2.2. Blade Element Theory Model

2.2.1. Overview

Based on Blade Element Theory, Flow360 provides 2 related solvers, which can be configured in BETDisks section of Flow360.json:

  • Steady blade disk solver

    To use the steady blade disk solver, the bladeLineChord needs to be set as 0, which is its default value if omitted.

  • Unsteady blade line solver

    To use the unsteady blade line solver, bladeLineChord has to be a positive value and initialBladeDirection also needs to be set.

In the BETDisks section of the Flow360.json, except the bladeLineChord and initialBladeDirection, other parameters are necessary for both solvers.

2.2.2. BET Loading Output

After the simulation is completed, a “bet_forces_v2.csv” file is created for the case, which contains the time history of the following quantities:

  1. Integrated x-, y-, z-component of non-dimensional forces and non-dimensional moments acted on each disk, represented by “Disk[diskID]_Force_x,_y,_z” and “Disk[diskID]_Moment_x,_y,_z” in the “bet_forces_v2.csv file” respectively. The non-dimensional force is defined as

(2.2.1)\[\text{Force}_\text{non-dimensional} = \frac{\text{Force}_\text{physical}\text{(SI=N)}}{\rho_\infty C_\infty^2 L_{gridUnit}^2}\]

The non-dimensional moment is defined as

(2.2.2)\[\text{Moment}_\text{non-dimensional} = \frac{\text{Moment}_\text{physical}\text{(SI=N$\cdot$m)}}{\rho_\infty C_\infty^2 L_{gridUnit}^3},\]

where the moment center is the centerOfRotation of each disk, defined in BETDisks of Flow360.json.

  1. Sectional thrust coefficient \(C_t\) and sectional torque coefficient \(C_q\) on each blade at several radial locations, represented by “Disk[diskID]_Blade[bladeID]_R[radialID]” with suffix “_Radius”, “_ThrustCoeff” and “_TorqueCoeff”. The number of radial locations is specified in nLoadingNodes.

The definition of \(C_t\) is

(2.2.3)\[C_t\bigl(r\bigr)=\frac{\text{Thrust per unit blade length (SI=N/m)}}{\frac{1}{2}\rho_{\infty}\left((\Omega r)^2\right)\text{chord}_{\text{ref}}}\cdot\frac{r}{R}\]

The definition of \(C_q\) is

(2.2.4)\[C_q\bigl(r\bigr)=\frac{\text{Torque per unit blade length (SI=N)}}{\frac{1}{2}\rho_{\infty}\left((\Omega r)^2\right)\text{chord}_{\text{ref}}R}\cdot\frac{r}{R}\]

where \(r\) is the distance between the node to the axis of rotation. \(\text{chord}_\text{ref}\) is the dimensional refererence chord length. \(R\) is the radius of the rotor disk.

Note

All the quantities in the right hand side of Eq.(2.2.1), Eq.(2.2.2), Eq.(2.2.3) and Eq.(2.2.4) are dimensional, which are different from the non-dimensional values in BETDisks (list) of Flow360.json.

Warning

For simulations of the steady blade disk solver, the resulting \(C_t\) and \(C_q\) are only saved on the first blade, named by “Blade0”. They are written as all zeros for other blades, because all the blades have the same sectional loadings in steady blade disk simulations. For the unsteady blade line solver, each blade has its own \(C_t\) and \(C_q\) values.

Here is an example of the header of a “bet_forces_v2.csv” file from a simulation containing two BET disks (assume nLoadingNodes = 20, numberOfBlades = 3 for each disk):

physical_step, pseudo_step,
Disk0_Force_x, Disk0_Force_y, Disk0_Force_z, Disk0_Moment_x, Disk0_Moment_y, Disk0_Moment_z,
Disk0_Blade0_R0_Radius, Disk0_Blade0_R0_ThrustCoeff, Disk0_Blade0_R0_TorqueCoeff,
Disk0_Blade0_R1_Radius, Disk0_Blade0_R1_ThrustCoeff, Disk0_Blade0_R1_TorqueCoeff,
...
Disk0_Blade0_R19_Radius, Disk0_Blade0_R19_ThrustCoeff, Disk0_Blade0_R19_TorqueCoeff,
Disk0_Blade1_R0_Radius, Disk0_Blade1_R0_ThrustCoeff, Disk0_Blade1_R0_TorqueCoeff,
Disk0_Blade1_R1_Radius, Disk0_Blade1_R1_ThrustCoeff, Disk0_Blade1_R1_TorqueCoeff,
...
Disk0_Blade1_R19_Radius, Disk0_Blade1_R19_ThrustCoeff, Disk0_Blade1_R19_TorqueCoeff,
Disk0_Blade2_R0_Radius, Disk0_Blade2_R0_ThrustCoeff, Disk0_Blade2_R0_TorqueCoeff,
Disk0_Blade2_R1_Radius, Disk0_Blade2_R1_ThrustCoeff, Disk0_Blade2_R1_TorqueCoeff,
...
Disk0_Blade2_R19_Radius, Disk0_Blade2_R19_ThrustCoeff, Disk0_Blade2_R19_TorqueCoeff,
Disk1_Force_x, Disk1_Force_y, Disk1_Force_z, Disk1_Moment_x, Disk1_Moment_y, Disk1_Moment_z,
...
...
...
Disk1_Blade2_R19_Radius, Disk1_Blade2_R19_ThrustCoeff, Disk1_Blade2_R19_TorqueCoeff

2.2.3. BET Visualization

An additional option betMetrics in volumeOutput is available to visualize the BET related quantities.