Volume flow rate calculation with implicit approach

Using the implicit approach, the solver defines the relationship between the fan's pressure rise and volume flow rate using a Taylor series expansion.

This expression for the expansion is:

where:

  • is a volume flow rate.
  • fP) represents the fan curve.
  • The superscripts n and n + 1 refer to the previous and current iterations, respectively.

The pressure rise, ΔPn, volume flow rate, , and gradient, , are evaluated from the solution at iteration, n. The updated volume flow rate, , is evaluated implicitly at the current iteration, n + 1.

In the implicit approach, the solver takes the fan curve data local to elements over the two faces on opposite sides of the fan and obtains a normal velocity vector for each element of a face to impose the Dirichlet boundary condition. The solver evaluates on the fan curve for a particular face element and obtains from the derivative of the fan curve at the specified operating point. In this approach, the solver inserts the local velocity into the solution matrix at a particular point based on the pressure difference across a face element. This gives a relationship between the velocity and pressure.