Mach number disperse phase

When St 1 the kinetic equation will be uncoupled from the gas phase and the disperse phase will behave as a granular gas. In the opposite limit where St c 1, p 0 and [/p u, so that the disperse-phase Mach number will be very large and 03 1. At intermediate values of the Stokes number, a rich variety of flow phenomena depending on all the values of the dimensionless parameters can be observed. 

For convenience, the relevant dimensionless numbers for gas-particle flow derived in this section are collected in Table 1.1. In practice, one must choose appropriate values for U and L corresponding to a particular problem. For example, they may be determined by the inlet and/or boundary conditions. However, one case of particular interest is particles falling in an unbounded domain for which convenient choices are T = t/p and U = ul = Up - f/gl = Tp g (i.e. the settling velocity). For this case, there is no source term for p and so it relaxes to zero at steady state due to the drag. The disperse-phase Mach number thus becomes infinite. For settling problems, the particle Archimedes number (see Table 1.1) is often used in place of the Froude number. 

Hydrodynamic interactions, which are not included in the kinetic equation for this example, can lead to a finite 0p. However, in gas article flows the disperse-phase Mach number will usually be very large. 

Mach number for continuous phase Mach number for disperse phase Morton number... 

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