Steady-state Temperature Field Research Articles

Transfer learning of convolutional neural network model for thermal estimation of multichip modules

This paper proposes a transfer learning approach to reduce the dependence of the neural network model on dataset size for multi-chip modules (MCMs) thermal estimation. The dataset that resembles the target task is used to pre-train a convolutional neural network model; then, it is fine-tuned using a much smaller dataset belonging to the target task. This process enables the model to adapt and refine its thermal estimation capabilities for the particular MCM under consideration with sparse data. Results show that the model effectively utilizes the geometric shapes and power details of MCMs to precisely predict steady-state temperature fields and junction temperatures. In a complex five-chip configuration, the fine-tuned model achieves a prediction error of only 1.17 % and accelerates inference speed by three orders of magnitude compared to traditional simulations. Additionally, the transfer learning model requires only 1/8 the dataset size and less than 1/3 the training time compared to a model with random initial parameters to achieve similar accuracy. The results indicate that this model can significantly enhance the utilization efficiency of historically accumulated MCM heat transfer datasets for new demands such as real-time thermal estimation and fast optimization of chip configuration.

A digital twin model of the axial temperature field of a DC cable for millisecond calculations

The most important features of digital twin technology for transmission and transformation equipment are symbiotic evolution and state prediction. In constructing the digital twin model for DC cables, the transient and steady-state temperature fields need to be considered comprehensively in the modeling process to consider the multi-physical field coupling, mathematical model, operational data, and environmental conditions in specific cases, which makes it difficult to satisfy the real-time requirements of the digital twin. To solve this problem, in this paper, a digital twin technology architecture for DC cables is proposed, and a neural network learning model is constructed to minimize the latency due to the complexity of the model simulation. Moreover, an efficient digital twin model that is based on the model-driven approach is developed for the fast computation of the axial temperature field of DC cables. The use of the Sequence-to-Sequence residual neural network algorithm for the reduced-order multi-physics field coupling modeling reduces the computational time and ensures as much accuracy as possible up to the finite element model simulation. The simulation results show that the use of the digital twin model reduces the simulation time from 275 s to 0.56 s, and the relative error between the accuracy of the digital twin model and the finite element model for the axial temperature field of the DC cable is 0.46 %. Finally, verification of the reasonableness and feasibility of the proposed method is carried out via an experimental platform according to the standard of CIGRE TB496. In particular, the maximum value of the DC cable temperature is verified to have a small error compared with the result of the Sequence-to-Sequence calculation under specific working conditions.

Experimental and numerical analysis of heat transfer mechanisms for two-phase oil-refrigerant flow process in the cylinder of rotary compressor

Investigating the heat transfer mechanisms in rolling piston type rotary compressors is crucial for improving their operational efficiency. A thermal test platform was established and steady-state temperature fields of key components were measured under various conditions, revealing a correlation between these temperatures and crank angles, except near the angle of 54° for the cylinder head-up. It provided important boundary conditions for simulation research. A novel three-dimensional fluid–solid-heat coupled simulation method was proposed, calculating heat transfer coefficients at fluid–solid interfaces. The two-phase heat transfer characteristics post oil–gas miscibility was studied, arising from the injection of lubricating oil into the working chamber. Two-phase oil-refrigerant mixtures, compared to single-phase refrigerant, increased heat transfer coefficients by 2.35 % in the suction channel and 2.99 % in the cylinder head-up, but decreased by 5.85 % in the cylinder head-down, 17.42 % in the piston, and 5.63 % in the cylinder. Oil injection was found to significantly enhance convective heat transfer in the suction chamber, increasing suction superheat in the cylinder by up to 29 K and reducing temperature of the compression chamber by up to 17 K. These results provide novel insights into the complex heat transfer in rotary compressors.

Nonlinear coupled multi-physics field analysis of permanent magnet synchronous motor combining finite element analysis with optimized meshless method

Aiming at significant disadvantages of finite element analysis (FEA) performed in coupled multiphysics field calculation, including high computing cost and strong dependency on meshing quality. Taking a high-speed permanent magnet synchronous motor (P MSM) as an example, an approach combining FEA with optimized meshless method is proposed to solve the heat transfer problem. Firstly, electromagnetic losses under rated and 1.2 times overloaded operation conditions are calculated using FEA respectively. Secondly, three-dimensional FEA flow models considering the influence of viscosity varying with temperature are established. Thirdly, convective heat transfer coefficients are calculated as the boundary condition, after which the electromagnetic losses as heat sources are mapped to the threedimensional steady-state temperature field calculations using FEA and conventional meshless method respectively. Applying the above two methods, a singular boundary method (SBM) is employed to replace the temporal derivative term of the transient calculation equation. Finally, to mitigate the illconditioned matrix appearing in the conventional meshless method coupled with FEA, an optimized meshless method is proposed to recalculate the heat transfer equation. After that, the calculation results of the above methods are compared with experimental results. This research is beneficial for the multiphysical coupling analysis of electrical equipment with complex structures considering nonlinear factors.

Exploration of Temperature Inversion in Intermediate Joints of 10 kV Three-Core Cable

In order to precisely ascertain the temperature at the hot spot within the intermediate joint of a three-core cable, this study focused on a 10 kV three-core cable joint as its primary subject. A three-dimensional finite element model of the cable joint was constructed, enabling the calculation of both the steady-state hot spot temperature field distribution and the transient temperature rise curve of the joint. Employing a one-dimensional transient thermal path model for the cable body, a radial inversion model for the cable core temperature was established. Through simulating the transient temperature field of the cable joint under varying currents, a fitting relationship was determined for the axial temperature points of the cable core. Subsequently, an inversion perception model was devised to calculate the hot spot temperature of the cable joint based on temperature measurements at specific points on the outer surface of the cable. Under both continuous and periodic loads, the inversion results revealed a consistent trend in the temperature at the joint crimping point with the finite element calculation outcomes, demonstrating a maximum error of within 3 degrees Celsius. This verification underscores the precision of the temperature combination inversion method when applied to three-core cable joints.

Thermal Simulation of Burned Nuclear Fuel Elements

An adjustable description of the temperature distribution in the nuclear fuel elements is evaluated to the prediction of the lifetime behavior of these components. The impact of the fuel and coolant temperature on the neutron reaction rates provides an incentive for accurate modelling of the temperature behavior under transient as well as steady-state operating conditions. This paper is to focus on the steady-state temperature field in the fuel elements. Many of the principles applied are also useful for describing the temperature field in the structure component.

Inverse Design of Axis Fan for Permanent Magnet Drive Motor for Special Vehicles

The control of mechanical energy loss is especially key in the design of permanent magnet drive motors for special vehicles. This paper takes a 300 kW high-efficiency motor as an example, and under the operating condition of 9000 rev/min, in order to control the size of the mechanical loss Pmech, improve the efficiency of the motor, as well as enhance the ventilation and heat dissipation performance of the motor, the structural parameters of the motor’s Axis fan are identified by using the Reverse Engineering (RE), and the fan performance is simulated and analysed by using the standard k-ε turbulence model of Computational Fluid Dynamics. The mechanical loss calculation model is investigated, and the effects of different blade numbers, wrap angles, and mounting angle parameters of the fan on the mechanical loss Pmech are derived. And finally, the scheme is calculated to show that when the blade number Z is 13, the wrap angle Δφ is 60°, the front mounting angle Φ1 is 45°, and the rear mounting angle Φ2 is 30°, the mechanical loss Pmech decreases from 8.0 kW to 2.54 kW, and the motor efficiency η0 is greatly improved, increasing from 94.2% to 96.1%. Meanwhile, based on finite element simulation experiments, the effects of the motor Axis fan on the steady-state temperature field of the pre-optimised and post-optimised fans are compared, and the optimised axis fan makes the motor ventilation and heat dissipation more reasonable. The maximum temperature of the motor under the same working condition decreased by 16.7 K, the efficiency η0 of this motor was greatly improved, and the efficiency η0 increased from 94.2% to 96.1%.

Seismic structure beneath the Avacha and Koryaksky volcanoes in Kamchatka based on the data of permanent and temporary networks

Avacha and Koryaksky are active volcanoes located in the vicinity of Petropavlovsk-Kamchatsky, the main city of Kamchatka, and they represent a serious hazard to the surrounding population and infrastructure. Here we investigate the upper-crustal structure beneath these volcanoes by implementing local earthquake tomography based on data from permanent seismic stations and from a temporary network installed in 2018–2019. Although the total amount of seismic rays recorded by the temporary network dataset is much lower, adding this data and attributing an appropriate weight lead to considerable increase of the resolution compared to the case of using merely the permanent network data. The resulting distributions of the P and S wave velocities, and especially the Vp/Vs ratio, reveal two magma reservoirs located below Avacha and Koryaksky volcanoes. Different depths of their upper limits explain differences in the eruption activity styles of these volcanoes. Below the Avacha Pass, we observe a thick layer of low-velocity soft volcaniclastic sediments formed due to the activity of both volcanoes. A conservative numerical estimate of a steady-state conductive temperature field around the magma source below Avacha demonstrates that the high temperature zone can be reached by drilling a well to a reasonable depth, thus suggesting that the area might be exploited as a source of geothermal energy.

Steady-State Temperature Field and Rolling Resistance Characteristics of Low-Speed and Low-Load Capacity Non-Pneumatic Tires

Rolling resistance (RR) is key research content for developing low-carbon energy-saving tires, and the resultant change in the tire temperature field exerts a crucial impact on tire performance. Currently, there is no accurate and systematic analysis method for solving the steady-state temperature field (SSTF) and RR of tires with complex patterns and non-pneumatic tires (NPTs), which are characterized by discontinuous structure in the circumferential direction. A solution strategy that entails SSTF and RR based on explicit transient rolling analysis and thermal-mechanical coupling is proposed and its accuracy is verified using the SSTF test pertaining to the low-speed and low-load capacity non-pneumatic tire (LSL-tire), which exhibits a 7.56% and 6.94% average temperature deviation for the outer surface center of the tread and for the outer surface center of spokes, respectively. Uniaxial tensile mechanical property tests and dynamic mechanical analysis (DMA) of the utilized rubber and polyurethane (PU) materials were conducted, and their specific heat capacity, thermal conductivity, and density were tested. Based on three-dimensional nonlinear finite element simulation and considering the characteristics pertaining to the loss factor of viscoelastic materials changing with temperature, the SSTF and RR of the LSL-tire under different loads and velocities were analyzed. The results indicate that the influence of load and speed on the SSTF of LSL-tire is quite significant, whereas the influence of speed on the RR is not apparent. For all conditions, the highest steady-state temperature points of the tread are located in its center, and in the spokes they are located in the joint between spokes and the outer ring; the spokes contribute the most to the RR, followed by the tread.

The research of a multi-stage roller type magnetorheological transmission device on temperature properties

Magnetorheological Transmission Device (MRTD) is a controllable power regulation device using magnetorheological fluid as the transmission medium. It has characteristics of fast response, a wide range of speed regulations, and a pollution-free environment. The traditional pairwise transmission structure has serious heat generation problems during operation, resulting in low transmission efficiency. Therefore, we innovatively propose a multi-stage roller type MRTD to improve the heat generation problem fundamentally. The steady-state and transient temperature fields of the multi-stage roller type MRTD are simulated using the thermal analysis module in ANSYS based on the temperature field formulation. The variations of internal temperature at different slip powers are obtained. The results show that the designed multi-stage roller type MRTD has a good suppression of temperature rise. This study can provide a new approach to improve the thermal performance of MRTD.

A fast computational method for internal temperature field in Oil-Immersed power transformers

In order to improve the computational efficiency of the steady-state temperature rise of oil-immersed power transformer windings, this paper proposes a temperature field reduced order model(ROM) based on proper orthogonal decomposition (POD) and response surface method(RSM). The method takes the operating conditions of the transformer as input and uses the POD method as a carrier, and establishes a fast calculation model of the steady-state temperature field through RSM, thus achieving fast calculation from transformer operating data to the entire temperature field. The paper first analyzes the reduction characteristics of the POD method, and then introduces the RSM to establish the correlation between the POD modal coefficients and the transformer conditions. Compared with traditional surrogate models, this method can obtain high-precision surrogate relationships with a small number of sample points, and the time cost of establishing is relatively low. The method aims to quickly obtain the POD modal coefficients through the winding conditions, thereby skipping the complex nonlinear calculation and efficiently reconstructing the winding temperature field with the reduced modal. The related examples show that the method has good computational accuracy and efficiency. In a 2D forced oil circulation cooling model, out of 100 test conditions, the error is not more than 2.0 K compared with the full-order calculation, and the total calculation time is only 3.13 s. Finally, based on a 35 kV natural oil circulation cooling transformer, a temperature rise test platform is constructed to verify the effectiveness of the method. The experimental results show that the calculated error of the ROM is not more than 5 K compared with the experimental results, and the single-step calculation time is only 0.73 s, which has greatly improved the computational efficiency compared with full-order calculation of the same scale. The proposed method in this study achieves a second-level calculation efficiency for the transformer winding temperature, providing a feasible solution for digital online monitoring of transformer temperatures.

Simulating the Electrochemical-Thermal Behavior of a Prismatic Lithium-Ion Battery on the Market under Various Discharge Cycles

In this paper, a computational fluid dynamics (CFD) model to predict the transient temperature distributions of a prismatic lithium-ion polymer battery (LiPo) cooled by natural convection at various discharge cycles is developed. The thermal behavior of a lithium-ion (Li-ion) battery cell is important for its safety, performance and degradation, and it requires both measurement and modeling. However, most existing thermal models for Li-ion battery cells only account for steady-state temperature fields, while the exercise of a Li-ion battery cell is usually transitory. The Newman’s pseudo-2D approach was used to perform an electrochemical CFD analysis. This approach treats the porous electrode as a collection of equal-sized, isotropic, homogeneous spherical particles. This simplifies the electrode microstructure and assumes a smooth and uniform lithium insertion/extraction in the electrode. The model has been validated through variable discharge rate experimental tests in a controlled chamber. Additionally, infrared images of the battery cell during discharging are taken and the experimental numerical gradient temperature was compared. We have validated the CFD simulations by comparing the temperature, state of charge and voltage curves with experimental data. The model predictions match the experimental data very well. The difficulty in CFD battery simulations with an electrochemical approach lies in the setting of many physical parameters that are difficult to find. In this work, the parameters’ characteristics of the simulated battery are assumed and validated; these can be useful for modeling batteries of the same type. Consequently, the model developed in this work can be applied to predict the temperature distribution of the LiPo prismatic battery and can be used by the battery designers and by the designers of all systems that include batteries.

An accurate and efficient implicit thermal network method for the steady-state temperature field

To calculate the temperature value accurately and efficiently, an implicit thermal network method (TNM) is developed in this study. The main idea of the method is the conversion of such time-varying observed variables as the thermal resistance and the heat source into latent variables to build the implicit thermal equilibrium equation. In the implicit TNM, the steady-state temperature is taken as an independent variable, then parameters related to the steady-state temperature can be expressed as the function of the independent variable. On this basis, implicit thermal equilibrium equations can be constructed. Finally, the steady-state temperature field can be obtained by Newton’s method in optimization. To validate the performance and effectiveness of the implicit TNM, case studies and the sensitivity analysis of algorithms are conducted. The result reveals that the implicit TNM outperforms conventional TNMs, the steady-state TNM and the transient TNM, in computation accuracy, computing time and allocated memory.

Temperature and humidity sensor monitoring of directly buried cable based on temperature field distribution simulation of power cable

Power cable is a piece of major transmission equipment, and its operating temperature as a major factor determines whether the cable system can operate safely and reliably and the current-carrying capacity. Therefore, it is of great significance to master the real-time temperature and the distribution of the power cable core. During the aging of cable insulation, temperature, as a major factor, directly determines the aging rate. One of the basic parameters on the power cable is the ampacity. If the ampacity is high, the cable will be overloaded. In this paper, the thermal circuit method is used to construct and calculate the cable, and the whale algorithm is used to estimate the temperature of the cable conductor. The conductor is estimated accurately within the allowable error range. The results are compared with the results of finite element simulation to verify the effectiveness of the finite element method. Through the experimental analysis, the model is established according to the cable trench on the spot. The steady-state temperature field is calculated through parameter setting. The average packet loss rate is 0.066 %, and the relative error is 0.32 %, which proves that this study can optimize the communication mode of the network and achieve a better monitoring effect. The method realizes the real-time temperature rise prediction of the cable core conductor by using the temperature rise of the outer skin. It can provide a certain theoretical basis for the online monitoring and engineering practical application of the cable core temperature and has practical significance.

Analytical solution for the steady-state temperature field of a linear three-pipe freezing system under hydrodynamic conditions

Artificial ground freezing construction under hydrodynamic conditions generally requires a longer period for the formation of a freezing curtain, bringing unique challenges in the prediction of the temperature distribution. In this study, a simple analytical formula for the steady-state temperature field in the freezing of a linear three-pipe system was derived based on the effect of multiple pipes and the principle of potential function superposition. The “partition and subsection” method was adopted to assume the freezing front shape of any single frozen steady-state temperature field in this system under hydrodynamic conditions and to further determine the temperature influence range of a single freezing pipe. To account for the effect of multiple pipes, the “superposition length ratio” was proposed to quantify the mutual effect of adjacent freezing pipes. An empirical formula for the superposition length ratio varying with different freezing pipe spacings and groundwater flow velocities was also presented. Finally, combined with a hydrothermal coupling numerical model and a linear three-pipe freezing model test under different hydrodynamic conditions, the analytical results were compared with the numerical and experimental results. The comparison results showed that the analytical model can effectively predict the steady-state temperature field of the linear three-pipe system under different hydrodynamic conditions, thus providing a theoretical basis for artificial freezing design under hydrodynamic conditions.

Mathematical Solution of Temperature Field in Non-Hollow Frozen Soil Cylinder Formed by Annular Layout of Freezing Pipes

With the wide application of the artificial ground freezing method in municipal underground engineering, the annular layout of freezing pipes is often adopted to form a frozen soil cylinder. However, there is still no analytical solution that can calculate the temperature distribution of frozen soil formed in this case. In this paper, a mathematical model of a steady-state temperature field of single-circle freezing is established, in which the inside of the freeze ring is completely frozen; that is, the temperature of all excavation sections is below the freezing point. Then, the analytical solution of temperature distribution is deduced through the complex variable method and potential superposition method. Comparison results of the analytical solution with those of the numerical simulation show that the analytical solution is precise enough. The temperature distribution of the main section and the intersection is approximately the same on the inner side, but the freezing effect of the main section is relatively better near the freezing pipes and outside the freeze ring. Besides, according to the derived analytical solution and common freezing parameters, a simplified formula to calculate the temperature field with enough accuracy was proposed, and the error can be controlled below 1‰. Finally, based on the simplified formula, a calculation method for frozen soil thickness and the average temperature is also given in this paper.

Research on digital twin based temperature field monitoring system for LNG storage tanks

The temperature distribution is a critical indicator of the health condition of liquefied natural gas (LNG) storage tanks. Point measurements are the main method of traditional LNG tank temperature field monitoring. To obtain more abundant temperature data and realize the digital transformation of temperature field monitoring, an LNG tank temperature field monitoring system was constructed, which consists of a model layer, a data layer, and an application layer, by combining sensing data with digital twin (DT) technology. First, the temperature distribution of the LNG storage tank under working and leaking conditions was simulated, and the sensing monitoring network was constructed by combining Fiber Bragg Grating (FBG) sensor temperature-sensing experiments. Second, a finite element calculation model of the steady-state temperature field of an LNG storage tank was developed, and the twin model was generated by fusing the sensing data to realize the inversion from local sensing data to the whole temperature field. Finally, an LNG temperature field monitoring system based on the DT was constructed. Based on physical field leakage simulations performed with the Fluent software, the functions of visual interaction, construction splitting, temperature chart analysis, leakage diagnosis, and historical data management of the twin models were realized, which provided system building samples for digital monitoring of new LNG storage tanks.

Effects of thermal dispersion on transient free convective flow in vertical porous channel filled with porous material

In this work, the effect of suction/injection on transient free convective flow in vertical porous (suction/injection on the channel surfaces) channel filled with porous material in the presence of thermal dispersion was studied. The Boussinesq assumption is applied and the nonlinear governing equations of motion and energy are developed. The time dependent problem is solved using implicit finite difference method while steady state problem is solved by perturbation technique method. The solution obtained is graphically represented and the effects of suction/injection, time, Darcy number, thermal dispersion, and Prandtl number on the fluid flow and heat transfer characteristics. During the course of computation, an excellent agreement was found between the well-known steady state solutions sand transient solutions at large value of time. Furthermore, the time required to reach steady state velocity and temperature field strongly dependent on suction/injection parameter, Prandtl number and thermal dispersion parameter. The introduction of suction/injection has distorted the symmetric nature of the flow formation.

A 3-D Finite Difference Method for Obtaining the Steady-State Temperature Field of a PCB Circuit

The temperature rise caused by the heat generated by the on-board LED driver module during work will lead to the rise of product failure rate. The thermal analysis of this drive module should not only consider the heat and packaging of the LED itself, but also the influence of other power components. Common commercial thermal simulation software, such as ANSYS ICEPAK or FLOTHEM, usually requires detailed thermal models for such printed circuit board (PCB)-level thermal simulation, and requires a large number of simulation parameter settings and a long simulation time to obtain temperature results that are barely close to the actual. In this article, a 3-D finite difference method is proposed to obtain the steady-state temperature field of PCB circuit. The model can be used to calculate the steady-state temperature field of PCB circuit by setting different component sizes, power, and thermal conductivity. This article uses this method to calculate the temperature field of PCB steady-state working with MATLAB. The experimental measurement of PCB is compared with thermal simulation by ANSYS ICEPAK. It proves that the temperature results obtained by this method are similar to the actual test temperature compared with ANSYS ICEPAK. The time required for calculation is greatly reduced.

Temperature Field and Stress Analysis of the Heavy-Concrete Transfer-Purge Chamber of the Nuclear Power Plant.

A transfer-purge chamber (TPC) is a double-steel-plate, heavy-concrete, curved-surface composite structure composed of steel plates, heavy concrete, and shear connectors. It is an important facility in the external refueling system of a nuclear power plant (NPP), providing a safe and reliable biological shielding space for reactor refueling operations. Temperature load is one of the most important factors that must be considered in the design of NPP structures. The temperature loads experienced by the TPC during its life cycle include those encountered in both normal and abnormal operation, which are distinct. In this study, we investigated the steady state and transient-state temperature fields and stresses of a TPC structure under normal operation and after 48 h of abnormal operation, respectively, which were calculated using Abaqus finite element software and the directly coupled method. During normal operation, the temperature field of the structure shows relatively uniform changes, and the temperature gradient of the internal concrete in the direction of its thickness has a constant value of 0.245 °C/cm. At the junction between the transfer and purge sub-chambers of the TPC, under the influence of wall curvature and deformation constraints, the maximum tensile strain of heavy concrete is 8.84 × 10-3, the maximum compressive strain is 2.04 × 10-3, the peak stress of the steel plate is 98.305 MPa, and the peak stress of the stud is 306.725 MPa. After 48 h of abnormal operation, the temperatures of the inner surface of the heavy concrete of the wall, the inner steel plate of the wall, the outer surface of the heavy concrete of the wall, and the inner steel plate of the wall increased by 8.12, 8.11, 0.31, and 0.30 °C, respectively. The tensile strain of the heavy concrete of the wall increased significantly by 52.64%, and the compressive strain of the concrete increased by 67.33%, whereas the stresses of the studs and steel plates increased by only 1.57% and 6.79%, respectively. These results show that the change in the temperature field greatly influences the stress and strain on the TPC structure. As measures for mitigating the development of this unfavorable situation of temperature stress concentration, the temperature operating range should be rationally controlled or the junction structure between the transfer and purge sub-chambers of the TPC optimized accordingly. The results of our study can provide basic data for a dynamic analysis of the TPC under conditions of combined earthquake and temperature loads.