Mixing, transport and combustion in sprays

We analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe. The idea is that the exchange of momentum in collisions between the grains and between the grains and the wall plays a significant role in the balance of forces in the particle phase. Consequently, the particle phase is considered to be a dilute system of colliding grains, in which the velocity fluctuations are produced by collisions rather than by the gas turbulence. The balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. The turbulence of the gas is treated using a one-equation closure. A numerical solution of the resulting governing equations provides velocity and turbulent energy profiles in agreement with the measurements of Tsuji et al. (1984).

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The role of particle collisions in pneumatic transport

A second order closure scheme is developed for the numerical prediction of isothermal, non-reacting, mono-dispersed, dilute gas-particle turbulent shear flows. The model is based on the two-equation (κ-ϵ) turbulence model developed for calculating the analogous gas-phase flows. Contrary to passive additives in a single phase flow, the particles will affect the turbulence structure of the continuous phase. Thus, the κ-ϵ model has been modified to account for the presence of the dispersed particles. In particular, the particles increase the dissipation rate because of the relative velocity fluctuations between the two phases. New proposals for these added effects based on particle size and loading are added to these equations. The resulting model is used to compute the axisymmetric jet in its developing region. The calculated jet spreading rate, centre-line velocity decay and entrainment rate are all in excellent agreement with published experimental data. Calculated turbulence quantities such as the kinetic energy and mean Reynolds shear stress are greatly reduced from their “clean jet” levels by the presence of the particles in good agreement with the available experimental data.



On a mis au point un schema de fermeture de second ordre pour la prevision numerique d'ecoulements de cisaillement en regime turbulent de systemes dilues gaz-particules, isothermes, non reagissantes et mono-dispersees. Le modele est base sur le modele de turbulence κ-ϵ, a deux equations, developpe pour calculer les ecoulements analogues en phase gazeuse. Contrairement aux adjuvants passifs dans un ecoulement monophasique, les particules affectent la structure de la turbulence de la phase continue. Aussi, on a modifie le modele κ-ϵ. pour tenir compte de la presence des particules dispersees. Les particules augmentent particulierement la vitesse de dissipation a cause des fluctuations de la vitesse relative entre les deux phases. On a ajoute a ces equations des elements nouveaux bases sur les dimensions des particules et sur la charge pour tenir compte de ces effets additionnels. Le modele resultant est utilise pour calculer par ordinateur, un jet axisymetrique dans la zone de developpement. La vitesse de deploiement du jet calculee, la diminution de la vitesse sur l'axe et la vitesse d'entrainement se comparent toutes tres bien avec les resultats experimentaux publies dans la litterature. Les quantites calculees relatives a la turbulence, telles que l'energie cinetique et la contrainte de cisaillement de Reynolds moyenne, sont fortement reduites par rapport a leurs valeurs dans le cas de “jets propres” a cause de la presence des particules et ce, en accord avec les resultats experimentaux disponibles.

A turbulence closure model for dilute gas-particle flows

A thermodynamical formulation for dispersed multiphase turbulent flows—1

Gas-particle two-phase turbulent flow in a vertical duct

A generalized eddy-viscosity function ν T , is introduced in order to express the Reynolds stress in an incompressible dusty gas as a linear combination of the Kronecker and rate-of-strain tensors. On the basis of Saffman's dusty-gas model a transport equation for the eddy viscosity is derived from the general turbulence energy equations, thereby introducing two additional functions, the specific turbulence kinetic energy E 1 , and a scale variable s . In order to determine the three variables modified Prandtl–Wieghardt relation among them is accepted and a transport equation for s is postulated in the same manner as in the clean-gas turbulence transport model (firstly proposed by Harlow & Nakayama 1967) but with the inclusion of an additional term accounting for the dust particles stabilizing action. We are considering values of loading (mass ratio of particles) of order of unity, with particle/gas density ratios of order of 10 3 and volume concentrations of the order of 10 −3 , so that particle–particle interactions are neglected. Supposing that the particles nearly follow the gas motion, following well at large scales and poorly at small, an application of the theory to problem of numerical calculations of the dusty-gas parameters such as mean velocity profile of turbulent pipe flow is given.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112080001954

Effects of the motion of dust particles on turbulence transport equations

In this paper we propose an exact solution of Vlasov and Maxwell's equations for a bounded hot plasma in order to derive the dispersion relation of the axially-symmetric surface waves propagating along a plasma column. Assuming specular reflexion of plasma particles from the boundary, expressions for the components of the electric displacement vector are obtained on the basis of the Vlasov equation. Their substitution in Maxwell's equations, neglecting the spatial dispersion in the transverse plasma dielectric function, allows us to determine the plasma impedance. The equating of plasma and dielectric impedances gives the wave dispersion relation which, in different limiting cases, coincides with the well-known results.

Kinetic theory of surface wave propagation along a hot plasma column

Thermal fluctuation field in an inhomogeneous nonisothermal medium

Using the second-order perturbation theory, we obtain an analytical expression for the electromagnetic field scattered from a dielectric surface with inhomogeneities that are shallow and small in comparison with the wavelength. This expression is used to analyze the critical phenomena in thermal radio emission of a periodically rough water surface, and the second order of the specific scattering cross section of radio waves, in the short and medium ranges of wavelengths, from a rough surface (in particular, from a sea surface with waves).

Zh. D. Genchev

Papers

Effects of the motion of dust particles on turbulence transport equations

Kinetic theory of surface wave propagation along a hot plasma column

Thermal fluctuation field in an inhomogeneous nonisothermal medium

Scattering of electromagnetic waves from a surface with small and shallow inhomogeneities