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.

Simulating the Influence of Supporting Electrolyte Concentration on Copper Electrodeposition in Microvias

Robust, void-free Cu electrodeposition in high-aspect ratio features relies on careful tuning of electrolyte additives, concentrations, and electrochemical parameters for a given feature dimension or wafer pattern. Typically, Cu electrodeposition in electronics manufacturing of microscale or larger features (i.e., microvias, through-holes, and high-density interconnects) employs a CuSO4 – H2SO4 electrolyte containing millimolar levels of chloride and, at a minimum, micromolar levels of a polyether suppressor. Research and optimization efforts have largely focused on the relationship between electrolyte additives and growth morphology, with less attention given to the impact of supporting electrolyte. Accordingly, a computational study exploring the influence of supporting electrolyte on Cu electrodeposition in microvias is presented herein. The model builds upon prior experimental and computational research on localized Cu deposition by incorporating the full charge conservation equation with electroneutrality to describe potential variation in the presence of ionic gradients. In accord with experimental observations, simulations predict enhanced current localization to the microvia bottom as H2SO4 concentration is decreased. This phenomenon derives from enhanced electromigration within recessed features that accompanies the decrease of conductivity with local metal ion depletion. This beneficial aspect of low acid electrolytes is also impacted by feature density, CuSO4 concentration, and the extent of convection.

Brown-York charges at null boundaries

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor Tij takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.

Under pressure: turbulent plumes in a uniform crossflow

Direct numerical simulation is used to investigate the integral behaviour of buoyant plumes subjected to a uniform crossflow that are infinitely lazy at the source. Neither a plume trajectory defined by the centre of mass of the plume $z_c$ nor a trajectory defined by the central streamline $z_{U}$ is aligned with the average streamlines inside the plume. Both $z_c$ and $z_{U}$ are shown to correlate with field lines of the total buoyancy flux, which implies that a model for the vertical turbulent buoyancy flux is required to faithfully predict the plume angle. A study of the volume conservation equation shows that entrainment due to incorporation of ambient fluid with non-zero velocity due to the increase in the surface area (the Leibniz term) is the dominant entrainment mechanism in strong crossflows. The data indicate that pressure differences between the top and bottom of the plume play a leading role in the evolution of the horizontal and vertical momentum balances and are crucial for appropriately modelling plume rise. By direct parameterisation of the vertical buoyancy flux, the entrainment and the pressure, an integral plume model is developed which is in good agreement with the simulations for sufficiently strong crossflow. A perturbation expansion shows that the current model is an intermediate-range model valid for downstream distances up to $100\ell _b$ – $1000 \ell _b$ , where $\ell _b$ is the buoyancy length scale based on the flow speed and plume buoyancy flux.

Gas flow modeling in wells

The topic of research is gas flow modeling in wells. The subject of the study is to determine the dynamic parameters of gas in a gas well, taking into account changes in the ambient temperature and gravity. Mathematical and numerical modeling of gas flow in a gas well is performed; a numerical algorithm to determine gas pressure in a gas well is built. This algorithm allows studying the state of production and injection wells with varying conditions at the wellhead and at the lower end of the well. Research methods are based on the energy equations of the transported gas; the mass conservation equation, which are the basic equations of gas flow; the methods of numerical and mathematical modeling. In the article, numerical and mathematical models of gas flow in a gas well are obtained, taking into account changes in the ambient temperature and gravity. A numerical algorithm and a program were built to determine the gas-dynamic characteristics of wells. The computational process was based on the “cycle in cycle” principle. Provisions were made to study the state of production and injection wells with varying conditions at the wellhead and at the bottom end of the well.

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.

Passive versus Active Transport of Saharan Dust Aerosols by African Easterly Waves

Theory and modeling are combined to reveal the physical and dynamical processes that control Saharan dust transport by amplifying African easterly waves (AEWs). Two cases are examined: active transport, in which the dust is radiatively coupled to the circulation; passive transport, in which the dust is radiatively decoupled from the circulation. The theory is built around a dust conservation equation for dust-coupled AEWs in zonal-mean African easterly jets. The theory predicts that, for both the passive and active cases, the dust transports will be largest where the zonal-mean dust gradients are maximized on an AEW critical surface. Whether the dust transports are largest for the radiatively passive or radiatively active case depends on the growth rate of the AEWs, which is modulated by the dust heating. The theoretical predictions are confirmed via experiments carried out with the Weather Research and Forecasting model, which is coupled to a dust conservation equation. The experiments show that the meridional dust transports dominate in the passive case, while the vertical dust transports dominate in the active case.

Prediction of 3-dimensional heat treatment model during the friction stir spot welding of AA 6061

In this research work, a die steel tool was used to join the two aluminium sheets together on a radial drill machine. For this, a cylindrical-shaped tool was fabricated. This tool is then clamped into the drill machine tool post. This rotating tool is then inserted/indented into the workpiece thus generating heat due to friction. The of the deformation of aluminium starts near the vicinity of the die steel tool impression. The tool transferred the soft material from the tip to the plunger. The plunger is in contact with the Aluminum sheet. Soften material is forged on the sheet with the help of a plunger and thus creating a solid phase joint between the Aluminum sheets. Three-dimensional numerical modelings were performed on Ansys software. A 3-D heat transfer model was used to solve the problem of friction stir spot welding (FSSW). This model was solved by applying the energy conservation equation. This model involves the heat generated at the boundary of the workpiece (AA) and the rotating tool and for study, the problem, steady-state heat transfer equation was used. The numerically computed and the measured values are compared to validate the results.

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.