Thermal-EHD contacts lubricated with oil/refrigerant solutions: a new cavitation modeling approach based on refrigerant solubility

A first cavitation modeling with thermal effects for oil/refrigerant solutions lubricated ElastoHydroDynamic (EHD) point contacts is reported in this work. The solubility of the oil/refrigerant system is introduced into the Generalized Reynolds equation coupled with the elasticity equation and the energy conservation equation. The numerical results show a very good agreement with the published experimental results concerning film thickness prediction. Moreover, the present model describes the cavitation region on a physical basis. A discussion with other cavitation models from the literature is proposed. It puts into light the necessity of taking into account the solubility of the refrigerant into oil for such problems. Compared to pure oil, oil/refrigerant solutions can potentially reduce the amount of liquid oil for the next contact due to its higher cavitation intensity.

Complete Equation of State Thermal Formulation for Simulation of CO2 Storage

Summary Storage of carbon dioxide (CO2) in depleted gas reservoirs or large aquifers is one of the available solutions to reduce anthropogenic greenhouse gas emissions. Numerical modeling of these processes requires the use of large geological models with several orders of magnitude of variations in the porous media properties. Moreover, modeling the injection of highly concentrated and cold CO2 in large reservoirs with the correct physics introduces numerical challenges that conventional reservoir simulators cannot handle. We propose a thermal formulation based on a full equation of state (EoS) formalism to model pure CO2 and CO2 mixtures with the residual gas of depleted reservoirs. Most of the reservoir simulators model the phase equilibriums with a pressure-temperature-based formulation. With this usual framework, it is not possible to exhibit two phases with pure CO2 contents. Moreover, in this classical framework, the crossing of the phase envelope is associated with a large discontinuity in the enthalpy computation, which can prevent the convergence of the energy conservation equation. In this work, accurate and continuous phase properties are obtained, basing our formulation on enthalpy as a primary variable. We first implement a new phase-split algorithm with input variables as pressure and enthalpy instead of the usual pressure and temperature, and we validate it on several test cases. This algorithm can model situations in which the mixture can change rapidly from one phase to the other at constant pressure and temperature. Then, treating enthalpy instead of temperature as a primary variable in both the reservoir and the well modeling algorithms, our reservoir simulator can model situations with pure or near pure components, as well as crossing of the phase envelope that usual formulations implemented in reservoir simulators cannot handle. We first validate our new formulation against the usual formulation on a problem in which both formulations can correctly represent the physics. Then, we show situations in which the usual formulations fail to represent the correct physics and that are simulated well with our new formulation. Finally, we apply our new model for the simulation of pure and cold CO2 injection in a real depleted gas reservoir from the Netherlands.

Transient analysis of power loss density with time-harmonic electromagnetic waves in Debye media

Due to the complex permittivity, it is difficult to directly clarify the transient mechanism between electromagnetic waves and Debye media. To overcome the above problem, the temporal relationship between the electromagnetic waves and permittivity is explicitly derived by applying the Fourier inversion and introducing the remnant displacement. With the help of the Poynting theorem and energy conservation equation, the transient power loss density is derived to describe the transient dissipation of electromagnetic field and the mechanism on phase displacement has been explicitly revealed. Besides, the unique solution can be obtained by applying the time-domain analysis method rather than involving the frequency-domain characteristics. The effectiveness of transient analysis is demonstrated by giving a comparison simulation on one-dimensional example.

A Case Study on the Deformation of Metro Foundation Pit in Silt Stratum in North China

Geological conditions of urban subway foundation pits are controllable factors in determining the deformation of pits. In this paper, the monitoring data and statistical data of a subway deep foundation pit in North China are presented and compared with those of Tianjin subway. The deformation characteristics of the proposed pit, open excavated with triple-layer steel supports, are introduced in detail. Based on the aforementioned information, the energy conservation equation of the mobilized strength design (MSD) method in which the compression deformation energy of internal support is considered is applied to predict the maximum lateral movement. The maximum lateral movement turns out to be 22.2 mm according to the improved MSD method, which is very close to the measured value.

Complete EOS Thermal Formulation for Simulation of CO2 Storage

Storage of CO2 in depleted gas reservoirs or large aquifers is one of the available solutions to reduce anthropogenic greenhouse gas emissions. Numerical modeling of these processes requires the use of large geological models with several orders of magnitude of variations in the porous media properties. Moreover, modeling the injection of highly concentrated and cold CO2 in large reservoirs with the correct physics is introducing numerical challenges that conventional reservoir simulators cannot handle. We propose a thermal formulation based on a full equation of state formalism to model pure CO2 and CO2 mixtures with the residual gas of depleted reservoirs. Most of the reservoir simulators model the phase-equilibriums with a pressure-temperature based formulation. With this usual framework, it is not possible to exhibit two phases with pure CO2 contents. Moreover, in this classical framework, the crossing of the phase envelope is associated with a large discontinuity in the enthalpy computation which can prevent the convergence of the energy conservation equation. In this work, accurate and continuous phase properties are obtained basing our formulation on enthalpy as a primary variable. We first implement a new phase-split algorithm with input variables as pressure and enthalpy instead of the usual pressure and temperature and we validate it on several test cases. This algorithm can model situations where the mixture can change rapidly from one phase to the other at constant pressure and temperature. Then treating enthalpy instead of temperature as a primary variable in both the reservoir and the well modeling algorithms, our reservoir simulator can model situations with pure or near pure components as well as crossing of the phase envelope that usual formulations implemented in reservoir simulators cannot handle. We first validate our new formulation against the usual formulation on a problem where both formulations can correctly represent the physics. Then we show situations where the usual formulations fail to represent the correct physics and that are simulated well with our new formulation. Finally, we apply our new model for the simulation of pure and cold CO2 injection in a real depleted gas reservoir from the Netherlands.

Drying of foods under intermittent supply of microwave energy: proposal for a mathematical model

Intermittent microwave drying improves the quality of the dehydrated product, because reduces the effect of microwave hot spots. Mathematical modelling is essential to understand the physics of this drying process and to optimize the operation conditions. However, there are few modelling studies about intermittent microwave drying. This work proposed a mathematical model based on mass balances of liquid and vapor water in which a non-equilibrium formulation described the water phase change. The microwave heating, described by Lambert’s law, was accounting as source term on the thermal energy conservation equation. The numerical solution used the finite element method, and the experimental drying of potato samples validated the simulated drying. The values of moisture content and temperature obtained by numerical solution of the model showed good agreement with experimental data. From this, it was observed the presence of three periods in the drying kinetics: an initial heating phase almost without drying, follow by a phase with constant drying rate, and final a decrease of drying rate and temperature increasement. The model results showed that the interior temperature was higher than the surface temperature of sample, and there was water evaporation inside the potato. In additional, the gradients of temperature were reduced due to intermittency of the microwave power. This redistribution of temperature could contribute to the improvement of product quality during drying.

Combustion of Flat Shaped Char Particles with Oxygen

Thin flat-shaped carbon black particles of 1.5 mm thickness by 22.5 mm diameter were combusted in pure oxygen at atmospheric pressures and temperatures in the range of 500 to 650 °C. One film kinetic-diffusion model was derived to characterize the kinetic and energy parameters for particles arranged in the form of a thin flat-shaped configuration. The kinetic and energy parameters, and operating regimes of thin flat-shaped char particles were characterized during the non-isothermal combustion process. The gasification regimes during preheating were also analyzed. Steady-state energy processes were considered to derive an energy conservation equation used for calculating the evolution of char surface temperatures as well as released peak energy rates and the specific energy, which are considered key engineering design parameters. The one-film kinetic-diffusion model showed that combustion of such particles was purely kinetic controlled under these conditions. The activation energy obtained varied between 50 to 74 kJ/mol using discrete time and linear fits to the Arrhenius equation. The total energies released per weight of char converted varied between 32.8 and 40.6 kJ/g. The highest peak energy rate released was 134 J/s when combusting char in O2 at a reactor temperature of 504 °C.

Dynamic Disintegration of Explosively-Driven Metal Cylinder with Internal V-Grooves

Machining V-shaped grooves to the internal surface of cylindrical shells is one of the most common technologies of controlled fragmentation for improving warhead lethality against targets. The fracture strain of grooved shells is a significant concern in warhead design. However, there is as yet no reasonable theory for predicting the fracture strain of a specific grooved shell; existing approaches are only able to predict this physical regularity of non-grooved shells. In this paper, through theoretical analysis and numerical simulations, a new model was established to study the fracture strain of explosively driven cylindrical shells with internal longitudinal V-grooves. The model was built based on an energy conservation equation in which the energy consumed to create a new fracture surface in non-grooved shells was provided by the elastic deformation energy stored in shells. We modified the energy approach so that it can be applicable to grooved shells by adding the elastic energy liberated for crack penetration and reducing the required fracture energy. Cylinders with different groove geometric parameters were explosively expanded to the point of disintegration to verify the proposed model. Theoretical predictions of fracture strain showed good agreement with experimental results, indicating that the model is suitable for predicting the fracture strain of explosively driven metal cylinders with internal V-grooves. In addition, this study provides an insight into the mechanism whereby geometric defects promote fracturing.

Nonisothermal conservative phase-field model for electric breakdown process

In this paper we consider phase-field model which describes electric breackdown process in solid dielectrics. The presented model extends the earlier presented one. The derived model includes energy conservation equation, accounts for nonisothermal effects (e.g., Joule heating) and consistently describes energy transformation during breakdown channel propagation. The consistent derivaton of the model is performed in the context of rational thermomechanics framework and M. Gurtin theory of microstresses and microforces.