Setting Up the Blade Element Method

Similar to the body force propeller method, the setup of the virtual disk for the blade element method does not require the creation of a separate region to which the method is then applied. Instead, you create the shape of the virtual disk by specifying the relevant parameters such as radius, thickness, and orientation to an existing mesh.

To verify the dimensions and orientation of the virtual disk, you can visualize it by using virtual disk-specific field functions.

To set up and run the blade element method:

Simcenter STAR-CCM+ supports two Time Option approached; Time Averaged and Time Accurate. The Time Accurate approach tracks the motion of the blades and adds source terms only at the location of the blades. By this means, the Time Accurate approach captures the time varying nature of the loads on the rotor blades and thus the time varying forces and moments. In contrast, the Time Averaged approach adds the averaged source terms over the entire rotor disk. For more information, see Time Option Specification.

Select the Virtual Disk > Time Option node and select the appropriate Source Term Distribution.

The Airfoil Sections node specifies the drag and lift coefficients as a function of Reynolds or Mach number and angle of attack. This information provides the virtual disk simulation with the effect of local blade aerodynamics data. An aerofoil section is a cross-section of the blade at a certain radial position. You can either specify one aerofoil section for the entire blade or subdivide the blade into several cross-sections and provide local drag and lift coefficient data. To specify the airfoil section:

Right-click the Virtual Disk > Airfoil Sections node and select New.
Select the Airfoil Sections > Airfoil Section 1 node and set the appropriate settings.
Import the airfoil data as a table.
There are two file format options available:
- File Table
  1. Right-click the Tools > Tables node and select New Table > File Table.
  2. Select the correct .csv file and click Open.
    The file contains a table with four comma-separated columns of the following format:
```
Angle of attack (degrees or radians), Lift coefficient, Drag coefficient, Mach number
```
    An example of a .csv file table is shown below:
```
"AoA (deg)","Cl","Cd","Mach"
-16,0,0,0
-16,-1.218,0.09183,0.2
-16,-1.316,0.08124,0.4
-16,-1.521,0.07389,0.6
...
```
  3. Select the Airfoil Section 1 > [Cl] or [Cd] nodes and set the Input Table.
  4. Set the remaining properties under the [Cl] and [Cd] nodes.
- C81 table
  1. Right-click the Virtual Disk > Airfoil Sections node and select Import C81 Airfoil Section Data...
  2. In the Open dialog, set the Airfoil Data Function to (alpha, [Mach]) and navigate to the C81 airfoil data file. The file contains the data for both the lift and the drag coefficient.
  3. Click Open.
    Two nodes for the lift and drag coefficients, respectively, are added to the Tools > Tables node.
  4. Select the Virtual Disk > Airfoil Sections > Airfoil Section 1 > [Cl (AoA, Mach)] node and set the appropriate properties.
    See Airfoil Section Properties.

The chord is a straight line connecting the leading and the trailing edge of the blade or airfoil. It describes the width of the blade at a given point. The chord length can either be specified as constant or as a function of the normalized span

\frac{r}{R}

. To specify the chord distribution:

Select the Virtual Disk > Chord Distribution node, and set the Method.
Within the corresponding sub-node set the required properties.

Rotor blade of a helicopter experience the effects of wave drag at the tip of the blades. Wave drag occurs when the air flow reaches the speed of sound edge at the tip of the blade. Therefore to avoid the occurrence of wave drag, the local velocity at the blade tip must be kept below the speed of sound. The wave drag also restricts the maximum achievable rotation rates in combination with the blade radius. To remedy this limitation and to reduce wave drag effects sweep-back rotor blades are introduced. Sweeping the blades reduces the local velocity by a factor of cosine of the sweep angle. The sweeping also increases the critical Mach number. To specify the sweep angle distribution:

Select the Virtual Disk > Sweep Angle Distribution node, and set the Method.
Within the corresponding sub-node set the required properties.

A blade can be built with twist to achieve different pitch angles between the hub and the tip. To specify the twist distribution:

Select the Virtual Disk > Twist Distribution node, and set the Method.
Within the corresponding sub-node set the required properties.

The disk for the blade element method is of a cylindrical shape. You must ensure that you specify a disk thickness between 10% and 15% greater than the cell size of the volume mesh where the disk is located. This ensures that the cells comprising the disk are continuous and that the disk is at least one cell layer thickness. It is not recommended that you specify a larger thickness for the disk, because a larger disk leads to smearing of the local effects of the blades.

To specify the disk geometry, select the Virtual Disk > Disk Geometry node, and set the relevant properties.

To specify the rotation rate:

Select the Virtual Disk > Rotation Rate node, and specify the appropriate properties.
If Ramp Method is set to Linear Ramp, set the appropriate properties within the Rotation Rate > Linear Ramp node.

For a rotor, the pitch angle of the blade

θ

determines the angle of attack of the blade with respect to the rotor disk. Due to the asymmetric nature of the rotor loading in forward flight, the pitch angle needs special treatment. You can either specify all three components of the pitch angle directly or you can select the trim algorithm to calculate them. When using the trim routine, you provide an initial guess for the angles. The values of the desired amount of thrust and the moments are used to calculate iteratively the new value of the pitch angles. For more information see Numerical Trim Algorithm.

Select the Virtual Disk > Disk Stick Specification, and set the properties described in Disk Stick Specification.
If Virtual Disk Trim Option is set to Trim Thrust Only or Trim Thrust and Moments, select the Trim Convergence Control, Target Thrust, Target Pitch and Roll Moment, and Time Accurate Trim Specification (only applicable for Time Accurate) nodes and set their relevant properties. See Virtual Disk Trim Option Reference and Using the Time-Accurate Approach with the Virtual Disk Trim Option.

Rotor blade flapping is a result of the dynamic equilibrium between the aerodynamic lift forces and the centrifugal force about the flap hinge acting on the blade. As a result of these two forces, the blade assumes a conical path instead of remaining in the plane perpendicular to the mast.

In hover flight mode, the lift distribution is symmetrical with respect to the blade azimuth angle. This symmetrical distribution results in a constant flapping angle that is independent of azimuth. This constant angle is known as the coning angle. In forward flight mode, the lift distribution is asymmetrical due to the unequal amount of lift on the advancing and the retreating side of the rotor. The flapping response of the blades thus depends on the azimuth. On the advancing side, the blade flaps up to reduce the angle of attack and to generate less lift. On the retreating side, the blade flaps down to increase the angle of attack and to generate more lift. In addition, the blades experience asymmetry in velocity due to the constant component of the flap angle in the front and the back of the rotor. The blade responds to this asymmetry by flapping upwards as it passes the front part and by flapping downwards as it passes the back part.

Simcenter STAR-CCM+ provides the functionality to specify the coning angle, the cyclic flapping components, and the flap hinge eccentricity. This functionality caters for a more realistic description of the rotor system being modeled. To specify the disk flap specification:

Select the Virtual Disk > Disk Flap Specification node, and set the relevant properties.

The blade element method requires an interpolation grid which is associated with the cells of the underlying volume mesh. Each element of the interpolation grid is called a bucket. Each bucket receives the local flow conditions from the associated volume cells and outputs a momentum source.

To set the Virtual Disk/Blade Resolution there are two different methods depending on the Time Option selected:

Time Average — the default interpolation method utilizes the source term strength of the four neighboring blade elements this providing a smoother distribution of source terms. To specify a 2D virtual disk interpolation grid in the radial and the azimuthal direction, do the following:
1. Select the Virtual Disk Resolution > Azimuthal Resolution node and set the Azimuthal Resolution.
2. Select the Radial Resolution and set the Radial Resolution and any distribution you wish to apply.

Time Accurate — the default interpolation method applies an internal linear grid along the blades to calculate the source terms for each of the blade elements. It interpolates the source term linearly and distributes source terms to the finite volume mesh using Bivariate Gaussian Distribution, thus providing a smoother distribution of source terms. To specify a 1D virtual blade interpolation grid in the radial direction:

Select the Virtual Blade Resolution > Radial Resolution node and set the Radial Resolution and any distribution you wish to apply.

注

In cases where you require backward compatibility with the nearest neighbor interpolation mode, select the Virtual Disks > Virtual Blade Resolution node and activate the Legacy Interpolation Mode. The Legacy Interpolation Mode does not support blade overlapping. If Simcenter STAR-CCM+ detects overlapping, it outputs a warning message. To avoid overlapping, you can adjust the inner radius.

To resolve flow effects near the tip efficiently without increasing the number of elements, you can activate radial distribution towards the outer radius of the virtual disk/blade:

Select the Virtual Disk/Blade Resolution > Radial Resolution node and set the Radial Distribution Function and Radial Stretch Mode.

To set the resolution such that each bucket is associated with at least one cell of the volume mesh, the virtual disk resolution must not be too fine. The resulting size of a bucket must approximately correspond to the cell size of the underlying volume mesh.

To approximate the trimmed cell size of the underlying volume mesh:
1. Calculate the length of the interpolation grid in the radial direction ( $r_{o u t} - r_{i n}$ ).
2. For a 2D interpolation grid, calculate the length in the azimuthal direction along the inner radius ( $2 π r_{i n}$ ).
3. Divide the lengths by the specified resolution in the respective direction.
The resulting value must approximately correspond to the volume mesh cell size in that area.
If you specified a virtual disk resolution that is too high, Simcenter STAR-CCM+ issues an error message. Reduce the grid resolution until the error message disappears. For more details, see Step 1: Cell Marking and the Allocation to the Blade Elements/Buckets Based on the Interpolation Grid.

A trailing vortex forms at the tip of each rotor blade. This vortex leads to a higher inflow near the tip, which effectively reduces the lift generation capacity of the blade in that region. This is known as tip loss. To specify the tip loss correction:

Select the Virtual Disk > Tip Loss Correction node, and set the Method.
In the corresponding sub-nodes, set the relevant properties.

To specify the source convergence control:

Select the Virtual Disk > Source Convergence Control node, and set the appropriate properties.
For more information see Blade Element Method Reference.