Numerical method of investigating nonstationary spatial motions of a compressible gas

Makhviladze, G. M.; Shcherbak, S. B.

doi:10.1007/bf00861052

Cited by 13 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…After all the particles have settled out, the gas continues its convective motion, whose characteristics coincide with those calculated in [3] . Thus, at t=t * when r"=1 .4 .…”

supporting

confidence: 80%

“…

…”

mentioning

confidence: 99%

“…The natural convection of clean gases in closed spaces has been studied fairly thoroughly (see, for example, [1][2][3]) . However, in many actual situations the gas contains foreign particles, which gives grounds for investigating dusty gas convection .…”

mentioning

confidence: 99%

“…The equations of the gas were integrated by means of an implicit finite-difference coordinate splitting scheme [3] . The solution was obtained by the following numerical method .…”

mentioning

confidence: 99%

See 3 more Smart Citations

Natural convection of a dusty gas

Makhviladze¹,

Мелихов²,

Soboleva³

1994

Fluid Dyn

Self Cite

View full text Add to dashboard Cite

The natural convection of a gas-particle suspension inside a two-dimensional square region is investigated within the framework of a two-velocity two-temperature model of the medium with allowance for phase relaxation and particle deposition .The natural convection of clean gases in closed spaces has been studied fairly thoroughly (see, for example, [1][2][3]) . However, in many actual situations the gas contains foreign particles, which gives grounds for investigating dusty gas convection . If the particles are so small that their temperature and velocity relaxation proceed much more rapidly than the process develops, then the system can be described by a one-velocity one-temperature model (homogeneous gas-particle suspension) . The convection behavior of such a medium was investigated in [4] . In this model limitations are imposed on the dimensions of the particles . Thus, for dust suspended in air under ordinary conditions within a square cell having a side length L= 10 -2 m the condition d< 10 -4 m (d is the particle diameter) must be satisfied [4], which corresponds to particles not more than a few microns in diameter .1 . We will consider a two-phase medium consisting of a viscous heat-conducting compressible gas (phase 1) and monodisperse spherical particles (phase 2), within a two-dimensional square domain . The volume fraction of the suspension is small, which means that particle collisions can be neglected. The temperatures on the lateral boundaries of the domain are kept constant but different . Under the influence of the force of gravity the system is set in motion : natural convection of the gas develops, entraining the particles, and at the same time particle sedimentation takes place, affecting the dynamics of the carrier phase .Within the framework of the basic assumptions of the mechanics of heterogeneous media [5] the gas-particle suspension can be treated as two interacting and interpenetrating continua . In dimensionless variables its motion is described by the equations

show abstract

“…After all the particles have settled out, the gas continues its convective motion, whose characteristics coincide with those calculated in [3] . Thus, at t=t * when r"=1 .4 .…”

supporting

confidence: 80%

“…

…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…The equations of the gas were integrated by means of an implicit finite-difference coordinate splitting scheme [3] . The solution was obtained by the following numerical method .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Natural convection of a dusty gas

Makhviladze¹,

Мелихов²,

Soboleva³

1994

Fluid Dyn

Self Cite

View full text Add to dashboard Cite

show abstract

“…v e e e ( 13) Equation (12) describes the rate of the pressure drop. equation (12) with the initial condition of leads to Integration of (t,)n+l n + 1 (14) This equation is only valid for the initial period and cannot be applied for the whole transient process.…”

Section: Experimental Work -The Initial Expansionmentioning

confidence: 99%

The Behaviour Of Heavy Gas And Particulate Clouds

Bettis¹,

Makhviladze²,

Nolan³

1986

Fire Saf. Sci.

View full text Add to dashboard Cite

Models have been applied to stages of two phase releases following the failure of pressurised vessels.The initial expansion stage has been modelled using an experimental apparatus involving the measurement of pressure histories and of Er eon-T l aerosol droplet sizes and velocities.The experimental data combined with a thermodynamic analysis has allowed estimations of the time dependent processes.The analytical description of the critical pressure decrease on the opening of the vessel is presented.The later evolution stage has been mathematically modelled by assuming that the two phases have separate velocities. The cloud motion characteristics have been shown to depend upon the degree of hydrodynamic interactions between the particles via the gaseous phase.For small particles> fractional volumes, this interaction is small and each particle behaves as a single particle corresponding to a "fi 1 t r a t i on" regime.

show abstract