Actuation disk

Table of Contents

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/m3]
\( A \) = Actuator disk planar surface area [m2]
\( \u_m \) = 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 (([86], Eqs. 5-6), ([87])):

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

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/m3]
\( A \) = Actuator disk planar surface area [m2]
\( \u_m \) = 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:

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:

Sample result

Actuator disk example

Source code:

History

  • Introduced in version 2.2.0