Problem Of Gas Flow Research Articles

Propagation of a Shock Wave through a Viscous Heat-Conducting Gas in a Long Microchannel

The problem of unsteady gas flow in a channel between parallel plates initiated by the initial discontinuity of the pressure and density (Riemann problem) in the channel cross-section at the high pressure drops and moderately low Knudsen numbers is solved numerically on the basis of the full system of Navier—Stokes equations. The finite-difference scheme of the second order with respect to the spatial variables and time is used. The effect of the gas viscosity and thermal conductivity on the velocity of the shock wave and the nature of flow behind it is studied under the conditions of long channel and low gas density in the low-pressure section. The numerical solution obtained is compared with the available experimental and computational data.

The influence of an oscillating wall on the position of oblique shocks in a 2D channel

In the paper we solve the problem of supersonic gas flow in a two-dimensional channel with the moving upper wall making oscillations according to the harmonic law. In order to obtain a numerical solution for gas dynamics equations we have implemented two difference schemes: the scheme with the space and time approximation of the first order and the scheme with the space approximation of the second order. The fluxes were computed using Van Leer’s method. A special form of fluxes in the gas dynamics equations is given, which enables to calculate fluxes on cell faces of difference mesh using Van Leer’s method. Depending on a type of the harmonic law and initial gas inflow conditions, the peculiarities of oblique-shock wave propagation in moving curvilinear domains have been investigated. It has been determined that under a particular oscillation frequency the presence of wall oscillation practically doesn’t have an effect on the flow regime inside the domain. The convergence of the obtained solution is shown by calculations using difference grids with different numbers of cells. While comparing the numerical solution obtained due to our program with the one obtained with Ansys Fluent solver we found that the constructed code operates correctly.

A generalized short-term unit commitment approach for analyzing electric power and natural gas integrated systems

This paper proposes a generalized short-term unit commitment approach for optimizing the hourly thermal generation scheduling by considering the existing interdependence between natural gas and electricity infrastructures. This generalized approach is formulated as a mixed-integer nonlinear optimization problem where a multi-period optimal gas and alternating current power flow model is incorporated into the thermal unit commitment problem. Contrary to all other proposals that ignore the reactive power dispatch and alternating current electricity network constraints for solving the unit commitment problem that considers the integrated electricity-natural gas system, the proposed solution approach simultaneously co-optimizes the active and reactive power scheduling and dispatch, while taking into account the set of physical and operational constraints associated with each infrastructure. This set of constraints includes reactive power generation limits, nodal voltage magnitude limits and dynamic gas flow constraints. The solution is obtained by decomposing this generalized optimization problem into two mutually connected optimization subproblems: one spatially separable related to the unit commitment problem and the other temporally separable associated with the unified co-optimization of both energy systems, which are sequentially solved until the same hourly generation dispatch in both subproblems is obtained. Hence, this solution is optimal for the unit commitment problem and the optimal gas and power flow problem. Study cases on two multi-energy systems are presented to numerically illustrate the suitability and main characteristics of the proposed approach.

Неизотермическое течение газа в эллиптическом канале с внутренним круговым цилиндрическим элементом в свободномолекулярном режиме

AbstractThe linearized problem of free-molecular gas flow in a long elliptic channel with a circular cylindrical element inside has been solved in the kinetic approximation. The flow in the channel is caused by temperature and pressure drops between its ends. The Boltzmann kinetic equation for collisionless gas has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The distribution of the mass velocity of the gas over the cross section of the channel has been obtained. The mass flow rate of the gas in the channel versus the temperature and pressure drops between its ends has been calculated. It has been found that the mass flow of the gas substantially depends on the radius of the inner cylinder.

Nonisothermal Free-Molecular Flow of Gas in an Elliptic Channel with a Circular Cylindrical Element Inside

The linearized problem of free-molecular gas flow in a long elliptic channel with a circular cylindrical element inside has been solved in the kinetic approximation. The flow in the channel is caused by temperature and pressure drops between its ends. The Boltzmann kinetic equation for collisionless gas has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The distribution of the mass velocity of the gas over the cross section of the channel has been obtained. The mass flow rate of the gas in the channel versus the temperature and pressure drops between its ends has been calculated. It has been found that the mass flow of the gas substantially depends on the radius of the inner cylinder.

Investigation on the Interface Smoothing of Coupled N–S/DSMC Method Using Image Processing Filters

Gas flow problems involving both continuum and rarefied regimes are common in many scientific and engineering applications. Coupled N–S/DSMC method is a major solution to simulate the continuum–rarefied transitional flow. Interface determination is one of the key aspects in developing coupled N–S/DSMC solver, which is often implemented using continuum breakdown parameters to indicate the rarefication level. Due to the statistics characteristic of DSMC method, distribution of the continuum breakdown parameters usually fluctuates, resulting in difficulty in locating the interface. Considering the similarity between continuum breakdown parameter smoothing and noise reduction in image processing, a general smoothing method is proposed in this paper, which employs the image filters to smoothen the distribution of continuum breakdown parameters. Two commonly used image filters, the mean filter and the median filter, are investigated. Several comparison studies are implemented by simulating a typical vacuum plume impingement flow problem. The median filter with 5 × 5 mask provides the best performance. The flow problem of flow over a 2D cylinder is used to validate the coupled N–S/DSMC solver using median filter to smoothen continuum breakdown parameter, which proves the accuracy of the coupled solver and validity of the smoothing method.

Development of a less-dissipative hybrid AUSMD scheme for multi-component flow simulations

In this study, a less-dissipative hybrid AUSMD scheme considering the linearized approximated solution around the material interfaces of compressible multi-component flows is proposed. A high-resolution reconstruction scheme, so-called MUSCL + THINC, has been devised by combining the MUSCL method with the Tangent of Hyperbola for Interface Capturing technique (THINC) under the boundary variation diminishing concept, which is used to determine the cell-interface values to evaluate the AUSMD flux. Several perfect gas and multi-component flow problems are selected as the benchmark test cases. The flow models we use here are the perfect gas Euler equations and the multi-phase five-equation flow model. We compared the proposed MUSCL + THINC-type AUSMD scheme with the original MUSCL-type AUSMD scheme to verify its capability of capturing shock waves, expansion fans, and material interfaces, which are identified as a well-defined sharp jump in volume fraction. Numerical results of all benchmark tests show that the MUSCL + THINC-type AUSMD solver is superior to the original MUSCL-type AUSMD in resolving shock waves, expansion fans, and interfaces. In particular, the solution quality for expansion fans and interfaces on coarse grids is greatly improved by the MUSCL + THINC-type AUSMD scheme.

Local Solvability of the Problem of the Van Der Waals Gas Flow Around an Infinite Plane Wedge in the Case of a Weak Shock Wave

Studying the problem of a stationary supersonic van der Waals gas flow around an infinite plane wedge, we prove the local-in-time well-posedness of the generalized statement of the problem.

ВЛАГОСОДЕРЖАНИЕ ПРИРОДНОГО ГАЗА В ПРИЗАБОЙНОЙ ЗОНЕ ПЛАСТА

Для модельной задачи отбора реального газа из скважины в центре кругового пласта с непроницаемыми кровлей и подошвой выполнен анализ влияния начальных пластовых условий на динамику распределения его влагосодержания. Использовалась математическая модель неизотермической фильтрации, в которой теплопроводность считалась пренебрежимо малой по сравнению с конвективным переносом. Для ее замыкания использовалась эмпирическая зависимость коэффициента несовершенства газа от давления и температуры, апробированная в предыдущих публикациях авторов. Связь между влагосодержанием, давлением и температурой газа описывалась эмпирическими зависимостями, основанными на формуле Бюкачека. Вычислительный эксперимент выполнялся следующим образом. Вначале из численного решения осесимметричной задачи неизотермической фильтрации реального газа определись давление и температура газа при заданном давлении на забое скважины. При этом условия на внешней границе пласта имитировали водонапорный режим отбора газа. Затем эти найденные функции времени и координат использовались для вычисления аналогичной зависимости для влагосодержания. Результаты эксперимента показали, что если пластовая температура существенно превышает равновесную температуру гидратообразования, то распределение влагосодержания в призабойной зоне будет практически идентично распределению температуры. В противном случае газ будет содержать пары воды только вблизи забоя скважины, а далее его влагосодержание будет практически равно нулю. Роль давления и в том и в другом случаях проявляется через интенсивность отбора газа, от которого, в свою очередь, зависят и интенсивность конвективного переноса тепла, и степень охлаждения газа за счет дросселирования.

Riemann problem and elementary wave interactions in dusty gas

The present paper concerns with the study of the Riemann problem for a quasi-linear hyperbolic system of partial differential equations governing the one dimensional isentropic dusty gas flow. The shock and rarefaction waves and their properties for the problem are investigated. We also examine how some of the properties of shock and rarefaction waves in a dusty gas flow differ from isentropic ideal gas flow. The solution of Riemann problem of dusty gas flow for different initial data is discussed. Under certain conditions, the uniqueness and existence of the solution of the Riemann problem has been analyzed. Finally, all possible interactions of elementary waves are discussed.

Recent Progress on Supercomputer Modelling of High-Speed Rarefied Gas Flows Using Kinetic Equations

Numerical solution of the Boltzmann equation for stationary high-speed flows around complex three-dimensional bodies is an extremely difficult computational problem. This is because of high dimension of the equation and lack of efficient implicit methods for the calculation of the collision integral on arbitrary non-uniform velocity grids. Therefore, the use of the so-called model (approximate) kinetic equations appears to be more appropriate and attractive. This article uses the numerical methodology recently developed by the second author which includes an implicit method for solving the approximating kinetic equation of E.M. Shakhov (S-model) on arbitrary unstructured grids in both velocity and physical spaces. Since most of model equations have a well-known drawback associated with the velocityindependent collision frequency it is important to determine the deviations of solutions of these equations from the solution of the complete Boltzmann equation or DSMC for high-speed gas flows. Our recent comparison of the DSMC and S-model solutions for monatomic gases with a soft interaction potential shows good agreement of surface coefficients of the pressure, heat transfer and friction, which are most important for industrial applications. In this paper, we compare the solution of model equations and the Boltzmann equation for the problem of supersonic gas flow around a cylinder when molecules interact according to the law of hard spheres. Since this law of molecular interaction is the most rigid, the difference in solutions can show the maximum error that can be obtained by using model equations instead of the exact Boltzmann equation in such problems. Our high-fidelity computations show that the use of model kinetic equations with adaptation in phase space is very promising for industrial applications.

Equilibrium of Interdependent Gas and Electricity Markets With Marginal Price Based Bilateral Energy Trading

The increasing interdependencies between natural gas systems and power systems create new business opportunities in coupled energy distribution markets. This paper studies the marginal price based bilateral energy trading on the equilibrium of coupled natural gas and electricity distribution markets. Convex relaxation is employed to solve a multiperiod optimal power flow problem, which is used to clear the electricity market. A successive second-order cone programming approach is utilized to solve a multiperiod optimal gas flow problem, which is used to clear the gas market. In addition, the line pack effect in the gas network is considered, which can offer storage capacity and provide extra operation flexibility for both networks. In both problems, locational marginal energy prices are recovered from the Lagrangian multipliers associated with nodal balancing equations. Furthermore, a best-response decomposition algorithm is developed to identify the equilibrium of the coupled energy markets with bilateral gas and electricity trading, which leverages the computational superiority of SOCPs. Cases studies on two test systems validate the proposed methodology.

Investigation on different discrete velocity quadrature rules in gas-kinetic unified algorithm solving Boltzmann model equation

Different discrete velocity quadrature rules are analyzed and applied in gas-kinetic unified algorithm (GKUA) for rarefied free-molecule transition to continuum flows, including the original and modified Gauss–Hermite quadrature rules, the composite Newton–Cotes integration methods, the multi-subinterval Gauss–Legendre numerical quadrature rule and the Gauss–Chebyshev integral rule. Mathematical description and basic procedures of GKUA are presented briefly in solving the gas flow problems covering various flow regimes on the basis of the direction solution to the unified kinetic model of the Boltzmann equation. The numerical analyses and the application conditions of these quadrature rules are given in detail, as well as the evaluating method for the discretized velocity ordinate (DVO) points and their corresponding weights of each rule. According to the comparisons for some Gauss-type function integrations, the original and modified Gauss–Hermite quadrature rules can obtain the integration results with enough accuracy by using least DVO points among these rules, while the impossibility of more nodes limits the application scope of these two quadrature rules. Other four rules can conduct the problems with a needful wide integral interval, even if they use more DVO points than the Gauss–Hermite rules. Besides, the multi-subinterval Gauss–Legendre and the Gauss–Chebyshev rules can use less DVO points to obtain accurate integration results than the other two rules, which demonstrate their advantage and are recommended to be applied in GKUA to solve the Boltzmann model equation efficiently.Numerical simulations for the Sod and Lax shock-tube problems and the shock-density wave disturbing interaction problems are conducted by using GKUA with the above quadrature rules to make comparison. All quadrature rules can obtain nice accurate results with different number of the DVO points. The original and modified Gauss–Hermite quadrature rules, using the least DVO nodes to obtain results with enough computed precision, are the best options for GKUA to simulate low mach number flow regimes, while the Gauss–Chebyshev quadrature rule, which can obtain results with adequate and controllable precision for a wide integral interval using little DVO nodes, is the most appropriate quadrature rule for GKUA solving some complex and high mach number flows covering various flow regimes.

Coefficient-by-Coefficient Averaging in a Problem of Laminar Gas Flow in a Well

Coefficient-by-Coefficient Averaging in a Problem of Laminar Gas Flow in a Well

Unsteady Rarefied Gas Flow with Shock Wave in a Channel

The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite volume. The effect of gas deceleration at the channel walls under the conditions of diffuse molecular reflection from the channel walls and end face is studied. Decay of a shock wave and disappearance of a homogeneous flow zone behind the shock wave is traced for three variants of conditions at the channel inlet: (1) gas enters the channel from a reservoir of infinite length and width (as the basic variant), the simultaneous motion in the reservoir and channel being studied; (2) the high-pressure reservoir represents a usual channel section; and (3) the motion of the gas in the reservoir is not considered at all, instead of this, the boundary conditions of the evaporation-condensation type under the conditions of gas at rest in the reservoir are imposed in the inlet cross-section.

Coefficient-by-Coefficient Averaging in a Problem of Laminar Gas Flow in a Well

This paper describes the problem of determining the temperature of laminar gas flow, in which the equation of convective heat transfer contains two variable coefficients, is reduced to nonclassical problems for zeroth and first asymptotic expansion coefficient with respect to a formal parameter. The Laplace–Carson transform are used to obtain analytical expressions for the temperature field of ascending laminar gas flow in a well with account for the relationships of density and velocity with spatial coordinates in zeroth and first asymptotic approximations. Expressions for the temperature asymptotically averaged along the cross section of the well and temperature distributions over the cross-sectional radius are obtained.

Calculation of the Maximum Slope Angles of the Temperature Curve for the Single-Flow Non-Stationary Method of Deriving the Thermal Characteristics of Heat Transfer Surfaces

Results are presented for the solution of the problem of gas flow in a porous body with the presence of a temperature “step” in the range 1–100 of the non-dimensional heat-transfer coefficient, while accounting for longitudinal thermal conductivity. The problem was solved using the numerical finite difference method. Maximum slope angles were derived for temperature curves that can be used to obtain the thermal characteristics of high-compact heat transfer surfaces with the single-flow non-stationary method. Recommendations were provided regarding the range of applicability of the method, taking into account the new received results.

Asymptotic far-field behavior of macroscopic quantities in a problem of slow uniform rarefied gas flow past a sphere

The asymptotic far-field behavior of macroscopic quantities in a problem of slow uniform rarefied gas flow past a sphere is investigated for the purpose of acquiring a function occurring in the second-order drag. The thermal force in the problem of thermophoresis of a sphere is also discussed.

DsmcFoam+: An OpenFOAM based direct simulation Monte Carlo solver

dsmcFoam+ is a direct simulation Monte Carlo (DSMC) solver for rarefied gas dynamics, implemented within the OpenFOAM software framework, and parallelised with MPI. It is open-source and released under the GNU General Public License in a publicly available software repository that includes detailed documentation and tutorial DSMC gas flow cases. This release of the code includes many features not found in standard dsmcFoam, such as molecular vibrational and electronic energy modes, chemical reactions, and subsonic pressure boundary conditions. Since dsmcFoam+ is designed entirely within OpenFOAM’s C++ object-oriented framework, it benefits from a number of key features: the code emphasises extensibility and flexibility so it is aimed first and foremost as a research tool for DSMC, allowing new models and test cases to be developed and tested rapidly. All DSMC cases are as straightforward as setting up any standard OpenFOAM case, as dsmcFoam+ relies upon the standard OpenFOAM dictionary based directory structure. This ensures that useful pre- and post-processing capabilities provided by OpenFOAM remain available even though the fully Lagrangian nature of a DSMC simulation is not typical of most OpenFOAM applications. We show that dsmcFoam+ compares well to other well-known DSMC codes and to analytical solutions in terms of benchmark results. Program summaryProgram title: dsmcFoam+Program Files doi:http://dx.doi.org/10.17632/7b4xkpx43b.1Licensing provisions: GNU General Public License 3 (GPL)Programming language: C++Nature of problem: dsmcFoam+ has been developed to help investigate rarefied gas flow problems using the direct simulation Monte Carlo (DSMC) method. It provides an easily extended, parallelised, DSMC environment.Solution method: dsmcFoam+ implements an explicit time-stepping solver with stochastic molecular collisions appropriate for studying rarefied gas flow problems.

A Unified Framework for Modeling Continuum and Rarefied Gas Flows

The momentum and heat transport in rarefied gas flows is known to deviate from the classical laws of Navier and Fourier in Navier-Stokes-Fourier (NSF) equations. A more sophisticated Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe gaseous and thermal transport both in continuum and rarefied gas flows. We first develop a unified numerical framework for modeling continuum and rarefied flows based on the NCCM model both in two and three dimensions. Special treatment is given to the complex highly nonlinear transport equations for non-conserved variables that arise from the high degree of thermal nonequilibrium. For verification and validation, we apply the present scheme to a stiff problem of hypersonic gas flows around a 2D cylinder, a 3D sphere, and the Apollo configuration both in continuum and rarefied situations. The results show that the present unified framework yields solutions that are in better agreement with the benchmark and experimental data than are the NSF results in all studied cases of rarefied problems. Good agreement is observed between the present study and the NSF results for continuum cases. The results show that this study provides a unified framework for modeling continuum and rarefied gas flows.