J. Aerosol Sci. Vol. 30, No. 1, pp. 51—69, 1999  1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0021-8502/98 $19.00#0.00 PII: S0021-8502(98)00017-2 DISTRIBUTION CHARACTERISTICS OF THE MASS CONCENTRATION OF COARSE SOLID PARTICLES IN A TWO-PHASE TURBULENT JET Felix Frishman, Medhat Hussainov, Alexander Kartushinsky* and U lo Rudi Estonian Energy Research Institute, Paldiski mnt.1, EE-0001, Tallinn, Estonia (First received 29 April 1997; and in final form 13 February 1998) Abstract—In the paper the results of the mathematical modelling a horizontal two-phase turbulent round jet carrying coarse solid particles are presented. The numerical results are compared with the experimental data obtained in our laboratory. The goal of these investigations is to describe the distribution characteristics of the mass concentration of particles moving with a velocity lag which starts from the pipe outlet. These features are based on the intensive diffusion of particles with the rapid decrease of their concentration from the initial stage of the jet (scattering effect) and the less intensive diffusion giving a wave-like distribution of the mass concentration along the axis of the jet (intermediate effect). Such particle distributions in the jet are related to the specific motion of coarse particles in the pipe expressed by their lagging behind the gas. For the mathematical description, an algebraic model for the closure of the equations for the dispersed phase which is based on the inter-particle collision is used since the solid admixture in our experiments is a polydispersed powder. Along with the inter-particle collision, turbulent interaction between the phases resulting in the Reynolds stresses in the dispersed phase is also taken into account. In addition, the Magnus lift force contributes to the model due to the particle rotation and the velocity lag of the particles which enter the jet.  1998 Elsevier Science Ltd. All rights reserved NOMENCLATURE AA transformation parameter of a coordinate in the radial direction C  ratio of the drag friction to the Stokes drag friction  " 24 ) C D  Re  "1#0.277 ) Re  #0.013875 Re   D pipe diameter D  , D  coefficients of pseudo-diffusion (inter-particle collision) and those of the turbulent diffusion of particles d particle diameter g  parameter in the pseudoviscosity coefficient "   /6 J  integral of the momentum conservation of jet J  integral of mass particle conservation k turbulent energy k  energy exchange by particle collision k  restitution coefficient for normal impact of particles k  restitution coefficient for oblique impact of particles l interparticle distance m mass of particle n  numerical concentration of jth particle fraction P probability of particle collision r radial coordinate R pipe radius Re the Reynolds number "u ) D/ Re  the particle Reynolds number  " (u!u  )#(v!v  ) d  )   Re  the Reynolds number determined by the shear rate ("d  /(4 ) AA) R) u/ ) Re * the Reynolds number calculated by the friction velocity ( " * R/) St the Stokes number (   d M  Re/18 C  ) St * the Stokes number determined by the friction velocity ["(2  /9) Re * d M  ] *Author to whom all correspondence should be addressed. 51