# Velocity Patch in FDS

As part of exploring options to model jet fans, we looked at using a Velocity Patch. The FDS User Manual discusses the concept of a velocity patch in the context of air entrainment by the spray from a sprinkler nozzle. The idea is that the spray droplets accelerate the gas through which they move and a velocity patch gives a way to specify the gas velocity. We were wondering if a velocity patch would work to model a jet fan.

## Velocity Patch Background

As described in the FDS User Manual (Section 15.3.3), “The details of the sprinkler head geometry and spray atomization are practically impossible to resolve in a fire calculation. As a result, the local gas phase entrainment by the sprinkler is difficult to predict. As an alternative, it is possible to specify the local gas velocity in the vicinity of the sprinkler nozzle.”

A velocity patch consists of: (1) a bounding volume, (2) a point (XYZ), and (3) polynomial coefficients that define the velocity using a second order Taylor expansion about the point XYZ. The polynomial is specified by the coefficients P0, PX(1:3), and PXX(1:3,1:3), which represent, respectively, the value of the velocity component (k), the first derivatives, and the second derivatives at point XYZ.

If we want a constant velocity, we only specify P0. The first line of the following FDS input defines the velocity component (in this case the X direction) and the constant value, P0. The second line defines a timer that activates the patch. The third line defines the geometry of the patch and links the patch to the previous data. By default the point XYZ is the center of XB, but as will be shown below, you can add a point definition to this line to shift the center of the expansion.

For a parabolic velocity in the X direction that varies in the Y-Z plane, the Taylor expansion simplifies to:

The plot shows the velocity for a patch that extends from Y=-1 to 1 and Z=-1 to 1, with P0=10 and P22=P33=-10.

This was tested in PyroSim using the following FDS input data:

and resulted in the following contours that match the expected results.

To demonstrate shifting the XYZ point for the Taylor expansion from the center to the edge at Y=1, we add XYZ data to the velocity patch device:

With the resulting velocity contour:

## Applications

The velocity patch makes it possible to define the gas velocity components within a given volume. For a sprinkler, this allows the user to specify the gas velocity caused by the spray droplets. We tested a model of a jet fan by making a shroud of thin obstructions and specifying the velocity of the gas along the axis of the fan using a velocity patch.

In the end, using a velocity patch to model a jet fan is probably not the best approach, but it does demonstrate one feature of FDS that is probably not used very often. A future post will discuss jet fan details.