Calculation Of Temperature Distribution Research Articles

Multi-physics coupling analysis of test heat pipe reactor KRUSTY based on MOOSE framework

The heat pipe reactor utilizes heat pipes for passive heat transfer, eliminating the need for any moving parts. This feature significantly enhances its safety characteristics. Given the intricate nature of the heat pipe reactor system, a comprehensive multi-physics coupling simulation is necessary to study its safety features. In this study, a high-fidelity multi-physics coupling analysis incorporating a neutronic-thermal–mechanical-heat pipe coupling model is conducted. The work is based on the multi-physics coupling framework MOOSE, which integrates the Monte Carlo code OpenMC for neutronic analysis and built-in modules for 3-dimensional thermal–mechanical analysis. Furthermore, a heat pipe simulation method called the Thermal Resistance Grid Method is implemented within the MOOSE framework and employed in the multi-physics coupling analysis. To facilitate transient analysis, the Point Kinetics method is also integrated into the MOOSE framework to account for the time-varying power factor during reactor transients. The various modules and physical fields are coupled together using either loose or tight coupling strategies. These coupling strategies are applied to assess a test heat pipe reactor known as KRUSTY. Steady-state simulations are conducted for both normal operation and single heat pipe failure conditions, enabling the calculation of fission power distribution, temperature distribution, stress and strain profiles, as well as power and temperature redistribution following a heat pipe failure. Moreover, a load-following transient of KRUSTY is simulated, demonstrating its capability for load following without reactivity control. The aforementioned calculations validate the feasibility of the coupling framework utilized in this study and highlight its ability to accurately capture local phenomena within the reactor core.

Numerical Investigation of Conjugate Heat Transfer Problems

Conjugate heat transfer (CHT) analysis has been carried out for laminar flow past flat plate and turbulent flow between parallel plates using a commercial CFD software CFX-TASCFlow. Navier-Stokes equations along with k-e turbulence model in the fluid and conduction equation in the solid have been solved simultaneously to obtain the flow features. The computed temperature distribution of the flow past flat plat matches very welL with analytical and other numerical results. For the turbulent flow between parallel plates, nondimensional temperature distribution and Nusselt number distribution matches very well with the analytical and experimental results for different values of Reynolds number and thickness of the heat transfer plate.

Numerical Analysis of Thermal Runaway in Copper-Plated Multifilament Coated Conductor

We have developed a numerical analysis model to simulate the thermal runaway in copper-plated multifilament coated conductors. We combined a circuit model to calculate current distribution in filaments and copper and a two-dimensional heat conduction model to calculate temperature distribution. The thermal runaway simulations of multifilament coated conductor with local defects were performed, and compared with the experimental results to validate the developed model. According to the simulation results, the effect of current sharing on the initiation of thermal runaway was determined.

Experimental Study of Inverse Heat Conduction Problem in a Kinetic Heating Facility

Estimation of unknown surface conditions using measured temperature time history inside or back wall of a solid body is known as inverse heat conduction problem. The purpose of present paper is to solve inverse heat conduction problem using iterative method in conjunction with measured thermocouple data. Exact solution of one-dimensional heat conduction equation is obtained to calculate temperature distribution inside a finite slab. An analytical expression of the sensitive coefficient is derived for constant wall heat flux. It is observed that the sensitive coefficient varies linearly with wall heat flux. Experiments were conducted in Kinetic Heating Facility to obtain temperature-time data. The facility works employing with close loop feed-back system with thyristor controlled thermac. Experimental results are compared with the estimated values and are found in good agreement. The Kinetic Heating Facility can easily be adopted to estimate the thermal diffusivity of material.

Thermomechanical Modeling of Material Flow and Weld Quality in the Friction Stir Welding of High-Density Polyethylene.

A thermomechanical model of the friction stir welding (FSW) of high-density polyethylene (HDPE) was developed by incorporating a Coupled Eulerian-Lagrangian (CEL) approach. A Johnson Cook (JC) material model of HDPE was developed through experimentally generated strain-rate- and temperature-dependent stress strain data. Two sets of FSW process parameters with minimum and maximum weld defects were numerically modeled. The numerically calculated temperature distribution, material flow and flash and potential defects were validated and discussed with the experimental results. Tracer particles allowed to visualize the material movement during and after the tool had traversed from the specified region of the workpiece. Both numerical models presented similar maximum temperatures on the upper surface of the workpiece, while the model with high traverse speed and slow rotational speed had narrower shoulder- and heat-affected zones than the slow traverse, high rotational speed model. This contributed to the lack of material flow, hence the development of voids and worm holes in the high traverse speed model. Flash and weld defects were observed in models for both sets of process parameters. However, slow traverse, high rotational speeds exhibited smaller and lesser weld defects than high traverse, slow rotational speeds. The numerical results based on the CEL approach and JC material model were found to be in good agreement with the experimental results.

Thermal Analysis of a Micro-Satellite in a Low Earth Orbit

The thermal design of a micro-satellite is presented in the paper. The theoretical studies are carried out to describe briefly the relationship among various design orbital parameters and are depicted graphically. Solar heating on a micro-satellite is considered as a thin walled circular cylinder rotating with uniform speed about its geometric axis is analyzed for a situation in which heat transfer by convection and heat exchange within the cylinder is negligible. The nonlinear ordinary differential equations for the thin walled cylinder are solved using fourth order Runge-Kutta method to compute temperature distribution. The results of the analysis are presented at various revolution per minute RPM of the micro-satellite. Radiation heat transfer inside the package is analyzed with networking method.

Coupled thermomechanical FE model of a railway disc brake for friction material wear calculations

The article presents a fully coupled 3D thermomechanical model of a railway vehicle disc brake for calculations of temperature, stress, contact pressure and wear distributions. Five specially designed composite organic friction materials associated with a cast-iron ventilated brake disc were analyzed. The performed computer simulations correspond to the operational parameters of braking carried out on a full scale dynamometer test stand at constant braking power and constant vehicle velocity. These conditions were obtained by correcting the clamping force in relation to changes in the coefficient of friction. In the finite element (FE) model of the disc brake, the pad wear depth distribution was determined on the basis of the Archard's law taking into account the specific wear rate, contact pressure and sliding velocity. To create the numerical model with the geometry deformation allowing for friction material loss due to wear, advanced techniques were adapted. The geometric model of the brake includes the complex shapes of the brake pad holder, brake pad and ventilated disc. The wear constants of the tested friction material were obtained by means of the FE simulation and the measurement of the pad weight loss before and after the test on a full scale dynamometer test stand. The distributions of temperature, stresses, contact pressure and accumulated wear depth, obtained from the finite element analysis, in combination with the measured changes in the clamping force and coefficient of friction during braking, enabled to establish relationships between the properties of materials, operational parameters of braking and geometrical features of the brake components.

Calculation of temperature distribution in heavy oil reservoirs by electromagnetic heating

The introduction of heat into a reservoir has proven to be an effective way to reduce the viscosity of heavy oils by increasing the temperature in the formation. The use of electromagnetic energy has proven to be particularly attractive because of its advantages vis-à-vis conventional heat recovery techniques. While extensive research has been conducted on this radiofrequency recovery method over the years, numerical simulation with reservoir industry applications has been rarely used for electromagnetic heating with heavy oil reservoirs when connected to strong-bottom aquifers. We propose a numerical scheme to estimate temperature variations in the reservoir by electromagnetic absorption, based on the calculation of the electro- magnetic wavefield amplitude and radiation heat diffusion coupling. The electrical and thermal properties of the reservoir were calculated considering the fractions and saturation of its phases. The results obtained from this RF heating simulation show a radially distributed temperature profile within the reservoir. The power and frequency of the incident wave were considered for an antenna located in the center of the formation. This allows to determine the required energy in kWh, and its influence on the antenna power, as well as the thermal and electrical properties of the medium such as aquifers. Numerical modelling allows reaching a stable temperature inside the reservoir, in days or months, despite the strong presence of water-saturated zones. The simulation shows that the presence of aquifers at bottom and partially saturated media affects reservoir heating. To make the numerical experiment reproducible and verifiable, the workflow is provided in code form.

Induction system for heating large rings before rolling

The paper considers the issues of designing an induction system for heating large-sized hollow cylindrical billets before rolling. The specific features of the billets heating process at the installation built into the technological processing line are noted. It is shown that for increasing the efficiency of the process of heating large-sized steel billets it is expedient to carry out the system of inductors with the use of a heat shield. A study of the process of heating of workpieces taking into account the nonlinear dependence of the physical characteristics of the metal of heated workpieces on the temperature changing in the process of heating is performed. The parameters of the induction system are calculated on the basis of a two-dimensional model. The geometric parameters of the circular billet resulted in a significant nonuniformity of the current density distribution along the axial coordinate of the billet due to the strongly pronounced boundary effects. The results of numerical calculation of the electromagnetic and thermal fields at different variations of the induction system design are presented. In order to substantiate and select the design of induction system that provides heating of the ring for the time caused by the work rate of the deforming equipment. A series of calculations was made, including three options: heating by an external cylindrical inductor; heating by two inductors: heating by inductor system with a heat shield. Analysis of efficiency of the investigated variants is based on multiple refinement of the results in the process of iterative design. Results of calculation of temperature distribution in the billet during heating are presented. The results of the research can be used to develop design and operating parameters of induction ring heating system in the rolling line.

Optimization of functionally graded plates under Thermo-elastic free vibration using nature-based algorithms

This article presents the parametric optimization of the free vibration characteristics of a functionally graded material (FGM) plate exposed to nonlinear thermal loading using the finite element method and nature-based algorithms. The one-dimensional (1D) Fourier heat conduction equation is used to calculate temperature distributions over the thickness of the plate. Using Lagrange’s equation, we get the dynamic equation of motion for the plate. An eight-noded iso-parametric plate element with five degrees of freedom per node is used in the finite element formulation based on first-order shear deformation theory. Rectangular plates have temperature-dependent material characteristics; the thickness of the plates is scaled using a straightforward power law distribution. Here, the investigation of the FGM plate is conducted with two different boundary conditions, such as simple support and fully clamped. Additionally, new hybrid optimization approaches, namely RSM-Composite Desirability Optimization (RSM-CDO), Whale Optimization Algorithm (WOA), Corrected Moth Search Optimization (CMSO), Lichtenberg Algorithm Optimization (LAO), Sunflower Optimization Algorithm (SFO), and Forensic-Based Investigation Algorithm (FBI), are utilised to determine the best optimal solution, and the obtained findings are validated using confirmatory tests.

Analytical model for temperature prediction of hot-rolled strip based on symplectic space Hamiltonian system

The cooling process of hot-rolled strip has an important influence on the mechanical and metallurgical properties of the final product. In particular, the uneven temperature of the hot-rolled strip in the run-out table cooling after rolling will lead to the formation of residual stress and eventually cause the flatness defects. Therefore, this study focused on the temperature distribution prediction of steel strips during run-out table cooling. For this purpose, an analytical model for calculating temperature distribution of strip width and thickness is presented. It is different from the traditional analytical models, this study introduces the two-dimensional heat conduction equation with an internal heat source under the traditional Lagrange system into the symplectic space Hamiltonian system to obtain the symplectic dual equations. Meanwhile, symplectic superposition method is used to deal with complex cooling boundary conditions. The symplectic analytical solution of the two-dimensional temperature field is calculated by strict derivation without any assumptions or predetermination of the solution forms. In order to verify the accuracy of the symplectic analytical solution, a temperature−phase transformation coupled finite element model for run-out table cooling of hot strip was established. Then the accuracy of the finite element model is verified by the measured data. Finally, it has been determined that the symplectic analytical solution exhibits a high degree of consistency with the computed results obtained from the finite element model.

ANALYSIS OF THE OPERATING RISKS OF HORIZONTAL FLARE UNITS UNDER UNSTEADY EQUIPMENT REGIME CONDITIONS

The article focuses on complications that arise when new water and gas injection wells are brought on regime and operation of horizontal flare units (HFU), which are part of the reservoir pressure maintenance (RPM) system in the simultaneous water and gas injection mode. In the process of bringing on regime there is a procedure to warm up and maintain working pressure in gas pipelines, for this purpose the associated petroleum gas is redirected to the HFU of the well pad. The existing design of the HFU does not allow maintaining technological parameters of gas injection into the well because of the lack of a regulating device in front of the HFU. The present article describes the measures aimed at ensuring stable operating pressure required when starting up new wells of the reservoir pressure maintenance system in the mode of simultaneous water and gas injection. Modernization of the existing HFU design with installation of a choke diaphragm, providing maintenance of operating pressure in the system of gas pipelines, is offered. The selection and calculation of the choke diaphragm were performed. The results of calculations of HFU with the new design of the choke diaphragm show the possibility of maintaining the working pressure in the gas pipeline when redirecting gas to the HFU during the launch, adding new water and gas injection wells in the system of reservoir pressure maintenance. Calculations of temperature distribution over the HFU surface are performed and dosages of hydrate inhibitor to ensure hydrate-free operation are specified.

Heat Transfer Analysis of the Tantalum-plated Barrel

Accurate calculation of temperature distribution in the barrel tube is of great importance for the barrel design. In this paper, a numerical heat conduction model of PCrNi3MoVA tube plated with tantalum coating at the inner surface is established. Based on the finite difference method, the temperature distribution of different coating schemes is calculated. The origin of rifling which is the most serious part of erosion and wear is selected as the object of study. When it comes to different coating thickness, we focused on the variation of temperature at the bore surface and the interface of Tantalum coating and steel substrate. The numerical results show that the thickness of the coating is of great significant to the temperature of the substrate.

Effect of a Parked Car Orientation on a Temperature Distribution and Cooling Load Calculation: Experimental Study

When a vehicle is left parked in the sun for an extended period, the gathered heat causes damage to several interiors within the cabin and causes discomfort for people and animals left inside the car. In the present work, the effect of the orientation of a parked white minibus on temperature distribution and cooling load calculation is studied experimentally in an open environment. Two different cases were studied facing south and facing east. For several hours, the temperature inside the car cabin had been monitored and measured at five separate locations. The cooling load calculations are carried out based on the experimental measurements. The results show that the overheating of parked cars always happens as a result of the radiation load especially when a car has a large surface glass area. Also, the ambient load is directly proportional to the ambient temperature, and the total load related directly to radiation load reaches the maximum value of 2358.1 W at 3:00 pm for 1st case and 2118.3 W at 11:00 am for 2nd case which shows an increase of 11.32 %. Thus, these results emphasized the fact that the orientation of the parked car may considerably affect the temperature distribution and the cooling load of the car cabin. Also, the study may be considered an essential step in designing any assisted ventilation or auxiliary air conditioning system that may enhance the car cabin conditions even while the car’s engine was off (parked automobile).

Fast calculation of temperature distribution in oil-immersed transformer windings based on U-net neural network

In this paper, a fast computational method based on the training of the U-net neural network is proposed to solve the fluid-thermal coupling problem of transformers. First, the input variables are selected according to the fluid-thermal coupling principle, and the finite volume method is applied to obtain the output results under different operating conditions and make them into training sets and test sets. Second, the training sets are normalized and input into the U-net neural network. At the same time, three hyperparameters that have more influence on the network training are discussed in detail, and the optimal combination of hyperparameters is determined. Finally, the prediction set is fed into the trained model for prediction computation, and the results are subjected to the inverse normalization operation, whose predictive results are consistent with those calculated by the finite volume method. In addition, the computational time is shortened from 300 to 0.07 s, and the prediction variance does not exceed 0.055 K2. The results show that the proposed method can be used to obtain the temperature of immersed transformer windings quickly, which provides an effective tool for real-time temperature simulation of the digital twin of power transformers.

Three-Dimensional Mechanistic Modeling of Time-Dependent Dielectric Breakdown in Polycrystalline Thin Films

Time-dependent dielectric breakdown (TDDB) is a crucial issue for the dielectric reliability. In this work, we present a full three-dimensional mechanistic model for calculation of the TDDB process in polycrystalline thin films. The model is based on the multiphonon trap-assisted tunneling theory and takes into account the intrinsic three-dimensional discreteness of traps at the dielectric grain boundaries. The leakage current density is calculated by solving coupled three-dimensional master equation and Poisson equation. The net phonon emission associated with each charge trapping and release event is treated as a local point heat source, which then enters the Fourier heat equation for three-dimensional temperature distribution calculation. The generated trap is determined by local temperature and electric field, which is subsequently included in the next round of calculation of electric and thermal properties. A positive feedback loop gradually leads to an increase of trap density, temperature, and leakage current density, and finally the dielectric breakdown. Our model can, to a good approximation, reproduce the experimental leakage current density-voltage characteristics and the Weibull distribution of time to breakdown at different dielectric thicknesses, stress voltages, and environmental temperatures. We find that in realistic devices, the three-dimensional trap-to-trap transport of electrons contributes a non-negligible part to the leakage current when the dielectric approaches breakdown. Our approach of three-dimensional mechanistic simulation is computationally efficient such that evolution of ${10}^{3}$ traps during the TDDB process can be easily performed on a standard desktop computer.

Calculation of termostabilization system led matrices by heat pipes

Using the method of electrothermal analogy, a mathematical model of the thermal stabilization system of the LED matrix with a heat pipe was developed. The system of differential equations is solved, including the stationary equation of heat conduction and the equation of heat generation, which are supplemented by boundary conditions of conjugation for heat fluxes and temperatures. The calculated temperature distribution in the structural elements of the thermal stabilization system depending on the power of the LED matrix, heat pipe parameters and the temperature of the environment. It is shown that the use of the proposed thermal stabilization system will allow to increase the luminous flux of the LED-matrix (increase the light power) without increasing the temperature of its active zone. This will allow to reduce the number of LED-matrix in the semiconductor lamp and its cost without shortening the service life.

Effect of the phase-transition fluid reaction heat on wellbore temperature in self-propping phase-transition fracturing technology

The key to the success of self-propping phase-transition fracturing (SPF) technology using two immiscible fluids to generate proppants in-situ in a reservoir lies in accurate calculations of temperature distribution. As the reaction heat of phase-transition fluid (PF) significantly affects wellbore temperature, reaction kinetic parameters were fitted by experimental data based on the Arrhenius equation, and the transient temperature model considering the reaction heat is established based on the first law of thermodynamics. This model is discretized by the finite difference method and solved by the successive over-relaxation iteration method. The results show that the reaction heat effect on wellbore temperature cannot be ignored. A temperature value and a phase transition time at the well bottom are the largest in the whole wellbore, so the phase transition ratio at the well bottom is the largest. Moreover, since the PF with incomplete phase transition in a wellbore is easier to enter fractures and prop fracture fronts, it is recommended to inject a pre-pad fracturing fluid before injecting PF to reduce wellbore temperature and prevent premature phase transition in the wellbore. These findings can help reveal the action mechanisms of different injection methods and parameters in a heat transfer process, which is of great significance for the theoretical research and field implementation of SPF technology.

Strength Failure of CO2 Injection Tubular Strings Considering CO2 Phase Transition

Compared with traditional injection tubular strings, the stresses on CO2 injection tubular strings are more complex. The results from field applications show that the phase transition of CO2 fluid in CO2 injection strings is an important factor in the calculation of temperature distribution and analysis of string mechanics. Therefore, we propose a strength analysis method for CO2 injection tubular strings that considers the CO2 phase transition. We selected four CO2 injection strings in an oil field in China as examples to evaluate their strength and safety. First, we established coupled differential equations for the temperature, pressure, and physical parameters of CO2 injection strings according to the theory of fluid flow and heat transfer. Then, we used an adaptive fuzzy neural network to construct the model for calculating the CO2 convection heat transfer coefficient and used this to obtain the high-precision convection heat transfer coefficients of tubular strings under conditions of CO2 flooding. We analyzed the injection-string deformations that resulted from the piston, spiral bending, expansion, friction and temperature effects according to the stress characteristics of the CO2 injection strings with packers under different working conditions. Finally, we performed mechanical analyses on the collapse resistance, internal pressure resistance, and tensile and triaxial stresses of the CO2 injection strings, and the results of these analyses provide a theoretical basis for the strength analysis of CO2 injection strings.

Calculation of microwave heating temperature distribution based on SVD truncation

In mathematical models of microwave heating with infinite-dimensional characteristics, it is difficult to use traditional numerical methods to improve computational efficiency. In this work, we propose a fast and accurate method to calculate the temperature distribution of materials under microwave heating. First, we analysed the relationship between the choice of model order and the solution accuracy by downscaling the infinite-dimensional heat conduction partial differential equation (PDE) model into a finite-dimensional ordinary differential equation (ODE) model. Additionally, the effect of different boundary conditions on the global temperature distribution was analysed. Second, the equilibrium conversion matrix was calculated using the singular value decomposition (SVD) truncation method under homogeneous boundary conditions. Using this matrix, a lower-dimensional microwave heating ODE model was further obtained. Finally, the numerical simulation results showed that the root mean square error (RMSE) was only 0.07 and the maximum relative error was only −0.85%. The computation time of the equilibrium conversion matrix was 2.12 ∼ 3.00 ms, and the model calculation time was reduced by 97.78%. We compared the calculated temperature rise curves with those obtained using the conventional COMSOL model. The SVD truncation method achieved an efficient and accurate solution for the microwave heating model.