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Show mathematical simplicity, its computational efficiency, and because it simulates a Gaussian distribution quite well without the computational overhead. Particle Transport Equations Two approaches for modeling the particle phase have been discussed in the literature - the Eulerian and Lagrangian methods. In the Eulerian method , the particles are treated like a fluid and partial differential equations similar to Equation 1 are solved for groups of particles of uniform diameters. In the Lagrangian treatment, formulated by Medgal and Agosta and extended by Crowe , the flights of the particles are tracked from the entry of the combustion chamber to the exit. The continuous distribution of particle sizes is represented by a number of particle streams that are each of uniform diameter. Each stream is characterized by a number and flow rate of particles and by initial position, mass, velocity, and temperature. The effect of the particles on the gas phase is included in the gas phase conservation (3) equations by source terms. Lockwood, et al. have stated the advantages of the Lagrangian method over the Eulerian method: 1) Particle slip is easily modeled 2) Computer storage does not increase with the number of particle size groups 3) The laws which govern the particle behavior are more obvious to apply However, as stated by Lockwood, turbulent diffusion is less easily modeled. Consequently, because of the overall advantages of the method, we chose the Lagrangian framework over the Eulerian one. Particle Momentum Equation. The equation of motion for a particle may be expressed as: dU A •* •> -> -> •* Vdt*) =cDpg<2 ) <ug- V I W +mPg (7) -8- |