Non-ideal Gas Flow Research Articles

Similarity Solutions of Cylindrical Shock Waves in Non-Ideal Magnetogasdynamics with Thermal Radiation

In the present work we have taken one-dimensional unsteady flow of non-ideal gas with magnetic effect under the presence of thermal radiation. The system is hyperbolic in nature and solved by similarity method using Lie Group of Transformations under the assumption that the system is constantly conformally invariant under the transformations. The similarity solutions are investigated behind a cylindrical shock which is a consequence of a sudden explosion or produced by an expanding piston. The shock is assumed to be strong and propagating into the medium which is at rest, with uniform density. The total energy of the shock is assumed to be time dependent and obeying the power law. By means of similarity method our system of PDEs transformed into the system of ordinary differential equations (ODEs), which in general are nonlinear. The effects of thermal radiation on the the flow variables velocity, density, pressure and magnetic field are investigated behind the shock.

Magnetogasdynamic Shock Waves in Non-ideal Gas Under Gravitational Field-Isothermal Flow

Self-similar solutions are obtained for one-dimensional unsteady isothermal flow of non-ideal gas with gravitational effects behind a spherical shock wave, in the presence of a spatially decreasing azimuthal magnetic field. The shock wave is driven out by a moving piston with time according to power law. The gas is assumed to be non-ideal having infinite electrical conductivity. The medium is under the influence of the gravitational field due to a heavy nucleus at the origin (Roche model). The effects of variation of the parameter of non-idealness of the gas, the Alfven–Mach number and the gravitational parameter on the flow-field behind the shock are investigated. It is shown that the presence of magnetic field, gravitational field and non-idealness of the gas has decaying effect on the shock wave. Further, it is investigated that the shock strength decreases due to an increase in the strength of magnetic field, gravitational and non-idealness parameter. The present study can be important for description of shocks in supernova explosions, in the study of a flare produced shock in the solar wind, central part of star burst galaxies, nuclear explosion, rupture of a pressurized vessel and explosion in the ionosphere etc.

Feasibility analysis of neutral stability for shock waves in a nonideal gas flow about a wedge

The feasibility of neutral stability for shock waves in the problem of a real gas flow about a wedge is studied by means of numerical experiments. A shock adiabat for a van der Waals gas is derived; that is, a relationship is found between the wedge and shock wave angles. A vast amount of numerical data is obtained, and some of them are summarized in tables. From these data, one can distinguish wedge flow regimes with neutrally stable shock waves.

Research on the inherent error of ultrasonic flowmeter in non-ideal hydrogen flow fields

For the widespread transmission, custody and utilization for hydrogen energy, accurate flow rate measurement is the precondition. The ultrasonic flowmeter has a prospect of wide application for the hydrogen flow measurement. To improve the measurement accuracy, this article researched the inherent error of the ultrasonic flowmeter in the non-ideal hydrogen gas flow. Computational fluid dynamics (CFD) had been used to simulate hydrogen flows downstream of the single right bend and an orifice plate at different Reynolds numbers. Based on the simulation results, this work investigated the inherent error of the ultrasonic flowmeter with different integrations and acoustic paths. The results show the errors become larger when the flowmeter position is closer to the disturbance sources. The increase in the number of acoustic paths can effectively reduce the error caused by the non-ideal flow. In the flow field downstream of the bend, the flowmeters adopting Tailored and Owics integration perform better than those with other integrations. Tchebychev and Owics integration cause less error in the front 4D (four times diameter) pipe downstream of the orifice plate, while Tailored and Owics cause less error in the rear 11D area.

Acceleration waves in non-ideal magnetogasdynamics

The problem of propagation of acceleration waves in an unsteady inviscid non-ideal gas under the influence of magnetic field is investigated. The characteristic solution to the problem in the neighbourhood of leading characteristics has been determined. An evolution equation governing the behaviour of acceleration waves has been derived. It is shown that a linear solution in the characteristic plane exhibits non-linear behaviour in physical plane. The effect of magnetic field on the formation of shock in non-ideal gas flow with planar and cylindrical symmetry is analysed. It is noticed that all compressive waves terminate into a shock wave. Further, we also compare/contrast the nature of solution in ideal and non-ideal magnetogasdynamic regime.

A pore network model for simulating non-ideal gas flow in micro- and nano-porous materials

The capability to simulate real gas flow in porous materials with micro- and nano-meter-scale pores is of importance in many applications, such as gas extraction from shale reservoirs, and the design of gas-based fuel cells. A node-bond pore-network flow model (PNFM) has been developed for gas flow where it is the only fluid phase. The flow conductance equation includes the usual Darcy flow terms, and additional terms that capture the contributions from slip flow to Knudsen diffusion. With respect to the case for a non-ideal gas, the extra contributions, which are necessary, to the coefficients of the Darcy and Knudsen terms, are expressed in terms of reduced temperature and pressure, using van der Waals’s two-parameter principle of corresponding states. Analysis on cylindrical pores shows that the coefficient deviates from that of the non-ideal gas case by more than 80% in the Darcy term, while between −80% and 150% in the Knudsen term, when the physical states approach to the critical state of the fluid. Although the deviations become smaller when the states are away from the critical state, they remain relatively large even at conditions relevant to practical applications. The model was applied to a pore network of a realistic 3D shale model to show slippage and Knudsen effects on the predicted permeability and the sensitivity to pore sizes. Simulations were carried out for methane under the operational conditions of typical shale-gas reservoirs, and nitrogen under the conditions of laboratory experiments. The results show that the ratio of gas and Darcy permeability correlates positively and strongly with the pore size but inversely with the gas pressure and Tangential Momentum Accommodation Coefficient (TMAC) in the slip term, which can impact gas permeability disproportionally. The results are in favour of controlling the rate of gas depressurisation to avoid early depletion in shale gas production. The methane permeability is shown to be 30% greater, relatively, than that when the ideal gas law is applied, even under normal field operational conditions, while the nitrogen permeability can only approximate the methane permeability within a certain range of field operational conditions when the slip flow is not dominating.

Shock dynamics of weak imploding cylindrical and spherical shock waves with non-ideal gas effects

The author (Anand 2012 Astrophys. Space Sci.342 377–88) recently obtained jump relations across a shock front in non-ideal gas flow taking into consideration the equation of state for a non-ideal gas as given by Landau and Lifshitz. In this paper an analytical solution for one-dimensional adiabatic flow behind weak converging shock waves propagating in a non-ideal gas is obtained by using Whitham's (1974 Linear and Nonlinear Waves (New York: Wiley)) geometrical shock dynamics approach. The effects of an increase in (i) the propagation distance from the centre of convergence, (ii) the non-idealness parameter and (iii) the adiabatic index of the gas, on the shock velocity, pressure, density, particle velocity, adiabatic compressibility and the change in entropy across the shock front, are analyzed. The results provided a clear picture of whether and how the non-idealness parameter and the adiabatic index affect the flow field behind the imploding shock front.

Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow

The generalized jump relations across the magnetohydrodynamic (MHD) shock front in non-ideal gas are derived considering the equation of state for non-ideal gas as given by Landau and Lifshitz. The jump relations for pressure, density, and particle velocity have been derived, respectively in terms of a compression ratio. Further, the simplified forms of the MHD shock jump relations have been obtained in terms of non-idealness parameter, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The aim of this paper is to contribute to the understanding of how shock waves behave in magnetized environment of non-ideal gases.

Jump relations across a shock in non-ideal gas flow

Generalized forms of jump relations are obtained for one dimensional shock waves propagating in a non-ideal gas which reduce to Rankine-Hugoniot conditions for shocks in idea gas when non-idealness parameter becomes zero. The equation of state for non-ideal gas is considered as given by Landau and Lifshitz. The jump relations for pressure, density, temperature, particle velocity, and change in entropy across the shock are derived in terms of upstream Mach number. Finally, the useful forms of the shock jump relations for weak and strong shocks, respectively, are obtained in terms of the non-idealness parameter. It is observed that the shock waves may arise in flow of real fluids where upstream Mach number is less than unity.

Growth and decay of acceleration waves in non-ideal gas flow with radiative heat transfer

Abstract The present paper is concerned with the study of the propagation of acceleration waves along the characteristic path in a non-ideal gas flow with effect of radiative heat transfer. It is shown that a linear solution in the characteristic plane can exhibit non-linear behavior in the physical plane. It is also investigated as to how the radiative heat transfer under the optically thin limit will affect the formation of shock in planer, cylindrical and spherically symmetric flows. We conclude that there exists critical amplitude such that any compressive waves with initial amplitude greater than the critical one terminate into shock waves while an initial amplitude less than the critical one results in the decay of the disturbance. The critical time for shock formation has been computed. In this paper we also compare/contrast the nature of solution in ideal and non ideal gas flows.

An Enskog based Monte Carlo method for high Knudsen number non-ideal gas flows

A Monte Carlo method based on the Enskog equation for dense gas is developed by considering high density effect on collision rates and both repulsive and attractive molecular interactions for a Lennard–Jones fluid. The appropriate internal energy exchange model is introduced with consistency with the collision model. The equation of state for a non-ideal gas is therefore derived involving the finite density effect and the van der Waals intermolecular force, changing from the Clapeyron equation to the van der Waals equation. In contrast to previous Monte Carlo approaches, the present predictions agree better with experimental data for the gas transport properties at high densities and in a wide temperature region. The numerical modeling of non-ideal gas flow in micro and nanochannels show that the high gas density affects greatly flow behavior and heat transfer characteristics. The high density of gas leads to a lower skin friction coefficient on the wall surfaces than the predictions by the perfect gas assumption.

A comparison of hyperbolic solvers for ideal and real gas flows

Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to second-order by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. These methods require the so-called Roe's average state, which is frequently difficult and sometimes impossible to obtain. Other methods that do not require the average state are best suited for complex equations of state. Of these, the VFRoe, AUSM+ and Hybrid Lax-Friedrich-Lax-Wendroff methods were compared for one-dimensional compressible flows of a Van der Waals gas. All methods were evaluated regarding their accuracy for given mesh sizes and their computational cost for a given solution accuracy. It was shown that, even though they require more floating points and indirect addressing operations per time step, for a given time interval for integration the second-order methods are less-time consuming than the first-order methods for a required accuracy. It was also shown that AUSM+ and VFRoe are the most accurate methods and that AUSM+ is much faster than the others, and is thus recommended for nonideal one-phase gas flows.

Nonideal gas flow and heat transfer in micro- and nanochannels using the direct simulation Monte Carlo method.

Subsonic nonideal gas flow and heat transfer in micro- and nanochannels for different Knudsen numbers are investigated numerically using the direct simulation Monte Carlo method modified with a consistent Boltzmann algorithm. The van der Waals equation is used as the equation of state. The collision rate is also modified based on the Enskog theory for dense gas. It is shown that the nonideal gas effect becomes significant when the gas becomes so dense that the ideal gas assumption breaks down. The results also show that the nonideal gas effect is dependent not only on the gas density, but also on the channel size. A higher gas density and a smaller channel size lead to a more significant nonideal gas effect. The nonideal gas effect also causes lower skin friction coefficients and different heat transfer flux distributions at the wall surface. The simulations presented in this work are helpful for a better understanding of micro- and nanoscale gas flows.

Nonideal Gas Effects for the Venturi Meter

A method for treating nonideal gas flows through a venturi meter is described. The method is an extension of a previous study reported in an earlier paper. The method involves the determination of the expansion factor which may then be used to determine the mass flow rate through the venturi meter. The method also provides the means for determining the critical pressure ratio as well as the maximum flow rate per unit throat area. The Redlich-Kwong equation of state is used, which allows for closed form expressions for the specific heat at constant volume and the change in entropy. The Newton-Raphson method is used to determine the temperature and specific volume at the throat. It is assumed that the following items are known: the upstream temperature and pressure and the ratio of the throat pressure to the upstream pressure. Results were obtained for methane gas. These results indicate that for the cases considered, the use of the ideal gas expression for the expansion factor would lead to an error in the determination of the mass flow rate; the error increases as the throat to inlet pressure ratio decreases. For the example reported in this study, the maximum percent difference in the critical pressure ratio between the ideal and nonideal gases was 5.81 percent, while the maximum percent difference in the maximum flow rate per unit throat area was 7.62 percent.

Nonideal Isentropic Gas Flow Through Converging-Diverging Nozzles

A method for treating nonideal gas flows through converging-diverging nozzles is described. The method incorporates the Redlich-Kwong equation of state. The Runge-Kutta method is used to obtain a solution. Numerical results were obtained for methane gas. Typical plots of pressure, temperature, and area ratios as functions of Mach number are given. From the plots, it can be seen that there exists a range of reservoir conditions that require the gas to be treated as nonideal if an accurate solution is to be obtained.

Hydraulic Analogy for Isentropic Flow Through a Nozzle

Modelling aspects of isentropic compressible gas flow using hydraulic analogy are discussed. Subsonic and supersonic flows through a typical nozzle are simulated as free surface incompressible water flow in an equivalent 2-D model on a water table. The results are first compared for the well known classical analogy in order to estimate experimental errors. Correction factors for pressure and temperature, to account for non-ideal compressible gas flow are presented and the results obtained on the water table are modified and compared with gas dynamic solution. Within the experimental errors, it is shown that the hydraulic analogy can be used as an effective tool for the study of two dimensional isentropic flows of gases.

The Solution of Nonlinear Equations

Abstract This paper presents procedures for treating problems involving transient flow of gases in porous problems involving transient flow of gases in porous media. The methods involve stepwise calculations using linearized equations derived from the nonlinear, second-order equations that describe transient flow of gas. The distribution of pressure around a gas well at various times can be readily calculated with a desk calculator or a small computer. Equations and procedures are offered for both infinite and limited reservoirs. Solutions by these new technique's are shown to be in good agreement with computer solutions available in the literature. Also discussed is a procedure using relatively few image wells for treating problems in reservoirs with curved, irregular boundaries. Introduction This paper is concerned with solving problems involving transient flow of gas in porous systems. The main contribution of this paper is the development of a technique that permits the effective use of a desk calculator for the computations. The methods presented here will permit individual engineers not having access to one of the larger computers to solve many practical problems that heretofore would have been intractable. problems that heretofore would have been intractable. The equation describing unsteady-state flow of a perfect gas in a horizontal reservoir is reported by perfect gas in a horizontal reservoir is reported by Katz to be (1) This equation is obtained by combining the continuity equation, Darcy's law, and the following density relationship for the gas. =...............................(2) The intractableness of Eq. 1 stems from the fact that it is a nonlinear, second-order differential equation for which no analytical solution is known. In 1953, a pioneering use of computers was presented by Bruce et al., who approximated the presented by Bruce et al., who approximated the differential equation with difference equations and solved these numerically. Their solutions developed for horizontal flow of a perfect gas for circular reservoirs were presented in terms of dimensionless parameters in plots of pressure vs radius for various parameters in plots of pressure vs radius for various times and flow rates. Later, Aronofsky and Porter, using computers, solved radial flow problems for nonideal gases, permitting gas properties to vary as linear functions of pressure. Recently, advances in solving problems involving the flow of nonideal gas have been made by Ramey and his colleagues, who have developed equations and computer solutions for real gases in terms of pseudo-reduced pressures. In the present paper, a method of solving the flow equations for gas is developed for both infinite and limited reservoirs. The methods, which make use of the analytical solutions for the corresponding linear differential equation for radial flow, can be used with a desk calculator or a small computer to solve problems characterized by nonradial as well as by radial reservoir geometry. An example solution is given to illustrate the method for the flow of a perfect gas in a circular, horizontal reservoir; the results have been compared with those of Bruce. The technique can also be applied to the flow of nonideal gases in nonuniform systems, as well as to oil reservoirs above the bubble-point pressure and to aquifers. In all cases, the results of the example problems obtained by the procedures presented in the text are compared with procedures presented in the text are compared with available published and accepted numerical or analytical results. Finally, a discussion is offered with the intent of guiding the reader toward successful application of the technique in solving practical reservoir problems.