a36082e62f
The external pressure p0 is now formally the static pressure in the presence of
tangential flow and the corresponding total pressure is calculated from this
static pressure using the tangential velocity obtained from the
pressureInletOutletVelocity boundary condition if available. In the case that
there is no external tangential flow the external total pressure is equal to the
static pressure p0 as before.
Description
Inflow, outflow and entrainment pressure boundary condition based on a
constant total pressure assumption.
For outflow the patch pressure is set to the external static pressure.
For inflow the patch pressure is evaluated from the patch velocity and the
external total pressure obtained from the external static pressure \c p_0
and external velocity \c U_0 which is looked-up from the the optional \c
tangentialVelocity entry in the \c pressureInletOutletVelocity velocity
boundary condition for the patch if that boundary condition is used,
otherwise \c U_0 is assumed zero and the external total pressure is equal to
the external static pressure.
The patch pressure is evaluated from the external conditions using one of
the following expressions depending on the flow conditions and
specification of compressibility:
1. incompressible subsonic:
\f[
p_p = p_0 + 0.5 |U_0|^2 - 0.5 |U|^2
\f]
where
\vartable
p_p | pressure at patch [m^2/s^2]
p_0 | external static pressure [m^2/s^2]
U | velocity [m/s]
U_0 | external velocity [m/s]
\endvartable
2. compressible subsonic:
\f[
p_p = p_0 + 0.5 \rho |U_0|^2 - 0.5 \rho |U|^2
\f]
where
\vartable
p_p | pressure at patch [Pa]
p_0 | external static pressure [Pa]
\rho | density [kg/m^3]
U | velocity [m/s]
U_0 | external velocity [m/s]
\endvartable
3. compressible transonic (\f$\gamma = 1\f$):
\f[
p_p = \frac{p_0 + 0.5 \rho |U_0|^2}{1 + 0.5 \psi |U|^2}
\f]
where
\vartable
p_p | pressure at patch [Pa]
p_0 | external static pressure [Pa]
\psi | compressibility [m^2/s^2]
\rho | density [kg/m^3]
U | velocity [m/s]
U_0 | external velocity [m/s]
\endvartable
4. compressible supersonic (\f$\gamma > 1\f$):
\f[
p_p = \frac{p_0 + 0.5 \rho |U_0|^2}
{(1 + 0.5 \psi G |U|^2)^{\frac{1}{G}}}
\f]
where
\vartable
p_p | pressure at patch [Pa]
p_0 | external static pressure [Pa]
\psi | compressibility [m^2/s^2]
\rho | density [kg/m^3]
G | coefficient given by \f$\frac{\gamma}{1-\gamma}\f$ []
\gamma | ratio of specific heats (Cp/Cv) []
U | velocity [m/s]
U_0 | external velocity [m/s]
\endvartable
The modes of operation are set by the dimensions of the pressure field
to which this boundary condition is applied, the \c psi entry and the value
of \c gamma:
\table
Mode | dimensions | psi | gamma
incompressible subsonic | p/rho | |
compressible subsonic | p | none |
compressible transonic | p | psi | 1
compressible supersonic | p | psi | > 1
\endtable
Usage
\table
Property | Description | Required | Default value
U | Velocity field name | no | U
phi | Flux field name | no | phi
rho | Density field name | no | rho
psi | Compressibility field name | no | none
gamma | (Cp/Cv) | no | 1
p0 | External pressure | yes |
\endtable
Example of the boundary condition specification:
\verbatim
<patchName>
{
type totalPressure;
p0 uniform 1e5;
}
\endverbatim
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