Inverse Heat Conduction Analysis Research Articles

Study of the Effect of Initial Plate Temperature in Jet Impingement Cooling Process

The microstructure characteristics and the properties of rolled steels are significantly affected by the heat transfer and boiling phenomena occurring during the jet impingement cooling on run‐out tables (ROT). In this study, experiments are conducted using a full industrial‐scale ROT facility with rectangular plates made of low‐carbon stainless steel (type 316L). The plate is heated up to a temperature ranging from to , then rapidly impinged using a single circular water jet, and the temperature drop is captured using an infrared thermal camera (FLIR A615 25°–50 Hz type). The dissipated heat flux, estimated experimentally using a 2D inverse heat conduction analysis, ranges from 6.1 to 3.4 MW m−2 across different zones along the plate surface. The impact of different initial plate temperature on the boiling behavior is studied by developing a 2D‐computational fluid dynamics (CFD) model, and the results are closely aligned with the experimental findings. The results reveal that when estimating the heat flux from CFD simulations, the best accuracy is obtained when considering fluid temperature at a point close to the plate surface (about 1 μm above the surface). Furthermore, the maximum extracted heat flux (MHF) is significantly influenced by the initial temperature of the plate. Increasing the initial plate temperature from 500 to 900 °C led to an increase of 82% in the MHF in stagnation zone, and 137% increase in the parallel‐flow region. The CFD model presented in this study and the full calculation of the boiling curves numerically will pave the road for investigating various practical parameters in jet impingement cooling.

Effect of constraint removal on single-crystal blade dimensions during investment casting

Single-crystal turbine blades, manufactured via investment casting, are key components of high-performance aero engines and gas turbines. The final dimensions of the blades depend on the cumulative effect of heat shrinkage at different stages, including the superalloy, mold shell, and ceramic core, etc. To clarify the effect of these stages on the blade dimensions, we first use the heat transfer coefficient calculated from inverse heat-conduction analysis to simulate the directional solidification. By extracting and mapping the final physical field from the previous stage to the next stage, four successive constraint removal processes are performed at different time points. Subsequently, we establish a time-varying model for the entire process of directional solidification and constraint removal. The errors of the extraction/mapping are consistently less than 0.002 mm in all three directions, thus confirming the feasibility of data transfer. Secondly, we analyze the dimensional deviation patterns of the casting after sequentially removing the mold shell, process rib, grain selector, and ceramic core constraints, with emphasis on the dimensional accuracy of the airfoil while disregarding the dovetail generated from machining. The final average deviations of Section 1, Section 2, and Section 3 of the airfoil are 0.1896 mm, 0.1723 mm, and 0.1909 mm, and the maximum deviations occur consistently at the trailing edge near the tip. Finally, three section deviations are validated via measurements performed using a vacuum furnace and industrial computed tomography. The results show that the proposed method improves the dimensional accuracy of hollow turbine blades.

Experimental artefacts affecting characterization of the evolving interfacial heat transfer coefficient in hot stamping of Al-Si coated 22MnB5 steel

In automotive hot stamping, knowledge of the interfacial heat transfer coefficient (HTC) between the blank and die is crucial for predicting the mechanical properties of the formed part. The HTC is derived from the ratio of the instantaneous heat flux between the blank and the die, and the corresponding difference between the blank and die surface temperatures. In many cases the heat flux and die surface temperatures are inferred from time-resolved subsurface temperature measurements using an inverse heat conduction analysis, while the blank is often modelled as thermally-lumped. This study highlights how seemingly subtle aspects of this experiment, like the positioning and time-constant of the thermocouples, may impact the inferred HTC. Furthermore, nonuniformity of the interfacial pressure appears to lower the target pressure at which the HTC saturates, and diminish the time-averaged HTC with increasing target pressures.

Two Coupled Analysis Strategies for Melt-Ablation Modeling of Thermal Protection Material in Supersonic Gas-Particle Two-Phase Impingement Flow

In this study, two analysis strategies were used to investigate the melt-ablation process of the copper specimen plate in the scaled ducted launcher. The reliability of the simulation results of the two analysis strategies was confirmed by comparing the two-way fluid-thermal-ablation coupled analysis (two-way FTA-CA) strategy with two-way fluid-thermal-ablation loosely coupled analysis (two-way FTA-LCA) strategy. Then, the accuracy of the FTA-LCA strategy was validated by comparing the simulation results of the FTA-LCA strategy and experimental results from the experimental scale test. Finally, the FTA-LCA strategy used in this study can not only estimate the impingement surface heat flux into the copper plate when the inverse heat conduction analysis (IHCA) is not possible, but also provide the analysis solution accuracy and the considerable gain in computational efficiency for predicting the long-duration ablation problem in supersonic gas-particle two-phase exhaust plume impingement flow.

Analysis of the local heat transfer of quenching of moving metal sheets made of different materials using flat spray nozzles

Experimental investigations have been performed for the cooling of hot moving metal sheets of thickness 2 mm and 5 mm with the initial temperature of 500 °C to 800 °C by two flat spray nozzles. Tap water at room temperature is used as a coolant. Experiments are carried out for nickel, nicrofer, and aluminum alloy AA6082 with varying sheet velocity( 5,10,15 mm/s) and nozzle inclination angle (45°,65°,90°). The temperature distribution on the backside of the sheet during the cooling is recorded with a high-speed infrared camera. The recorded thermal data are used in the inverse heat conduction analysis to estimate the local heat fluxes and temperatures on the quenched surface. The thermal images obtained are used to analyze the length of the pre-cooling, transition boiling, and nucleate boiling. The maximum heat flux, the DNB temperature, and the rewetting temperature are presented for researched parameters. The nozzle inclination angle has a weak influence. The higher the velocity and the thickness of the sheet are, the higher the maximum heat flux and the shorter the pre-cooling region. The reason is that the position of the max. heat flux is shifted downstream near to impingement region.

DAMAGE EVALUATION METHOD OF STEEL DAMPERS SUBJECTED TO SEISMIC RESPONSE BEHAVIOR BY USING MICROCOMPUTER

After the severe seismic disaster, to investigate the damage states of buildings, the experts go to the disaster area, however, they encounter some difficulties. To solve the above problems, this study suggests a damage evaluation system for steel structures, which adopts the concept of Internet of Things (IoT). This system makes it possible for us to hold on damage of a building without going there after an earthquake. It has been recognized that the temperature change occurs on steel materials during inelastic behavior. In other study, the effectiveness of the damage evaluation method was confirmed by using the heat generation of steel at unsteady plastic amplitude. Here, the experimental study and discuss is performed to investigate the effectivity of evaluation method with the history of voltage by thermoelectric devices measured by a microcomputer when subjected to seismic response behavior. The cumulative plastic strain can be estimated from the relationship between temperature and strain of steel using the inverse heat conduction analysis. By dividing the cumulative plastic strain into half cycles, the strain amplitude per half cycle can be estimated, and the degree of damage can be calculated from the strain amplitude. By conducting the above analysis, we could predict damage level of the steel from the history of voltage by thermoelectric devices under the seismic response behavior. In addition, it was also shown that the microcomputer can be used to track the temperature rise of plastic heating in steel.

Quenching of a heated wall with spatial temperature gradient using a liquid film through oblique jet impingement

The quenching of a heated aluminum alloy plate with a spatial temperature gradient by water jet impingement was experimentally investigated to examine the effect of the liquid mass flow rate and liquid jet velocity by varying the nozzle diameter. The behavior of the liquid film formed by jet impingement was observed by high-speed imaging, and the temperature profile of the test plate was measured by infrared imaging. In addition, the surface heat flux and the amount of the heat removal, from the test plate to the liquid film, were calculated by inverse heat conduction analysis to investigate the heat transfer characteristics between the liquid film and test plate and to estimate the mass fraction of the injected liquid contributing to cooling. Results indicated that the wetting front propagation was affected by the mass flow rate, rather than by the liquid jet velocity. From the estimated results obtained by inverse heat conduction analysis, it was found that the values of the maximum heat flux, whose position lay near the wetting front, were almost the same under the same mass flow rate condition even though the liquid jet velocity was about 2.5 times different. In addition, from the estimation of the amount of heat removal, it was found that about 90% of the injected liquid was splashed away from the test plate without evaporation.

Intrinsic effects of Cr-layered accident-tolerant fuel cladding surface on reflood heat transfer

A transient flow quench experiment was conducted to investigate the reflood heat transfer of a Cr-layered vertical tube, which is considered to be the most promising candidate for an accident-tolerant fuel cladding application. Cr was physically deposited on a stainless-steel tube by using DC magnetron sputtering. Owing to the increased nanoscale features of the Cr coating, the surface showed an enhanced capillary wicking potential with superhydrophilic characteristics. In addition, an oxidized Cr-coated specimen was prepared to examine the effects of oxidation during normal operations and blowdown phases in a loss-of-coolant accident. After being heated to 740 °C, the specimens were subjected to a continuous flow of deionized water and heat generation with varying coolant subcooling. The temperature history during quenching was recorded, and the quench behavior was visualized using a high-speed camera. The quench performance, including the quench temperature, critical heat flux, film boiling heat transfer coefficient, and quench front velocity, was analyzed for each specimen by performing an inverse heat conduction analysis. The effects of the Cr coating and oxidation were found to have different impacts on the quench performance, depending on the coolant subcooling and boiling regimes.

Experimental investigation of hot AISI 304 steel plate with very‐high mass‐flux varying water temperature spray

AbstractThe spray cooling is investigated for very high mass‐flux coolants at different temperatures. First, the intended spray is characterized for its role in the cooling enhancement, which reveals that droplet detachment frequency, droplet residence time, liquid film, and vapor film wavelength influence heat‐transfer performance for high‐temperature very‐high mass‐flux spray. After that, the furnace heated 6‐mm thick steel plate at 1030°C is quenched using spray possessing average impingement density (231 kg/m2s) and coolant temperatures (30°C, 40°C, and 50°C). The heat transfer performance is analyzed using inverse heat conduction analysis, wherein temperature‐dependent steel thermophysical properties are considered. The heat transfer performance assessment through parameters such as cooling rate, surface heat flux, and heat transfer coefficient curves shows improvement in cooling performance. For 50°C coolant temperature, we observed the maximum improvement in cooling rate, 141°C/s, and critical heat flux, 3.64 MW/m2. The efficiency analysis reveals that coolant at the highest temperature is the most efficient. Also, an approximate cost assessment suggests enhanced coolant temperature as an economical alternative for heat transfer enhancement than additives‐based coolant.

A novel domain propulsion and adaptive modified inversion method for the inverse geometry heat conduction analysis of FGMs

A novel domain propulsion and adaptive modified inversion method based on the least square error method and the precise integration finite element method is firstly proposed to identify the geometries of two-dimensional and three-dimensional models made of functional gradient materials. After introducing concept of virtual boundary, the inverse geometry problems can be solved only by the two processes, which are the domain propulsion process and the adaptive modified process. The first process is getting a better shape and position of virtual boundary through propulsion scheme. After that, the geometry can be identified by modifying the shape of virtual boundary and searching the isotherm or isothermal surface. To improve the ill-posedness of problems, the truncated singular value decomposition method and the coefficient expending scheme are adopted in inversing process. The results of some typical numerical examples show that the present method can obtain the great performance on both the inversing accuracy and the computing efficiency by discussing the influence of some factors such as the different approximation functions, the measurement errors, the number of measurement points and so on.

A meshless collocation scheme for inverse heat conduction problem in three-dimensional functionally graded materials

This short communication documents the first attempt to apply the generalized finite difference method (GFDM) for inverse heat conduction analysis of functionally graded materials (FGMs). The fact that the GFDM is a meshless collocation method makes it particularly attractive in solving problems with complex geometries and high dimensions. By employing the Taylor series expansion and the moving least-squares technique, the method produces sparse and banded matrix which makes it possible to perform large-scale simulations. Three benchmark examples are provided to demonstrate the accuracy and adaptability of the GFDM approach in solving the inverse Cauchy problems. The convergence and stability of the method with respect to the amount of noise added into the input data are analyzed.

An experimental approach based on inverse heat conduction analysis for thermal characterization of phase change materials

A new method based on solution to inverse heat conduction problem for the assessment of solidification parameters of PCM salts has been proposed. The method estimates the mold -salt interfacial heat flux and it is used to calculate the latent heat of salt PCMs using calorimetry based energy balance equations. This method is more accurate compared to Computer Aided Cooling Curve Analysis (CACCA) techniques as it eliminates the drawbacks involved with base line fitting calculations and errors introduced due to the improper selection of solidification points. Pure salt PCMs such as KNO3 and solar salt were used for the validation of this technique. Both air and furnace cooling were adopted to demonstrate the effect of cooling rate on solidification characteristics. The wettability of salt samples on mild steel surface was analyzed to account for the difference in the thermal behavior of salts.

Determination of thermophysical properties and density volume fractions of Al2O3/Y-ZrO2 layered composite materials using transient thermography and two-stage inverse nonlinear heat conduction analysis

In the present study, transient thermography, a nondestructive imaging technique, is applied to evaluate the transient temperature response in a graded medium without the use of embedded thermocouples. A layered composite sample was fabricated from Al2O3 and Y-ZrO2 powders using powder metallurgy (PM). This sample was irradiated on one side with a direct current laser while the transient temperature was measured along its depth by a midinfrared camera. Also, a MATLAB code based on the truly meshless radial point interpolation method (t-RPIM) was developed and implemented to solve the problem of quasilinear transient heat transfer in PM solids. In the t-RPIM formulation, the Cartesian transformation method and the Crank-Nicolson scheme were used for the evaluation of domain integrals and time discretization, respectively, thereby yielding a truly mesh-free technique. In the conducted experiment, the thermophysical properties were assumed to be independent of temperature because of the small amount of temperature increase. These properties and the volume fractions of the constituent powders were determined using a combination of the t-RPIM and the damped Gauss-Newton method in an inverse analysis. Good agreement was found between the measured temperature and the reconstructed temperature profile using the identified thermal parameters and volume fractions, thus validating the accuracy and ability of the applied t-RPIM as a tool in an inverse scheme to solve the inverse transient heat conduction problem in nonhomogeneous media.

Natural convection of plate finned tube heat exchangers with two horizontal tubes in a chimney: Experimental and numerical study

This study uses a hybrid method of computational fluid dynamics (CFD) and inverse heat conduction analysis (IHCA) combined with experimental temperatures to investigate the natural convection of plate finned tube heat exchangers with two horizontal tubes located in a chimney. The influence of the position of the two heated tubes on the results obtained is considered. IHCA combined with experimental temperatures is used to estimate h¯ and h¯b. Subsequently, the CFD commercial software combined with the obtained inverse results and experimental temperatures is employed to get the present results. The results reveal that the zero-equation turbulence model can be applied to determine more accurate results than the other two flow models. Therefore, the appropriate flow model for this study is the zero-equation turbulence model. The fringe pattern for each heated tube is mainly aligned in the vertical direction and the two plumes are slightly inclined toward the inward direction. The obtained velocity pattern and air temperature contour are consistent with existing interferometric images or isotherms. The proposed correlation between Ra and Nu agrees with the obtained inverse and CFD results.

Effects of wall thickness and material property on inverse heat conduction analysis of a hollow cylindrical tube

In this study, we examined the effects of a hollow cylindrical tube’s thickness and material properties on estimated time delay and waveform distortion in a one-dimensional inverse heat transfer analysis model using the thermal resistance method and an input estimation algorithm. Results indicated a persistent time delay for various heat flux amounts applied to different tube thicknesses. As the tube thickness increased, the numerically determined temperature data also experienced a time delay, which affected the inverse heat transfer response curve. Results also indicated that the transient heat flux waveform estimated for different material properties showed higher levels of distortion for materials having relatively low thermal conductivity. These materials also exhibited greater time delays. To address these issues, we applied a Fourier number (a dimensionless number representing the tube’s thickness and material properties) and proposed an equation to calculate sharpness, which can subsequently be used to predict probable time delays and heat flux waveform distortion. In conclusion, a correction is required when a low Fourier number is used in inverse heat transfer analysis.

Design of Thermal Protection System for Reusable Hypersonic Vehicle Using Inverse Approach

In this study, an inverse heat conduction analysis based on the Levenberg-Marquardt method is applied to reconstruct the aerothermal heating and thermal protection material response of a reusable hypersonic vehicle (RHV) from the knowledge of temperature measurements taken within the thermal protection system (TPS). In addition to reconstruction of TPS material response, a lightweight passive TPS for the RHV based on these predictions is designed. In this analysis, the experimental temperature data are generated by a direct approach; this is due to the lack of real experimental setup that is used to measure the temperature. The direct analysis has performed by an explicit one-dimensional finite difference code to analyze the in-depth temperature response of the TPS. The temperature data determined from the direct approach are used to simulate the temperature measurements. The influence of measurement errors upon the accuracy of the inverse results is also investigated. Finally, results show that the Levenberg-Marquardt method is an effective technique to design a lightweight passive TPS for an RHV by using the inverse approach.

Development of Inverse Analysis Method of Heat Conduction and Thermal Stress for Elbow—Part II

An inverse heat conduction analysis method for piping elbow was developed to estimate the temperature and stress distribution on the inner surface by measuring the outer surface temperature. In the paper, the accuracy for the thermal stress calculation using the inverse heat conduction analysis method was confirmed by comparing with the reference results from normal FE heat conduction and thermal stress analyses. In the case of the measured-basis fluid temperature input from a high temperature–pressure test, the inverse analysis method estimated the maximum stress change by 7% conservative comparing with the normal FE analyses.

Development of Inverse Analysis of Heat Conduction and Thermal Stress for Elbow (Part I)

High temperature stratified flow sometimes caused thermal fatigue cracking in power plants. To prevent fatigue damage by stratified flow, it is important to know temperature distribution history in a pipe. In this study, inverse heat conduction analysis method for an elbow model was developed to estimate the inner surface temperature from the measured outer surface temperature. In the method, the transfer function database inter-relating the inner surface temperature with the outer one was used. For several patterns of the temperature history, the inverse analysis simulations were performed and the accuracy of the estimated inner surface temperature was shown.

Reconstruction of aero-thermal heating and thermal protection material response of a Reusable Launch Vehicle using inverse method

A transient inverse heat conduction analysis based on Lavenberg–Marquardt method is presented to reconstruct the aero-thermal heating and thermal protection material response of a Reusable Launch Vehicle (RLV), from the knowledge of temperature measurements taken within the thermal protection system. In this analysis, due to the lack of real experimental set-up to measure the temperature however it is generated by direct approach using real heating profile on the surface of RLV developed at NASA Langley Research Center. The direct analysis is performed by an explicit one-dimensional finite difference code to determine the in-depth temperature response of Integrated Thermal Protection System (ITPS) of RLV. The temperature data determined from direct approach is used to simulate the temperature measurements. The effects of thermocouple arrangement and measurement error upon the stability of inverse results are investigated. Results show that the Lavenberg–Marquardt is an effective technique to predict aero-thermal heating of RLV by using inverse approach.

Characterization of defects in carbon fiber-reinforced plastics by inverse heat conduction analysis using transfer matrix between layers

In this study, inverse analyses of the defects in carbon fiber-reinforced plastics (CFRPs) are performed using the transfer matrix approach. The material properties used in the calculation were obtained on the basis of mixture laws for epoxy resin and carbon fibers. The accuracy of the inverse analysis was confirmed by calculations employing numerical models of CFRP plates with PAN-based and pitch-based carbon fibers containing defects. The inverse analysis was conducted based on the temperature distribution of CFRP laminates with PAN-based carbon fibers, which was obtained by infrared measurements. The analyses successfully estimated the positions of defects, and the effectiveness of the transfer matrix method for CFRPs was demonstrated through the inverse analysis.