The open source CFD toolbox
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]


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