the cs_user_head_losses function is used to compute the values of the head loss term, and is called at each time step for each previously defined head loss volume zone.
(cs_user_zones.c and cs_user_head_losses.c)
Volume zones may be defined using the GUI, or through the cs_user_zones (in cs_user_zones.c).
cku is the local head loss term.
It appears on the momentum as follows:
\[ \rho \der{\vect{u}}{t} = - \grad p + \vect{headloss} \: (+\: \text{other terms})\]
with
\[ \vect{headloss} = - \rho \tens{cku}\cdot \vect{u} \,\: (\text{in } kg\cdot m^{-2} \cdot s^{-1})\]
For a distributed head loss, let \({ \tens{\xi_l} = \dfrac{\tens{dh_l}}{(0.5 \rho u^2)}}\) given by the litterature ( \( \tens{dh_l} \) is the head loss per unit length)
the source term tspdc
is equal to \(\tens{dh_l} = - \tens{\xi_l}(0.5\rho\vect{u}^2)\)
we have \( \tens{cku} = 0.5\tens{\xi_l}|\vect{U}| \)
For a singular head loss, let \(\tens{\xi_l} = \dfrac{\tens{dh_s}}{0.5\rho\vect{u}^2}\) given by the litterature ( \(\tens{dh_s} \) is the singular head loss)
the source term tspdc
is equal to
\[\frac{\tens{dh_s}}{L} = - \frac{\tens{\xi_l}}{L} (0.5 \rho\vect{u}^2)\]
. We have
\[\tens{cku} = 0.5\frac{\tens{\xi_s}}{L}|\vect{u}|\]
where \( L \) is the length over which we have chosen to represent the singular head loss.
Here is the list of examples: