Non-isothermal Gas Flow Research Articles

Nonisothermal multiphase flow of brine and gas through saline media: S. Olivella, J. Carrera, A. Gens & E. E. Alonso, Transport in Porous Media, 15(3), 1994, pp 271–293

Nonisothermal multiphase flow of brine and gas through saline media: S. Olivella, J. Carrera, A. Gens & E. E. Alonso, Transport in Porous Media, 15(3), 1994, pp 271–293

Space-Time Spectral Element Methods for One-Dimensional Nonlinear Advection-Diffusion Problems

The following space-time Galerkin spectral element methods are developed and applied to solve the Burgers equation with small viscosity: (a) coupled methods, consisting of an explicit method for hyperbolic dominated equations and an implicit method for parabolic dominated equations; (b) two splitting methods which solve the hyperbolic substep explicitly and the parabolic one implicitly (one uses spectral elements in the explicit part and the other uses the Adams-Bashforth multistep method). A subcycling technique, in which several convective steps are taken for each implicit viscous step was also investigated for the two splitting methods. A stability analysis of the four methods is performed and subsequent results are debated. A convergence study and a comparison of computer execution time for the four methods is made and the results are discussed. Comparative study leads to the conclusion that the space-time spectral element splitting method with subcycling is superior to the other methods presented in terms of robustness and computer execution time. The number of subcycles should be kept low (2-3) in order to avoid significant loss of accuracy. The coupled explicit method is also applied to the solution of the one-dimensional coupled continuity, momentum, and energy equations for non-isothermal flow of an ideal gas with temperature dependent properties in a cylindrical duct of variable radius.

Thermal venting to recover less-volatile hydrocarbons from the unsaturated zone, 2. Model applications

The first part (Kaluarachchi and Islam, this issue) of this two-part series of papers developed the theoretical framework of analysis describing thermal venting using nonisothermal gas flow, heat energy transport and multicomponent mass transport. The work presented in this paper demonstrated the applicability of thermal venting through a series of numerical simulations in one- and two-dimensional flow domains. In both cases, a four-component hydrocarbon mixture consisting of volatile benzene, moderately-volatile n-dodecane, and less-volatile naphthalene and n-hexylbenzene in equal mass fraction was used. The results from the one-dimensional laboratory-scale column simulations showed a total recovery of naphthalene, n-dodecane and n-hexylbenzene by thermal venting, where as corresponding removal by normal venting was < 33% for the same time period. Effect of thermal energy was negligible with volatile benzene due to high ambient vapor pressure. Similar results were obtained from the two-dimensional field-scale simulations too. The temperature distribution in the subsurface was affected by simultaneous evaporation of contaminants and moisture condensation from humid air. The simulations also considered the parameter sensitivity to overall recovery. The overall results of this theoretical analysis suggested that thermal venting may be a powerful remediation technique that is applicable to the unsaturated zone when normal soil venting fails to recover the less-volatile fraction of the residual plume. However, the results of this analysis need to be experimentally validated for complete evaluation of the overall technology.

Thermal venting to recover less-volatile hydrocarbons from the unsaturated zone, 1. Theory

Thermal venting is a remediation technique suitable to the liquid unsaturated zone to enhance recovery of less-volatile residual hydrocarbon contaminants. Thermal venting is different to traditional soil venting because heated air instead of air at ambient conditions is applied to the contaminated zone. The vapor pressure of a less-volatile contaminants is typically increased by temperature causing the gas-phase concentrations to increase by three- to five-fold over a temperature increase of 20–30°C. The work described in this first paper provides the theoretical framework of analysis related to thermal venting. The analysis included nonisothermal gas flow, thermal energy transport and multicomponent mass transport in a multiphase porous medium. The transient gas flow analysis included the effect of temperature on fluid properties and gas compressibility. The heat energy transport analysis was performed under the thermodynamic equilibrium condition with phase-summed effective thermal properties. Multi-component mass transport was performed under local equilibrium for partitioning between phases. Model verification was performed to the extend possible using analytical and available experimental data for different physical processes. The second paper of this two-part series will demonstrate the applicability of thermal venting technique through numerical simulations of hypothetical laboratory and field-scale scenarios.

Nonisothermal multiphase flow of brine and gas through saline media

We propose a general formulation for nonisothermal multiphase flow of brine and gas through saline media. The balance equations include mass balance (three species), equilibrium of stresses and energy balance (total internal energy). Salt, water and air mass balance equations are established. The balance of salt allows the establishment of the equation for porosity evolution due to solid skeleton deformation, dissolution/precipitation of salt and migration of brine inclusions. Water and air mass balance equations are also obtained. Two equations are required for water: total water in the medium and water present in solid phase brine inclusions. The mechanical problem is formulated through the equation of stress equilibrium. Finally, the balance of internal energy is established assuming thermal equilibrium between phases. Some general aspects of the constitutive theory are also presented.

Nonisothermal rarefied gas flow through a narrow slit

The nonisothermal flow of gas through a narrow slit under the influence of small pressure and temperature differences is investigated. The flow field and the mass and heat fluxes are found. It is shown that the heat transfer between the gas and the diaphragm, caused by the pressure difference, leads to a thermal polarization effect. The Onsager reciprocity relation is checked.

Nonsteady nonisothermal flow of compressible gas in a channel with track sampling

A method is proposed for forming a linear mathematical model of a pulsating gas flow with entropy waves, in the case of gas sampling distributed along a channel, and the sampling are compared with experimental data.

Nonisothermal flow of a polyatomic gas in a channel and the thermomolecular pressure difference effect

Nonisothermal flow of a polyatomic gas in a channel and the thermomolecular pressure difference effect

Slow nonisothermal flow of a viscous gas between two coaxial disks

Slow nonisothermal flow of a viscous gas between two coaxial disks

Nonisothermal flow of a rarefied multiatomic gas in a channel

The authors consider the slow flow of a polyatomic gas in a plane channel, bounded at x = + or - d/2 by two infinite parallel planes. Interest in nonisothermal flow in channels and the thermomolecular pressure difference produced by conductivity, which give experimental data on the total thermal conductivity of polyatomic gas provides an independent source of data on internal energy relation times, which are usually determined by experiments on ultrasound absorption or other methods.

Nonisothermal flow of a rarefied gas in a circular cylindrical channel

Using a method which averages the system of moment equations over the channel section, the authors have obtained expressions for Poiseuille flow and thermal creep flow in a capillary at intermediate Knudsen numbers (Kn⩽0.25).

Derivation of the equations of slow nonisothermal gas flows

In recent years, some new phenomena have been predicted theoretically on the basis of the Burnett approximation. These include thermal-stress and concentration-stress convection [1–3], and also effects due to the influence of a magnetic field in a multiatomic gas (viscomagnetic heat flux, etc., [4]). It has been shown theoretically (see [5]) that under certain conditions various terms of the Burnett approximation must be taken into account in the expression for barodiffusion. The conclusions relating to a viscomagnetic heat flux have recently been confirmed experimentally [4]. The predicted phenomena follow rigorously from the Burnett equations. However, many hydrodynamicists adopt a sceptical attitude to these equations, which is due partly perhaps to attachment to the classical Navier-Stokes equations, which have served theoreticians without fail for a century and a half. In this connection, we discuss the evolution of ideas relating to the validity of the Burnett approximation. We discuss the minimal assumptions which must be made in order to derive the equations of “slow” [Reynolds number R = 0(1)], essentially nonisothermal [▽ ln T = 0(1)] flows of a gas as a continuous medium (Knudsen number K → O) in the case when the derivatives of the thermal Burnett stresses in the momentum equation have the same order of magnitude as the Euler and Navier-Stokes terms of this equation [1–3].

Calculation by the Krylov-Bogolyubov method of the velocity profile and fluxes in the nonisothermal flow of a rarefied gas in a cylindrical capillary

The Krylov-Bogolyubov numerical method is used to solve integral transfer equations obtained from the kinetic equation with the BHC (Bhatnagar—Cross—Krook) model of the collision operator. The velocity profiles and the thermal-creep flows and Poiseuille flow are calculated in different modes of flow under conditions of incomplete accommodation of the tangential momentum of molecules at the wall.

Theoretical investigation of nonisothermal flow of a rarefied gas in a cylindrical capillary

This paper calculates thermocreep and Poiseuille flow in a cylindrical capillary using the Bubnov-Galerkin method. Asymptotic formulas are obtained for flow in the viscous regime with slip.

The effect of large temperature difference on the turbulent heat and momentum transfer in an air flow inside a circular tube.

This paper presents the results of analytical and experimental investigations of the local behaviour of turbulent heat and momentum transfer in a hot air flow through a cooled circular tube with a steep radial temperature gradient. It is concluded that in the turbulent core region the profiles of mixing length are not different from isothermal ones. It is presumed that the damping of mixing length near the wall is expressed by extending the Van Driest model to non-isothermal flow of gas. It is shown that the analytical prediction correlates the results of the measurements satisfactorily, and that in the cooling turbulent gas flow of low Reynolds number the deviations of the Nusselt number and friction factor from isothermal ones are negligibly small when they are correlated by using physical properties at bulk temperature.

The Flow of Rarefied Gases in Vacum Systems and Problems of Standardization of Measuring Techniques

The problem of rarefied gas flow in vacuum systems and particularly the effects of non-uniform gas distributions likely to occur in practice have been the subject of many recent detailed investigations. The results of these studies have in turn influenced the techniques used in obtaining meaningful measurements. A brief review of recent activities is followed by a discussion of dynamic gas flow conditions as they affect the various recommendations for standardization of system parameters, measurements and calibration techniques. Methods have been agreed for the determination of volume rate offlow for pumps. Some of the remaining problems are concerned with measurements involving non uniform and possibly non-isothermal gas flow in systems containing localised or distributed sources of gas and cryogenic, sorbing or gettering surfaces as pumps.

Hydrate formation during gas flow in pipes

The problem of crystalline hydrate formation during nonisothermal stationary flow of an ideal gas in a circular inclined pipe is studied. A model is proposed for the growth of the hydrate layer on the pipe walls.

Pyrometric method of measuring instantaneous velocities in nonisothermal gas flows

Pyrometric method of measuring instantaneous velocities in nonisothermal gas flows

The problem of the linearization of the equations of the nonstationary nonisothermal flow of a real gas in pipelines

The analysis of numerical solutions is the basis for investigating the effect of various terms in the equations of the nonstationary nonisothermal motion of a real gas on the nature of the solution and its results in order to simplify and linearize the original equations to a form permitting analytical solution.

On estimating the influence of the terms characterizing the change in velocity head in the equations governing the transient nonisothermal motion of gas in pipelines

A system of equations describing the transient, nonisothermal flow of gas in pipelines is considered, and the effect of the terms characterizing the change in the velocity head on the character of the solution is analyzed. A comparison is drawn between the numerical solution of these equations with and without allowing for the changes in the velocity head, and some corresponding estimates of the differences between these are presented.