The previous part (Part 1) focuses on the definitions. This part aims to explain what k-factor is and its relation to coefficient of discharge by deriving with equations.

The K-factor, minor loss coefficient, is a dimensionless value that expresses the aerodynamic resistance of the grille/duct or other impediments to the airflow. It can be derived from the coefficient of discharge.

To understand the fundamentals of the k-factor further, we dive deeper and express the phenomena in physical expressions. A pressure difference of ΔP between two ends of an opening can ideally generate a maximum velocity, v_{dyn}.

When an element (filter, louvre etc.) is added to the opening a certain pressure, P_{loss}, is lost due to resistance of the element while the fluid velocity is at v_{f}. The amount of the pressure loss is expressed as:

The actual velocity in the opening can also be expressed as:

This expression which involves the pressure loss (k-factor) can also be incorporated into the discharge coefficient . The discharge coefficient is the ratio of actual flow rate (v_{f}) to the theoretical flow rate (v_{dyn}). Therefore C_{d} is:

**Application in CFD**

In CFD applications it is often impractical to model grilles in full detail with all geometrical details. Instead, the k-factor is used as a volumetric loss coefficient in a volume representing the grille. The streamwise loss is given by the K-factor divided by the width of the volume representing the grille. Inlet and outlet losses are not incorporated into the applied k-factor since they are already present in the CFD simulation due to the air flow near the object.

In the last part of this blog a few worked examples about defining the equivalent area and choosing the right grille size with the right *C _{d}* value are demonstrated.

Continue reading Part 3