A Numerical Pseudoviscosity Algorithm for Calculating Cylindrically Symmetric Gas Flows on Irregular Difference Grids

The performance of laser beam welding strongly depends on the education of the machine operator. The development of processing parameters for each machine installation and trouble-shooting are time and cost intensive. CALas, a fast simulation software of the laser beam welding process is presented.The physical basis and its appearance in the numerical algorithm is discussed. The model considers the fundamental physical processes, absorption of laser radiation at the keyhole surface including multiple reflections, heat conduction in liquid and solid phases, melt flow and gas flow, absorption of laser radiation in the vapor phase and heat conduction in the plasma volume. Integral formulations are used in order to decrease the calculation time and to preserve the most important features of the experimental results. The results are compared with off-line measurements of the welding depth, the seam width and the cooling time.The welding process is far from its stationary state and experimentally observed quantities are intrinsically time dependent. Therefore, already the setup of a stationary model requires some knowledge about the dynamics.The fundamental physical processes are ordered by their typical time-scales. On-line measurement of plasma emission and numerical simulation of an evolving capillary are presented.The performance of laser beam welding strongly depends on the education of the machine operator. The development of processing parameters for each machine installation and trouble-shooting are time and cost intensive. CALas, a fast simulation software of the laser beam welding process is presented.The physical basis and its appearance in the numerical algorithm is discussed. The model considers the fundamental physical processes, absorption of laser radiation at the keyhole surface including multiple reflections, heat conduction in liquid and solid phases, melt flow and gas flow, absorption of laser radiation in the vapor phase and heat conduction in the plasma volume. Integral formulations are used in order to decrease the calculation time and to preserve the most important features of the experimental results. The results are compared with off-line measurements of the welding depth, the seam width and the cooling time.The welding process is far from its stationary state and experimentally observed quant...

High energy gas fracturing is a simple approach of applying high pressure gas to stimulate wells by generating several radial cracks without creating any other damages to the wells. In this paper, a numerical algorithm is proposed to quantitatively simulate propagation of these fractures around a pressurized hole as a quasi-static phenomenon. The gas flow through the cracks is assumed as a one-dimensional transient flow, governed by equations of conservation of mass and momentum. The fractured medium is modeled with the extended finite element method, and the stress intensity factor is calculated by the simple, though sufficiently accurate, displacement extrapolation method. To evaluate the proposed algorithm, two field tests are simulated and the unknown parameters are determined through calibration. Sensitivity analyses are performed on the main effective parameters. Considering that the level of uncertainty is very high in these types of engineering problems, the results show a good agreement with the experimental data. They are also consistent with the theory that the final crack length is mainly determined by the gas pressure rather than the initial crack length produced by the stress waves.

This thesis deals with the development of mathematical models and numerical schemes for simulating the hydrodynamic pressure and temperature rise of compliant foil bearings lubricated by a thin gas film in between its compliant bearing surface and the rotating shaft. The model accounts for the compressibility of gas, the compliance of the bearing surface, and the interaction between the pressure field and temperature field of the gas film in the bearing system. Numerical solutions obtained over a fairly large range of operating speeds show excellent agreement with existing experimental data from both load performance test and bearing temperature measurement. A series of parametric study is presented to illustrate the utility of the developed algorithms for characterization of foil bearing performance and guidance of foil bearing design. The numerical algorithm can handle high speeds and high eccentricity ratios, which allows the prediction of realistic performance and characteristics of foil bearings under extreme operating conditions.

Assessment of the environmental and economic performance of a safety valve requires information about the flow of the substance through the valve when it is actuated. The goal of this paper was to determine the flow rate of the discharged substance and the mass flow rate of the substance entering the safety valve when it is actuated.Proposed a mathematical model to describe the processes occurring in the valve. The model includes a system of differential equations describing the physical laws of conservation in the internal volume of the valve and differential equations, which link the value of gas flow through the valve with the pressure and the amount of movement of the shut-off disk. Used a modified method by S.K. Godunov to solve gasdynamic equations.Established that the determination of the flow and power characteristics of the valve requires the preliminary construction of a mathematical model of the safety valve operation. Based on this, proposed a method for determining the flow rate of the discharged substance and the mass rate of the substance entering the safety valve when it is actuated.Obtained the flow characteristics of the valves under review and the dynamics of movement of the shutoff disc of the valve, as well as the dependence of the pressure change on the opening time of the valve. Comparison of the calculated values with available experimental data gives good agreement of results (no more than 5.6 % for a gas flow rate, under 10 % for the movement of the valve and change the arrival of gas in time using the standard deviation function of the flow characteristics of 0.6 %), confirms the correctness of the defined mathematical model, used numerical schemes and algorithms, as well as the proposed method and recoverability of the arrival of gas in a pressure–time curve.

The initial stage of collapse of symmetric gaseous prisms

Phase distribution phenomena in two-phase bubble column reactors

To design space vehicles aimed for returning payloads from a geostationary orbit, the Moon and other large or small planets of Solar system, a knowledge of the total (convective and radiative) heating from an environment is required. It is well known that the radiative heat load on a space vehicle moving through the atmosphere increases as the speed and the size increase, therefore, in many of these missions the large part of the trajectory will pass at high altitude, where the low atmospheric density can lead to significant thermal, chemical and physical nonequilibrium effects. Physical models and computational codes used to predict the aerothermodynamics must account for not only high temperature equilibrium thermodynamics (as a rule, within the framework of the local thermodynamic equilibrium (LTE) approach), but also for nonequilibrium one. Therefore, an accurate prediction of radiative heating as well as convective one under both equilibrium and nonequilibrium conditions becomes important to designers and space mission planners. To develop a prediction computational fluid dynamics (CFD) tool for reentry flows, where dissociation, ionization and radiation are important, some major areas are addressed. The most significant of them are following: (1) physical-chemical kinetics of high temperature dissociated and ionized gases, (2) transport properties of the gas mixtures, (3) spectral radiation properties of high temperature gases and low-temperature plasmas, (4) numerical simulation algorithms for prediction of nonequilibrium gas mixtures dynamics and radiation heat transfer in volumes of various geometry, and (5) models of physical and chemical processes accompanied by interaction of gas flows and radiation with thermoprotection systems (TPS) of space vehicles (including their thermochemical destruction, ablation, sublimation, etc.). In literatures (See Refs. (Park, C, 1990, Nonequilibrium Hypersonic Aerothermodynamics, Willey-Interscience Publication, J. Wiley & Sons, New York; Park, C., 1993, “Review of Chemical Kinetic Problems of Future NASA Missions. I: Earth Entries,” J. Thermophys. Heat Transfer, 7(3), pp. 385–398; Park, et al., 1994, “Review of Chemical-Kinetic Problems of Future NASA Missions, II: Mars Entries,” J. Thermophys. Heat Transfer, 8(1), pp. 9–23; Sarma, G., 2000, “Physico-Chemical Modelling in Hypersonic Flow Simulation,” Prog. Aerosp. Sci., 36, pp. 281–349; Huo, and Thuemmel, 1995, Electron-Air Molecule Collisions in Hypersonic Flows. Molecular Physics and Hypersonic Flows, Capitelli M., ed., Kluwer Academic Publishers, pp. 115–138.)) one can find reviews of governing equations used in the aerophysics, boundary conditions and the associated inputs using the physical-chemical models and their partially successful applications. This article presents the states of the art of models of electronic kinetics in the nonequilibrium low-temperature plasma of complex chemical compositions (air and carbon dioxide mixtures) widely met in various aerospace applications. Special attention is given to electronic kinetics of atoms and diatomic molecules within the framework of the radiative-collisional models.

The macroscopic chemistry method for modelling non-equilibrium reacting gas flows with the direct simulation Monte Carlo (DSMC) method is developed and tested. In the macroscopic method, the calculation of chemical reactions is decoupled from the DSMC collision routine. The number of reaction events that must be performed in a cell is calculated with macroscopic rate expressions. These expressions use local macroscopic information such as kinetic temperatures and density. The macroscopic method is applied to a symmetrical diatomic gas. For each dissociation event, a single diatom is selected with a probability based on internal energy and is dissociated into two atoms. For each recombination event, two atoms are selected at random and replaced by a single diatom. To account for the dissociation energy, the thermal energies of all particles in the cell are adjusted. The macroscopic method differs from conventional collision-based DSMC chemistry procedures, where reactions are performed as an integral part of the collision routine. The most important advantage offered by the macroscopic method is that it can utilise reaction rates that are any function of the macroscopic flow conditions. It therefore allows DSMC chemistry calculations to be performed using rate expressions for which no conventional chemistry model may exist. Given the accuracy and flexibility of the macroscopic method, it has significant potential for modelling reacting non-equilibrium gas flows. The macroscopic method is tested by performing DSMC calculations and comparing the results to those obtained using conventional DSMC chemistry models and experimental data. The macroscopic method gives density profiles in good agreement with experimental data in the chemical relaxation region downstream of a strong shock. Within the shock where strongly non-equilibrium conditions prevail, the macroscopic method provides good agreement with a conventional chemistry model. For the flow over a blunt axisymmetric cylinder, which also exhibits strongly non-equilibrium conditions, the macroscopic method also gives reasonable agreement with conventional chemistry models. The ability of the macroscopic method to utilise any rate expression is demonstrated by using a two-temperature rate model that accounts for dissociation-vibration coupling effects that are important in non-equilibrium reacting flows. Relative to the case without dissociation-vibration coupling, the macroscopic method with the two-temperature model gives reduced dissociation rates in vibrationally cold flows, as expected. Also, for the blunt cylinder flow, the two-temperature model gives reduced surface heat fluxes, as expected. The macroscopic method is also tested with a number density dependent form of the equilibrium constant. For zero-dimensional chemical relaxation, the resulting relaxation histories are in good agreement with those provided by an exact Runge-Kutta solution of the relaxation behaviour. Reviews of basic DSMC procedures and conventional DSMC chemistry models are also given. A method for obtaining the variable hard sphere parameters for collisions between particles of different species is given. Borgnakke-Larsen schemes for modelling internal energy exchange are examined in detail. Both continuous rotational and quantised vibrational energy modes are considered. Detailed derivations of viscosity and collision rate expressions for the generalised hard sphere model of Hassan and Hash [Phys. Fluids 5, 738 (1993)] and the modified version of Macrossan and Lilley [J. Thermophys. Heat Transfer 17, 289 (2003)] are also given.

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

Gas-kinetic numerical study of complex flow problems covering various flow regimes

This article is concerned with the transient behavior and thermal performance of a porous matrix combustor-heater in which combustion and heat transfer among the different phases (i.e., the solid matrix, the gas flowing in the packed bed, and the coolant flowing through the tubes) are considered. The governing equations for describing combustion and heat transfer processes are nonlinear and coupled. Under the assumption that axial flow of the gas is predominant, these equations are numerically solved for a typical cell in order to obtain the transient three-dimensional distributions of temperatures and of the fuel mass fraction. The numerical algorithm developed provides the tools for analyzing the effects of operating and geometrical parameters on the performance of a porous matrix combustor-heater and for optimizing design and operation of the unit. Numerical results for some examples are given.

On constructing the contour of minimum wave drag in an inhomogeneous supersonic flow: PMM vol. 37, n≗3, 1973, pp. 469–487

This paper presents a semi-analytical solution for one-dimensional advection-diffusion equation coupled with a linear partial differential equation with constant coefficients. The mathematical model describes a grain-fumigant-air system during fumigation processes, where fumigant gas transports through a storage silo. The coupled system considers both diffusion and advection mechanisms with constant velocity and diffusivity parameters. The solution methodology employs the Laplace transformation technique to convert the partial differential equations into ordinary differential equations in the Laplace domain. The Stehfest numerical algorithm is subsequently applied to invert the Laplace transforms and obtain the time-domain solution. Numerical computations are performed using MATLAB software to simulate the fumigant concentration distributions. Graphical results illustrate the fumigant gas concentration in air versus vertical height within the silo for different time intervals. Additional plots demonstrate the fumigant concentration absorbed by grain particles over time. The analysis examines effects of varying initial gas concentration and flow velocity on the transport process. Results indicate that higher initial concentrations and increased velocities accelerate the fumigation process, requiring less time to fill the silo completely. The proposed solution provides a mathematical framework for optimizing fumigation parameters in agricultural storage applications.

Smoothed Particle Hydrodynamics (SPH) is a grid-free numerical particle method for the simulation of the compressible flow of gases and fluids. The SPH-Method provides a numerical algorithm for solving a system of coupled partial differential equations for continuous field magnitudes. The method transfers this system of equations to a system of coupled common differential equations for magnitudes at discrete sampling points, the locations of the SPH-particles.

Physical and comprehensive numerical studies of the generation of plasma bunches with a high specific energy have been carried out with the use of a plasma gun. The parameters of the plasma bunch upon exit from the plasma accelerator and during propagation in the ionosphere (h > 200 km) to considerable distances (≈100 km) have been calculated. A special numerical algorithm is presented to determine the results of the impact of a rarefied high-velocity gas flow ( $${v}$$ ∼ 5 × 107 cm/s) on the surface of crystalline and amorphous solid bodies.