8.2.1. BET Disk and BET Line

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. A case study on the XV-15 rotor using blade element theory can be found at XV15 BET Disk.

Note

1. In the BETDisks section, all input quantities are non-dimensional, except the twists and alphas (both in degrees). The convention for non-dimensional inputs in Flow360 can be found at Non-Dimensional Inputs.

2. For users of XROTOR and DFDC, we have a translator script that will convert the XROTOR/DFDC inputs in Flow360 BET inputs.

Some input parameters related to BET solver in Flow360 are explained:

8.2.1.1. radius

All grid points enclosed by the cylinder defined by “radius”, “center” and “axisOfRotation” will have aerodynamic forces imposed on them according to blade element theory.

8.2.1.2. rotationDirectionRule

leftHand or rightHand. It depends on the design of the rotor blades: whether the blades follow curl left hand rule or the curl right hand rule to generate positive thrust. The following 2 figures show the curl left hand rule and curl right hand rule. The fingers follow the spinning of the blades and the thumb points to the thrust direction. By default, it is rightHand.

8.2.1.3. axisOfRotation

It is the direction of your thumb (thrust) described in “rotationDirectionRule”.

8.2.1.4. omega

The non-dimensional rotating speed. It should be positive in most cases, which means the leading edge moves in front and the rotation direction of the blades in BET simulations is consistent with the curling fingers described in “rotationDirectionRule” to generate positive thrust. A negative “omega” means the blades rotate in a reverse direction, where the trailing edge moves in front.

The following 4 pictures give some examples of different rotationDirectionRule and axisOfRotation with positive omega. The curved arrow follows the same direction in which rotor spins. The straight arrow points to the direction of thrust.

"rotationDirectionRule":"leftHand",
"axisOfRotation":[0,0,1],
"omega": 0.3

---

"rotationDirectionRule":"leftHand",
"axisOfRotation":[0,0,-1],
"omega": 0.5

---

"rotationDirectionRule":"rightHand",
"axisOfRotation":[0,0,1],
"omega": 0.5

---

"rotationDirectionRule":"rightHand",
"axisOfRotation":[0,0,-1],
"omega": 0.5

---

Note

In the above 4 examples, if the omega is negative, the rotor rotates in the opposite direction of what is shown.

8.2.1.5. chords and twists

The sampled radial distribution of chord length and twist angle. The “twist” affects the local angle of attack. The “chords” affects the amount of lift and drag imposed on the blade (or fluid). For a radial location where chord=0, there is no lift or drag imposed. It should be noted that for any radial location within the given sampling range, the chord or twist is linearly interpolated between its two neighboring sampled data points. For any radial location beyond the given sampling range, the chord or twist is set to be the nearest sampled chord or twist, i.e. constant extrapolation. Here are 3 examples of the given “chords” and the corresponding radial distribution of chord length:

Example 1. The root of blade starts at r=20 with chord length=15. The chord shrinks to 10 linearly up to r=60. The chord keeps as 10 for the rest of blade. In this setting, the chord=0 for r in [0,20], there is no aerodynamic lift and drag imposed no matter what the twist angle it has, so this setting fits the rotor without hub.

[
    {
        "radius": 19.9999,
        "chord": 0
    },
    {
        "radius": 20,
        "chord": 15
    },
    {
        "radius": 60,
        "chord": 10
    },
    {
        "radius": 150,
        "chord": 10
    }
]

Example 2. The root of blade starts at r=0 with chord=0. The chord expands to 15 linearly up to r=20, then shrinks to 10 linearly up to r=60. The chord keeps as 10 for the rest of blade. This setting could be used for a mesh with the geometry of hub. Because the chord length changes gradually near the root region, there won’t be tip vortices in root region.

[
    {
        "radius": 0,
        "chord": 0
    },
    {
        "radius": 20,
        "chord": 15
    },
    {
        "radius": 60,
        "chord": 10
    },
    {
        "radius": 150,
        "chord": 10
    }
]

Example 3. This is an exmpale of wrong setting of chords, because the chord length at r=0 is not 0, so the local solidity is infinity, which is not realistic.

[
    {
        "radius": 20,
        "chord": 15
    },
    {
        "radius": 60,
        "chord": 10
    },
    {
        "radius": 150,
        "chord": 10
    }
]

Note

The number of sampling data points in chords and twists doesn’t have to be the same. They are served as sampled data for interpolation of chord length and twist angle respectively and separately.