totalPressure

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:

• windAroundBuildings

Source code:

• supersonicFreestream

API:

• Foam::totalPressureFvPatchScalarField

History: Introduced in version 1.5