Submodel of rotational motions in gas dynamics

An invariant submodel of the equations of gas dynamics constructed on a one-dimensional subalgebra consisting of the sum of operators of rotation and translation in time is studied within the framework of the SUBMODELS program. The system of equations of the submodel is brought to symmetric form. Hyperbolicity conditions for the system are derived. Group analysis is performed and an invariant solution is considered. Isobaric flows are listed. For the simplest of them, characteristics and strong discontinuities are considered. Necessary conditions for existence of solutions without singularities on the axis are derived. Institute of Mechanics, Ural Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 37–45, November–December, 1998.     

Galilean-invariant axisymmetric self-similar submodel of gas dynamics without swirling

This paper deals with one insufficiently studied submodel of invariant solutions of rank 1 of the equations of gas dynamics. It is shown that, in cylindrical coordinates, the submodel without swirling reduces to a system of two ordinary differential equations. For the equation of state with additional invariance, a self-similar system is obtained. A pattern of phase trajectories is constructed, and particle motion is studied using asymptotic methods. The obtained solutions describe unsteady flows over axisymmetric bodies with possible strong discontinuities. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 46–52, March–April, 2009.     

Projective Submodel of the Ovsyannikov Vortex

A submodel of the Ovsyannikov vortex with projective symmetry is studied. Integration of the factor system of the submodel reduces to solving a first-order differential equation which is not solved with respect to the derivative. The properties of the solutions of this equation are studied. It is shown that the submodel describes gas ow with a nonstationary source and a nonstationary sink. The problem of the motion of a gas volume between pistons of cylindrical shapes is studied, and its solution with an invariant shock wave is obtained.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 3–16, July–August, 2005.     

Ovsyannikov plane vortex: The equations of the submodel

A submodel of the equations of ideal magnetohydrodynamics is constructed that generalizes the classical motion of an ideal continuous medium with plane waves. It is shown that, in contrast to classical motion, in this submodel the velocity and magnetic-field vectors can change direction in a plane orthogonal to a distinguished spatial direction. The submodel is described by a system of equations with two independent variables and a finite relation specifying the orientation of the vector fields in space. The solutions of the submodel define substantially spatial processes and singularities in the motion of continuous media which cannot be studied in the classical one-dimensional formulation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 27–40, September–October, 2008.     

On a gas source in a constant force field

The nonbarochronic regular partially invariant submodel of the equations of gas dynamics is studied. The submodel reduces to an implicit ordinary differential equation of the first order for an auxiliary function X = X(x). The physical quantities (velocity, density, and pressure) are expressed in terms of the function X. The properties of the solutions of the equation are investigated and interpreted physically in terms of gas motion. The existence of a shock-wave solution is proved. The properties of the shock adiabat are studied. It is shown that the results obtained are new and differ significantly from the results for the case of no constant force. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 3–16, November–December, 2006.     

Solution with a linear velocity field for a submodel of one-dimensional gas motions

A method for finding exact solutions of the equations of gas dynamics with a linear velocity field is proposed. This method was used to find exact solutions for one submodel of the evolutionary type which was fully integrated for the case of a polytropic gas. Examples of particle motion for the obtain exact solutions are given.     

Partially invariant solutions in gas dynamics and implicit equations

This paper studies a nonbarochronic, regular, partially invariant solution (submodel) of rank one and defect two to the equations of gas dynamics which describes spatial unsteady gas motion. The equations of gas dynamics are reduced to an implicit ordinary differential equation of the first order for an auxiliary function and to an integrable system. A complete classification of the irregular singular points of the key equation according to a parameter characterizing the gas flow is given, and transformations of the irregular singular points with variation in the parameter are obtained. Qualitative properties of the solution are investigated and physically interpreted in terms of gas motion. It is shown that there are two modes of motion, one of which is supersonic, and in the second modes, a continuous transition through the speed of sound is possible.     

Continuous Restricted Radial Motion of a Gas under the Action of a Piston

The possibility of continuous conjugation of the straightline radial motion of a gas sphere toward the center and away from the center with the motion where the gas in the entire sphere stops simultaneously is shown. The motion is described by an invariant submodel of rank 1. Time reflections allow one to construct a solution that describes a periodic continuous restricted motion of the gas sphere under the action of a piston.     

Front Regime of Heat and Mass Transfer in a Gas Hydrate Reservoir under the Negative Temperature Conditions

The analytical self-similar solution to the nonlinear problem of the front regime of heatand- mass transfer in a gas hydrate reservoir under the negative temperature conditions is obtained. In the initial state the reservoir is assumed to be saturated with a heterogeneous gas hydrate–ice–gas mixture. In particular cases there may be no ice or/and gas. The ice and gas are formed behind the gas hydrate dissociation front. The calculations are presented for a stable hydrate–gas system. The critical curves are constructed in the well-pressure–reservoir-permeability plane. These curves separate the domains of the front regime and the regime of volume gas hydrate dissociation ahead of the front. The velocity of the gas hydrate dissociation front is investigated as a function of various problem parameters. The characteristic temperature and pressure distributions corresponding to various regimes on the diagram are investigated.     

Gas Flows with Spiral and Helical Level Lines

An invariant submodel of rank 1 describing flows with spiral and helical level lines is considered. It is shown that, for the case of spiral level lines, there is a smooth gas flow in a twisted Laval nozzle. For the case of helical level lines, two flows are conjugated via the helical surface of the shock wave.     

Class of differentially invariant solutions of the submodel of axisymmetric flows of an ideal gas

A class of differentially invariant solutions of a problem with the pressure independent of the radial coordinate is considered for a submodel of steady axisymmetric flows of a polytropic gas. The overdetermined system turns out to be compatible and is integrated. All solutions defining transonic and supersonic flows with a limiting surface are found. These solutions are compared with invariant solutions obtained previously.     

Plane ovsyannikov vortex: Motion properties and exact solutions

The physical properties of ideal plasma flow described by the Ovsyannikov plane vortex are studied. The particle trajectories and magnetic lines are shown to be plane curves, and an algorithm for describing the motion in three-dimensional space is proposed. Some exact solutions of the submodel are obtained and studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 55–68, November–December, 2008.     

Turbine adapted maps for turbocharger engine matching

This paper presents a new representation of the turbine performance maps oriented for turbocharger characterization. The aim of this plot is to provide a more compact and suited form to implement in engine simulation models and to interpolate data from turbocharger test bench.The new map is based on the use of conservative parameters as turbocharger power and turbine mass flow to describe the turbine performance in all VGT positions. The curves obtained are accurately fitted with quadratic polynomials and simple interpolation techniques give reliable results.Two turbochargers characterized in an steady flow rig were used for illustrating the representation. After being implemented in a turbocharger submodel, the results obtained with the model have been compared with success against turbine performance evaluated in engine tests cells. A practical application in turbocharger matching is also provided to show how this new map can be directly employed in engine design.     

Decay of a plane shock wave in a two-parameter medium with arbitrary equation of state

Special curves, called shock polars, are frequently used to determine the state of the gas behind an oblique shock wave from known parameters of the oncoming flow. For a perfect gas, these curves have been constructed and investigated in detail [1]. However, for the solution of problems associated with gas flow at high velocities and high temperatures it is necessary to use models of gases with complicated equations of state. It is therefore of interest to study the properties of oblique shocks in such media. In the present paper, a study is made of the form of the shock polars for two-parameter media with arbitrary equation of state, these satisfying the conditions of Cemplen's theorem. Some properties of oblique shocks in such media that are new compared with a perfect gas are established. On the basis of the obtained results, the existence of triple configurations in steady supersonic flows obtained by the decay of plane shock waves is considered. It is shown that D'yakov-unstable discontinuities decompose into an oblique shock and a centered rarefaction wave, while spontaneously radiating discontinuities decompose into two shocks or into a shock and a rarefaction wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 147–153, November–December, 1982.     

基于子模型法的大跨斜拉桥扁平钢箱梁应力分析

为了掌握扁平流线型钢箱梁应力水平及其分布,本文以润扬斜拉桥为工程背景,建立了整体有限元模型和局部有限元子模型。在对整体有限元模型进行分析的基础上,应用子模型法对润扬斜拉桥主梁各关键截面进行了有限元受力分析,运用试验结果验证了有限元结果的可靠性。在此基础上研究了主梁各关键截面的应力水平及其分布特点,并进一步总结了试验荷载下润扬斜拉桥扁平钢箱梁的受力特点。结果表明了子模型法应用于扁平钢箱梁局部应力分析的有效性和可靠性,其结果可为润扬斜拉桥扁平钢箱梁的安全监测提供科学依据。     

SIMULATION OF PARTICLE COATING IN THE SUPERCRITICAL FLUIDIZED BED

Fluidized bed technology using supercritical carbon dioxide both as a fluidizing gas and as a solvent for the coating material makes possible the production of thin, uniform and solvent-free coatings. But operation at low fluidizing velocities, which is favorable to facilitate gas cleaning under the high pressure conditions, may lead to uneven distribution of the coating in the fluidized bed and to unstable operation due to agglomeration. Therefore a model has been developed which describes local fluid dynamics within the high pressure fluidized bed. Based on this model, the coating process is described and the distribution of the coating inside the fluidized bed is calculated. Furthermore a submodel for the calculation of local concentrations of liquid paraffin has been set up, which may be used as a basis for the prediction of agglomeration and thus stability of operation.     

Numerical Simulation of Pulverized Coal MILD Combustion Using a New Heterogeneous Combustion Submodel

The scope of this investigation is the application and analysis of a recently developed submodel (Schulze et al., Oil Gas Science Technol, 2013, doi:10.2516/ogst/2012069) for char particle combustion and gasification. The distinguishing feature of this model is a detailed representation of the diffusion and convection processes as well as the homogeneous reactions in the boundary layer around the char particle. These processes are fully coupled to the heterogeneous particle kinetics. The model was implemented into the CFD code ANSYS-Fluent. The coupled solver is used for simulating the IFRF full scale pulverized coal combustion MILD furnace, for which detailed experimental data are available for model evaluation (Orsino et al., IFRF Doc. No F46/y/3, 2000) The new model yields improved agreement with measured data as compared to the standard modeling approach. This can be directly related to the prediction of the char burnout rate. For further analysis, the mixing field in the IFRF furnace is investigated in detail by introducing four mixture fractions for pyrolysis products, char burn-off gases, primary and secondary air, respectively. The solutions of the respective transport equations are used to define the local stoichiometry both in the gas phase and on the particle surface in such a multi-stream system. The conditions in the particle surrounding gas phase as well as on the particle surface are used to define the regime of particle-gas interaction based on the simulations with the new submodel. It can be shown that for certain conditions the homogeneous reactions in the particle boundary must be accounted for.     

An ocean modelling system with turbulent boundary layers and topography: numerical description

The Sandia ocean modelling system (SOMS) is a system of three-dimensional, fully conservative, partially implicit numerical models based on primitive equations and a staggered Arakawa ‘c’ grid. A thin-shell bottom boundary layer submodel coupled to a free-stream submodel resolves boundary layers together with realistic topography. Both submodels use stretched vertical co-ordinates and an optional Mellor-Yamada level-2·5 turbulence closure. Rigid top pressures are determined by vertical integration of the conservation equations using a hydrostatic approximation. SOMS reproduces previously published results, but with notable advantages in speed and economy.     

Regular submodels of types (1,2) and (1,1) of the equations of gas dynamics

Partially invariant solutions of types (1, 2) and (1, 1) for gas-dynamic equations are regularly divided into two classes: for the first class, the invariant independent variable is the time, i.e., this class contains barochronic solutions, and for the second class, the invariant variable necessarily depends on spatial coordinates. The barochronic submodel of gas-dynamic equations, as well as a passive subsystem for solutions of the second class, is integrated in finite form. In the latter case, the invariant subsystem is reduced to an ordinary differential equation and quadratures. Integration of the submodels is illustrated by a number of examples. The following common properties of barochronic gas flows are described: rectilinear trajectories of gas particles, the possibility of collapse of density on a manifold, and stratification of the space of events. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 40–49, March–April, 1999.     

Numerical simulation of a dense solid particle flow inside a cyclone separator using the hybrid Euler–Lagrange approach

This paper presents a numerical simulation of the flow inside a cyclone separator at high particle loads. The gas and gas–particle flows were analyzed using a commercial computational fluid dynamics code. The turbulence effects inside the separator were modeled using the Reynolds stress model. The two phase gas–solid particles flow was modeled using a hybrid Euler–Lagrange approach, which accounts for the four-way coupling between phases. The simulations were performed for three inlet velocities of the gaseous phase and several cyclone mass particle loadings. Moreover, the influences of several submodel parameters on the calculated results were investigated. The obtained results were compared against experimental data collected at the in-house experimental rig. The cyclone pressure drop evaluated numerically underpredicts the measured values. The possible reason of this discrepancies was disused.