TWO FLUID MODEL FOR TWO-PHASE TURBULENT JETS

摘要

An Eulerian multidimensional model for a cylindricaltwo-phase dispersed particle jet is proposed and compared withexperimental data. The averaged equations of mass andmomentum are solved for each phase and the turbulent kineticenergy equation is solved for the continuous phase.The phase distribution is controlled by the interfacialforces and the Reynolds stress gradient. The two fluid modelaveraging procedure developed by Reeks (1992) results in aturbulent diffusion force. This force is constituted for the caseof homogeneous turbulent flow. Furthermore, it is proposedthat the eddies interact primarily with those particles that aresmaller than them, i.e., only bigger eddies can trap particles anddeflect their path. The constitutive relations for the turbulentkinetic energy of the continuous phase consists of a k-ε modelwhich has been modified for two-phase flows.Once the constitutive relations have been defined, thetwo-fluid model is implemented in a computational fluiddynamics code. The results are compared against experimentaldata for an air jet with 39 μm glass particles. Because thefluid flow around these particles is well understood, theyrepresent a good starting point for the development of a twophaseturbulence model. The particles are assumed to follow adrag law consistent with Oseen’s equation. Furthermore, theseparticles have very small turbulent wakes so they producenegligible additional turbulence. Their effect on turbulencemodulation is primarily dissipative due to viscous shear in theflow field around them.In the vicinity of the jet source the time constant of theglass particles is significantly larger than the time constant ofthe turbulent eddies. Therefore, the trajectories of the particlesare quite different from those eddies and the turbulent diffusionforce may be validated at conditions where the classicalgradient-diffusion approximation is not very good. It has beenshown that the present model is equivalent to Taylor’s gradientdiffusionequation when the particle-gas flow approachesturbulent equilibrium.Good agreement between the model and the data isobtained. The sensitivity of the results to the turbulence timeconstant definition is discussed. Furthermore, the effect ofturbulence anisotropy is also considered.