Analytical Solving a Nonlinear Model of the Glow Discharge

A nonlinear model has been introduced for the positive column of DC glow discharge in apure sealed, or low flow, gas media by including the diffusion, recombination, attachment, detachment,process and having the two-step ionization process of the metastable excited states, too. By thecombination of the system of the nonlinear continuity equations of the system, using some physicalestimations, and degrading the resulted nonlinear PDE in polar and rectangular systems of coordinatethe steady-state nonlinear ODE have been derived. Using a series-based solution, an innovativenonlinear recursion relation has been proposed for calculating the sentence of series. Using the stateof elimination of free charge on the outer boundary of the discharge vessel, the universal equation ofthe characteristic energy of the electrons versus the similarity variable, using the maximum degree ofionization as the parameter, has been derived.

A simple model of ozone–temperature coupling in the tropical lower stratosphere

Observations show strong correlations between large-scale ozone and temperature variations in the tropical lower stratosphere across a wide range of timescales. We quantify this behavior using monthly records of ozone and temperature data from Southern Hemisphere Additional Ozonesonde (SHADOZ) tropical balloon measurements (1998–2016), along with global satellite data from Aura microwave limb sounder and GPS radio occultation over 2004–2018. The observational data demonstrate strong in-phase ozone–temperature coherence spanning sub-seasonal, annual and interannual timescales, and the slope of the temperature–ozone relationship (T / O3) varies as a function of timescale and altitude. We compare the observations to idealized calculations based on the coupled zonal mean thermodynamic and ozone continuity equations, including ozone radiative feedbacks on temperature, where both temperature and ozone respond in a coupled manner to variations in the tropical upwelling Brewer–Dobson circulation. These calculations can approximately explain the observed (T / O3) amplitude and phase relationships, including sensitivity to timescale and altitude, and highlight distinct balances for “fast” variations (periods < 150 d, controlled by transport across background vertical gradients) and “slow” coupling (seasonal and interannual variations, controlled by radiative balances).

HYDRODYNAMIC CALCULATION OF CONTACTLESS SEALS WITH PLANE SLOTS IN DRIVES OF ELECTRIC POWER SYSTEMS

Non-contact seals with fl at slott ed gaps of drives of electric power systems used in switchgears of hydraulic units, as well as in pumps and hydraulic motors have been investigated. Calculation of seals based on average clearance results in an underestimation or overestimation of the leakage rate compared to the operational values. The regularity of the distribution of pressure and fl ow rate in the gap of a fl at conical slot is determined, and formulas for the fl ow rate (leakage) and friction forces acting on the walls of the conical slot are found. To solve the problem, the approximate Navier-Stokes and fl ow continuity equations are used. Several special cases of the fl ow of the working fl uid in diff erent gaps are considered: a plane-parallel gap with an oscillating wall and at a constant pressure gradient and a conical gap at diff erent ratios of the pressure drop and the frictional action of the moving channel wall. When the wall oscillates in a conical gap and constant pressure, the presence of an extremum is characteristic. In this case, an excess pressure appeared in the slott ed gap, creating a supporting force, and the pressure value became high enough. When the lower wall of the conical slot moves in the direction of the increasing gap, the pressure inside the slott ed channel, under certain conditions, can reach a complete vacuum, the value of which is limited by the bulk strength of the liquid and the pressure of saturated vapor at a given temperature. When the pressure drop and oscillations of the wall of the conical gap are additive, then at a suffi ciently high velocity of the wall movement, the pressure inside the slot can even increase and exceed the value of the supplied pressure.

Numerical validation of pressure and flow characteristics across a control valve in a feed line

This work is intended to understand the variation of pressure and flow at the pump inlet of liquid rocket engine. The opening and closure of the valve upstream of the pump features complex phenomenon. The opening and closing of the valve cause pressure and flow variations at the pump inlet which may lead to combustion instabilities in combustion chamber of engine, hydraulic transients in feedlines, and off-design operation of turbo-pumps which are fundamental to the efficient testing and operation of engine. A numerical model to predict the pressure and flow transients across a control valve for different rate of opening in fluid feed systems has been developed using first-order finite difference technique. In case of flow in pipes, the velocity and pressure is governed by momentum and continuity equations. A computer code for the prediction of fluid transients is developed based on method of characteristics for one-dimensional fluid flow in pipelines and compared with test data for validation. The control valve is considered to be in-line with the feed line and modeled based on the valve coefficient vs. percent opening of valve. This model can subsequently be used to predict the effect of opening/closing time of the valve on pressure surges across the control valve and corresponding flow rate in the feedline for different opening of the valve.

A higher-order numerical analysis to study the flow physics and to optimize the design of a short-dwell blade coaters for higher efficiency

Blade coaters are most commonly used for coating of paper and paperboard with higher efficiency. The efficiency of short-dwell blades coaters depends on many factors such as the properties of the coating material, design of the coating reservoir, the types of flow behaviour taking place inside the reservoir, etc. In this work, we have proposed an optimal design of the reservoir to improve the efficiency of short-dwell coaters. The reservoir has been modeled as flow inside a two-dimensional rectangular cavity. Incompressible Navier-Stokes equations in primitive variable formulation have been solved to obtain the flow fields inside the cavity. Spatial derivatives present in the momentum, and continuity equations are evaluated using a sixth-order accurate compact scheme whereas the temporal derivatives are calculated using the fourth-order Runge-Kutta method. The actual rate of convergence of the numerical scheme has been discussed in detail. In addition, the accuracy and stability of the used numerical method are also analysed in the spectral plane with the help of amplification factor and group velocity contour plot. The obtained numerical solutions have been validated with the existing literature. Four different aspect ratio cases (L/H = 3/4,4/3,4/5 and 5/4) have been considered for the simulations including the case of square cavity. It has been observed that L/H = 5/4 case provides best results among all others.

Diffusion treatment of quantum mechanics and its consequences

Localized ensemble of free microparticles spreads out as in a frictionless diffusion satisfying the principle of relativity. An ensemble of classical particles in a fluctuating classical scalar field diffuses in a similar way, and this analogy is used to formulate diffusion quantum mechanics (DQM). DQM reproduces quantum mechanics for homogeneous and gravity for inhomogeneous scalar field. Diffusion flux and probability density are related by Fick’s law, diffusion coefficient is constant and invariant. Hamiltonian includes a “thermal” energy, kinetic energies of drift and diffusion flux. The probability density and the action function of drift form a canonical pair and canonical equations for them lead to the Hamilton-Jacobi-Madelung and continuity equations. At canonical transformation to a complex probability amplitude they form a linear Schrödinger equation. DQM explains appearance of quantum statistics, rest energy (“thermal” energy) and gravity (“thermal” diffusion) and leads to a low mass mechanism for composite particles.

Modelling of a Non-Transferred Plasma Torch Used for Nano-Silica Powders Production

In this study, a two-dimensional numerical model was developed to simulate operation conditions in the non-transferred plasma torch, used to synthesis nanosilica powder. The turbulent magnetohydrodynamic model was presented to predict the nitrogen plasma flow and heat transfer characteristics inside and outside the plasma torch. The continuity, momentum, energy, current continuity equations, and the turbulence model were expressed in cylindrical coordinates and numerically solved by COMSOL Multiphysics software with a finite element method. The operation conditions of the mass flow rate of ionized gas ranging from 78 sccm to 240 sccm and the current varying between 50 A to 200 A were systematically analyzed. The variation in the electrothermal efficiency with the gas flow rate, the plasma current, and the enthalpy was also reported. The results revealed that the increase in working current lead to a raise in the effective electric power and then an increase in the distribution of plasma velocity and temperature. The efficiency of the torch was found to be between 36% and 75%. The plasma jet exited the nozzle torch with a larger fast and hot core diameter with increasing current. The numerical results showed good correlation and good trends with the experimental measurement. This study allowed us to obtain more efficient control of the process conditions and a better optimization of this process in terms of the production rate and primary particle size. X-ray diffraction (XRD) and transmission electron microscopy (TEM) were used to characterize the primary nanosilica powder that was experimentally collected. The arc plasma method enabled us to produce a spherical silicon ultra-fine powder of about 20 nm in diameter.

Modeling of wave processes in closed water areas of shallow water areas

The article presents the developed non-stationary two-dimensional hydrostatic model of wave propagation in the water area of the port of the Bay of Five Hunters, protected by a coastal protection structure in the form of a jetty. The tasks of the work included the development of a model based on the Navier-Stokes and continuity equations and a long-range assessment of the possible impact of the wave situation on marine objects in the port area. At present, the provision of hydrometeorological predictive information is one of the most important factors in the effective operation of port waters. The results are presented graphically using a geographic information system, where different wave heights and maximum wave amplitudes are displayed using a color palette. The consistency of the obtained results is shown, and refraction, diffraction, and interference are noted for the incoming wavefront.