Basic Conservation Laws Research Articles

The bohmion method in nonadiabatic quantum hydrodynamics

Starting with the exact factorization of the molecular wavefunction, this paper presents the results from the numerical implementation in nonadiabatic molecular dynamics of the recently proposed bohmion method. Within the context of quantum hydrodynamics, we introduce a regularized nuclear Bohm potential admitting solutions comprising a train of δ-functions which provide a finite-dimensional sampling of the hydrodynamic flow paths. The bohmion method inherits all the basic conservation laws from its underlying variational structure and captures electronic decoherence. After reviewing the general theory, the method is applied to the well-known Tully models, which are used here as benchmark problems. In the present case of study, we show that the new method accurately reproduces both electronic decoherence and nuclear population dynamics.

Analysis of Characteristics of Damping Valve Based on High-Order Discrete Scheme

In this paper, based on the high-order discrete scheme, a two-way fluid-solid coupling numerical simulation is for the damping valve plate. According to the discrete method, the governing equations of fluid structure coupling of damping valve plate are studied, including the basic conservation laws; Meanwhile, it analyzes the discretization of the control equation, including the discretization method and the high-order discretization format when the finite volume method is adopted. And based on this discrete format, a numerical simulation was performed on the damping valve, the oil flow condition is analyzed, and the velocity of the throttling hole at different time points and the throttling pressure are analyzed.

A bioconvection model for viscoelastic nanofluid confined by tapered asymmetric channel: implicit finite difference simulations.

As part of the growing evolution in nanotechnology and thermal sciences, nanoparticles are considered as an alternative solution for the energy depletion due to their ultra-high thermal effectives. Nanofluids reflect inclusive and broad-spectrum significances in engineering, industrial and bio-engineering like power plants, energy source, air conditioning systems, surface coatings, evaporators, power consumptions, nano-medicine, cancer treatment, etc. The present study describes the bio-convective peristaltic flow of a third-grade nanofluid in a tapered asymmetric channel. Basic conservation laws of mass, momentum, energy, and concentration as well as the microorganism diffusion equation are utilized to model the problem. The simplified form of the modeled expressions is accounted with long wavelength assumptions. For solving the resulting coupled and nonlinear equations, a well-known numerical method implicit finite difference scheme has been utilized. The graphical results describe the velocity, temperature and concentration profiles, and the density of motile microorganisms at the nanoscale. Furthermore, microorganism concentration lines are analyzed.

Динамика рабочих процессов в автоматических регуляторах давления прямого действия пневматических систем космических аппаратов

The purpose of the study was by means of modern software to explore working processes taking place in automatic direct-acting pressure regulators of pneumatic spacecraft systems. As a result, we developed a general mathematical model of the pressure regulator. The design of the regulator is shown in the form of a block diagram, composed of a set of channels, cavities, and stages. The elements of the block diagram are interconnected by the basic laws of conservation of energy and mass. The mathematical model was evaluated in the Amesim software package. Findings of the full-scale and computational experiments led to the conclusions about the effect the heat exchange between the working fluid and the environment produces on the parameters of the pressure regulator, and about the use of the Amesim software package for further research of working processes in the valve units of pneumatic systems.

A comparative study on micropolar, Williamson, Maxwell nanofluids flow due to a stretching surface in the presence of bioconvection, double diffusion and activation energy

Prime aim of current study is to explore the comparative outcomes for mass and thermal transportation of various fluids models namely Newtonian, micropolar, Williamson and Maxwell due to extending surface. This exploration is concerned to the effect of double diffusion and applied magnetic field. The bioconvection may improve the settling of nanoparticles and the double diffusion effects are considered to be more realistic on the part of this work. The mixture of base fluids with nanoparticles and gyrotactic micro-organisms is homogenous. By the implementation of basic conservation laws, the governing partial differential equations are organized which are then reformed into corresponding ordinary differential equations. For the physical insight, Runga-Kutta method with shooting technique is utilized. The controlling parameters of buoyancy ratio, thermophoresis, magnetic field, Brownian movement, Lewis number and Prandtl number are varied in acceptable ranges to evaluate their impacts on temperature, momentum, concentration field and micro-organisms concentration. The notable outcomes indicated that micropolar fluid takes the highest value for velocity and then Newtonian fluid, Williamson fluid and Maxwell fluid in descending order. The results related to different three non-Newtonian nano-fluids with effective heat transfer can find applications in heat transfer processes such as heat exchanger.

High-accuracy thrust measurements of the EMDrive and elimination of false-positive effects

The EMDrive is a proposed propellantless propulsion concept claiming to be many orders of magnitude more efficient than classical radiation pressure forces. It is based on microwaves, which are injected into a closed tapered cavity, producing a unidirectional thrust with values of at least 1 mN/kW. This was met with high scepticism going against basic conservation laws and classical mechanics. However, several tests and theories appeared in the literature supporting this concept. Measuring a thruster with a significant thermal and mechanical load as well as high electric currents, such as those required to operate a microwave amplifier, can create numerous artefacts that produce false-positive thrust values. After many iterations, we developed an inverted counterbalanced double pendulum thrust balance, where the thruster can be mounted on a bearing below its suspension point to eliminate most thermal drift effects. In addition, the EMDrive was self-powered by a battery-pack to remove undesired interactions due to feedthroughs. We found no thrust values within a wide frequency band including several resonance frequencies and different modes. Our data limit any anomalous thrust to below the force equivalent from classical radiation for a given amount of power. This provides strong limits to all proposed theories and rules out previous test results by at least two orders of magnitude.

Analysis of the influence of geometric parameters on working processes in a two!stage hybrid power machine of positive displacement without a gas cap with a profiled working chamber of the second stage

A principal scheme is considered and a mathematical model of work processes is developed in a two-stage hybrid power machine of positive displacement without a gas cap with a profiled working chamber of the second stage. The mathematical model is based on the basic laws of conservation of energy, volume and mass for a dropping liquid and a compressible gas in the second stage. The diameter of the supply pipeline and the initial radius of the profiled working chamber in the second stage are selected as the main geometric parameters that have the greatest influence on the work processes. The response functions are found that determine the dynamics of the fluid flow in the machine under study and its main integral characteristics. Keywords: work process, cooling, reciprocating compressor, hybrid power machine of positive displacement, profiled working chamber Scherba_V_E@list.ru

Construction of Higher-Order Metric Fluctuation Terms in Spacetime Symmetry-Breaking Effective Field Theory

We examined the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws were used as constraints on a generic series of terms in an expansion around a flat background. We found all such terms for a two-tensor coupling to cubic order in the metric and tensor field fluctuations. The results are presented in a form that can be used for phenomenological calculations. One key result is that if we preserve the underlying diffeomorphism symmetry in a spontaneous-symmetry breaking scenario, one cannot decouple the two-tensor fluctuations from the metric fluctuations at the level of the action, except in special cases of the quadratic actions.

Modelling of hydrogen-air supersonic mixing and combustion in near-wall region

Abstract Turbulent mixing, ignition, and flame stabilization in the non-premixed supersonic hydrogen-air flow is numerically modelled in a near-wall region. Mixing algorithm based on the turbulence approach SARANS (Reynolds Averaged Navier–Stokes equations closed with Spalart–Allmaras turbulence model) with a diffusion model and a detailed kinetic model for hydrogen-air chemical reactions are employed. The system of governing equations that consists of basic conservation laws and the turbulence model equation is solved in a coupled manner with the LU–SGS–GMRES method. The model is applied to simulate the process of hydrogen injection into a M = 2.44 air flow with their subsequent mixing, ignition, and combustion in the Burrows– Kurkov chamber. The results are compared to available experimental and reference computational data. All calculations are carried out on the ‘MVS-10P’ JSCC RAS supercomputer cluster.

The calculating model of microstructured flat plate wettability during evaporation into the stagnation flow

The results of the analysis of the problem of wetting the microstructured flat wall surface during adiabatic liquid evaporation into a boundary layer of air flowing at right angles are presented. The basic conservation laws are formulated in the form of differential equations that allow calculating the velocity and height of liquid rise in capillaries, wetting dynamics, depth and mass of the liquid in capillaries, and the evaporation surface area.

Explicit-Iterative Scheme for the Time Integration of a System of Navier–Stokes Equations

We propose a new explicit-iterative scheme for time integrating the multidimensional Navier–Stokes equations of a compressible environment through splitting into convective and diffusive stages, which are performed sequentially at each time step. The convective stage is implemented using the Godunov scheme; and the diffusive stage, using the Chebyshev explicit-iterative LI-M scheme, which has no restriction on the time step. The resulting scheme ensures that the basic conservation laws hold on arbitrary irregular grids. The explicit nature of the calculations ensures that the scheme can be efficiently used in various parallel technologies.

Weakly nonlinear acoustic theory on pressure propagation in bubbly flows with different cases of nonuniform distribution of initial flow velocities of gas and liquid phases

Three cases of weakly nonlinear propagation of plane progressive pressure waves in flowing water containing many uniformly separated spherical microbubbles are theoretically investigated, with a particular focus on different cases of initial flow patterns. The gas and liquid phases initially have a high velocity with uniform distribution, and a low velocity with nonuniform distribution for each phase. Basic conservation laws based on a two-fluid model are employed to govern different velocity distributions for gas and liquid phases. From the method of multiple scales with perturbation expansions, we derive three cases of nonlinear wave equation describing the long-range propagation of waves: (i) the KdVB (Korteweg–de Vries–Burgers) equation for a long wave, (ii) the NLS (nonlinear Schrödinger)-I equation for a short wave in slow nonuniform flow, (iii) the NLS-II equation for a short wave in fast nonuniform flow. As a result, all the initial velocities contribute to an advection effect of waves, initial nonuniform flow distribution induces a variable coefficient of advection term into the KdVB, NLS-I, and NLS-II equations, and an important role of relative velocity between the gas and liquid phases is clarified.

Mathematical problem in the construction of kinetic equations of alternative fuel oxidation in an internal combustion engine

In this paper, when solving problems of non-equilibrium gas dynamics, the source terms associated with the presence of physical and chemical transformations are taken into account, primarily in the mass balance equations. Based on the method of splitting by physical processes, a computational scheme is constructed in which the influence of the chemical source is taken into account separately from other terms included in the laws of mass conservation of the components of the mixture. This ensures the independence of the formulation of the accepted kinetic problem. Naturally, in a number of cases, the solution of a chemical-kinetic problem can have independent significance. The independence of the formulation of the “purely” chemical-kinetic problem is, however, very relative, since the basic conservation laws of the hydrodynamic model of a reacting continuous medium are a system of strongly coupled equations. For this reason, the chemical-kinetic problem is consistently formulated only for the spatially homogeneous case.

A Numerical Simulation for Transport of Hybrid Nanofluid

Hybrid nanofluids are used to enhance therapeutic effects and reduce the side effects in tumour therapy. These nanoparticles are transported nearest to the cancer’s tissues under the action of the peristaltic waves generated on the walls of the blood vessel. The motion of hybrid nanoparticles in non-uniform vertical channel having flexible boundaries is numerically elaborated in present study. Poisson equations are used on the basis of electro-osmotic theory to encounter the phenomena of applied electric field on the walls of the channel. Lubrication approach and Debye–Huckel linearization approximations are utilized to obtain the system of coupled ordinary differential equations from the basic conservation laws which are solved by using implicit finite difference scheme which is commonly known as Keller–Box method and MATLAB built in subroutine Bvp5c. The impact of electro-osmotic parameter on all features of flow of nanoparticles observed through several graphs and various tables. The current study is applicable and helpful in the design of micropumps and nanomedicine technologies.

Collaborative Computing Methods for One-Dimensional and Three-Dimensional Problems of Computational Fluid Dynamics

This article presents a method of collaborative one-dimensional (1D)–three-dimensional (3D) modeling of computational fluid dynamics. The method is based on the simultaneous calculation of 3D and 1D areas and linking the two parts of the problem by transferring the boundary conditions. The 3D approximation region is modeled based on the solution of Navier-Stokes equations. The 1D regions are calculated using the basic conservation laws and the empirical characteristics of elements. The proposed solutions are validated through several tasks. For each task, the results are compared with the available analytical solutions or the experimental data.

Oscillatory slip flow of Fe3O4 and Al2O3 nanoparticles in a vertical porous channel using Darcy's law with thermal radiation

AbstractThe heat transfer phenomena and oscillatory flow of an electrically conducting viscous nanofluid (NF) in a channel with porous walls and saturated porous media exposed to the thermal radiation are studied. The nanoparticles (NPs) Fe3O4 and Al2O3 are taken with water as base fluid along with nonuniform temperature and velocity slip at the wall of channel (y′ = 0). The basic laws of momentum and energy conservation are converted into the dimensionless system of the partial differential equations (PDEs) using similarity variables. Closed‐form solutions of these coupled PDEs are constructed for all values of time by taking the oscillatory pressure gradient. The physical insight of involved parameters on the fluid velocity, temperature profile, heat transfer rate, and surface friction is studied and analyzed graphically. It is noted from this study that the fluid velocity shows a decreasing behavior with the volume fraction of NPs. Furthermore, the amplitude of the oscillatory motion in case of skin friction decreases for a large magnetic field.

Generalized indicator-based determination of solution pH

pH indicators can be used both fast responsive as well as long-term stable sensors. They have been extensively used for monitoring pH changes in fast kinetic reactions as well as slowly changing pH in oceanic waters. If the pH range that needs to be covered is narrow it is possible to use only one indicator of appropriate protonation constant; otherwise, mixtures of two or more indicators are used for monitoring pH values covering a broad range of pH. In this paper we presented a new methodology for determining pH of solutions using mixtures of pH indicators. The pH calculation is based on the strict application of the basic laws of mass action and mass conservation. The proposed method was evaluated by the successful determination of the pH values of solutions containing three indicators (neutral red, phenol red (two different protonation constants), and methyl orange) covering a wide range of pH values from 0.5 to 9. The method was also applied for rapid monitoring of pH changes in stopped-flow measurements, investigating the reactions of CO2 in aqueous amine solutions.

Physical and mathematical models for space objects breakup and fragmentation in hypervelocity collisions

The paper presents results of analysis of existing mathematical models for orbital debris fragments breakup in high velocity collisions. The breakup models are modified and updated taking into account the latest breakup criteria, experimental data and basic conservation laws. The model examples are analyzed, the criterion is developed for distinguishing fragments, which will stay in orbit after collision event.

Darcy–Boussinesq Model of Cilia-Assisted Transport of a Non-Newtonian Magneto-Biofluid with Chemical Reactions

The model developed in this study presents a mathematical approach to the physiological transport of seminal liquid due to ciliary movements, which are attached with the lumen of the ductile efferent in the male reproductive system. The rheological properties of the seminal liquids were described using the Jeffrey liquid model. The problem described an electromagnetic mixed convective flow of a Jeffrey liquid through a vertical channel with heat and mass transfers. The effects of chemical reactions and the external heat generation were included in the formulation. The flow took place through an active porous medium (due to thick cilia mat and other deposits) and was influenced by the Lorentz magnetic force. Four basic conservation laws of mass, momentum, energy, and concentration were utilized in the mathematical modeling. These are highly nonlinear equations, which were simplified due to a physiologically valid approach known as LAT (lubrication approximation theory). Analytical solutions for temperature, concentration, and velocity profiles were evaluated. The expressions describing the pressure–volume flow rate relationships were also obtained. Analysis of various physical and geometrical factors affecting the pressure–volume (pumping) characteristics was also presented. One of the main findings of our study is that the difference between our calculated values of the flow rate and the estimated values of the flow rate in the ductile efferent was negligibly small. Moreover, our results can be implemented in the artificial cilia pumping systems in microchannels.

Thermal analysis of an Eyring-Powell fluid flow-through a constricted channel

This paper is aimed to investigate the entropy generation in a MHD convective flow of Eyring-Powell fluid through a mildly constricted channel. The constriction is assumed to be of regular or irregular shape and is presented inside the channel wall. Mathematical model is developed using the basic laws of conservation of mass, momentum, and energy. The governing equations are normalized using appropriate set of dimensionless variables and solutions are obtained by regular perturbation technique. The solutions are further used to calculate the entropy expression associated with the Second law of thermodynamics. The heat transfer characteristics, like, temperature, isotherms, entropy generation number entropy lines and the Bejan number are analyzed for the variation in magnetic field, shape parameter, and material constants. It is observed that entropy production is maximum in the narrow part of the channel. Moreover, entropy generation rate is higher for the regular parabolic shape as compared to irregular shapes of constriction.