Dynamic Inflow (3-State)

R2026b

Compute inflow of air through rotor disc

Since R2026a

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Dynamic Inflow (3-State) block

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Libraries:
Aerospace Blockset / Rotor Systems / Inflow Models

Description

The Dynamic Inflow (3-State) block computes the normal induced velocity through the rotor disc by solving three ordinary differential equations with mean, lateral, and longitudinal inflow as the state variables. The model used in the Dynamic Inflow (3-State) block is developed from incompressible flow Euler equations with the rotor modeled as an actuator disc.

The Dynamic Inflow (3-State) block captures first harmonic variation of inflow in the azimuthal direction and linear variation of inflow along the blade span. The block enables the computation of the induced velocity required for computation of blade forces and moments at a low computational cost.

Note

Use this inflow model when potential flow equations apply and incompressible flow assumptions are valid. The Dynamic Inflow (3-State) block does not monitor local Mach numbers or enforce incompressibility limits, so you can apply a wide range of input parameters. Verify that your operating conditions remain within the typical range for incompressible flow to achieve the best results.

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.

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 the sentinel value -1 (default) to use uniform distribution, or as a real nonnegative strictly increasing vector with values in [0 1] for custom distribution. 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 that 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. The accuracy of the computed inflow distribution can be influenced by the radial discretization, including the number and spacing of blade elements, as well as the portion of the aerodynamically effective blade span represented by the specified radial segments.

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

Algorithms

The Dynamic Inflow (3-State) block implements the three‑state dynamic inflow model using the coupled first‑order system

$$M\left[\begin{array}{c}{\dot{\lambda }}_0\\ \dot{\lambda }c\\ \dot{\lambda }s\end{array}\right]+V{L}^{-1}\left[\begin{array}{c}{\lambda }_0\\ \lambda c\\ \lambda s\end{array}\right]=\left[\begin{array}{c}{C}_T\\ -C_{M_x}\\ -C_{M_y}\end{array}\right]$$

where M is the apparent mass matrix, V is the mass-flow matrix, and L is the influence coefficient matrix. All the matrices have closed form representations as shown in [2]. The aerodynamic coefficients C_T, C_Mx, and C_My are computed from the elemental force distribution input.

The induced-velocity field is reconstructed from the three inflow states using $${\lambda }_i(\overline{r},\psi ,t)={\lambda }_0+{\lambda }_c\overline{r}\cos \psi +{\lambda }_s\overline{r}\sin \psi$$, with r̅ as the nondimensional radial location and ψ as the azimuth angle. The block evaluates r̅ from either a uniform or custom radial distribution.

This formula captures the mean inflow and the first harmonic variation in the azimuthal direction, with linear variation in the radial direction. The model is a simplified approach that is suitable for real-time simulation and stability analysis [2].

References

[1] Peters, David A., and Ha Quang Ninh. “Dynamic Inflow for Practical Applications.” Journal of the American Helicopter Society 33, no. 4 (1988): 64–68.

[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): 11001–11001.

Version History

Introduced in R2026a