As the cavity size increases,the enhancement of heat transfer by the cavity mouth is suppressed by the heat accumulation effect at the heater bottom.The liquid rewetting process during bubble departure is the reason for the fluctuation of the space-averaged heat flux,and the heater thermal conductivity determines the fluctuation amplitude.The evaporation of liquid in the cavity with high thermal conductivity walls is more intense,resulting in shorter waiting time and higher bubble departure frequency.

Investigation of the Conjugate Heat Transfer and Flow Field for a Flat Plate with Combined Film and Impingement Cooling

Film cooling combined with internal impingement cooling is one of the most effective technologies to protect the gas turbine vanes and blades from the hot gas. In this study, conjugate heat transfer CFD study was undertaken for a flat plate with combined film cooling and impingement cooling. An experiment on conjugate heat transfer of a flat plate with combined film and impingement cooling was performed to validate the code. Then the effects of several parameters including Biot number, blowing ratio, film hole shape and impingement hole diameter on the overall cooling effectiveness were numerically studied. The results show that for a specific combined cooling scheme and a given blowing ratio, the coolant potential can be reasonably allocated to the internal and the external cooling to achieve the overall cooling effectiveness. As the blowing ratio increases, the overall cooling effectiveness trends to reach a maximum value. For different film hole geometrical, the maximum values of the overall cooling effectiveness at high blowing ratio approximate to the same value. At a given mass flow rate of coolant, the increase of the impingement hole diameter leads to the reduction of the overall cooling effectiveness.

Conjugate heat transfer investigation of cooled turbine using the preconditioned density-based algorithm

The preconditioned density-based conjugate heat transfer(CHT)algorithm was used to investigate the heat transfer characteristics of a cooled turbine vane.Fluid domain provided boundary heat flux for solid domain and obtained boundary temperature from it for the coupling strategy.The governing equations were solved by the preconditioned density-based finite-volume method,with preconditioning matrix,improved Abu-Gharmam Shaw(AGS)transition model,matrix dissipation scheme and four kinds of turbulence models.The grid system is multi-block structured grids for fluid domain and unstructured grids for solid domain,with full-matched grids at the fluid-solid interfaces.The effects of turbulence model,outlet Mach number,outlet Reynolds number,inlet turbulence intensity and the temperature ratio of blade surface/gas on the local heat transfer performance were studied.Results indicate that the k-o shear-stress transport(SST)and AGS model can predict the conjugate heat transfer better than others.The Mach number and Reynolds number have relatively obvious influences on the heat transfer,while the turbulence intensity and temperature ratio only have slight influences.Comparisons with experimental data demonstrate the applicability and accuracy of the numerical algorithm.

Conjugate heat transfer investigations of turbine vane based on transition models

The accurate simulation of boundary layer transition process plays a very important role in the prediction of turbine blade temperature field. Based on the Abu-Ghannam and Shaw （AGS） and c-Re h transition models, a 3D conjugate heat transfer solver is developed, where the fluid domain is discretized by multi-block structured grids, and the solid domain is discretized by unstructured grids. At the unmatched fluid/solid interface, the shape function interpolation method is adopted to ensure the conservation of the interfacial heat flux. Then the shear stress transport （SST） model, SST ＆ AGS model and SST ＆ c-Re h model are used to investigate the flow and heat transfer characteristics of Mark II turbine vane. The results indicate that compared with the full turbulence model （SST model）, the transition models could improve the prediction accuracy of temperature and heat transfer coefficient at the laminar zone near the blade leading edge. Compared with the AGS transition model, the c-Re h model could predict the transition onset location induced by shock/boundary layer interaction more accurately, and the prediction accuracy of temperature field could be greatly improved.

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.

Unified Solution of Conjugate Fluid and Solid Heat Transfer-Part I.Solid Heat Conduction

A unified solution framework is proposed for efficiently solving conjugate fluid and solid heat transfer problems.The unified solution is solely governed by the compressible Navier-Stokes(N-S)equations in both fluid and solid domains.Such method not only provides the computational capability for solid heat transfer simulations with existing successful N-S flow solvers,but also can relax time-stepping restrictions often imposed by the interface conditions for conjugate fluid and solid heat transfer.This paper serves as Part I of the proposed unified solution framework and addresses the handling of solid heat conduction with the nondimensional N-S equations.Specially,a parallel,adaptive high-order discontinuous Galerkin unified solver has been developed and applied to solve solid heat transfer problems under various boundary conditions.

Numerical Investigation of Flow and Heat Transfer in Vane Impingement/Effusion Cooling with Various Rib/Dimple Structure

By investigating heat transfer and flow structures of dimples,orthogonal ribs,and V-shaped ribs in the impingement/effusion cooling,the article is dedicated to selecting a best-performing internal cooling structure for a turbine vane.The overall cooling effectiveness and coolant consumption are adopted to evaluate the cooling performance.To analyze the influence of structural modification,the flow field is investigated on chordwise/spanwise sections and the target surface.The blockage effect on crossflow can protect jet flow,resulting in higher heat transfer performance of the target surface.Ribs own a stronger blockage effect than dimples.Compared with the blockage effect,the influence of the rib shape is negligible.By installing dimples between ribs,heat transfer is augmented further.The introduction of ribs/dimples leads to higher discharge coefficients of jet nozzles but lower discharge coefficients of film holes.Thus,the film cooling deteriorates.Meanwhile,the installation of the ribs and dimples decreases total coolant consumption.The effect of ribs/dimples on heat transfer and effusion condition of internal and external cooling is analyzed.The best-performing cooling structure is the target surface with dimples and orthogonal ribs,which decreases the wall temperature and coolant consumption by 14.57-28.03 K and 1.19%-1.81%respectively.This article concludes the flow mechanism for dimples and influence factors on the cooling performance,which may serve as guidance for the turbine vane design.

Evaluation and development of a predictive model for conjugate phase change heat transfer of energy storage system partially filled with porous media

The present study proposes a predictive model to explore the effect of partially filled porous media on the con-jugate heat transfer characteristic of phase change material(PCM)with interfacial coupling conditions between pure fluid region and porous region.The enthalpy-porosity method,local thermal non-equilibrium model and Darcy-Forchheimer law are comprehensively considered to describe the convective heat transfer process in porous media.The modified model is then validated by benchmark data provided by particle image velocimetry(PIV)ex-periments.The phase change behavior,heat transfer efficiency and energy storage performance are numerically investigated for different partial porous filling strategies in terms of filling content,position,height of porous foam and inclination angles of cavity.The results indicate that due to the resistance in porous region,the shear stress exerted by the main vortex(natural convection)in pure fluid region and the momentum transferred,a secondary vortex phenomenon appears in the porous region near the fluid/porous interface.Moreover,such dis-continuity of permeability and fluid-to-porous thermal conductivity results in the cusp of phase change interface at the horizontal fluid/porous boundary.Among four partial porous filling cases,the lower porous filling one has more desirable heat transfer performance,and the 3/4H lower porous filling configuration is the best solution for optimization of the latent heat thermal energy storage(LHTES)systems.For tilted cavity,the increase of inclination angle positively affects the heat transfer efficiency as well as the energy storage rate of the LHTES system,where the performance of 3/4H lower porous filling configuration is further highlighted.

Study on seepage and deformation characteristics of coal microstructure by 3D reconstruction of CT images at high temperatures

To study the seepage and deformation characteristics of coal at high temperatures,coal samples from six different regions were selected and subjected to computed tomography(CT)scanning studies.In conjunction with ANSYS software,3 D reconstruction of CT images was used for the establishment of fluidsolid conjugate heat transfer model and coal thermal deformation model based on the microstructures of coal.In addition,the structure of coal was studied in 2 D and 3 D perspectives,followed by the analysis of seepage and deformation characteristics of coal at high temperatures.The results of this study indicated that porosity positively correlated with the fractal dimension,and the connectivity and seepage performances were roughly identical from 2 D and 3 D perspectives.As the porosity increased,the fractal dimension of coal samples became larger and the pore-fracture structures became more complex.As a result,the permeability of coal samples decreased.In the meantime,fluid was fully heated,generating high-temperature water at outlet.However,when the porosity was low,the outlet temperature was very high.The average deformation of coal skeleton with different pore-fracture structures at high temperatures showed a trend of initial increase and subsequent decrease with the increase of porosity and fractal dimension.The maximum deformation of coal skeleton positively correlated with connectivity but negatively correlated with the fractal dimension.

Radiator Optimization Design for Planar Motors Based on Parametric Components

Focusing on the design problem of high-performance radiators for planar motors in the wafer stage of the lithography machine,a thermal-fluid coupling optimization scheme based on parametric solid components was proposed.The mapping method between component parameters and pseudo-density values was established.An analytical solution for the sensitivity of pseudo-density to component parameters was given.The conjugate heat transfer function with the shallow channel approximation term was solved through the pseudo-density information.In the optimization example,circular components were selected,and the position and the size of solid components were chosen as design variables.In order to eliminate calculation errors caused by pseudo-density,an optimized pseudo-density field was converted into the result based on parametric components.Compared to the reference motor radiator,the average surface temperature rise of the optimized water-cooling motor radiator is reduced by 22.4%,which verifies the feasibility and effectiveness of the proposed method.

Numerical simulation of HP rotor cooling configuration using parameterized method

This paper implemented cooling configuration design on certain gas turbine HP rotor using parameterized method.It is convenient for complicated gas turbine blade modeling using parameters and also benefit for the geometry modify in later period.Parameterized modeling is the foundation of air cooling turbine blade design method engineering application.Mesh quality can be awarded when generated complicated cooling configuration blade grids,and also the increase of calculation error can arise by many mesh blocks.Film cooling and serpentine passage can effectively enhance the cooling effectiveness and protect blade.

Comparative Study on Different Methods for Prediction of Thermal Insulation Performance of Thermal Barrier Coating Used on Turbine Blades

As turbine inlet temperature gets higher and higher,thermal barrier coating(TBC) is more and more widely used in turbine blades.For turbine blades with TBC,it is of great significance to evaluate the temperature distribution of its substrate metal quickly and accurately,especially during the design stage.With different degrees of simplification such as whether to consider the change of the geometric size of the fluid domain by TBC and whether to consider the planar heat conduction in TBC,three different methods used in conjugate heat transfer(CHT) simulation to model the TBC of the turbine blades have been developed and widely used by researchers.However,little research has been conducted to investigate the influence of the three methods on the temperature distribution of turbine blade.To fill this gap,three geometric models were designed.They are a solid conduction model with a substrate metal layer and a TBC layer,a transonic turbine vane with internal cooling and TBC,and a plate cylindrical film hole cooling model with TBC.Different methods were used in these geometric models and their differences were carefully analyzed and discussed.The result shows that for the conduction model used in this paper,with the same TBC surface temperature distribution,the difference between the three methods is very small and can be ignored.For a transonic turbine vane with internal cooling,regarding the local maximum temperature of the substrate-TBC interface,the largest difference between the method in which TBC is considered as a thermal resistance or a virtual layer of cells and the method in which three-dimensional heat conduction equation of TBC is solved occurs at the trailing edge.The difference near the leading edge is below 2K.When employed to the film cooling model,the difference of the laterally averaged temperature of the substrate-TBC interface can be 8 K which is mainly due to the change of the length to diameter ratio of the film cooling hole by TBC.If the substrate thickness is reduced by the thickness of TBC when three-dimensional heat conduction equation of TBC is solved,the temperature difference between the three methods will be quite limited.

Conjugate calculation of a film-cooled blade for improvement of the leading edge cooling configuration

Great efforts are still put into the design process of advanced film-cooling configurations.In particular,the vanes and blades of turbine front stages have to be cooled extensively for a safe operation.The conjugate calculation technique is used for the three dimensional thermal load prediction of a fim-cooled test blade of a modern gas turbine.Thus,it becomes possible to take into account the interaction of internal flows,external flow,and heat transfer without the prescription of heat transfer ooefficients.The focus of the investigation is laid on the leading edge part of the blade.The numerical model consists of all internal flow passages and cooling hole rows at the leading edge.Furthermore,the radial gap flow is also part of the model.The comparison with thermal pyrometer measurements shows that with respect to regions with high thermal load a qualitatively and quantitatively good agreement of the conjugate results and the measurements can be found.In particular,the region in the vicinity of the mid-span section is exposed to a higher thermal load,which requires further improvement of the cooling arrangement.Altogether the achieved results demonstrate that the conjugate calculation technique is applicable for reasonable prediction of three-dimensional thermal load of complex cooling configurations for blades.

Numerical Analysis of Microchannels Designed for Heat Sinks

Conjugate heat transfer is numerically investigated using a three-dimensional computational fluid dynamics approach in various microchannel geometries to identify a high-performance cooling method for piezoelectric ceramic stacks and spindle units in high-precision machines.Straight microchannels with rectangular cross sections are first considered,showing the performance limitations of decreasing the size of the microchannels,so other solutions are needed for high applied heat fluxes.Next,many microchannel designs,focusing on streamwise geometric variation,are compared to straight channels to assess their performances.Sinusoidally varying channels produce the highest heat transfer rates of those studied.Thus,their optimization is considered at a channel width and height of 35 and 100μm,respectively.Heat transfer increases as the amplitude and spatial frequencies of the channels increase due to increased interfacial surface area and enhanced Dean flow.The highest performance efficiencies are observed at intermediate levels of amplitude and frequency,with efficiency decreasing as these geometric parameters are increased further at the onset of flow separation.The sinusoidal channel geometries are then optimized with respect to minimizing the system’s pressure drop for all applied heat fluxes between 5690 and 6510 kW/m2.Doing so created an optimal geometry curve and showed that all geometries in this region had amplitudes close to 40μm.Therefore,imposing a fixed heat flux requirement for a case study of cooling piezoelectric ceramics,the optimized sinusoidal geometry decreases the system pressure drop by 79%relative to a straight channel while maintaining a larger minimum feature size.