Full Numerical Solution Research Articles

Lubrication mechanism of graphene nanoplates as oil additives for ceramics/steel sliding components

Tribological behavior of Si3N4 ceramic/GCr15 steel components under lubrication of graphene was investigated and found that friction reduction and wear resistance of the sliding pairs were improved by 27% and 43%, respectively, after adding 0.075 wt% of graphene into the base oil. Herein, the lubrication mechanism of graphene nanoplates as oil additives was focused on to promote the practical application of graphene in hybrid ceramic bearings industry. In order to investigate the effect of oil film thickness on tribological properties, the viscosity of blended lubricating oil containing different concentration of graphene was measured and the oil film thickness between rubbing surfaces was calculated using a full numerical solution in point contacts. In addition, the rubbing surfaces were analyzed with combination of EDS and Raman technique. The results demonstrated that the viscosity of base oil and oil film thickness increased with addition of graphene. Graphene entered rubbing interface and prevented ceramic/steel pairs from mechanical contact. Lubrication mechanism including interlayer shearing, surface mending and protective film formation contributed to reduce the friction coefficient and worn scar diameter.

Microconfined electroosmotic flow of a complex fluid with asymmetric charges: Interplay of fluid rheology and physicochemical heterogeneity

Abstract We report a study on the micro-confined electroosmotic flow of an Oldroyd-B fluid over a surface having asymmetric charge modulation. We have employed a combination of regular and matched asymptotic expansion to obtain the analytical solution. We have also carried out a full numerical simulation of the physicochemical problem in order to assess the full parameter space of the problem. The analytical solution is shown to be in excellent agreement with the full numerical solution in the limiting conditions of thin electrical double layers and weakly viscoelastic fluids. We have used these solutions to describe the complex fluid flow pattern and the modified electroosmotic slip velocity. We have also highlighted the alteration in the net volumetric throughput and ionic current. We have subsequently presented the numerical solutions for the velocity field, flow rates, and streaming current by varying the physicochemical conditions at the surface and viscoelastic properties of the fluid. We report an augmentation in the electroosmotic slip velocity with the increase in relative strength. The symmetry breaking of flow and stress distributions are shown to affect the net-throughput and streaming current, which is indicative of the combined effect of phase angle, magnitude of charge distribution, and the fluid viscoelasticity. We have shown that the thickness of electrical double layer considerably affects the net-throughput and streaming current generation in the microchannel. Our results hold the key towards understanding the complex bio-fluid transport in a microchannel utilizing the electric field in the presence of non-uniform surface charge distribution.

Application of Successive Linearisation Method on the Boundary Layer Flow Problem of Heat and Mass Transfer with Radiation Effect

In this paper, we applied the successive linearization method (SLM) in solving highly system of nonlinear boundary value problem. The method is presented in detail by solving the problem of free convective heat and mass transfer of an incompressible fluid past a moving vertical plate in the presence of radiation effect. The governing partial differential equations are converted into system of non linear ordinary differential equations by a similarity transformation, which are converted into system of linear ordinary differential equations using SLM. The linear system is solved using the Chebyshev spectral method to find solutions that are accurate and converge rapidly to the full numerical solution. Comparison with previously published works are performed to test the validity of the obtained results with focus on the accuracy and convergence of the solution. The effects of selected fluid parameters on the velocity as well as the temperature and concentration distribution are determined and discussed.

Relativistic effects in photoionizing a circular Rydberg state in the optical regime

We study the photoionization process of a hydrogen atom initially prepared in a circular Rydberg state. The atom is exposed to a two-cycle laser pulse with a central wavelength of 800 nm. Before the atom approaches saturation, at field intensities of the order of ${10}^{17}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$, relativistic corrections to the ionization probability are clearly seen. The ionization is predominantly driven by the radiation pressure in the propagation direction of the laser field, not by the electric field. Direct comparisons with the full numerical solution of the time-dependent Dirac equation demonstrate quantitative agreement with a semirelativistic approximation, which is considerably easier to implement.

Detecting Nonclassical Correlations in Levitated Cavity Optomechanics

Nonclassical optomechanical correlations enable optical control of mechanical motion beyond the limitations of classical driving. Here we investigate the feasibility of using pulsed cavity-optomechanics to create and verify nonclassical phase-sensitive correlations between light and the motion of a levitated nanoparticle in a realistic scenario. We show that optomechanical two-mode squeezing can persist even at the elevated temperatures of state-of-the-art experimental setups. We introduce a detection scheme based on optical homodyning that allows revealing nonclassical correlations without full optomechanical state tomography. We provide an analytical treatment using the rotating wave approximation (RWA) in the resolved-sideband regime and prove its validity with a full numerical solution of the Lyapunov equation beyond the RWA. We build on parameters of current experiments for our analysis and conclude that the observation of nonclassical correlations is possible today.

Linear theory of current driven ion acoustic instability at the distance 0.3 to 1 AU from the Sun

Several kinds of instabilities are often observed in the solar wind. We studied the linear theory of the current-driven electrostatic ion acoustic instability at frequencies near the ion cyclotron frequency at distances from the Sun over 0.3 to 1 AU. The properties of current driven electrostatic ion-acoustic instability are investigated. The instability parameters, such as angular wave frequency, the critical drift velocity and the growth rate are calculated. We used the dispersion relation in hot magnetized plasma to calculate the current driven ion acoustic instability properties. To determine the critical drift velocity and the growth rate a full numerical solution of the dispersion relation equation is carried out. Since the growth rate of instability depends on the wave normal angle, the drift velocity of the electron along the magnetic field and the ion thermal cyclotron radius, the calculation is carried out for ranging of the wave normal angles, drift velocities and ion thermal cyclotron radius. The results show that the growth rate of instability increases with increasing distance from the Sun. The growth rate of instability increases with decreasing the wave normal angle, but the critical drift velocity decreases with decreasing the wave normal angle.

Variational theory for the ground state and collective excitations of an elongated dipolar condensate

We develop a variational theory for a dipolar condensate in an elongated (cigar shaped) confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.

An efficient hybrid model for thermal analysis of deep borehole heat exchangers

The deep borehole heat exchanger (DBHE) shows great potential in seasonal thermal energy storage and its high performance efficiency with smaller land occupancy attracts increasing attention as a promising geothermal energy exploitation technique. With respect to a vertical BHE with extremely long length pipes buried underground, thermal analysis of the unsteady heat transfer process of the system is quite complicated. Due to the high temperature underground, the deeper part of BHE can extract more heat from the rock, which leads to a higher heat extraction rate. The heterogeneous distribution of heat flux density and geothermal gradient cannot be described properly by the existing analytical models. Although a full 3D numerical solution can reflect these features, it always requires high computational resources and presents numerical instabilities. In this paper, we propose a hybrid modeling method with high efficiency to simulate the temperature evolution inside the DBHE, and the heat propagation front in the surrounding rock mass. The temperature evolution inside the DBHE is solved by finite difference schemes, while the heat propagation in the surrounding rock is determined by an analytical formulation of thermal impacted radius. The coupling is achieved via source/sink term by incorporating the heat flux between the DBHE and the surrounding rock. Furthermore, an innovative analytical formulation describing the heat flux density is also presented, which accounts for the key parameters affecting the thermal performance of the DBHE system. Our proposed model is further verified against results with full 3D numerical solution under the same configurations. It is demonstrated that the proposed model can capture the key physical process of the heat transfer problem, while maintaining the calculation accuracy required by the engineering application. Regarding the calculation speed, the model results are around 30 times faster when compared to the full 3D numerical solution.

Improved opacity expansion for medium-induced parton splitting

We present a new expansion scheme to compute the rate for parton splittings in dense and finite QCD media. In contrast to the standard opacity expansion, our expansion is performed around the harmonic oscillator whose characteristic frequency depends on the typical transverse momentum scale generated in the splitting. The first two orders account for the high frequency regime that is dominated by single hard scatterings together with the regime of multiple soft scatterings at low frequency. This provides the tools to go beyond the leading logarithmic approximation and compare to the full numerical solution to the corresponding Schrödinger equation across a wide range of gluon frequencies. We investigate the sensitivity of our results to varying the separation scale that defines the leading order. Finally, the application to Monte Carlo event generators is discussed.

Influences of transient impact and vibration on the lubrication performance of spur gears

In this paper, the mathematical model of gear elastohydrodynamic lubrication is presented. The transient impact operating condition and underdamped load condition are considered. Taking thermal effect and squeeze effect into account, the full numerical solution of gear pairs is obtained. In this numerical calculation, multigrid method is applied to compute the film pressure; multigrid integration technique is used to calculate the solid surface deformation; column by column scanning technique is employed to calculate temperature. The simulation results show that an entrapped film dimple forms under transient impact condition; transient impact causes remarkable increases in film pressure and film temperature. Compared with the normal case the minimum thickness of the impact case is smaller, which is not beneficial to teeth lubrication. Thermal effect induces some decreases in film thickness because of the viscosity–temperature relationship. Vibrational load with high damped frequency causes greater increases in film thickness and greater decreases in the coefficient of friction than that of low damped frequency. However, the film temperature of high damped frequency is higher than that of low damped frequency.

Erratum: Early kinetic decoupling of dark matter: When the standard way of calculating the thermal relic density fails [Phys. Rev. D 96 , 115010 (2017)

Calculating the abundance of thermally produced dark matter particles has become a standard procedure, with sophisticated methods guaranteeing a precision that matches the percent-level accuracy in the observational determination of the dark matter density. Here, we point out that one of the main assumptions in the commonly adopted formalism, namely local thermal equilibrium during the freeze-out of annihilating dark matter particles, does not have to be satisfied in general. We present two methods for how to deal with such situations, in which the kinetic decoupling of dark matter happens so early that it interferes with the chemical decoupling process: i) an approximate treatment in terms of a coupled system of differential equations for the leading momentum moments of the dark matter distribution, and ii) a full numerical solution of the Boltzmann equation in phase-space. For illustration, we apply these methods to the case of Scalar Singlet dark matter. We explicitly show that even in this simple model the prediction for the dark matter abundance can be affected by up to one order of magnitude compared to the traditional treatment.

Coupled tribo-dynamic modelling of linear guideways for high precision machining application

Linear guideways play a crucial role in determining precision of machine tools. Understanding their dynamic response is essential for objectively controlling their behavior and performance in operation. Due to highly loaded lubricated contacts, mixed-elastohydrodynamic regime is dominant. The mixed-elastohydrodynamic film maintains the coupling between horizontal degree of freedom (feed velocity) and vertical degree of freedom (loading direction). This paper presents a novel tribo-dynamic solution for linear guideways, taking in to account the lubricant effects and coupling between horizontal and vertical degrees of freedom. An analytical tribology model is used implicitly within the dynamic model. For in-depth tribological quantities including pressure and film thickness distribution, an explicit full numerical solution for mixed-elastohydrodynamic is utilized. Results show that the coupled solution of vertical and horizontal degrees of freedom taking in to account lubricated contacts is essential. It is shown that at moderate and light loads, the effect of this coupling and presence of lubricant is more pronounced.

The Effect of Working Parameters upon Elastohydrodynamic Film Thickness Under Periodic Load Variation

There are a number of widely used machine components, such as rolling element bearings, gears and cams, which operate in the lubrication regime known as Elastohydrodynamics (EHD), where lubricant film thickness is governed by hydrodynamic action of convergent geometry, elastic deformation between non-conformal contacting surfaces, and the increase of lubricant viscosity with pressure. Variable loading conditions occur not only in all the machine components mentioned above, but also in natural joints such as hip or knee joints of humans or many vertebrates. Experimental studies of the behaviour of EHD films under variable loading are scarce and to authors’ knowledge systematic studies of the evolution of lubricant film thickness in EHD contacts subjected to forced harmonic variation of load are even less common. The aim of the present study is to explore the effect of load amplitude on the EHD film behaviour. This is done in alternating cycles with the load varying about a fixed, preset value at various amplitudes. Experimental results are compared with a simple theoretical analysis based on the speed of change of contact’s dimensions, a semi-analytical solution which includes both speed variation and squeeze effect, and finally with a full numerical solution.

Transient heat transfer in fibrous multi-scale composites: A semi-analytical model and its numerical validation

This article presents the development and validation of a semi-analytical (hybrid) model to describe transient heat conduction in a composite material reinforced with long unidirectional cylindrical inclusions. The development of the model relies on the existing analytical solution at the particle-scale, subject to a locally uniform but time-evolving surface temperature; this solution is used to calculate the local heat exchange with the matrix material. Following this, spatial discretization (using N nodes) at the macroscale leads to a system of Ordinary Differential Equations, yielding the matrix temperature and the surface temperature of the inclusions at each node. n0 is the number of the terms in the Bessel expansion computed without recourse to approximation. The intra-fiber thermal response is recovered analytically from the above. A fully numerical two-dimensional model of a unidirectional composite containing 1000 randomly placed fibers is developed on the OpenFOAM platform, using Gmesh for generation of the computational meshes. Comparison of the predictions of the proposed semi-analytical model with the results of several 100s of numerical simulations, spanning a large range of size ratios (macro-scale to fiber diameter) and conductivity ratios, shows excellent agreement between the semi-analytical model and the numerical results. The proposed model is portable and executable on mid-level workstations, requiring minutes of CPU time for cases in which a full numerical solution would require 10s of CPU hours. It therefore provides an attractive and accurate alternative in modeling transient heat transfer in multi-scale fibrous composites.

A Fast Simulation Approach to the Thermal Recovery Characteristics of Deep Borehole Heat Exchanger after Heat Extraction

Necessary intermittence after heat extraction for a deep borehole heat exchanger (DBHE) is beneficial for sustainable operation. This paper centers on the fast simulation for thermal recovery characteristics of DBHE under intermittent condition. First of all, in view of the existing temperature gradient and multi-layer heterogeneity of rock underground that could never be ignored for DBHE, we extend the classical finite line source model based on heat source theory and superposition principle to account for the vertical heat flux distribution varying along depth and heterogeneous thermal conductivities in the multi-layer rock zone. Moreover, a fast simulation approach for heat transfer analysis inside the borehole coupled with the extended finite line source model is put forward to depict the transient thermal response and dynamic thermal recovery of rock outside borehole. To the authors’ knowledge, no such algorithm for deep BHE has yet been suggested in the previous literature. This approach has proven to be reliable and efficient enough for DBHE simulation under the intermittent condition. Simulation results show that at least 65 days of intermittence for the model in study should be spared after the heating season to achieve sustainable heat extraction in the next cyclic operation. Compared to the detailed solution based on full discretization numerical schemes, the relative error for borehole bottom temperature was 0.79%. In addition, comparison of the simulation results for thermal performance during the heating season in a three-year cyclic operation with 205 days intermittence shows that both the outflow temperature and heat extraction rate in the subsequent cycle after intermittence are in good agreement with the full 3D numerical solution in the reference (with a relative error of 6.36% for the outflow temperature and 9.3% for the heat extraction rate). Regarding the calculation speed, around a 13 times acceleration can be achieved. Finally, it is also promising to be applicable for thermal recovery simulation after heat extraction of vertical closed loop borehole heat exchangers at arbitrary length from shallow to deep.

Electroosmosis of a viscoelastic fluid over non-uniformly charged surfaces: Effect of fluid relaxation and retardation time

We investigate the electroosmotic flow of a quasi-linear viscoelastic fluid over a surface having charge modulation in narrow confinements. We obtain analytical solutions using a combination of regular and matched asymptotic expansions in order to describe the viscoelastic flow field and apparent slip velocity besides pinpointing variations of the flow rate and ionic currents due to the surface charge modulation. We demonstrate excellent agreement between the asymptotic analytical solution for the flow field and the full numerical solution in the limiting condition of a thin electrical double layer and weakly viscoelastic fluid. For a wide range of flow governing parameters, we analyze the flow velocity, vortex dynamics, flow rates, and streaming current. We demonstrate that the magnitude of the observed electroosmotic slip velocity is more sensitive to the thickness of the electrical double layer rather than the viscoelasticity of the fluid. We have observed that the contribution of fluid elasticity is prominent in breaking the axial symmetry in the electroosmotic flow with the presence of periodic charge distributions, which is in contrast to the symmetric electroosmotic flow field of a Newtonian fluid over the same charge modulated walls. The results hold the key toward understanding the flow of biological fluids in microfluidic flows by leveraging electrokinetic transport over charge modulated surfaces. We believe that the results of net throughput, streaming current, and vortex dynamics will aid our understanding of the complex fluid behavior and microfluidic mixers.

A computational study of the properties of the quasi-perpendicular fast forward shock event during solar maximum

MHD shock waves and discontinuities are often observed in the solar wind. We studied a strong shock wave event on 7 June 2014, during a solar maximum. The properties of forward shock are investigated and all physical parameters of interplanetary shock are analyzed. The upstream parameters, such as Alfven velocity and sound speed are calculated, and the angle ( $${\theta }$$ ) between the upstream magnetic field direction and the shock normal is estimated. To determine the propagation speed of the shock, a full numerical solution of shock adiabatic equation is carried out. The thermal pressure for electrons and ions are calculated and also the pressure ratio and the entropy change across the shock are estimated. The results show that the shock strength is about 3.88 with $${\theta }\approx \text{72 }^{\circ }$$ (a quasi-perpendicular case), and shock propagation velocity is about 678 km/s. The increase in the specific entropy is also evaluated.

Full structure of the thermal plasma including the ion isothermal drag

In order to study the ion temperature effect on the space-charge structure and the plasma variables on the wall, the ion thermal force has been added to the ion motion equation in the plasma fluidal model. In the eigenvalue problem of plasma, the plasma equations are numerically solved in a whole area from the plasma center to the wall and it is displayed that the ion temperature has significant effects on the plasma structure and floating variables. However, the fluidal theory of plasmas introduces a singular point among the space charge of plasma boundary layer if the static pressure and the inertial mass of the thermal ions are taken into account at the same time. Finding a full numerical solution for the thermal plasma equations needs to cross the singular point. The singular point and how crossing the point will be depicted too.

Tribological and thermal properties of a crowned gear pair with high-speed and heavy-load in thermal micro-elastohydrodynamic lubrication

The oil film stiffness, temperature rise of oil film, flash temperature and frictional loss ratio of a crowned gear pair with non-Newtonian transient thermal elastohydrodynamic lubrication of rough surfaces in high-speed and heavy-load operating conditions are investigated. The pressure, film thickness, coefficient of friction and temperature rise are calculated along the action line of spur gears to verify the validity of full numerical solution. Subsequently, the effects of high-speed, heavy-load and roughness on those tribological and thermal properties of a crowned gear drive are discussed. The results show that in high-speed, heavy-load and rough surface contact, the crown modification is in favor of stability improvement of gear drive due to smoother curve of oil film stiffness. The temperature rise of the oil film and flash temperature on tooth surface are quite high which are prone to result in gear scuffing. Moreover, small flash temperature and frictional loss ratio occur in the domains near the start of active profile and the tip due to the effect of crown modification.

Stability and variational analysis of cavity solitons under various perturbations

We theoretically investigate the dynamics and stability of a temporal cavity soliton (CS) excited inside a silicon-based microresonator that exhibits free-carrier generation as a result of two-photon absorption (TPA). The optical propagation of the CS is modeled through a mean-field Lugiato-Lefever equation (LLE) coupled with an ordinary differential equation accounting for the generation of free carriers owing to TPA. The CS experiences several perturbations (like intrapulse Raman scattering (IRS), TPA, free-carrier absorption (FCA), free-carrier dispersion (FCD), etc.) during its round-trip evolution inside the cavity. We develop a full variational analysis based on a Ritz optimization principle which is useful in deriving simple analytical expressions describing the dynamics of individual pulse parameters of the CS under perturbation. TPA and FCA limit the efficient comb generation and modify the stability condition of the CS. We determine the critical condition of stability modified due to TPA and derive closed-form expressions of the saturated amplitude and width of stable CS. We perform detailed modulation-instability analysis and obtain stability condition against perturbations of steady-state solution of LLE. The CS experiences FCD which leads to a temporal acceleration resulting in spectral blueshift. Exploiting the variational analysis, we estimate these temporal and spectral shifts. We also include IRS in our perturbation theory and analytically estimate the frequency redshifting. Finally, we study the effect of pump-phase-modulation on a stable CS. All our analytical results are found to be in good agreement with the data obtained from the full numerical solution of LLE.