This force is caused by the fact that the particle has to accelerate some of the surrounding fluid, leading to an additional drag of the following form:

(6–21)

If the virtual mass force is included, the coefficient is normally set to 1. However, when the virtual mass force is not included, then effectively has the value zero, and is equal to 1. The second part of the right hand side contains the particle velocity deviation, hence, it can be brought to the left hand side of the particle momentum equation (see Equation 6–7), leading to a modified effective mass. Considering only steady-state flows, the remaining term can be written as

(6–22)

leading to the following contribution to the right hand side of Equation 6–7:

(6–23)

with

(6–24)

necessary if the particles are solved in a rotating system. The term is shifted to the rotation term (see Equation 6–19), therefore, the implemented virtual mass term reduces to

(6–25)

The particle momentum source due to the virtual mass force is computed from:

(6–26)