The available boundary conditions, as noted in Section 22.10, include the following:
The particle rebounds the off the boundary in question with a change in its momentum as defined by the coefficient of restitution. (See Figure 22.13.1.)
The normal coefficient of restitution defines the amount of momentum in the direction normal to the wall that is retained by the particle after the collision with the boundary [ 366]:
where is the particle velocity normal to the wall and the subscripts 1 and 2 refer to before and after collision, respectively. Similarly, the tangential coefficient of restitution, , defines the amount of momentum in the direction tangential to the wall that is retained by the particle.
A normal or tangential coefficient of restitution equal to 1.0 implies that the particle retains all of its normal or tangential momentum after the rebound (an elastic collision). A normal or tangential coefficient of restitution equal to 0.0 implies that the particle retains none of its normal or tangential momentum after the rebound.
Nonconstant coefficients of restitution can be specified for wall zones with the "reflect'' type boundary condition. The coefficients are set as a function of the impact angle, , in Figure 22.13.1.
Note that the default setting for both coefficients of restitution is a constant value of 1.0 (all normal and tangential momentum retained).
The trajectory calculations are terminated and the fate of the particle is recorded as "trapped''. In the case of evaporating droplets, their entire mass instantaneously passes into the vapor phase and enters the cell adjacent to the boundary. See Figure 22.13.2. In the case of combusting particles, the remaining volatile mass is passed into the vapor phase.
The particle is reported as having "escaped'' when it encounters the boundary in question. Trajectory calculations are terminated. See Figure 22.13.3.
The direction and velocity of the droplet particles are given by the resulting momentum flux, which is a function of the impingement angle, , and Weber number. See Figure 22.13.4.
The "wall-jet" type boundary condition assumes an analogy with an inviscid jet impacting a solid wall. Equation 22.13-2 shows the analytical solution for an axisymmetric impingement assuming an empirical function for the sheet height ( ) as a function of the angle that the drop leaves the impingement ( ).
where is the sheet height at and is a constant determined from conservation of mass and momentum. The probability that a drop leaves the impingement point at an angle between and is given by integrating the expression for
where is a random number between 0 and 1. The expression for is given in Naber and Reitz [ 258] as
The "wall-jet" type boundary condition is appropriate for high-temperature walls where no significant liquid film is formed, and in high-Weber-number impacts where the spray acts as a jet. The model is not appropriate for regimes where film is important (e.g., port fuel injection in SI engines, rainwater runoff, etc.).
This boundary condition consists of four regimes: stick, rebound, spread, and splash, which are based on the impact energy and wall temperature. Detailed information on the wall-film model can be found in Section 22.4.
This boundary condition means that the particles will pass through the internal boundary. This option is available only for internal boundary zones, such as a radiator or a porous jump.
It is also possible to use a user-defined function to compute the behavior of the particles at a physical boundary. See the separate UDF Manual for information about user-defined functions.
Because you can stipulate any of these conditions at flow boundaries, it is possible to incorporate mixed discrete phase boundary conditions in your FLUENT model.
Discrete phase boundary conditions can be set for boundaries in the panels opened from the Boundary Conditions panel. When one or more injections have been defined, inputs for the discrete phase will appear in the panels (e.g., Figure 22.13.5).
Select reflect, trap, escape, wall-jet, or user-defined in the Boundary Cond. Type drop-down list under Discrete Phase Model Conditions. (In the Walls panel, you will need to click on the DPM tab to access the Discrete Phase Model Conditions.) If you select user-defined, you can select a user-defined function in the Boundary Cond. Function drop-down list. For internal boundary zones, such as a radiator or a porous jump, you can also choose an interior boundary condition. The interior condition means that the particles will pass through the internal boundary.
If you select the reflect type at a wall (only), you can define a constant, polynomial, piecewise-linear, or piecewise-polynomial function for the Normal and Tangent coefficients of restitution under Discrete Phase Reflection Coefficients. See Section 22.13.1 for details about the boundary condition types and the coefficients of restitution. The panels for defining the polynomial, piecewise-linear, and piecewise-polynomial functions are the same as those used for defining temperature-dependent properties. See Section 8.2 for details.
Default Discrete Phase Boundary Conditions
FLUENT makes the following assumptions regarding boundary conditions:
The coefficient of restitution can be modified only for wall boundaries.