3D FE model of frictional heating and wear with a mutual influence of the sliding velocity and temperature in a disc brake

Numerical simulation of frictional heating in a disc brake of a typical passenger vehicle based on the equation of motion and the boundary-value problem of heat conduction was carried out. An influence of temperature-dependent coefficient of friction on the sliding velocity, braking time, braking distance and the thermomechanical wear was studied. Two materials of the pad combined with the cast-iron brake disc were examined. The dependencies of the coefficient of friction and wear rate on the temperature and contact pressure were derived from experimental measurements and implemented to the computational model of the brake. Comparisons of temperature for validation purposes calculated using the contact model developed in this study were made with the model introducing an approach based on the heat partition adopted from other studies.     

Three-dimensional non-isothermal model development of high temperature PEM Fuel Cells

A three-dimensional non-isothermal mathematical model is developed in a triple mixed serpentine flow multichannel domain for a high temperature PEM Fuel Cell having a phosphoric acid doped PBI membrane as electrolyte and an active area of 25 cm² within Comsol Multiphysics. The inlet temperatures of cathode and anode reactants are taken as 438 K. Model predicts pressure, and temperature distribution along the channels and membrane current density distribution over the membrane electrodes. The model results are obtained at two different operation voltages, 0.45 V and 0.60 V. Resulting average current densities are respectively 0.313 A cm^?2 and 0.224 A cm^?2. The non-isothermal model results are compared to isothermal model results from a previous study and various other single channel non-isothermal model results available in the literature. The pressure drop at cathode compartment is predicted to be 6500 Pa, whereas it is found to be 6400 Pa for the isothermal model. The temperature difference within the system is found to be 0.18 K for the operation voltage of 0.6 V, whereas this value increases to 0.31 K for the operation voltage of 0.45 V. The temperature difference isocontours are illustrated for the whole cell. Considering changes in temperature, one can employ isothermal operation assumption for this system as an approximation and simplification for the governing equations, since the variation in the temperature within the cell is less than 1 K. It should be emphasized that multichannel model predictions are more realistic compared to single channel models. The model developed here can be extended to larger electrode active area and different multichannel configurations.     

Wellbore temperature and pressure calculation model for supercritical carbon dioxide jet fracturing

A new numerical calculation model for wellbore temperature and pressure for SC-CO₂ jet fracturing was proposed in this research. In our model, the impact of tubing, casing, and cement on heat transfer, and the heat generated by fluid friction losses are all taken into consideration. The CO₂ physical properties are calculated by the Span–Wagner and Vesovic models. Based on our calculation model, the factors that may affect the wellbore temperature and pressure are discussed. The results indicated that ignoring the influence of the cement sheath thermal resistance on heat transfer would lead to a wellbore temperature higher than the actual value. The wellbore CO₂ pressure is always higher than its critical value, but the CO₂ temperature at the jet point in some cases is lower than its critical value. The wellbore CO₂ temperature is increased with the increase in injection temperature and cement sheath thermal conductivity and the decrease in annulus injection rate and coiled tubing injection rate. However, the decrease in the coiled tubing injection rate and increase in the cement sheath thermal conductivity are the only effective ways to ensure that the CO₂ temperature at the jet point exceeds its critical value.     

Three-dimensional layered electrochemical-thermal model for a lithium-ion pouch cell

Performance of lithium-ion pouch cell cannot be evaluated only by its external characteristics, such as the surface temperature and potential, as the internal electrochemical and thermal properties of the cell can significantly affect its performance. However, it is difficult to observe the internal thermal and electrochemical characteristics by means of experiment. Within this study a layered three-dimensional electrochemical-thermal coupled model of a lithium-ion pouch cell is proposed, then it is verified by experimental method at several discharge rates. According to this model, the spatial distribution of temperature field and heat generation rate are analyzed at four discharge rates, a fitted surface equation is presented for this battery to roughly predict the heat generation rate according to the discharge rate and depth of discharge. Afterward, several representative electrochemical properties (electric potential, electrolyte concentration, electrode current density, and mass transfer process) are investigated from the spatial perspective, which reveals the transfer process of lithium-ion and current clearly inside the battery. It is also concluded that there exists a gradient both at the plane and thickness of the electrode, and the gradient in the thickness direction is larger than that in the plane. A large gradient in temperature, lithium-ion concentration, electrode potential and current density distribution are located at the connection between tabs and electrodes.     

Wellbore temperature and pressure calculation model for coiled tubing drilling with supercritical carbon dioxide

To better control the state of carbon dioxide during supercritical carbon dioxide drilling, a mathematical model is established to analyze the wellbore carbon dioxide temperature and pressure influencing factors. In this model, the influences of formation temperature change and fluid-friction-generated heat on wellbore temperature distribution are considered. Additionally, the impact of casing, tubing, and cement sheath thermal resistance on heat transfer are considered. The model is validated by comparing the wellbore temperature data calculated from this model with data from previous models. Based on the model, the factors that may affect the wellbore carbon dioxide temperature and pressure are analyzed. The results show that the downhole temperature decreases with the decrease in nozzle diameter and geothermal gradient, and with the increase in injection rate. The injection temperature significantly affects the wellbore temperature near the wellhead, but it does not affect the downhole temperature. Therefore, for low geothermal gradient formation, reducing the injection rate and increasing the nozzle diameter are two effective methods to maintain the CO₂ at the downhole in the supercritical state. The pressure inside the coiled tubing increases with the increase in injection rate and decrease in nozzle diameter, but the injection temperature and geothermal gradient has little effect on the pressure inside both the coiled tubing and annulus.     

Three-dimensional driven-cavity flows with a vertical temperature gradient

Numerical studies of three-dimensional flows in a cubical container with a stable vertical temperature stratification are carried out. Flows are driven by the top lid, which slides in its own plane at a constant speed. The top wall is maintained at a higher temperature than the bottom wall. The end walls and the side walls are thermally insulated. Numerical solutions are obtained over a wide range of physical parameters, i.e. 10² ≤ Re ≤ 2 × 10³, 0 ≤ Ri ≤ 10.0 and Pr = 0.71, where the mixed-convection parameter Ri Gr. Re⁻². Systematical comparison of the three-dimensional numerical solutions with the previously reported two-dimensional results illuminates the impact of thermal stratification on the three-dimensional flow characteristics. When Ri < O(1), the effect of the vertical temperature gradient is minor, and the flow structures are similar to those of the non-stratified fluid flows in a conventional lid-driven cavity flow. Fluids in the primary vortex are well mixed, and the temperature is fairly uniform in the main circulating region. When Ri ≥ O(1), the stable temperature distribution tends to suppress the vertical fluid motion. Much of the fluid motion takes place in the vicinity of the top sliding lid and the bulk of the cavity region is nearly stagnant. When Ri > O(1), the fluid motion exhibits vertically layered vortex structures. The Nusselt number is computed at the top and bottom wall, and this also illustrates the varying flow characteristics as Ri encompasses a broad range. Extensive numerical flow visualizations are conducted. Plots demonstrating the primary flows in the (x−y) plane and the secondary flows in the (y−z) plane are presented. These display the influences of Re and Ri on the basic character of the flow and the three-dimensional effects.     

Three-dimensional model for stacks of tubular high temperature proton exchange membrane fuel cells incorporating a thin layer approach for the membrane electrode assembly

A three-dimensional, non-isothermal, steady state model for stacks of tubular high temperature proton exchange membrane fuel cells (HT PEM FCs) is developed. It is based on a thin layer approach for the membrane-electrode assembly while retaining Butler-Volmer kinetics, concentration and Ohmic losses on both electrodes. It solves for flow, temperature and concentration fields as well as locally resolved current densities for multiple cells. Single cell results for the polarization curve compare well with experimental data for single tubular HT PEM FCs. The model allows for efficient simulations of stacks of multiple tubular HT PEM FCs with a shared air channel in which the interactions between local FC performance and flow, temperature and concentration fields pose a major design challenge. The effects of flow field design, flow rate and cell distance in a stack of 7 tubular cells are investigated and basic approaches for the design of such stacks are derived.     

A simple improvement of a tip loss model for actuator disc simulations

The loading of a wind turbine decreases towards the blade tip because of the velocities induced by the tip vortex. This tip loss effect has to be taken into account when performing actuator disc simulations, where the single blades of the turbine are not modeled. A widely used method applies a factor on the axial and tangential loading of the turbine. This factor decreases when approaching the blade tip. It has been shown that the factor should be different for the axial and tangential loading of the turbine to model the rotation of the resulting force vector at the airfoil sections caused by the induced velocity. The present article contains the derivation of a simple correction for the tangential load factor that takes this rotation into account. The correction does not need any additional curve fitting but just depends on the local airfoil characteristics and angle of attack. Actuator disc computations with the modified tip loss correction show improved agreement with results from actuator line, free wake lifting line, and blade element momentum simulations.     

Heat conduction calculation for a model of the surface of the moon

Four layers, a dust layer, an anorthosite layer, a basalt layer and a dunite layer, have been used to model the surface of the Moon 4·6 billion years ago. The equations describing heat conduction with or without radioactive heating have been written and Laplace transform techniques have been applied. The thermal history of the imbedded basalt-like material has been found by numerical inversion of the Laplace transform. The objective of the present analysis is to determine whether the solidification of the basalt could be delayed about 1 billion years to produce the observed age difference between the dust and the crystalline rocks found on the surface of the Moon.     

动力电池内部温度梯度反演计算

电池在充放电过程中内部温度的分布特征对于锂离子电池热管理系统的设计十分重要。根据电池的物理结构,将圆柱型电池内部平均分成若干等温层,建立了电池沿径向的产热和传热模型,将测试获得的电池表面温度和热流密度作为边界条件,假设热量从中心向外传递过程中等温层之间的热流密度线性增加,提出了一种计算电池沿径向内部温度分布的方法,并在电池内部中心放置热电偶,验证了该方法的准确性。计算结果表明,电池内部温度并非线性分布,在靠近电池中心位置处相邻等温层之间的温度梯度较小,而在靠近电池表面区域附近相邻等温层之间的温度梯度较大。该计算方法在20～40 ℃环境温度区间内具有较高的精度,而在−10 ℃环境温度下误差会偏大些。     

Analysis of wake states by a full-field actuator disc model

Various wake status have been analysed by a numerical method that combines the actuator disc principle with the Navier–Stokes equations. Results are compared with one-dimensional momentum theory and experiments. The computations are in excellent agreement with one-dimensional momentum theory for rotors working in the windmill brake state as well as in the propeller and hover states. The computations demonstrate that the turbulent wake and vortex ring states are unstable regimes for a rotor with constant loading and that these states, after a complicated transient phase, settle to a steady state. Copyright © 1998 John Wiley & Sons, Ltd.     

八轴机车轴箱三维结构设计及强度计算

轴式为C0-C0的DF4、DF8和DF11系列内燃机车已不适应于牵引5 000 t重载列车,开发大功率的八轴内燃机车是一种较好的技术措施.采用B0-B0 B0-B0轴式的八轴机车的动力学性能,尤其是曲线通过性能较好.但这种结构由于增加了两个动力轮对和两个过渡构架及三系悬挂,增加了车体的长度和机车总体高度,为了满足机车限界要求,给轴箱设计带来了很大困难,因而轴箱结构型式与常用的转臂式轴箱不同.强度计算表明,八轴机车轴箱新型结构型式满足强度要求.     

On the calculation of the temperature distribution in a packed bed for solar energy applications

Calculations utilizing the exact solutions for the temperature distributions of the solid in and the fluid flowing through a packed bed with arbitrary initial bed temperature and arbitrary inlet fluid temperature have been carried out. The computational method allows a reversal of the direction of the flow at arbitrary times. The influence of the nondimensional frequency of a periodic flow reversal on the bed and fluid temperatures at the steady periodic state are presented.     

Three-dimensional model of a 50 cm high temperature PEM fuel cell. Study of the flow channel geometry influence

In this work, a three-dimensional half-cell model for a 50 cm² high temperature polyelectrolyte membrane fuel cell (HTPEMFC) has been implemented in a Computational Fluid Dynamics (CFD) application. It was solved for three different flow channel geometries: 4-step serpentine, parallel and pin-type. Each geometry leads to a very well defined current density profile which indicates that current density distribution is directly linked to the way reactants are spread over the electrode surface. The model predicts that parallel flow channels present a significant lower performance probably due to the existence of preferential paths which makes the reactant gases not to be well distributed over the whole electrode surface. This results in lower output current densities when this geometry is used, especially at high oxygen demand conditions. This behavior was also detected by experimental measurement. Serpentine and pin-type flow channels were found to perform very similarly, although slightly higher limit current densities are predicted when using serpentine geometry. Inlet flow rate as well as temperature influence were also studied. The model predicts mass transfer problems and low limit current densities when the fuel cell is fed with small oxygen flow rates, whereas no differences regarding average flow rates are noticed if it is over increased. Better fuel cell performance is predicted while temperature grows as it could be expected.     

New optimized model for water temperature calculation of river-water source heat pump and its application in simulation of energy consumption

The energy consumption calculation plays an important role in the analysis of project economic and social benefits. In order to calculate energy consumption accurately, this research presents a water temperature of condenser inlet calculation model of river-water source heat pump unit. The feasibility and calculation error of the model had been analyzed. Additionally, the new water temperature calculation model had been validated via an engineering case. The results showed that the hourly water temperature in 24 h could be replaced by daily average water temperature due to little change of the daily water temperature change. In this case, the calculation error could be less than 5%. It is found that despite water temperature has many influenced factors, there is a remarkable relationship between the daily average water temperature and daily average outdoor dry bulb temperature by data analysis (R² ≈ 0.9). The influence of river sampling location on water temperature calculation of condenser inlet could be ignored due to slight temperature changes (within 0.15 °C). The method proposed in this paper met the engineering accuracy and provided a very effective method for the engineering calculation of energy consumption of water chilling unit.     

A model for the calculation of solar global insolation

A theoretical model is described that is designed to give the total global insolation falling on the earth's surface and the transmission of the atmosphere. It is compared to a model by Braslau and Dave[1] and found to agree to within a few percent in all cases. Climatogical values of total pricipitable water, turbidity, and surface albedo are required as the model inputs, and the sources of these data are described. The model has been applied to 26 stations in the National Weather Service (NWS) pyranometer network, where measured true solar noon atmospheric transmission values are available, as part of the NOAA program to rehabilitate the old pyranometer observations. For three of these stations where reliable true solar noon irradiance and transmission values are available, the model calculations and observations are compared. At 18 locations the calculated and measured daily mean insolation values are compared for clear days. At one location (Boulder, Colorado) calculated and measured radiation climatologies for all weather conditions are compared. In all comparisons the model and observations differ by no more than 2.7 per cent, which is within the experimental accuracy (±5 per cent) of the pyranometers. Possible sources of errors are discussed.     

Analysis of models for calculation of temperature of anode plasma electrolytic heating

Plasma electrolytic processes used for treatment of materials are based on their heating in a vapor–gaseous medium. This work is concerned with the thermal models for calculation of the steady-state temperature of anode heating, which are based on solution of the heat conduction equation in a continuous and stable vapor–gas envelope (VGE). These models provide the decreasing current–voltage (CVC) and the increasing temperature–voltage (TVC) characteristics of anode heating, which are qualitatively agreed with experimental data in the voltage region corresponding to stationary heating up to 400–1000 °C. The analysis of assumptions accepted in these models has shown that the agreement between calculated and experimental data can be improved by taking into account the temperature dependence of thermal conductivity coefficient of vapor. This agreement remains unchanged when taking into account the role of the space charge in the envelope. Mean estimates of a value of effective electrical conductivity of the vapor envelope (2.13 × 10^?3 S/m) and the mobility of ions in the envelope (1.6 × 10^?4 m²/(Vs)) with the experimental data for aqueous solutions of ammonium nitrate in the concentration ranging from 1 to 3 mol/l have been obtained.     

Three-dimensional,two-phase,CFD model for the design of a direct methanol fuel cell

This study presents a computational fluid dynamics (CFD) model for modelling gas evolution and current distribution in a direct methanol fuel cell (DMFC). The improved two-phase model includes a new sub-model for estimating the interface mass transfer without empirical correlations. Simulation results in a horizontal channel of the DMFC agree with typical trends reported in the literature for bubbly flows. The increase in inlet flow rate is found to lead to a decrease in the gas content in the outlet of the anode channels. A case study illustrates applications of the CFD model for modelling gas evolution and current distribution in a DMFC with a parallel flow-field design. Simulation results with a improved two-phase model provide an explanation of experimental observations of a transparent DMFC with parallel channels. An improved three-dimensional CFD model includes all relevant phenomena and is valuable for gas management in a DMFC design.     

Three-dimensional computational fluid dynamics model of a tubular-shaped PEM fuel cell

A full three-dimensional, non-isothermal computational fluid dynamics model of a tubular-shaped proton exchange membrane (PEM) fuel cell has been developed. This comprehensive model accounts for the major transport phenomena in a PEM fuel cell: convective and diffusive heat and mass transfer, electrode kinetics, and potential fields. In addition to the tubular-shaped geometry, the model feature an algorithm that allows for more realistic representation of the local activation overpotentials which leads to improved prediction of the local current density distribution. Three-dimensional results of the species profiles, temperature distribution, potential distribution, and local current density distribution are presented. The model is shown to be able to understand the many interacting, complex electrochemical, and transport phenomena that cannot be studied experimentally.     

Thermodynamic calculation and reference electrode calibration for high temperature molten salts

Abstract

Molten salts are important reaction media for chemical and electrochemical processing and have recently attracted attention for their potential in reprocessing and partitioning spent nuclear fuels. Electrochemical measurements are a convenient tool for exploring thermodynamic and kinetic properties of molten salts, but inconsistency in acquired data may arise from the use of inaccurate reference electrodes and differences in thermodynamic calculations. A thermodynamic approach to the calculation of half cell potentials for reactions in molten salts is proposed. As examples, chlorine/chloride and lithium ion/lithium half cell potentials in LiCl–KCl eutectic are thermodynamically analysed. The Ag/AgCl reference electrode is discussed as an example of a high temperature reference electrode. A technique involving in situ transient reduction of constitutive metal ions for the calibration of high temperature reference electrodes is developed which may enable the consistency of acquired data using different reference electrodes in a variety of molten salts. The thermodynamic approach and calibration technique may be extended to ionic liquid and other media at high and low temperatures.