| OCR Text |
Show The kinematic definition of w is \1xV=w (2) The continuity equation is \1·V=O (3) For the present case of axisymmetric flow, Eqn.(3) is satisfied directly by the introduction of a stream function 'l/J, such that (4) where e3 is a unit base vector perpendiculat to the plane of the flow. The governing equation for'l/J is then obtained using equations (2) and (4). The formulation is based on global conservation of mass, momentum, and energy. A clustered conformal coordinate transformation procedure is used to establish a surface-oriented orthogonal coordinate system, with grid clustering/stretching characteristics in the physical flow domain. A novel grid-point placement, the selected mesh size, and the time step ensure proper flow resolution and the flow numerical diffusion. More technical details of the formulation are given in references [10] and [1]. 2.2 Particulate phase Lagrangian equations are used to describe the motion and heating of each individual particle as it traverses the combustion chamber. The usual assumptions are used to derive these equations. The particles are assumed to be non-deformable and spherical, with density much higher than that of the fluid. Virtual mass force, pressure gradient force, and Basset force are all neglected. Particle-particle interaction and other force fields such as gravity are also presently not included in the analysis. The drag is treated empirically, assuming quasisteady flow for spherical particles. Several different formulae have been proposed, which indicate the uncertainties associated with the Lagrangian model. The governing equation for the particle flight, in nondimensional form, is then written as: dVp 1 + 0.15Re;,3 ( ) dt= 'YT Vf-Vp (5) 5 |
