Propulsion

class tuduam.propulsion.BEM(data_path: str, propclass: Propeller, rho: float, dyn_vis: float, V_fr: float, n_stations: int, a: float, T=None, P=None)

Bases: object

A class for performing Blade Element Momentum (BEM) analysis on a propeller. For initialization of the BEM class please keep the number of stations above 20. Also, if any error occurs with the propeller class, carefully check whether all parameters have been properly loaded in. Please specify either a thrust level or power level.

Parameters:

data_pathstr

Path to the directory containing all Xfoil data for the various Reynolds numbers. Please note the format of the file names given to polar files. They should only contain the Reynolds number in the name, no other numbers such as the airfoil code.

propclassPropeller

The propeller data structure with the propeller radius, number of blades, RPM cruise, and non-dimensional hub radius specified.

rhofloat

Density at the cruise height [kg/m^3].

dyn_visfloat

Dynamic viscosity [N s/m^2].

V_frfloat

Freestream velocity [m/s].

n_stationsint

Number of stations to calculate [-] (preferably > 20).

afloat

Speed of sound [m/s].

Tfloat, optional

Thrust delivered by the propeller [N], defaults to None.

Pfloat, optional

Power delivered to the propeller [W], defaults to None.

Attributes:

propellerPropeller

The propeller data structure.

Bint

Number of blades.

Rfloat

Propeller radius.

Dfloat

Propeller diameter.

Omegafloat

Angular velocity in rad/s.

xi_0float

Non-dimensional hub radius.

rhofloat

Density at the cruise height [kg/m^3].

dyn_visfloat

Dynamic viscosity [N s/m^2].

Vfloat

Freestream velocity [m/s].

lambfloat

Speed ratio.

N_sint

Number of stations to calculate [-].

afloat

Speed of sound [m/s].

dir_pathstr

Path to the directory containing all Xfoil data.

alpha_interpNearestNDInterpolator

Interpolator for angle of attack based on CL and Reynolds number.

cd_interpNearestNDInterpolator

Interpolator for CD based on CL and Reynolds number.

F(r, zeta)

Prandtl relation for tip loss factor.

Parameters:

rfloat

Radial position.

zetafloat

Induced inflow ratio.

Returns:

float

Tip loss factor.

F_int(xi, zeta)

Tip loss factor for integration.

Parameters:

xifloat

Non-dimensional radius.

zetafloat

Induced inflow ratio.

Returns:

float

Tip loss factor for integration.

G_int(xi, zeta)

G function for integration.

Parameters:

xifloat

Non-dimensional radius.

zetafloat

Induced inflow ratio.

Returns:

float

G function value for integration.

I_prim_1(xi, zeta, eps)

Integral I_prim_1 for internal variable calculation.

Parameters:

xifloat

Non-dimensional radius.

zetafloat

Induced inflow ratio.

epsfloat

Average value.

Returns:

float

Integral I_prim_1 value.

I_prim_2(xi, zeta, eps)

Integral I_prim_2 for internal variable calculation.

Parameters:

xifloat

Non-dimensional radius.

zetafloat

Induced inflow ratio.

epsfloat

Average value.

Returns:

float

Integral I_prim_2 value.

J()

Advance ratio.

Returns:

float

Advance ratio.

J_prim_1(xi, zeta, eps)

Integral J_prim_1 for internal variable calculation.

Parameters:

xifloat

Non-dimensional radius.

zetafloat

Induced inflow ratio.

epsfloat

Average value.

Returns:

float

Integral J_prim_1 value.

J_prim_2(xi, zeta, eps)

Integral J_prim_2 for internal variable calculation.

Parameters:

xifloat

Non-dimensional radius.

zetafloat

Induced inflow ratio.

epsfloat

Average value.

Returns:

float

Integral J_prim_2 value.

M(r)

Mach number as a function of radius.

Parameters:

rfloat

Radial position.

Returns:

float

Mach number.

PG(M)

Prandtl-Glauert correction factor.

Parameters:

Mfloat

Mach number.

Returns:

float

Prandtl-Glauert correction factor.

RN(Wc)

Reynolds number as a function of local speed and chord.

Parameters:

Wcfloat

Local speed times chord.

Returns:

float

Reynolds number.

Wc(F, phi, zeta, Cl)

Product of local speed at the blade and chord.

Parameters:

Ffloat

Tip loss factor.

phifloat

Angle of local velocity.

zetafloat

Induced inflow ratio.

Clfloat

Lift coefficient.

Returns:

float

Product of local speed and chord.

Xi(r)

Non-dimensional radius.

Parameters:

rfloat

Radial position.

Returns:

float

Non-dimensional radius.

efficiency(Tc, Pc)

Calculate propeller efficiency.

Parameters:

Tcfloat

Thrust coefficient.

Pcfloat

Power coefficient.

Returns:

float

Propeller efficiency.

f(r, zeta)

Exponent used in the Prandtl tip loss factor calculation.

Parameters:

rfloat

Radial position.

zetafloat

Induced inflow ratio.

Returns:

float

Exponent value.

f_int(xi, zeta)

Exponent used in the Prandtl tip loss factor calculation for integration.

Parameters:

xifloat

Non-dimensional radius.

zetafloat

Induced inflow ratio.

Returns:

float

Exponent value for integration.

optimise_blade(zeta_init)

Optimize the blade design by iteratively running the BEM design procedure and updating the inflow ratio (zeta) until convergence is achieved.

Parameters:

zeta_initfloat

Initial inflow ratio.

Returns:

dict

Dictionary containing the results of the BEM analysis, including chord, pitch, alpha, drag-to-lift ratio, effective velocity, solidity, Cl, Cd, propeller efficiency, thrust coefficient, power coefficient, and updated zeta.

phi(r, zeta)

Angle of local velocity of the blade with respect to the disk plane.

Parameters:

rfloat

Radial position.

zetafloat

Induced inflow ratio.

Returns:

float

Angle of local velocity.

phi_int(xi, zeta)

Angle of local velocity for integration.

Parameters:

xifloat

Non-dimensional radius.

zetafloat

Induced inflow ratio.

Returns:

float

Angle of local velocity for integration.

phi_t(zeta)

Pitch angle of the blade tip.

Parameters:

zetafloat

Induced inflow ratio.

Returns:

float

Pitch angle of the blade tip.

run_BEM(zeta)

Runs the design procedure for the propeller using Blade Element Momentum (BEM) theory from an arbitrary start zeta.

Parameters:

zetafloat

Initial inflow ratio.

Returns:

dict

Dictionary containing the results of the BEM analysis, including chord, pitch, alpha, drag-to-lift ratio, effective velocity, solidity, Cl, Cd, propeller efficiency, thrust coefficient, power coefficient, and updated zeta.

x(r)

Non-dimensional speed.

Parameters:

rfloat

Radial position.

Returns:

float

Non-dimensional speed.

class tuduam.propulsion.OffDesignAnalysisBEM(dir_path: str, propclass: Propeller, V: float, rpm: float, rho: float, dyn_vis: float, a: float)

Bases: object

A class encapsulating the arbitrary analysis of a propeller blade as described in Adkins and Liebeck (1994).

General notes

1. Interferences factors were clipped to -0.7 and 0.7. Viterna and Janetzke11 give empirical arguments for clipping the magnitude of a and a’ at the value of 0.7 in order to better convergence. See a_fac and a_prime_fac

Future improvement

1. TODO: Also compare to sample example in original paper of Adkins and Liebeck (1994)

2. TODO: Refactor such that rpm and V can be changed in the self.analyse_propeller method. Reinstantiating the class would not be necessary in that case

3. TODO: Make the off design analysis robust enough so a scipy.optimize could perhaps be used in the future.

Cx(Cl, Cd, phi)

Cy(Cl, Cd, phi)

F(r, phi_t)

K(Cl, Cd, phi)

K_prim(Cl, Cd, phi)

M(W)

PG_correct(M)

RN(W, c)

W(a, a_prim, r)

Xi(r)

a_fac(Cl: ndarray, Cd: ndarray, phi: ndarray, c: ndarray, r: ndarray, phi_t: ndarray) → ndarray

Returns the rotational interferene factor. Note that Viterna and Janetzke11 give empirical arguments for clipping the magnitude of a and a’ at the value of 0.7 in order to better convergence.

Viterna, A., and Janetzke, D., “Theoretical and Experimental Power from Large Horizontal-Axis Wind Turbines,” Proceedings from the Large Horizontal-Axis Wind Turbine Conference, DOE/NASA-LeRC, July 1981.

Parameters:

• Cl (np.ndarray) – _description_

• Cd (np.ndarray) – _description_

• phi (np.ndarray) – _description_

• c (np.ndarray) – _description_

• r (np.ndarray) – _description_

• phi_t (np.ndarray) – _description_

Returns:

_description_

Return type:

np.ndarray

a_prim_fac(Cl, Cd, phi, c, r, phi_t)

Returns the rotational interferene factor. Note that Viterna and Janetzke11 give empirical arguments for clipping the magnitude of a and a’ at the value of 0.7 in order to better convergence.

Viterna, A., and Janetzke, D., “Theoretical and Experimental Power from Large Horizontal-Axis Wind Turbines,” Proceedings from the Large Horizontal-Axis Wind Turbine Conference, DOE/NASA-LeRC, July 1981.

Parameters:

• Cl (_type_) – _description_

• Cd (_type_) – _description_

• phi (_type_) – _description_

• c (_type_) – _description_

• r (_type_) – _description_

• phi_t (_type_) – _description_

Returns:

_description_

Return type:

_type_

analyse_propeller(delta_pitch: float, max_iter=100, abs_extrapolation=0) → dict

Analyse the propeller according to the procedure specified in Adkins and Liebeck (1994), returns a dictionary with the keys as specified below.

Parameters:

delta_pitch – A change in pitch of the entire blade in radians. A positive value will further in crease the pitch

and vice versa. :type delta_pitch: float :param abs_extrapolation: The maximum extrapolation out of the given dataset allowed before a near zero thrust is returned in degrees :type abs_extrapolation: float :return: A dictionary with the following keys:

“thrust”: thrust created by the propeller, “torque”: torque required for the propeller , “eff”: propulsive efficiency of the propeller, “thrust_coeff”: thrust coefficient of the propeller, “power_coeff”: power coefficien of the propeller, “AoA”: Angle of attack at each station of the propeller, “lift_coeff”: Lift coefficient at each station of the propeller, “drag_coeff”: Drag coefficient at each station of the propller,

Return type:

dict

eff(C_T, C_P)

f(r, phi_t)

phi(a, a_prim, r)

solidity_local(c, r)

class tuduam.propulsion.PlotBlade(propclass: Propeller, path_coord: str)

Bases: object

A class to plot the blade of a propeller based on its specifications and airfoil coordinates.

Parameters:

propclassPropeller

Propeller class with all the attributes defined.

path_coordstr

Path to the coordinates of the airfoil in the format starting at the top trailing edge, moving to the top leading edge and then looping back to the bottom trailing edge.

Attributes:

chordsnp.ndarray

Array of chord lengths at different radial positions.

pitchsnp.ndarray

Array of pitch values at different radial positions.

radial_coordsnp.ndarray

Array of radial coordinates from the hub to the tip of the blade.

Rfloat

Radius of the propeller.

xi_0float

Twist angle at the root of the blade.

tc_ratiofloat

Thickness-to-chord ratio of the airfoil.

path_coordstr

Path to the airfoil coordinate file.

load_airfoil() → ndarray

Returns an array using a path to the coordinate file of the airfoil.

Returns:

np.ndarray

Array with the airfoil coordinates.

plot_3D(tst=False)

Plot a 3D plot of one propeller blade. The user can drag the mouse around to see the blade from various angles.

Parameters:

tstbool, optional

A boolean used for testing to suppress the output, defaults to False.

Returns:

None

plot_3D_plotly(tst=False)

Plot a 3D plot of one propeller blade. The user can drag the mouse around to see the blade from various angles.

Parameters:

tstbool, optional

A boolean used for testing to suppress the output, defaults to False.

Returns:

None

plot_blade(tst=False) → None

Returns two plots: one top-down view of the propeller showing the amount of twist and the various chords, and one plot showing a side view of the propeller.

Parameters:

tstbool, optional

A boolean used for testing to suppress the output, defaults to False.

Returns:

None

tuduam.propulsion.alpha_xfoil_interp(dir_path: str) → NearestNDInterpolator

Interpolates the angle of attack (alpha) from Xfoil output data.

Parameters:

dir_pathstr

The path of the directory to read from; can be absolute or relative.

Returns:

NearestNDInterpolator

Interpolator for angle of attack based on CL and Reynolds number.

tuduam.propulsion.cd_xfoil_interp(dir_path: str) → NearestNDInterpolator

Interpolates the drag coefficient (CD) from Xfoil output data.

Parameters:

dir_pathstr

Directory of the files containing the Xfoil polar data.

Returns:

NearestNDInterpolator

Interpolator for CD based on CL and Reynolds number.

tuduam.propulsion.cl_xfoil_interp(dir_path: str) → NearestNDInterpolator

Interpolates the lift coefficient (CL) from Xfoil output data.

Parameters:

dir_pathstr

Directory of the files containing the Xfoil polar data.

Returns:

NearestNDInterpolator

Interpolator for CL based on angle of attack and Reynolds number.

tuduam.propulsion.extract_data_dir(dir_path: str) → ndarray

This function pulls data from multiple files within a directory as outputted by Xfoil and puts them in one array. Information on how to do this can be found in the notebooks.

Assumptions

1. The function expects the name to at least have Rexxxx where the x’s represent the Reynolds number.

Parameters:

dir_pathstr

The path of the directory to read from; can be absolute or relative.

Returns:

np.ndarray

An m x 8 array where the columns are the following: [alpha, CL, CD, CDp, CM, Top_xtr, bot_xtr, Reynolds number].