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7.20.1 Fan Equations



Modeling the Pressure Rise Across the Fan


A fan is considered to be infinitely thin, and the discontinuous pressure rise across it is specified as a function of the velocity through the fan. The relationship may be a constant, a polynomial, piecewise-linear, or piecewise-polynomial function, or a user-defined function.

In the case of a polynomial, the relationship is of the form


 \Delta p = \sum_{n=1}^{N}{f_n v^{n-1} } (7.20-1)

where $\Delta p$ is the pressure jump, $f_n$ are the pressure-jump polynomial coefficients, and $v$ is the magnitude of the local fluid velocity normal to the fan.

figure   

The velocity $v$ can be either positive or negative. You must be careful to model the fan so that a pressure rise occurs for forward flow through the fan.

You can, optionally, use the mass-averaged velocity normal to the fan to determine a single pressure-jump value for all faces in the fan zone.



Modeling the Fan Swirl Velocity


For three-dimensional problems, the values of the convected tangential and radial velocity fields can be imposed on the fan surface to generate swirl. These velocities can be specified as functions of the radial distance from the fan center. The relationships may be constant or polynomial functions, or user-defined functions.

figure   

You must use SI units for all fan swirl velocity inputs.

For the case of polynomial functions, the tangential and radial velocity components can be specified by the following equations:


 U_\theta = \sum_{n=-1}^{N} {f_n r^{n}} ; -1 \leq N \leq 6 (7.20-2)


 U_r = \sum_{n=-1}^{N} {g_n r^{n}} ; -1 \leq N \leq 6 (7.20-3)

where $U_\theta$ and $U_r$ are, respectively, the tangential and radial velocities on the fan surface in m/s, $f_n$ and $g_n$ are the tangential and radial velocity polynomial coefficients, and $r$ is the distance to the fan center.


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