400
12. Special Topics
much smaller than the actual number in the fluid. Each computational particle then represents a number (or packet) of actual particles; these are called
packet methods. If phase change and combustion are not present and the
loading is light, the effect of the dispersed phase on the carrier flow can be
neglected and the latter can be computed first. Particles are then injected and
their trajectories are computed using the pre-computed velocity field of the
background fluid. (This approach is also used for flow visualization; one uses
massless point particles and follows their motion to create streaklines.) This
method requires interpolation of the velocity field to the particle location; the
interpolation scheme needs to be at least as accurate as the methods used
for time advancement. Accuracy also requires that the time step be chosen
so that particles do not cross more than one cell in one time step.
When the mass loading of the dispersed phase is substantial, the influence of particles on the fluid motion has to be taken into account. If a packet
method is used, the computation of particle trajectories and fluid flow must
be done simultaneously and iteration is needed; each particle contributes
momentum (and energy and mass) to the gas in the cell in which it is located. Interaction between particles (collision, agglomeration, and splitting)
and between particles and walls needs to be modeled. For these exchanges,
correlations based on experiment have been used but the uncertainties may
be rather large. These issues require another book to be described in any
detail; see the newly published work by Crowe et al. (1998) for a description
of most widely used methods.
For large mass loadings and when phase change takes place, an Eulerian
approach (the two-fluid model) is applied to both phases. In this case, both
phases are treated as continua with separate velocity and temperature fields;
the two phases interact via exchange terms analogous to those used in the
mixed Eulerian-Lagrangian approach. A function defines how much of each
cell is occupied by each phase. The principles of two-fluid models are described
in detail by Ishii (1975); see also Crowe et al. (1998) for a description of some
methods for gas-particle and gas-droplet flows. The methods used to compute
these flows are similar to those described earlier in this book, except for the
addition of the interaction terms and boundary conditions and, of course,
twice as many equations need to be solved.
12.8 Combustion
Another important problem area deals with flows in which combustion i.e.
chemical reaction with significant heat release plays an important role. Some
of the applications should be obvious to the reader. Some combustors operate
at nearly constant pressure so the principal effect of heat release is reduction
of the density. In many combustion systems it is not unusual for the absolute
temperature to increase by a factor of five to eight through the flame; the
density decreases by the same factor. In such a case, there is no possibility
12. Special Topics
much smaller than the actual number in the fluid. Each computational particle then represents a number (or packet) of actual particles; these are called
packet methods. If phase change and combustion are not present and the
loading is light, the effect of the dispersed phase on the carrier flow can be
neglected and the latter can be computed first. Particles are then injected and
their trajectories are computed using the pre-computed velocity field of the
background fluid. (This approach is also used for flow visualization; one uses
massless point particles and follows their motion to create streaklines.) This
method requires interpolation of the velocity field to the particle location; the
interpolation scheme needs to be at least as accurate as the methods used
for time advancement. Accuracy also requires that the time step be chosen
so that particles do not cross more than one cell in one time step.
When the mass loading of the dispersed phase is substantial, the influence of particles on the fluid motion has to be taken into account. If a packet
method is used, the computation of particle trajectories and fluid flow must
be done simultaneously and iteration is needed; each particle contributes
momentum (and energy and mass) to the gas in the cell in which it is located. Interaction between particles (collision, agglomeration, and splitting)
and between particles and walls needs to be modeled. For these exchanges,
correlations based on experiment have been used but the uncertainties may
be rather large. These issues require another book to be described in any
detail; see the newly published work by Crowe et al. (1998) for a description
of most widely used methods.
For large mass loadings and when phase change takes place, an Eulerian
approach (the two-fluid model) is applied to both phases. In this case, both
phases are treated as continua with separate velocity and temperature fields;
the two phases interact via exchange terms analogous to those used in the
mixed Eulerian-Lagrangian approach. A function defines how much of each
cell is occupied by each phase. The principles of two-fluid models are described
in detail by Ishii (1975); see also Crowe et al. (1998) for a description of some
methods for gas-particle and gas-droplet flows. The methods used to compute
these flows are similar to those described earlier in this book, except for the
addition of the interaction terms and boundary conditions and, of course,
twice as many equations need to be solved.
12.8 Combustion
Another important problem area deals with flows in which combustion i.e.
chemical reaction with significant heat release plays an important role. Some
of the applications should be obvious to the reader. Some combustors operate
at nearly constant pressure so the principal effect of heat release is reduction
of the density. In many combustion systems it is not unusual for the absolute
temperature to increase by a factor of five to eight through the flame; the
density decreases by the same factor. In such a case, there is no possibility