Engee documentation

Rotor

Calculation of the aerodynamic force and torque of the propeller.

blockType: SubSystem

rotor

Path in the library:

/Aerospace/Propulsion/Rotor

Description

Block Rotor calculates the components of the aerodynamic force and the aerodynamic torque generated by the propeller. The block can also take into account the tilt of the propeller disc due to the swing movement of the blades in horizontal flight.

The components of aerodynamic force:





where

  • — thrust coefficient of the screw;

  • — air density;

  • — the radius of the screw;

  • — the angular velocity of the screw.

Components of the aerodynamic moment:





where — the torque coefficient of the screw.

If the check box is selected Compute CT and CQ The unit calculates the thrust and torque coefficients of the propeller according to the theory of the blade element.

In accordance with the simplified method of accounting for end losses proposed by Prandtl, the thrust coefficient of the elementary section of the blade is found by the formula:

where

  • — a function reflecting the load drop factor in the end section of the blade;

  • — flow rate;

  • — the relative radius of the section.

The exponential function indicator included in the formula , is equal to

where — the number of blades, determined by the parameter Number of blades.

According to the theory of the blade element, the thrust coefficient of the elementary section of the blade is found by the formula:

where

  • — fill factor;

  • — the chord defined by the parameter Chord, [m];

  • — the radius defined by the parameter Radius, [m];

  • — the slope of the lifting force curve, determined by the parameter Lift curve slope (per rad);

  • — the angle of installation at the end of the blade, determined by the parameter Twist distribution.

After equating the right sides of the equations, the resulting equation it is solved numerically with respect to . Knowing the flow coefficient, it is possible to determine the thrust coefficient of the entire blade using the integral formula.

The algorithm for calculating the torque coefficient is similar. The torque coefficient is related to the thrust coefficient of the elementary section of the blade by the following relationship:

Limitations

  • The block does not simulate the swing and cyclic movement of the blades.

  • The block uses the ideal and linear laws of changing the rotation of the blades, set by the parameter Twist distribution. In this case, the chord and the slope of the lifting force curve of the blades are considered constant.

Ports

Entrance

# Ωb(rad/s) is the angular velocity of the screw

+ scalar

Details

The angular velocity of rotation of the propeller around its axis relative to the body (fuselage), rad / s.

Типы данных

Float64
Support for complex numbers

None

# rb(kg/m3) is the density of air

+ scalar

Details

Air density, kg/m 3. The value must be greater than zero.

Типы данных

Float64
Support for complex numbers

None

# Vb(m/s) — screw speed

+ a 3-by-1 vector

Details

The components of the screw velocity in the associated coordinate system, m/s.

Dependencies

To use this port, set the parameter Modeling meaning With flap effects.

Типы данных

Float64
Support for complex numbers

None

# ωb(rad/s) is the angular velocity of the aircraft

+ a 3-by-1 vector

Details

The components of the angular velocity of the aircraft in the associated coordinate system, rad/s.

Dependencies

To use this port, set the parameter Modeling meaning With flap effects.

Типы данных

Float64
Support for complex numbers

None

Output

# Fxyz(N) — aerodynamic force

+ a 3-by-1 vector

Details

The components of the aerodynamic force in the associated coordinate system, defined as a vector. Vector elements:

  1. — longitudinal force;

  2. — traction force;

  3. — lateral force.

They are measured in units of force.

Типы данных

Float64
Support for complex numbers

None

# Mxyz(N-m) — aerodynamic moment

+ a 3-by-1 vector

Details

The components of the aerodynamic moment in the associated coordinate system, defined as a vector. Vector elements:

  1. — transverse moment;

  2. — a normal moment;

  3. — the longitudinal moment.

They are measured in units of moment.

Типы данных

Float64
Support for complex numbers

None

# CT — thrust coefficient

+ scalar

Details

Thrust coefficient.

Dependencies

To use this port, check the box Output computed CT and CQ.

Типы данных

Float64
Support for complex numbers

None

# CQ is the torque coefficient

+ scalar

Details

The torque coefficient.

Dependencies

To use this port, check the box Output computed CT and CQ.

Типы данных

Float64
Support for complex numbers

None

Parameters

Main group

# Modeling — the method of calculating the thrust force
Without flap effects | With flap effects

Details

The method of calculating the thrust force:

  • Without flap effects — without taking into account the geometry of the blades;

  • With flap effects — taking into account the geometry of the blades and the tilt of the propeller disc in horizontal flight.

Values

Without flap effects | With flap effects
Default value

Without flap effects
Program usage name

modelMode
Tunable

No
Evaluatable

Yes

Rotor

# Number of blades — number of blades

Details

The number of blades. The value must be greater than zero.

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects.

Default value

2.0
Program usage name

Nb
Tunable

No
Evaluatable

Yes

# Compute CT and CQ — calculation of thrust and torque coefficients

Details

Check this box so that the thrust and torque coefficients of the screw are calculated inside the unit.

Default value

false (switched off)
Program usage name

CTcheck
Tunable

No
Evaluatable

Yes

# Output computed CT and CQ — output of calculated thrust and torque coefficients

Details

Check this box to add new output ports to output the calculated thrust and torque coefficients of the propeller.

Dependencies

To use this option, check the box Compute CT and CQ.

Default value

false (switched off)
Program usage name

CTout
Tunable

No
Evaluatable

Yes

# Thrust coefficient (CT) — thrust coefficient

Details

The thrust coefficient of the screw. The value must be greater than zero.

Dependencies

To use this option, uncheck the box. Compute CT and CQ.

Default value

0.0107
Program usage name

CT
Tunable

No
Evaluatable

Yes

# Torque coefficient (CQ) — torque ratio

Details

The torque coefficient of the screw. The value must be greater than zero.

Dependencies

To use this option, uncheck the box. Compute CT and CQ.

Default value

0.00078263
Program usage name

CQ
Tunable

No
Evaluatable

Yes

Blade

# Radius, [m] — radius

Details

The radius of the screw, m. The value must be greater than zero.

Default value

0.033
Program usage name

R
Tunable

No
Evaluatable

Yes

# Chord, [m] — The chord

Details

Horta of the screw, m. The value must be greater than zero.

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects.

Default value

0.01
Program usage name

c
Tunable

No
Evaluatable

Yes

# Hinge offset, [m] — removal of the horizontal hinge

Details

The distance from the axis of rotation of the screw to the axis of the hinge, which ensures the swing movement of the blade. It is measured in meters. The value must be greater than or equal to zero.

As a rule, the value for propellers is zero.

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects.

Default value

0.0
Program usage name

e
Tunable

No
Evaluatable

Yes

# Lift curve slope (per rad) — slope of the lifting force curve

Details

The derivative of the lift coefficient with respect to the angle of attack. The value must be greater than zero.

Changing the value depending on the angle of attack is not taken into account.

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects.

Default value

5.5
Program usage name

clalpha
Tunable

No
Evaluatable

Yes

# Lock number — mass characteristics

Details

Mass characteristic of the propeller blade. The value must be greater than zero.

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects.

Default value

0.6051
Program usage name

gamma
Tunable

No
Evaluatable

Yes

# Twist distribution — the law of twist change
Linear | Ideal

Details

The law of twist change:

  • Linear — linear.

    The model of geometric blade rotation is described by the dependence .

  • Ideal — perfect.

    The model of geometric blade rotation is described by the dependence .

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects.

Values

Linear | Ideal
Default value

Linear
Program usage name

twistType
Tunable

No
Evaluatable

Yes

# Blade root angle, [rad] — installation angle of the section

Details

Angle of installation of the section of the propeller blade I’m glad. The value must be greater than zero.

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects, and for the Twist distribution parameter, set the value Linear.

Default value

0.2548
Program usage name

theta0
Tunable

No
Evaluatable

Yes

# Blade twist angle, [rad] — twist angle

Details

Angle of rotation of the section of the propeller blade I’m glad.

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects, and for the Twist distribution parameter, set the value Linear.

Default value

-0.1361
Program usage name

theta1
Tunable

No
Evaluatable

Yes

# Blade tip angle, [rad] — installation angle

Details

Angle of installation of the propeller blade I’m glad. The value must be greater than zero.

Dependencies

To use this option, check the box Compute CT and CQ or set for the parameter Modeling meaning With flap effects, and for the Twist distribution parameter, set the value Ideal.

Default value

0.1018
Program usage name

thetaTip
Tunable

No
Evaluatable

Yes

Literature

  1. Pounds, P. E. I. (2007). Design, construction and control of a large quadrotor micro air vehicle (Doctoral dissertation, Australian National University).

  2. Riether, F. (2016). Agile quadrotor maneuvering using tensor-decomposition-based globally optimal control and onboard visual-inertial estimation (Doctoral dissertation, Massachusetts Institute of Technology).

  3. Alayan O. M. Aerodynamics and dynamics of helicopter flight: Textbook / O. M. Alayan, V. F. Romasevich, V. S. Sovgirenko; Edited by Candidate of Technical Sciences A.M. Zagordan. — M.: Voenizdat, 1973. — 445 p.: ill.

  4. Shaidakov V. I., Maslov A.D. Aerodynamic design of propeller blades: Textbook. Moscow: Publishing House of MAI, 1995. 68 p.: ill.

  5. B. N. Yuriev. Aerodynamic calculation of helicopters. The State Publishing House of the Defense Industry. Moscow, 1956.