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 andinitialBladeDirection
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:
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
The non-dimensional moment is defined as
where the moment center is the centerOfRotation
of each disk, defined in BETDisks of Flow360.json.
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
The definition of \(C_q\) is
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.