Dynamic Inflow (Finite-State)

Compute inflow of air through rotor disc

Since R2026a

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Libraries:
Aerospace Blockset / Rotor Systems / Rotor Aerodynamics

Description

The Dynamic Inflow (Finite-State) block computes the normal induced velocity through the rotor disc by solving a set of ordinary differential equations. The number of state variables depends on the number of harmonics and number of radial modes used in the computation. The model used in the block is developed from incompressible flow Euler equations with the rotor modeled as an actuator disc.

The Dynamic Inflow (Finite-State) block models the azimuthal variation of inflow using trigonometric functions and the radial variation using Legendre functions. The block also computes the induced velocity required for blade force and moment calculations with good accuracy while avoiding heavy computation. The method is designed for integration into flight-control and simulation architectures, providing a balance of fidelity and efficiency for analysis and real-time applications.

Note

This inflow model is based on potential flow equations and is designed for conditions where incompressible flow assumptions are valid. The block does not automatically monitor local Mach numbers or enforce incompressibility limits, allowing flexibility for a wide range of input parameters. For best results, it is recommended to verify that their operating conditions fall within the typical range for incompressible flow.

Ports

Input

f_z — Elemental force distribution

real array

Elemental force distribution, specified as an array of size N_b-by-N_r, where N_b is the number of blades and N_r is the number of radial locations along the blade span where the force has been computed. It is expected that the force values provided corresponds to mid points of the radial segments used in the computation.

The unit is either N/m or lbf/ft.

The input values should represent the force per unit length calculated at various radial locations, using methods such as blade element theory. The input port does not support variable-size signals.

Dependencies

The unit of fz depends on the value of the Units parameter.

Data Types: double

μ — Rotor advance ratio

real scalar in range [-1,4]

Rotor advance ratio, specified as a real scalar in the range [-1,4]. This parameter is dimensionless and represents the ratio of the forward flight speed to the tip speed of the rotor blades. The rotor advance ratio is defined as $$\mu =\frac{V\cos i}{\Omega R}$$, where:

• i is the rotor disc plane incidence angle.

• V is the rotor velocity with respect to air.

• Ω is the angular velocity of the rotor, measured in radians per second.

• R is the rotor radius, which is the distance from the center of the rotor hub to the tip of the rotor blades.

Data Types: double

μ_z — Normal velocity ratio

real scalar in range [-1,4]

Normal velocity ratio, specified as a real scalar in the range [-1,4]. This argument is defined as $${\mu }_z=\frac{V\sin i}{\Omega R}$$, where:

• i is the rotor disc plane incidence angle.

• V is the rotor velocity with respect to air.

• Ω is the angular velocity of the rotor, measured in radians per second.

• R is the rotor radius, which is the distance from the center of the rotor hub to the tip of the rotor blades.

Data Types: double

ρ — Density

positive nonzero scalar

Density of air, specified as a positive nonzero scalar in kg/m³ or slug/ft³.

Dependencies

The unit of Density depends on the value of the Units parameter.

Data Types: double

Ω — Angular velocity of rotor

real scalar

Angular velocity of the rotor, specified as a real scalar in radians per second.

Dependencies

To enable this port, set the Rotor rotational speed source parameter to Port.

Data Types: double

Output

λ_i — Normal induced velocity ratio

real array

Normal induced velocity ratio, returned as a nondimensional array of dimension N_b-by-N_r, where N_b is the number of blades and N_r is the number of radial locations at which inflow is computed. The size of output will be same as that of input force distribution.

Data Types: double

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Units — Input and output units

Metric (MKS) (default) | English

Input and output ports and parameter units, specified as Metric (MKS) or English.

Units	Radius	Elemental Force Distribution	Density
Metric (MKS)	Meters	N/m	kg/m3
English (Velocity in ft/s)	Feet	lbf/ft	slug/ft3

Programmatic Use

Block Parameter: units

Type: character vector

Values: Metric (MKS) | English

Default: Metric (MKS)

Rotor rotational speed source — Source of angular velocity of the rotor

Dialog (default) | Port

Source of the angular velocity of the rotor, specified as one of Dialog or Port.

Programmatic Use

Block Parameter: omegaSrc

Type: character vector

Values: Dialog | Port

Default: Dialog

Rotor rotational speed — Rotational speed of rotor

41.2596 (default) | real scalar

Rotational speed of rotor, specified as a real scalar in radians per second.

Dependencies

This parameter is visible when the Rotational Speed Source parameter is set to Dialog.

Programmatic Use

Block Parameter: omega

Type: double

Values: 41.2596 | real scalar

Default: 41.2596

Rotor radius — Rotor radius

5.08 m (default) | real positive scalar

Rotor radius, specified as a nonzero scalar in m or ft. This is the distance from the center of the rotor hub to the tip of the rotor blades, specified by R in the equations for μ, μ_z and λ_i.

Dependencies

The unit of Blade radius depends on the value of the Units parameter.

Programmatic Use

Block Parameter: radius

Type: double

Values: 5.08 m | real positive scalar

Default: 5.08 m

Radial locations source — Source of radial locations

Uniform distribution based on force input (default) | Custom distribution

Source of radial locations, specified as one of Uniform distribution based on force input or Custom distribution. This parameter determines how the radial positions along the rotor blade are specified for aerodynamic computations.

• Uniform distribution based on force input - The entire length of the rotor blade is divided into equal segments based on the number of radial locations N_r specified in the force input. For example, if the number of columns in force input is 10, the blade span will be divided into 10 equal segments, as shown in the figure.

  

• Custom distribution - You can specify non-uniform radial positions along the blade, using the parameter Non-dimensional radial element edges (default: -1 for uniform distribution).

Programmatic Use

Block Parameter: radSrc

Type: char vector

Values: Uniform distribution based on force input | Custom distribution

Default: Uniform distribution based on force input

Non-dimensional radial element edges (default: -1 for uniform distribution) — Custom radial locations

-1 (default) | real scalar | real nonnegative strictly increasing vector with values in [0 1]

Custom radial segment limits (non-dimensional), specified as a real scalar (-1) or real nonnegative strictly increasing vector with values in [0 1]. The length of the vector should be one greater than N_r, the number of columns in the force input. It is expected that the input force values are computed or obtained at the mid-points of the radial segments specified through the parameter. For example, if the user inputs the parameter as, [r₀ r₁ r₂ r₃ r₄ r₅ r₆ r₇ r₈ r₉ r₁₀], with r₀>=0, and r₁₀<=1, a sample blade segment distribution is as shown in the figure and N_r will be 10. It is expected than the range r₀ to r₁₀ is the aerodynamically effective region of the blade and the integration to compute force is done only in this region.

If this parameter is set to -1 (default value), uniform distribution approach is followed.

Dependencies

This parameter is visible when Radial locations source is set to Custom distribution.

Programmatic Use

Block Parameter: radDistr

Type: double

Values: real scalar | real nonnegative strictly increasing vector with values in [0 1]

Default: -1

Highest harmonic index — Number of harmonics

2 (default) | nonnegative scalar

Highest harmonic variation to be considered in the modeling of azimuthal variation of inflow through the rotor disc, specified as a non-negative scalar in the range [0,6].

Tips

When you increase the number of harmonics, you enhance model fidelity but also raise computational demands. Therefore, choose the number of harmonics to balance the need for accuracy with the limitations of computational resources.

Programmatic Use

Block Parameter: indexHarmonic

Type: double

Values: 2| nonnegative scalar

Default: 2

Compute spatial modes — Method to compute number of radial modes per harmonic

Consistently upgraded (default) | Constant

Method to compute number of radial modes per harmonic, specified as one of Consistently upgraded or Constant.

Programmatic Use

Block Parameter: methodSpatialModes

Type: char

Values: Consistently upgraded| Constant

Default: Consistently upgraded

Number of spatial modes per harmonic — Number of spatial modes per harmonic

2 (default) | real positive scalar

Number of spatial modes per harmonic, specified as a real positive scalar.

Programmatic Use

Block Parameter: numSpatialModes

Type: double

Values: 2| real positive scalar

Default: 2

References

[1] He, Chengjian. Development and Application of a Generalized Dynamic Wake Theory for Lifting Rotors. PhD diss., Georgia Institute of Technology, 1989.

[2] Peters, David A. “How Dynamic Inflow Survives in the Competitive World of Rotorcraft Aerodynamics.” Journal of the American Helicopter Society 54, no. 1 (2009): 011001.

Version History

Introduced in R2026a