| OCR Text |
Show where m and A are the particle mass and cross-sectional area, K ->• respectively, U and U are the gas and particle velocities, p is the gas density, g is the gravitational acceleration and Cn is the drag (18) coefficient from Crowe . The solution of Equation 7 is accomplished step-wise through a computational cell. Integration of the equation is performed analytically using the average particle mass at that time step, and is followed by another integration which defines the new particle position. The net source of momentum to the gas phase equations for a single particle stream can be written as follows: SM = " 6 ( mp V " " mp 9 At <8> where n is the number flow rate of particles in the particular stream and 5(m V ) represents the change of the particle momentum between the " " -> inlet and exit. The change in momentum due to gravity (m q) does not P contribute to the momentum transport of the gas phase. Particle Energy Equation. The heat transfer to or from a particle can be represented as: dT_ Nu k , m Cn HT2 • -A MTn - TJ + K A ( G - 4aT: ) (9) P P dt dp P 9 P P P where the first term on the right-hand side represents convective heat transfer, and the second term represents radiation heat transfer to or from the particle. Equation 9 is solved for a new time step by calculating an upper and lower bound on temperature. As long as the bounds are within a preselected error, the temperature is taken as the average value. Otherwise, the time step is decreased and the temperatures are recomputed. The effect on particle temperature of the change in particle mass is evaluated. If the effect is significant, the time step is decreased and the energy equation is resolved. The net source of heat per unit time to the gas phase for a single particle stream can be expressed as: -9- |
