∇

Description

The totalPressure is a boundary condition that 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 (\(\phi\)).

Four variants are possible:

Incompressible subsonic

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

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

where:

Property Description
\(p_p\) Incompressible pressure at patch [m^2/s^2]
\(p_0\) Incompressible total pressure [m^2/s^2]
\(\u\) Velocity

Compressible subsonic

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

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

where:

Property Description
\(p_p\) Pressure at patch [Pa]
\(p_0\) Total pressure [Pa]
\(\rho\) Density [kg/m^3]
\(\u\) Velocity

Compressible transonic (\(\gamma = 1\))

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

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

where:

Property Description
\(p_p\) Pressure at patch [Pa]
\(p_0\) Total pressure [Pa]
\(\psi\) Compressibility [m^2/s^2]
\(\u\) Velocity

Compressible supersonic (\(\gamma > 1\))

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

\[p_p = \frac{p_0}{\left(1 + \frac{\gamma - 1}{2} \psi \mag{\u}^2\right)^{\frac{\gamma}{\gamma - 1}}}\]
Property Description
\(p_p\) Pressure at patch [Pa]
\(p_0\) Total pressure [Pa]
\(\psi\) Compressibility [m^2/s^2]
\(G\) Coefficient given by \(\frac{\gamma}{1-\gamma}\)
\(\u\) Velocity

The modes of operation are set by the dimensions of the pressure field to which this boundary condition is applied, the psi entry and the value of gamma:

Mode Dimensions psi gamma
Incompressible subsonic p/rho - -
Compressible subsonic p none -
Compressible transonic p psi 1
Compressible supersonic p psi > 1

Usage

The condition requires entries in both the boundary and field files.

Boundary file 

<patchName>
{
    type            patch;
    ...
}

Field file 

<patchName>
{
    // Mandatory entries
    type            totalPressure;

    // Conditional entries

        // Incompressible subsonic
        rho             none;
        p0              uniform 0;

        // Compressible subsonic
        p0              uniform 100000;

        // Compressible transonic
        psi             psi;
        p0              uniform 100000;

        // Compressible supersonic
        psi             psi;
        gamma           1.4;
        p0              uniform 100000;

    // Optional entries
    U               <word>;
    phi             <word>;
    rho             <word>;
    psi             <word>;

    // Inherited entries
    ...
}

where:

Property Description Type Required Default
type Type name: totalPressure word yes -
p0 Total pressure field scalarField yes -
U Name of velocity field word no U
phi Name of flux field word no phi
rho Name of density field word no rho
psi Name of compressibility field word no none
gamma Heat capacity ratio scalar conditional -

Further information

Tutorial:

Source code:

API:

History:

  • Introduced in version 1.5