in this paper, the present state of knowledge about axial mixing in gasliquid reactors is reviewed. a brief outline of the methods for measuring residence time distribution(rtd)of various phases in a multiphase reactor is presented. this is followed by a short description of differential and stage-wise models for characterizing back mixing from rtd measurments. backmixing characteristics of som...

Numerical analysis of hypersonic continuum and rarefied gas flows near blunt probes is presented under conditions of intensive gas blowing from the surface. Nonequilibrium parameters in the multicomponent flows were evaluated for slot and uniform injections of air, helium, and hydrogen. Numerical results indicate that the most effective cooling of the probe surface occurs at moderate uniform in...

An accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics. The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term. The...

In this work, we introduce a new class of numerical schemes for rarefied gas dynamic problems described by collisional kinetic equations. The idea consists in reformulating the problem using a micro-macro decomposition and successively in solving the microscopic part by using asymptotically stable Monte Carlo methods. We consider two types of decompositions, the first leading to the Euler syste...

The present paper completes an earlier result by S. Ukai, T. Yang, and S.-H. Yu [Commun. Math. Phys. 236 (2003), 373−393] on weakly nonlinear half-space problems for the steady Boltzmann equation with hard-sphere potential. 1. Statement of the Problem & Main Result Boundary layers are an important class of flows in the kinetic theory of gases. One of the most significant problems in this contex...

The present paper completes an earlier result by S. Ukai, T. Yang, and S.-H. Yu [Commun. Math. Phys. 236 (2003), 373−393] on weakly nonlinear half-space problems for the steady Boltzmann equation with hard-sphere potential. 1. Statement of the Problem & Main Result Boundary layers are an important class of flows in the kinetic theory of gases. One of the most significant problems in this contex...

Airflow over a flat plate at zero incidence is investigated as a function of the Reynolds number Re and the Mach number M under subsonic, low-Reynolds-number conditions. The flows are simulated using the direct simulation Monte Carlo (DSMC) method and the information preservation (IP) method that is a modified DSMC method developed for low-speed rarefied gas flows. Good agreement is obtained be...