Total pressure

Table of Contents

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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