Propeller
Propeller that converts torque into thrust
- Library:
Simscape / Driveline / Engines & Motors
Description
The Propeller block represents a propeller with fixed or controllable blades that converts rotational mechanical energy into translational mechanical energy. You can parameterize the propeller by using constants, polynomials, or tabulated data to characterize the thrust and torque coefficients. Propellers that allow negative pitch or are designed to operate in reverse may include thrust and torque coefficient curves specific to the astern direction, which you can use in the parameterization.
You can include the wake effects of the vessel hull in the block. You can specify a constant wake fraction or enable a physical signal port, and the block will calculate the wake effects automatically.
You can use a physical signal to control the blade pitch.
This terminology is helpful for understanding the block:
Wake fraction is the difference between the vessel velocity and the advance velocity expressed as a ratio of the vessel velocity.
Advance velocity is the speed of the flow through the propeller, Va.
Advance ratio is the speed of the flow through the propeller with respect to the propeller tip angular speed expressed as a ratio.
Quadrant is the relative two-dimensional location of the propeller operating condition where the vertical axis is Va and the horizontal axis is ω.
First quadrant: +Va, +ω
Second quadrant: +Va, -ω
Third quadrant: -Va, -ω
Fourth quadrant: -Va, +ω
Pitch is the ideal translational propeller advance distance for a single revolution.
Open water is when the effects of the hull are not present.
Equations
The block equations refer to these quantities:
T(t) is the smoothed propeller thrust.
Q(t) is the smoothed propeller torque.
ρ, ρ(t) is the fluid density, which can function with time. You can specify the fluid density with the Density parameter or the Rho port.
P is the pitch.
D is the propeller diameter. This value is equivalent to the Propeller diameter parameter.
ω(t) is the propeller angular speed input at port R. For more information about using angular units in Simscape™, see Angular Units.
n(t) is the propeller angular speed in revolutions per second, which serves to consistently nondimensionalize the torque and thrust. Here, ω = 2πn(t).
nThr is the Rotational speed threshold parameter.
kT is the thrust coefficient. This value is equivalent to the Thrust coefficient, kT parameter.
kQ is the torque coefficient. This value is equivalent to the Resistive torque coefficient, kQ parameter.
pkT is the kT polynomial coefficients (pN...p0) parameter.
pkQ is the kQ polynomial coefficients (pN...p0) parameter.
kThr is the nondimensional coefficient threshold. This value is equivalent to the Saturation threshold for nondimensional coefficients parameter.
J is the advance ratio.
Va is the advance velocity. You can specify the advance velocity using the Va port.
η is the smoothed efficiency.
The block smooths the propeller thrust and torque with respect to the rotational speed such that:
The block uses coefficients of thrust and torque to parameterize the performance of the propeller. You can provide static coefficients, or you can specify the coefficients as a polynomial that acts as a function of the advance ratio. The block defines the advance ratio as:
where the propeller rotational speed n is linearized with the angular speed threshold nThr for smoothing.
When you set Parameterization to Polynomial
fit
, the block calculates the thrust and torque coefficients as:
respectively, where pkT and pkQ represent the polynomial coefficients.
When you set Efficiency sensor to
On
, the block outputs the smoothed efficiency:
You can choose different options to parameterize the propeller
kT and
kQ based on the fidelity you
desire or the type of information that is available to you. If you want to
parameterize the propeller performance as a function of J,
you can set Parameterization to Polynomial
fit
or Tabulated coefficients
. If
you want to use an asymmetrical parameterization for negative values of
J, you must set Parameterization to
Tabulated coefficients
.
Constant coefficients
— This simple parameterization does not function with J. You specify kT and kQ as constants.Polynomial fit
— You can specify a vector of polynomial coefficients in descending degree. For example, if you enter[.063, -.19, -.25, .37]
for the kT polynomial fit coefficients (pN...p0) parameter, the block interprets this vector as kT = .063J3-.19J2-.25J+.37. The block saturates J to be between 0 and the first positive root of the polynomial and restricts kT and kQ to always be positive.Tabulated coefficients
— You can specify tabulated values for kT and kQ for given values of J and P/D. You must select this option if you want to use negative coefficients.
When you set Translational connections to
Conserving
, the block uses a constant wake
fraction to relate the vessel velocity to the advance velocity. You input the
thrust and velocity of the vessel using the R2 and
C2 ports. The block computes the advance velocity
as:
where:
V is the vessel velocity. You can specify the vessel velocity relative to the reference using the R2 and C2 ports, where V = VR2-VC2..
w is the wake fraction. This is equivalent to the Wake fraction parameter.
When you set Translational connections to
Physical connections
, you can use the
Va port to supply the advance velocity as a physical
signal. The block outputs the propeller thrust as a physical signal from the
Th port.
When you set Blade pitch type to
Controlled
, you can parameterize the propeller
over a range of pitch-diameter ratios, P/D. You must specify
the P/D range as a vector in the Pitch-diameter
ratio vector, P/D parameter, where each element corresponds to a
row in the kT and
kQ matrices.
Assumptions and Limitations
When you set Parameterization to
Polynomial fit
, the block assumes that the propeller torque and thrust coefficients are symmetric with the first quadrant.When you set Parameterization to
Tabulated coefficients
, the block assumes identical torque and thrust coefficients in the first quadrant and third quadrant as well as identical torque and thrust coefficients in the second quadrant and fourth quadrant.
Variables
Use the Variables tab to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.
Ports
Inputs
Outputs
Conserving
Parameters
Model Examples
References
[1] Bernitsas, Michael M., D. Ray, P. Kinley. "Kt, Kq and Efficiency Curves for the Wageningen B-Series Propellers." Report 237. Department of Naval Architecture and Marine Engineering. College of Engineering. University of Michigan, 1981.
[2] Carlton, J. S. Marine Propellers and Propulsion. Second edition. Oxford: Elsevier, 2007.