Actuation disk

Properties

• The actuationDiskSource applies sources on velocity, i.e. U, to enable actuator disk models for aero/hydro thrust loading of rotary disks (e.g. propellers, horizontal-axis wind/tidal turbines, or helicopter rotors) on surrounding flow field in terms of energy conversion processes.
• The actuationDiskSource is applied on the volume cells (not on faces). This nuance might be important since theoretical actuator disks possess zero-thickness.
• The actuationDiskSource inherits the traits of the fvOption, and cellSetOption.

Corrections applied to:

U : Velocity [m/s]

Required fields:

U : Velocity [m/s]

Model equations

The actuationDiskSource possesses two options for force computations:

Froude : Froude's one-dimensional ideal actuator disk method

variableScaling : Variable-scaling actuator disk method

Froude's method

The model expressions for Froude method (8, Eq. 3.9):

$$T = 2 \rho_{\ref} A | \u_m \cdot \vec{n} |^2 a (1-a)$$

with

$$a = 1 - \frac{C_p}{C_T}$$

Where:

$T$ : Thrust magnitude [N]

$\rho_{\ref}$ : Monitored incoming fluid density [kg/m$^3$]

$A$ : Actuator disk planar surface area [m$^2$]

$\u_m$ : Incoming velocity spatial-averaged on monitored region [m/s]

$\vec{n}$ : Surface-normal vector of the actuator disk pointing upstream [-]

$a$ : Axial induction factor [-]

$C_p$ : Power coefficient [-]

$C_T$ : Thrust coefficient [-]

Variable-scaling method

The model expressions for variableScaling method ((31, Eqs. 5-6), (30)):

$$T = 0.5 \rho_{\ref} A | \u_o \cdot \vec{n} |^2 C_T^*$$

with

$$C_T^* = C_T \left( \frac{ | \u_m | }{ | \u_o | } \right)^2$$

Where:

$T$ : Thrust magnitude [N]

$\rho_{\ref}$ : Monitored incoming fluid density [kg/m$^3$]

$A$ : Actuator disk planar surface area [m$^2$]

$\u_m$ : Incoming velocity spatial-averaged on monitored region [m/s]

$\u_o$ : Incoming velocity spatial-averaged on actuator disk [m/s]

$\vec{n}$ : Surface-normal vector of the actuator disk pointing upstream [-]

$a$ : Axial induction factor [-]

$C_p$ : Power coefficient [-]

$C_T$ : Thrust coefficient [-]

$C_T^*$ : Calibrated thrust coefficient [-]

Operands

Operand	Type	Location
input	-	-
output file	dat	$POST=$FOAM_CASE/postProcessing/<FvO>/<time>/<file>

Usage

Example of the fvOptions specification using constant/fvOptions file:

actuationDiskSource1
{
    // Mandatory entries (unmodifiable)
    type            actuationDiskSource;

    // Mandatory (inherited) entries (unmodifiable)
    selectionMode   <mode>;    // e.g. cellSet as shown below
    cellSet         <cellSetName>;

    // Mandatory entries (runtime modifiable)
    diskArea        40.0;
    diskDir         (1 0 0);
    Cp              <Function1>;
    Ct              <Function1>;

    // Conditional optional entries (unmodifiable)
    monitorMethod   <points|cellSet>;
    monitorCoeffs
    {
        // Option-1
        points
        (
            (p1x p1y p1z)
            (p2x p2y p2z)
            ...
        );

        // Option-2
        cellSet     <monitorCellSet>;
    }

    // Optional entries (unmodifiable)
    variant         <forceMethod>;

    // Optional entries (runtime modifiable)
    sink            true;
    writeFileStart  0;
    writeFileEnd    100;

    // Optional (inherited) entries
    ...
}

where the entries mean:

Property	Description	Type	Required	Default
type	Type name: actuationDiskSource	word	yes	-
diskArea	Actuator disk planar surface area	scalar	yes	-
diskDir	Surface-normal vector of the actuator disk pointing upstream	vector	yes	-
Cp	Power coefficient	Function1	yes	-
Ct	Thrust coefficient	Function1	yes	-
monitorMethod	Type of incoming velocity monitoring method - see below	word	no	points
variant	Type of the force computation method - see below	word	no	Froude
sink	Flag for body forces to act as a source (true) or a sink (false)	bool	no	true
writeFileStart	Start time for file output	scalar	no	0
writeFileEnd	End time for file output	scalar	no	VGREAT

The inherited entries are elaborated in:

• fvOption
  • cellSetOption
• writeFile
  • Function1

Options for the monitorMethod entry:

points  | Monitor incoming velocity field at a given set of points
cellSet | Monitor incoming velocity field at a given cellSet

Options for the variant entry:

Froude          | Froude's one-dimensional ideal actuator disk method
variableScaling | Variable-scaling actuator disk method

Further information

Tutorial:

• turbineSiting

Sample result

Source code:

• actuationDiskSource

History: Introduced in version 2.2.0