Blade Element Method Reference

• Time Option
• Airfoil Sections
• Chord Distribution
• Sweep Angle Distribution
• Twist Distribution
• Disk Geometry
• Rotation Rate
• Disk Stick Specification
• Trim Convergence Control
• Target Thrust
• Target Pitch and Roll Moment
• Disk Flap Specification
• Virtual Disk/Blade Resolution
• Tip Loss Correction
• Source Convergence Term

Time Option

Specifies how the source term distribution is applied to the disk. This can either be done using a Time Averaged approach or a Time Accurate approach. For the time averaged approach the source term is averaged and then applied onto the rotor disk. For the time accurate approach the source term is added to the blades through tracking the motions. See also: 时间选项指定.

Airfoil Sections

Allows you to specify the local aerodynamic coefficients as a function of angle of attack and either Mach Number or Reynolds Number on a specific radial point along the blade as specified by the Normalized Disk Span. The normalized disk span is defines the dimensionless radial coordinates along the blade. It is calculated by $\frac{r}{R}$ where r is the radial coordinate and R is the maximum blade radius.

To fully define the aerodynamic coefficients, complete the properties on the corresponding child nodes. For more information see Airfoil Section Properties.

Chord Distribution

Allows you to define the chord distribution on the rotors. You can either provide this data as a constant value, a polynomial as a function of the normalized disk span or as table. You are also able to specify the dimensions used for defining the chord.

Method	Child Node
Constant	Constant Sets a constant chord value.
Polynomial in (r/R)	Polynomial in (r/R) Specifies the chord distribution as a function of the dimensionless disk span in the form of a polynomial.
Table (r/R)	Table (r/R) Allows you to specify a table of data to represent the chord distribution and define which columns represent the normalized span and chord data.

Sweep Angle Distribution

Allows you to define the sweep angle distribution on the rotors. You can either provide this data as a constant value, a polynomial as a function of the normalized disk span or as table. You are also able to specify the dimensions used for defining the chord.

Method	Child Node
Constant	Constant Sets a constant sweep angle value.
Polynomial in (r/R)	Polynomial in (r/R) Specifies the sweep angle distribution as a function of the dimensionless disk span in the form of a polynomial.
Table (r/R)	Table (r/R) Allows you to specify a table of data to represent the sweep angle distribution and define which columns represent the normalized span and chord data.

Twist Distribution

Allows you to define the twist distribution on the rotors. You can either provide this data as a constant value, a polynomial as a function of the normalized disk span or as table. You are also able to specify the dimensions used for defining the chord.

Method	Child Node
Constant	Constant Sets a constant blade twist value.
Polynomial in (r/R)	Polynomial in (r/R) Specifies the blade twist distribution as a function of the dimensionless disk span in the form of a polynomial.
Table (r/R)	Table (r/R) Allows you to specify a table of data to represent the blade twist distribution and define which columns represent the normalized span and chord data.

Disk Geometry

See Virtual Disk Model Reference

Rotation Rate

Specifies the rotation rate of the disk. The rotation rate can either be specified as a constant value or be ramped linearly to a maximum value specified. If Linear Ramp has been selected the following sub-node is available.

Sub-node

Properties

Linear Ramp

Start Counter Specifies the iteration or time-step at which to begin any rotation. Stop Counter Specifies the iteration or time-step on which to the full rotation rate is imposed. Initial Value Specifies the slow rotation rate value with which to begin the ramping. Ramp Counter Shows which counter is used to control the ramping of Rotation Rate. The Time Option determine the counter type: Iteration when Time Averaged is selected Time Step when Time Accurate is selected.

Disk Stick Specification

Specifies the initial orientation of the blades through the following three components of the pitch angle of the blade, which are defined in Eqn. (4997):

Collective Pitch ( ${\theta }_0$ )

Specifies the pitch angle component generated through vertical lift or descent of the swash plate, which is everywhere constant in the azimuthal direction.

Cyclic Pitch: Cosine Component (Lateral Cyclic Pitch ${\theta }_{1c}$ )

Specifies the tilting of the rotor disk to left/right with respect to the flying direction. It is generated through the left/right tilting of the swash plate and results in a roll tilting of the helicopter.

Cyclic Pitch: Sine Component (Longitudinal Cyclic Pitch ${\theta }_{1s}$ )

Specifies the tilting of the rotor disk to front/back with respect to the flying direction. It is generated through the front/back tilting of the swash plate, which results in a nose down or tail down tilting of the helicopter.

Virtual Disk Trim Option

If any target thrust or/and moments are required, the Simcenter STAR-CCM+ trim solver calculate the control input — the required collective pitch, lateral cyclic pitch, and longitudinal cyclic pitch to achieve the desired thrust and moments.

The trim solver calculates the control input iteratively from the initial pitch values until convergence. See Numerical Trim Algorithm.

You can follow the iterative development of the pitch angle components by using the Virtual Disk Angle report. See Reporting Virtual Disk Results.

Options	Corresponding Child-Nodes
No Trimming No trimming is performed. All parts of the pitch angles are fixed through the initial values.	None
Trim Thrust Only The iterative trim algorithm adjusts the collective pitch angle only to achieve the desired thrust value.	Trim Convergence Control When the virtual disk trim option is set to Trim Thrust or Trim Thrust and Moment, allows you to set the Trim Under Relaxation Factor and Trim Tolerance to the desired values. This speeds up the convergence of the numerical trimming algorithm. For more information, see Overview of the Source Term Update. Target Thrust When the virtual disk trim option is set to Trim Thrust, allows you to set the Target Rotor Thrust. Rotor Thrust indicates the lift generated through the rotor blades.
Trim Thrust and Moments The iterative trim algorithm adjusts all parts of the pitch angle (collective, longitudinal cyclic, and lateral cyclic pitch angle) to achieve the desired thrust and moment values.	Target Pitch and Roll Moment When the virtual disk trim option is set to Trim Thrust and Moment, allows you to set the Target Rotor Pitch Moment, which results in a nose down or tail down tilting of the helicopter, and, the Target Rotor Roll Moment, which results in a left/right roll tilting of the helicopter. The trim solver calculates iteratively the corresponding three components of the pitch angle to achieve the desired moments.
If the Trim Thrust Only or Trim Thrust and Moments options are combined with the time option Time Accurate	Time Accurate Trim Specification Revolution Input Runs the trim calculation with respect to the number of revolutions, where you set Start Trim Revolution to specify the start revolution of the data collecting after the periodic flow regime is reached. To specify the elapsed revolutions before you update the control input, you set the Revolutions between corrections. Data collecting lasts exact one revolution. For example, Start Trim Revolution 3 and Revolutions between corrections 2 indicate that the data collecting starts at the 3rd revolution. At the 4th revolution, the data collecting is complete and the first correction is done. The correction happens every two revolution, which are the 4th, 6th, 8th revolution and so on. Tolerance Input Runs the iterative trim calculation by specifying the Source Term Tolerance, which must be satisfied to launch a new trim calculation. Data collecting starts when the tolerance is fulfilled. First correction happens one revolution after the data collection. The subsequent data collecting starts when the tolerance is fulfilled again.

Disk Flap Specification

Specifies the components used to define the lift distribution around the blades as a result of rotor blade flapping. These components are:

• Coning Angle: The angle that is formed between the span wise axis of a helicopter rotor blade, when the rotor system is producing lift, and a plane at right angles to the rotor mast. The coning angle is caused by the relationship between the centrifugal force acting on the rotor blade and the lift that is produced by the blades. This angle corresponds to ${\delta }_0$ in Eqn. (4993).
• Cyclic Flap: Cosine Component: This angle corresponds to ${\delta }_{1c}$ in Eqn. (4993).
• Cyclic Flap: Sine Component: This angle corresponds to ${\delta }_{1s}$ in Eqn. (4993).
• Flap Hinge Eccentricity: The distance between the horizontal hinge of a helicopter rotor system (the flapping hinge) and the hub. The hinge allows the blades to move up and down in a flapping motion that compensates for asymmetry in the lift force.

Virtual Disk/Blade Resolution

Specifies the resolution of the interpolation grid used for the blade element method. The resolution depends on the time option selected. For the Time Average approach, the default interpolation method utilizes the source term strength of the four neighboring blade elements thus providing a smoother distribution of source terms. For the Time Accurate approach, 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. The following sub-nodes are available:

Sub-Node	Properties
Azimuthal Resolution Only available for the Time Averaged Approach	Azimuthal Resolution The resolution of the two-dimensional virtual disk interpolation grid in the azimuthal direction.
Radial Resolution	Radial Resolution The resolution of the two-dimensional virtual disk interpolation grid in the radial direction. Radial Distribution Function Selects the method by which the grid lines of the interpolation grid are clustered towards the outer radius of the virtual disk. Determine how the grid lines are distributed radially. The options are: Constant: Specifies an equidistant distribution of radial grid lines. Geometric: Specifies a geometric progression for the distribution of the radial grid lines. Distributes the bucket layers using simple geometric relationships. The stretch factor between adjacent bucket layers is always a constant value. Hyperbolic Tan:Specifies a hyperbolic function for the distribution of the radial grid lines. Distributes the bucket layers according to a one-parameter hyperbolic tangent stretching function: $$s\left(n_i\right)=1+\frac{\tanh \left[F_s(n_i/N-1)\right]}{\tanh \left(F_s\right)}$$ where N is the total number of layers, $n_i$ is the current node, $F_s$ is the overall stretch factor, and $s\left(n_i\right)$ is the distribution value for node $n_i$ . Note that $0\le n_i\le N$ , so that for 5 layers, $n_i$ takes the values 0, 1, 2, 3, 4, 5. Radial Stretch Mode Selects how the factor is defined that determines the density of the radial grid line distribution for the non-constant radial distribution function. The options are: None: Deactivates radial stretching Stretch Factor: Defined as the ratio of spacing at bucket layer n to the spacing at bucket layer n+1 Ratio Factor: Ratio of spacing between the last bucket layer and the first bucket layer.

Tip Loss Correction

The tip-loss correction defines a factor $F$ within a range of 0 to 1 that is multiplied with a chosen correction variable to yield a corrected lift force towards the tip of the blade. This correction factor is specified as a function of the dimensionless normalized disk span $r^{\prime }=r/R$ . The factor ranges from 0 to 1 where $r$ is the radial position and $R$ is the outer radius of the virtual disk (corresponding to the blade tip radius).

There are several methods to define the tip loss correction factor:

Method	Sub-Node	Properties
Constant Provides backward compatibility. On import of simulation files created prior to Simcenter STAR-CCM+ 12.04 and with tip correction active (0 < Tip Correction < 1), this method is set automatically. The tip-loss factor has the shape of a step function with a value of 1 until the radial starting point, and a value of 0 thereafter. The corrected lift force is obtained by multiplying lift force with the tip-loss factor.	Constant	Radial Start Point Defines the radial position on the virtual disk from which the tip loss correction is applied. For previously restored simulation files it take the value previously set Tip Correction.
Cosine From the radial starting point onwards, sets the tip-loss factor in the form of a half-cosine function: $$F=\{\begin{array}{ccc}1& ,& 0\le r^{\prime }<{r^{\prime }}_{\mathrm{start}}\\ \cos \left[\frac{\pi }{2}\left(\frac{r^{\prime }-{r^{\prime }}_{\mathrm{start}}}{R-{r^{\prime }}_{\mathrm{start}}}\right)\right]& ,& {r^{\prime }}_{\mathrm{start}}\le r^{\prime }\le R\end{array}$$ (250) This function provides a gradual decrease in tip-loss factor from the radial starting point onwards to the outer radius of the virtual disk. The corrected lift force is obtained by multiplying with lift force with the tip-loss factor.	Cosine	Radial Start Point Defines the radial position on the virtual disk from which the tip-loss correction is applied. Corresponds to ${r^{\prime }}_{\mathrm{start}}$ in Eqn. (250).
User-Defined Sets the tip-loss factor in the form of user-defined field functions. Both the radial starting point and the user-defined tip-loss factor can vary in space.	User-Defined	Correction Variable Specify the correction variable with which the tip-loss factor is multiplied. The options are: Lift: Apply a user-defined field function as lift correction, which scales the initial lift force computed by the solver. Angle of Attack: Correction factor is returned by a user-defined field function for Angle of Attack Correction applied to the initial angle of attack computed by the solver. Lift and Drag: Both lift and drag are corrected according to the factors provided in the lift correction and drag correction field functions. These corrections are applied to the initial lift and drag computed by the solver. The factors can be the same or different according to the formulation. For sub-node properties see, Correction Variable Properties

Source Convergence Term

Allows you to specify the Source Under Relaxation Factor and the Source Tolerance for the source terms.

Airfoil Sections Properties

When Airfoil Section Function Specification is set to Reynolds Number the following node and properties appear in the simulation tree within the Airfoil Section > [Airfoil Section] node.

When Airfoil Section Function Specification is set to Mach Number the following node and properties appear in the simulation tree within the Airfoil Section > [Airfoil Section] node.

Correction Variable Properties

All three correction variables require the radial start point, which defines the radial position on the virtual disk from which the tip-loss correction is applied. Using your own field function, you can set the starting point as a constant or varying around the circle swept by the blade.

To create a dependance on angular position, use the built in field function Cell Azimuth of [Virtual Disk].