The open source CFD toolbox
Total pressure

# Properties

• Wrapper around the fixed condition to set the static pressure from a definition of the total pressure
• Applicable to the pressure field

# Usage

The condition sets the static pressure at the patch $$p_p$$ based on a specification of the total pressure, $$p_0$$. The mode of operation is determined via the input entries and the dimensions of the convective flux, phi ( $$\phi$$).

## Subsonic incompressible

Patch pressure described by subtracting the dynamic pressure from the total pressure, where the flux has dimensions of $$m^3/s$$.

$p_p = p_0 - \frac{1}{2}\mag{\u}^2$

Field file entries:

<patchName>
{
type            totalPressure;
rho             none;
p0              uniform 0;
value           uniform 0;

// Optional entries
U               U;
phi             phi;
}


## Subsonic compressible

Patch pressure described by subtracting the dynamic pressure from the total pressure, where the flux has dimensions of $$kg/s$$.

$p_p = p_0 - \frac{1}{2}\rho\mag{\u}^2$

Field file entries:

<patchName>
{
type            totalPressure;
p0              uniform 100000;
value           uniform 100000;

// Optional entries
U               U;
phi             phi;
rho             rho;
}


## Transonic compressible

Ratio of specific heats, $$\gamma = C_p/C_v$$ equal to 1.

$p_p = \frac{p_0}{1 + \frac{1}{2} \psi \mag{\u}^2}$

Field file entries:

<patchName>
{
type            totalPressure;
psi             psi;
p0              uniform 100000;
value           uniform 100000;

// Optional entries
U               U;
}


## Supersonic compressible

Ratio of specific heats, $$\gamma = C_p/C_v$$ greater than 1.

$p_p = \frac{p_0}{\left(1 + \frac{\gamma - 1}{2 \gamma} \psi \mag{\u}^2\right)^{\frac{\gamma}{\gamma - 1}}}$

Field file entries:

<patchName>
{
type            totalPressure;
psi             psi;
gamma           1.4;
p0              uniform 100000;
value           uniform 100000;

// Optional entries
U               U;
}


# Further information

Source code:

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