Prediction Of Heat Flux Research Articles

Prediction of Critical Heat Flux of Mixtures Flowing in Channels

Boiling of mixtures in channels is involved in many chemical processes, and refrigerant mixtures are finding a rapidly increasing use in the refrigeration industries. Hence, reliable prediction of CHF (critical heat flux) is needed. There is no published method that has been verified over a wide range of parameters. In this study, available data for CHF in tubes and annuli were compared to general correlations for tubes and annuli, which are well-verified for single-component fluids. This paper presents the results of this comparison. It was found that general correlations for single-component fluids were in satisfactory agreement with data for mixtures. The data included mixtures of refrigerants and chemicals, reduced pressure 0.02 to 0.8597, mass flux 200 to 3798 kgm−2s−1, temperature glide 2.1 to 21.9 K, and critical quality −0.46 to 0.99. The data for annuli were predicted with a MAD (mean absolute deviation) of 13.6%, and the data for tubes had a MAD of 13.9% when compared to the Shah correlations for single-component fluids. Based on the results of the present data analysis and results of research on pool boiling, a range is identified in which pure fluid correlations can be used for mixtures. This will be useful in the design of heat exchangers involving the boiling of mixtures in channels.

Effect of surface radiation on the surface heat flux of two-dimensional hypersonic panel flow

This article investigates the effect of surface radiation on the surface heat flux of a two-dimensional hypersonic panel flow by comparing the surface heat fluxes of penetrating-radiative-equilibrium cases with those of constant-wall-temperature cases. A Du Fort–Frankel-type difference scheme is applied to cases with different external flow properties and is verified by comparing the results under a constant-wall-temperature boundary condition with self-similar solutions. Both laminar and turbulent flows are considered, and turbulence is modeled using a Baldwin–Lomax turbulence model with the assumption that full-scale turbulence is reached at the leading edge. The results show that the surface heat fluxes for laminar penetrating-radiative-equilibrium cases are greater by the order of 10% than those for constant-wall-temperature cases with the same temperature value at the corresponding points. Though turbulent instances are substantially more difficult, surface heat fluxes of penetrating-radiative-equilibrium cases are fairly similar to those of constant-wall-temperature cases. These results serve as the foundation for a brief discussion of how parameters affect the outcome and the proposal of a modified reference enthalpy method that can be used to predict heat flux when surface radiation causes a streamwise variation in wall temperature.

Analysis of Mars 2020 Entry Vehicle Aerothermal Flight Data

The Mars 2020 entry vehicle’s thermal protection system included measurements of in-depth temperature on the heatshield and backshell, and surface heating on the backshell. This paper describes the flight data and resulting analysis: subsurface temperatures at 11 heatshield and 6 backshell locations, measured total heat flux at two backshell locations, and a radiometer on the backshell to measure shock layer radiation. All temperatures were within allowable material limits. Total surface heat flux was derived from the in-depth temperature measurements at the thermocouple locations. Turbulent boundary-layer conditions occurred at nine heatshield locations and the radiometer provided evidence that heating from shock layer radiation significantly exceeded convective heating on the backshell. Computational results on the reconstructed entry trajectory are compared to the flight data. After boundary-layer transition, total heat flux from algebraic turbulence model calculations qualitatively matches the reconstructed heating, but with lower peak magnitudes. On the backshell, laminar heat flux predictions generally exceed the as-flown values by less than , with shock layer radiation predicted to contribute the majority of heating. At the radiometer location, the maximum predicted radiative heat flux exceeds the measurement, with the measured value likely suppressed by ablation products on the sapphire window.

Effect of orthogonal channel structure on the heat transfer in pool boiling and its heat flux prediction model

Pool boiling has a heat transfer performance far exceeding that of traditional heat transfer methods, so it has broad application prospects. At present, the mainstream means to improve the boiling performance are mainly to change the heat transfer surface and to change the liquid working medium. Previously, a T-shaped microchannel structure has been designed, whose maximum heat flux was 338% of that of a smooth surface, and whose maximum boiling heat transfer coefficient was 184.7% of that of a smooth surface. The structure of this paper is further developed on the basis of this structure. It is found that the orthogonal channel structure can better improve the heat transfer effect. Specifically, within a certain range, the promotion effect of heat transfer is positively correlated with the increase of fin length. When the wall superheat is 12.3 K, the heat flux of the best orthogonal channel structure S4 is 358% of that of the smooth surface. The maximum heat transfer coefficient of S4 is 11.9 W/(cm2·K), which is 281.3% of that of the smooth surface. In addition, a prediction model is proposed for the structure of this paper, and its prediction error is within 25% under medium and high heat flux.

Computational Optimization of a Loosely-Coupled Strategy for Scale-Resolving CHT CFD Simulation of Gas Turbine Combustors

The accurate prediction of heat fluxes and, thus, metal wall temperatures of gas turbine (GT) combustor liners is a complicated and numerically expensive task. Computational Fluid Dynamics (CFD) support for the design of cooling systems is essential to ensure safe and proper operation of the entire gas turbine engine. Indeed, it is well known how complicated, and, at the same time, expensive it is to carry out experimental campaigns inside combustors operating under working conditions, and, therefore, pressurized and having high temperatures. The correct prediction of thermal fluxes in a CFD simulation depends on the proper modeling of all the involved phenomena and their interactions with each other. For this reason, Conjugate Heat Transfer (CHT) simulations are mandatory in gas turbine cooling system applications. Multiphysics and multiscale simulations, based on loosely-coupled approaches, have emerged as extremely effective numerical tools, providing enormous computational time savings, as compared with standard CHT simulations. The fundamental advantage of such approaches is based on the fact that each heat transfer mechanism is solved with the most suitable numerical setup, which leads to the use of spatial and temporal resolutions following the characteristic time scales of each phenomenon to be solved. For industrial applications, where the availability of numerical resources is limited and, at the same time, the timelines with which to obtain results are rather tight, having robust and easy-to-use loosely-coupled solutions available for the design of combustion chamber cooling systems would be extremely valuable. In this context, the objective of this work was to perform an initial optimization step for the multiphysics and multiscale tool, U-THERM3D, developed at the University of Florence to revise the coupling strategy workflow with a view to making the numerical tool faster and easier to use. The revised methodology was applied to the RSM gas turbine combustor model test case developed with cooperation between the Universities of Darmstadt, Heidelberg, Karlsruhe, and the DLR. In particular, all experimental tests were conducted by the Institute of Reactive Flows and Diagnostics (Reaktive Strömungen und Messtechnik) of the Department of Mechanical Engineering at TU Darmstadt, from which the gas turbine combustor model takes its name. The newly obtained results were compared and analyzed, both qualitatively and in terms of computational time savings, with those previously achieved with the current version of the U-THERM3D tool already studied by the authors and available in the literature. Moreover, an analysis of computing times was carried out relative to the super-computing center used for the different adopted methodologies.

Dimensional Analysis in Error Reduction for Prediction of Nucleate Boiling Heat Flux by Artificial Neural Networks for Limited Dataset

Abstract In this work, artificial neural networks (ANNs) is used to predict nucleate boiling heat flux by learning from a dataset of twelve experimental parameters across 231 independent samples. An approach to reduce the number of parameters involved and to increase model accuracy is proposed and implemented. The proposed approach consists of two steps. In the first step, a feature importance study is performed to determine the most significant parameters. Only important features are used in the second step. In the second step, dimensional analysis is performed on these important parameters. Neural network analysis is then conducted based on dimensionless parameters. The results indicate that the proposed feature importance study and dimensional analysis can significantly improve the ANNs performance. It also show that model errors based on the reduced dataset are considerably lower than those based on the initial dataset. The study based on other machine learning models also shows that the reduced dataset generate better results. The results conclude that ANNs outperform other machine learning algorithms and outperform a well-known boiling correlation equation. Additionally, the feature importance study concludes that wall superheat, gravity and liquid subcooling are the three most significant parameters in the prediction of heat flux for nucleate boiling. Novel results quantifying parameter significance in surface tension dominated (SDB) and buoyancy dominated (BDB) boiling regimes have been reported. The results show that surface tension and liquid subcooling are the most significant parameters in SDB regime with a combined contribution percentage of 60%, while wall superheat and gravity are the most significant parameters in BDB regime with a combined contribution percentage of 70%.

Experiments and qualitative analysis by artificial neural network approach on pool boiling of FC-72 on finned surfaces confined by an unheated horizontal wall

Heat transfer measurements were taken during nucleate pool boiling of FC-72 (a saturated liquid utilized for thermal control of electronic components) from extended finned surfaces placed in a horizontal channel. The influence of channel width on boiling behavior for various extended finned surfaces was experimentally investigated. These finned surfaces have an array of uniformly or non-uniformly spaced straight spines with a square cross-section. The fins had a length of 3 mm or 6 mm. Starting from a uniform configuration, for which the width spacing of the spines was 0.4 mm, non-uniform surfaces were obtained by regularly removing some rows of spines. The effects of channel width (0.5–20 mm) and spines distribution were analyzed. The case of an extended unconfined surface was investigated and used as a reference to compare the effect of the confinement. An Artificial Neural Network (ANN) with one hidden layer was trained with the experimental data to predict the heat flux. An optimization algorithm was implemented to calculate the geometry that maximizes the predicted heat flux operating near the maximum temperature limit under different constrictions as fixed fin height or fixed channel width.

Critical heat flux correlations for tube and annulus geometries under inclination and rolling conditions

In floating nuclear reactors, critical heat flux (CHF) prediction is crucial because the CHF can be influenced under heaving, rolling, and inclination conditions, unlike in land-based reactors. Hence, the existing land-based empirical correlations of the CHF can be invalid under some conditions in marine reactors. Therefore, empirical correlations of the flow boiling CHF were developed in this study to predict the CHF under inclination and rolling motions in tubes and annuli. Available experimental CHF data (616 points) were collected including our previous experimental data (405 points) and their trends under marine conditions were analyzed. The CHF variation was expressed using two types of modified Froude numbers depending on the CHF regime—departure from nucleate boiling and dryout. These parameters were used in correlations for the CHF under inclination. CHF correlations under rolling conditions were developed. Rolling was found to attenuate the CHF variation through the inclination. This observation was reflected in the newly developed rolling CHF correlation. The proposed correlations adequately described the existing CHF experimental data under inclination and rolling within an uncertainty of 9.5%. The developed CHF correlations can be used for the safety analysis and reactor core thermal–hydraulic design of marine reactors.

Study on smoke blocking and thermal radiation attenuation by water curtain in tunnel fire

A 1:10 scale model tunnel with a length, height and width of 9 m, 0.6 m and 0.8 m, respectively, was set up in this paper. A water curtain system was installed in the model to investigate the effect of water curtain systems on smoke flow and heat propagation. A reduced-scale experimental and theoretical study was carried out by varying the heat release rate of the fire source, the water curtain pressure, and the number of water curtain rows. A series of tests were carried out for various setups to quantify each mechanism of interaction between the water mist and hot smoke, to propose a method for qualitatively analysing water curtain systems blocking the propagation of heat radiation and the flow of smoke from combustion, and to propose a method for predicting heat fluxes. The study found that the pressure of the water curtain, the number of rows, and the heat release rate of the fire source all had an effect on the smoke blocking effect of the water curtain system. This effect decreased as the heat release rate of the fire source increased and increased significantly with the pressure of the water curtain and the number of rows. The smoke blocking effect was quantified using conservation of momentum by establishing a dimensionless parameter R to represent the ratio of water curtain momentum to smoke momentum, as well as the ratio of heat flux before and after the water curtain to represent the smoke blocking capacity delta of the water curtain. The smoke blockage rate delta ranges between 40 and 75%, and the smoke blockage rate increases as the momentum R increases. Finally, in tunnel fires, a predictive model for the attenuation of heat radiation by water curtains has been developed, providing theoretical support for the quantitative study of the smoke and thermal blockage effects of water curtains, which is beneficial to the protection of human life in confined spaces.

Compact Thermal Modelling of Magnetic Components using an Admittance Matrix Approach

Unlike semiconductor devices, the thermal modelling of magnetic components has not been standardized. Due to this lack of standardization in the academic community, most proposed magnetic component thermal models have not been evaluated for boundary condition independence. Hence, they cannot be classified as Compact Thermal Models (CTMs). In this study, CTMs of a PQ 30/40 inductor are developed using an admittance matrix-based approach. First, a Detailed Thermal Model (DTM) of the inductor under direct current excitation is developed and validated using experimental test results for power dissipation varying from 2.6 to 11.9 W. Following this, a single heat source CTM is developed from the DTM data using the admittance matrix approach. The thermal performance of the deduced CTM is evaluated for fifteen different boundary condition scenarios with surface heat transfer coefficients varying between 1 to 200 . The surface temperature and heat flux predictions were within 5% of the DTM results, while the junction temperature error was 10%. Most magnetic components like transformers and inductors have multiple loss sources. Hence, the DTM and CTM were re-evaluated for multiple heat sources. The resulting multi-heat source CTM was also observed to accurately predict surface temperatures and heat fluxes.

A HYBRID SOLVER FOR THE RADIATIVE TRANSFER EQUATION IN NONGRAY COMBUSTION GASES

The discrete ordinates method (DOM) or its variant, the finite angle method (FAM), is a popular solution method for the radiative transfer equation (RTE). Accurate solution to the RTE using the DOM or FAM requires many solid angles (directions) in multidimensional geometry. In combustion gases, where the absorption coefficient oscillates wildly and the RTE must be solved repeatedly, this method becomes computationally intractable. Here, the FAM is hybridized with the P<sub>1</sub> approximation, which is efficient since it requires solution to a single partial differential equation as opposed to a set of directional RTEs in the FAM. The P<sub>1</sub> approximation is accurate when the intensity field is fairly isotropic, as evidenced in optically thick media. Hence, the hybridization employs the FAM for optically thin and intermediate spectral intervals and employs the P<sub>1</sub> approximation for optically thick spectral intervals. The objective of the present study is to determine optimal parameters for hybridization that can provide the best compromise between accuracy and efficiency. Using a narrowband-based box model for carbon dioxide and water vapor, the nongray radiative transfer equation is solved in media with nonuniform properties enclosed in multidimensional enclosures. Two different approaches-cutoff and filter optical thickness-are investigated for hybridizing. Several problems, both two- and three-dimensional, and with and without coupling to other modes of heat transfer are considered. The filter approach was found to be the best choice for prediction of the radiative source and temperature (in the case of a coupled mode), while the cutoff approach was found to be the best for prediction of wall radiative heat fluxes.

Assessment study of different radiation models in the simulation of 1 m methanol pool fire

Pool fires are one of the most commonly encountered flame types in fire disasters, and the accurate and detailed modeling of pool fires is beneficial for the hazard analysis and assessment of liquid-related fire accidents. The radiation model is known to be the critical component in the accurate simulation of various fire scenarios. Therefore, to develop a proper radiation model, an LES study of a large-scale methanol pool fire was performed in this work by coupling four different radiation models into the open-source fire simulation code FDS and solving the radiation intensity transport equation using the discrete ordinates method. The impact characteristics of different radiation models are evaluated in detail with the NIST experiments, where the comparative analysis was carried out. Regarding the temperature calculations, the WSGG (weighted-sum-of-gray-gases)-based radiation model and Cassol’s model performed better. In addition, all models predict pulsation frequencies well. However, regarding the prediction of the radiative heat fluxes, Cassol’s two models and the FDS default model outperformed the other models, which indicates that the database for obtaining the spectral information of each species and the method to determine the WSGG coefficient of mixed gases are significant factors for the successful prediction of flame radiation.

Evaporation of a water layer under local non-isothermal heating

• Water layer evaporation under local heating was investigated. • Gas convection effect was several times greater than diffusion and buoyancy of vapor. • Local heating allowed achieving high values of the heat transfer coefficient. • Obtained results were important for the development of new methods of heat exchange enhancement. The evaporative behavior of a water layer and the heat transfer under local heating were investigated. Non-stationary and non-isothermal heat exchange conditions were created by laser heating. The thermal field on the free surface of the layer was registered using thermal imaging technology. Changes in the liquid mass due to evaporation were determined using the gravimetric method. The key factors affecting water evaporation were estimated and the characteristic heat fluxes associated with evaporation, radiation and convection are compared. The effect of free convection in the gas phase on the evaporation rate of the water film is several times higher than the effect of diffusion and buoyancy of vapor. The local heating allowed achieving high values of the heat transfer coefficient and heat fluxes at considerably smaller liquid temperatures and heating area, which is advantageous from an energy point of view. The obtained results were important for the development of new methods of heat exchange enhancement, as well as for the prediction of heat fluxes and hydrodynamic flows and evaluation of non-isothermal, non-stationary and inhomogeneous heat exchange.

Peak heat flux prediction of hypersonic flow over compression ramp under vibrationally excited free-stream condition

In hypersonic shock tunnel experiments, the high-temperature reservoir gas expands and accelerates so rapidly that there is not enough time for vibrational energy relaxation. As a result, thermal nonequilibrium gas flow is frequently encountered in the test section, and this significantly affects the measured heat flux. In this paper, hypersonic compression-ramp flows are studied numerically to investigate the effect of incomplete vibrational energy accommodation on the separation flow structure and peak heat flux in the reattachment region under low-to-medium Reynolds number and high Mach number conditions. Numerical results and theoretical analysis suggest that the vibrational energy accommodation has no noticeable impact on the length scale of the separation zone, but strongly influences the peak heat flux of the separated ramp flows. Decomposing the peak heat flux into translational–rotational energy and vibrational energy components, qtr and qv, respectively, we find that qv/qtr characterizes the nonequilibrium degree of the vibrational energy accommodation. A formula for predicting the peak heat flux is then proposed, taking the effect of incomplete vibrational energy accommodation into consideration. Finally, surface heat flux measurements in a hypersonic shock tunnel indicate that a deviation of up to 13% in total peak heat flux could arise if vibrational energy accommodation is not considered under the vibrationally excited free-stream condition.

Experimental Investigations of Heat-Flux and Temperature Predictions by New Inverse Technique

This paper describes the developed method for predictions of transient internal surface temperatures and heat-flux obtained from thermocouples, which are installed through the wall of the rocket motor nozzle. Heat-Flux was estimated by using the prediction of internal surface temperatures from numerical solutions of the inverse heat conduction problem (IHCP). Three Heat-Flux gauges are manufactured and used in convergent, throat, and divergent sections. The temperatures are measured with starting operation of the rocket motor along the gauges where the thermocouples are connected to the data acquisition system interfacing with the PC. The measured unsteady temperature behavior is approximated by polynomials third degree in space and time. The measurement results indicate that the maximum reading temperatures are at the throat section. No differences in time were appearing in curves to reach maximum prediction surface temperatures.

Numerical Study of Liquid Metal Turbulent Heat Transfer in Cross-Flow Tube Banks

Heavy liquid metals (HLM) are attractive coolants for nuclear fission and fusion applications due to their excellent thermal properties. In these reactors, a high coolant flow rate must be processed in compact heat exchangers, and as such, it may be convenient to have the HLM flowing on the shell side of a helical coil steam generator. Technical knowledge about HLM turbulent heat transfer in cross-flow tube bundles is rather limited, and this paper aims to investigate the suitability of Reynolds Average Navier–Stokes (RANS) models for the simulation of this problem. Staggered and in-line finite tube bundles are considered for compact (a=1.25), medium (a=1.45), and wide (a=1.65) pitch ratios. The lead bismuth eutectic alloy with Pr=2.21×10−2 is considered as the working fluid. A 2D computational domain is used relying on the k−ω Shear Stress Transport (SST) for the turbulent momentum flux and the Prt concept for the turbulent heat flux prediction. The effect of uniform and spatially varying Prt assumptions has been investigated. For the in-line bundle, unsteady k−ω SST/Prt=0.85 has been found to significantly underpredict the integral heat transfer with regard to theory, featuring a good to acceptable agreement for wide bundles and Pe≥1150. For the staggered tube bank, steady k−ω SST and a spatially varying Prt has been the best modeling strategy featuring a good to excellent agreement for medium and wide bundles. A poor agreement for compact bundles has been observed for all the models considered.

Machine Learning Strategy for Wall Heat Flux Prediction in Aerodynamic Heating

The efficient and accurate prediction of the aeroheating performance of hypersonic vehicles is a challenging task in the thermal protection system structure design process, which is greatly affected by grid distribution, numerical schemes, and iterative steps. From the inspiration of the theoretical analysis and machine learning strategy, a new wall heat flux prediction framework is proposed first by establishing the relationship between the wall heat flux and the flow variables at an extreme temperature point (ETP) in the normal direction of the corresponding wall grid cell, which is named the machine learning (ML)-ETP method. In the training phase, the flow properties and their gradients at the ETP and the distance from the ETP normal to the wall are employed as feature values, and the accurate wall heat flux predicted by the converged fine grid is regarded as the tag value. With the assistance of the trained regression model, the heat flux of the same configuration with a coarse grid in the wall-normal direction could be predicted accurately and efficiently. Moreover, test cases of different configurations and inflow conditions with a coarse grid are also carried out to assess the model’s generalization performance. All comparison results demonstrate that the ML-ETP strategy could predict wall heat flux more rapidly and accurately than the traditional numerical method due to its nonstrict grid distribution requirements. The improvement of the predictive capability of the coarse-graining model could make the ML-ETP method an effective tool in hypersonic engineering applications, especially for unsteady ablation simulations or aerothermal optimizations.

A theoretical approach for prediction of temperature and heat flux of copper beads on wood surfaces

AbstractThe present research is dedicated to investigating the fire hazard risks of molten metal particles from electrical wires or devices, in enclosed places (houses, factories, etc.). A mathematical model is proposed for the calculation of the temperature of the molten particles as well as the heat flux they can transfer to the attached surface and the temperature of the attached surface. It is concluded that the probability of fire ignition for a specific bed is a function of the molten particles' diameter and the ratio of the contact to total surface. The proposed model can be used for fire investigation analysis in indoor places due to potential electric faults.

Pool boiling experiment with Novec-649 in microchannels for heat flux prediction

Boiling dissipates significant amounts of heat as a result of small temperature differences between a wall and a fluid. For this reason, the heat transfer process is widely used across many industries, e.g. for cooling electronic devices, power sources, etc. In practice, heat dissipation from an electronic device occurs mainly during the controlled heat flux loss through the wall to the coolant. This mechanism was studied for boiling Novec-649 (GWP = 1) at atmospheric pressure on copper surfaces with 0.2 to 0.5 mm deep grooves milled in parallel. The resultant microchannels and the spaces between them were 0.2 mm, 0.3 mm, and 0.4 mm wide. The maximum heat flux for the surface with 0.4 mm deep and 0.3 mm wide microchannels was 274 kW/m2. The highest heat transfer coefficient, 22.3 kW/m2K, was obtained for the surface with a 0.5 mm deep and 0.3 mm wide microchannel. A twofold increase in the maximum heat flux and a fivefold increase in heat transfer coefficient were obtained compared to the smooth surface. The effect of geometric parameters on the heat exchange process was investigated for the heat flux density range of 6.6–274 kW/m2. Diameters and frequencies of departing vapor bubbles were determined experimentally with the use of a high-speed camera. A simplified model was proposed to determine the diameters, frequencies, and heat fluxes at different superheats. The model provided a heat flux prediction with a maximum mean deviation of 35 %.

Thermal Performance Estimation of Nanofluid-Filled Finned Absorber Tube Using Deep Convolutional Neural Network

Numerical simulations are usually used to analyze and optimize the performance of the nanofluid-filled absorber tube with fins. However, solving partial differential equations (PDEs) repeatedly requires considerable computational cost. This study develops two deep neural network-based reduced-order models to accurately and rapidly predict the temperature field and heat flux of nanofluid-filled absorber tubes with rectangular fins, respectively. Both network models contain a convolutional path, receiving and extracting cross-sectional geometry information of the absorber tube presented by signed distance function (SDF); then, the following deconvolutional blocks or fully connected layers decode the temperature field or heat flux out from the highly encoded feature map. According to the results, the average accuracy of the temperature field prediction is higher than 99.9% and the computational speed is four orders faster than numerical simulation. For heat flux estimation, the R2 of 81 samples reaches 0.9995 and the average accuracy is higher than 99.7%. The same as the field prediction, the heat flux prediction also takes much less computational time than numerical simulation, with 0.004 s versus 393 s. In addition, the changeable learning rate strategy is applied, and the influence of learning rate and dataset size on the evolution of accuracy are investigated. According to our literature review, this is the first study to estimate the temperature field and heat flux of the outlet cross section in 3D nanofluid-filled fined absorber tubes using a deep convolutional neural network. The results of the current work verify both the high accuracy and efficiency of the proposed network model, which shows its huge potential for the fin-shape design and optimization of nanofluid-filled absorber tubes.