Simulation

Classes

class libmurosim.Atmosphere

Object describing basic atmosphere attributes. Make sure units are consistent with everything else.

Constructor:

Parameters

density – Atmospheric density.
dynamic_viscosity – Atmospheric dynamic viscosity.

density: atmospheric density

dynamic_viscosity: atmospheric dynamic viscosity

kinematic_viscosity: atmospheric kinematic viscosity

Functions

libmurosim.step(ac_state, aircraft, ac_input_state, inflows, wake_history, atmo, iteration, dt)

Step the simulation by one timestep

Parameters

ac_state – AircraftState object holding the current state of the aircraft
aircraft – Aircraft object describing the aircraft geometry
ac_input_state – AircraftInputState describing the aircrafts inputs
inflows – a list of Inflow objects. One for each rotor
wake_history – WakeHistory object containing the current and past wake states
atmo – Atmosphere object describing ambient atmospheric conditions
iteration – the current iteration
dt – the current timestep size

libmurosim.basic_aircraft_rotor_dynamics(input_state, dt)

Update all rotor azimuthal positions using a basic dynamics equation with simple forward Euler integration:

\(\frac{\mathrm{d}\psi}{\mathrm{d}t} = \Omega + \dot\Omega \Delta t\)

Parameters

input_state – The AircraftInputState to update
dt – The current time step size

libmurosim.basic_single_rotor_dynamics(input_state, dt)

Updates a single rotor azimuthal positions using a basic dynamics equation with simple forward Euler integration:

\(\frac{\mathrm{d}\psi}{\mathrm{d}t} = \Omega + \dot\Omega \Delta t\)

Parameters

input_state – The RotorInputState to update
dt – The current time step size

libmurosim.chunk_size(): Returns the chunk size used by the internal data structures

Geometry

Classes

class libmurosim.Aircraft

This class allocates and holds an array of rotors for the aircraft.

Constructor:

Parameters: num_rotors – The number of rotors the aircraft has.

rotors: An array of RotorGeometry, one for each rotor on the aircraft

class libmurosim.RotorGeometry

This class allocates and holds all the blades and other rotor geometric data.

Constructor:

Parameters

num_blades – Number of blades the rotor has.
origin – The global origin of the rotor. This is where the center of the hub is located.
radius – The dimensional radius of the rotor.
solidity – The solidity of the rotor.

blades: An array of BladeGeomtery, one for each blade of the rotor

origin: The global origin of the rotor. This is where the center of the hub is located.

radius: The dimensional radius of the rotor.

solidity: The solidity of the rotor.

class libmurosim.BladeGeometry

This class allocates and holds the blade geomteric parameters.

Constructor:

Parameters

num_elements – The number of spanwise blade elements.
azimuth_offset – The azimuthal offset that this blade has relative to its rotor.
average_chord – The average chord of the blade.

average_chord: The dimensional average chord of the blade

azimuth_offset: The azimuthal offset for this blade. This is added to the RotorInputState azimuth.

chunks

class libmurosim.BladeGeometryChunk

C_l_alpha

alpha_0

chord

r

twist

Functions

libmurosim.set_r(bg, data)

Set the spanwise radial stations (non-dimensional) of a BladeGeometry from a linear array.

Parameters

bg – BladeGeometry object to apply twist to.
data – List of radial stations

libmurosim.set_twist(bg, data)

Set the spanwise twist distribution of a BladeGeometry from a linear array.

Parameters

bg – BladeGeometry object to apply twist to.
data – List of twist angles (in radians) for each radial station

libmurosim.set_chord(bg, data)

Set the spanwise chord distribution (non-dimensional) of a BladeGeometry from a linear array.

Parameters

bg – BladeGeometry object to apply twist to.
data – List of chord lengths (non-dimensional) for each radial station

libmurosim.set_C_l_alpha(bg, data)

Set the spanwise lift curve slope (\(C_{L_{\alpha}}\))(per radian) distribution of a BladeGeometry from a linear array.

Parameters

bg – BladeGeometry object to apply twist to.
data – List of lift curve slope (per radians) for each radial station

libmurosim.set_alpha_0(bg, data)

Set the spanwise 0 lift angle (\(\alpha_0\))(in radians) distribution of a BladeGeometry from a linear array.

Parameters

bg – BladeGeometry object to apply twist to.
data – List of \(\alpha_0\) (in radians) for each radial station

libmurosim.set_sweep(bg, data)

Set the spanwise sweep angle (in radians) distribution of a BladeGeometry from a linear array.

Parameters

bg – BladeGeometry object to apply twist to.
data – List of sweep angles (in radians) for each radial station

State

Classes

class libmurosim.AircraftState

This is the top level class that holds the current aerodynamic state of an aircraft.

Constructor:

Parameters

num_rotors – The number of rotors on this aircraft
num_blades – The number of blades on each rotor
num_elements – The requested number of spanwise elements. This will be rounded up to the nearest chunk_size().
ac – The Aircraft object associated with this state

rotor_states: An array of RotorState, one for each rotor on the aircraft

class libmurosim.RotorState

This class holds the current aerodynamic state of the rotor.

Attention

This never needs to be explicitly constructed as it will be constructed by AircraftState

C_T: The current thrust coefficient of this rotor

advance_ratio: The current advance ratio of this rotor

axial_advance_ratio: The current axial advance ratio of this rotor

blade_states: An array of BladeState, one for each blade of this rotor

class libmurosim.BladeState

This class holds the current aerodynamic state of the blade.

Attention

This never needs to be explicitly constructed as it will be constructed by AircraftState

C_D: The current drag coefficient contribution from this blade

C_L: The current lift coefficient contribution from this blade

C_Mx: The current x moment coefficient contribution from this blade

C_My: The current y moment coefficient contribution from this blade

C_Q: The current power/torque coefficient contribution from this blade

C_T: The current thrust coefficient contribution from this blade

azimuth: The current azimuthal angle of this blade

chunks

class libmurosim.BladeStateChunk

aoa: A chunk of spanwise sectional angle of attack

dC_D: A chunk of spanwise sectional drag coefficient

dC_L: A chunk of spanwise sectional lift coefficient

dC_Q: A chunk of spanwise sectional power/torque coefficient

dC_T: A chunk of spanwise sectional thrust coefficient

d_gamma: A chunk of spanwise sectional change in circulation

gamma: A chunk of spanwise sectional circulation

Functions

libmurosim.get_dC_T(blade_state)

Extract blade spanwise thrust coefficient to a linear array.

Parameters: blade_state – the BladeState to extract the spanwise \(dC_T\) from
Returns: List of spanwise \(dC_T\) values

libmurosim.get_dC_Q(blade_state)

Extract blade spanwise torque coefficient to a linear array.

Parameters: blade_state – the BladeState to extract the spanwise \(Cd_Q\) from
Returns: List of spanwise \(dC_Q\) values

libmurosim.get_aoa(blade_state)

Extract blade spanwise angle of attack (\({\alpha}\)) to a linear array.

Parameters: blade_state – the BladeState to extract the spanwise \({\alpha}\) from
Returns: List of spanwise \({\alpha}\)

libmurosim.get_gamma(blade_state)

Extract blade spanwise bound circulation (\({\Gamma}\)) to a linear array.

Parameters: blade_state – the BladeState to extract the spanwise \({\Gamma}\) from
Returns: List of spanwise circulation values

libmurosim.get_d_gamma(blade_state)

Extract blade spanwise change in bound circulation (\({\Delta}\)\({\Gamma}\)) to a linear array.

Parameters: blade_state – the BladeState to extract the spanwise \({\Delta}\)\({\Gamma}\) from
Returns: List of spanwise \({\Delta}\)\({\Gamma}\) values

libmurosim.get_dC_L(blade_state)

Extract blade spanwise lift coefficient (\(dC_L\)) to a linear array.

Parameters: blade_state – the BladeState to extract the spanwise \(C_L\) from
Returns: List of spanwise \(dC_L\) values

libmurosim.get_dC_D(blade_state)

Extract blade spanwise drag coefficient (\(dC_D\)) to a linear array.

Parameters: blade_state – the BladeState to extract the spanwise \(C_D\) from
Returns: List of spanwise \(dC_D\) values

Input State

Classes

class libmurosim.AircraftInputState

This class represents the input parameters for the entire aircraft.

Contructor:

Parameters

num_rotors – Number of rotors the aircraft has.
num_blades – The number of blades each rotor has.

rotor_inputs: An array of RotorInputState, one for each rotor

class libmurosim.RotorInputState

angle_of_attack: Angle of attack of the rotor in radians

angular_accel: The angular acceleration of the rotor in \(mathrm{rad}/s^2\)

angular_velocity: The angular velocity of the rotor in \(mathrm{rad}/s\)

azimuth: The current azimuthal position of the rotor in radians

blade_flapping: An array of blade flapping angle in radians

blade_flapping_rate: An array of blade flapping rates in \(mathrm{rad}/s\)

blade_pitches: An array of blade pitches taken at the 75% spanwise location in radians

freestream_velocity: The dimensional freestream velocity

r_0: The initial non-dimensional tip vortex core size

Functions

Inflow Models

Classes

class libmurosim.HuangPeters

This class instantiates a dynamic inflow model for a single rotor. One of these will be needed for each rotor in the aircraft.

Constructor:

Parameters

Mo – The number of odd modes used in the model. 4 typically works well.
Me – The number of even modes used in the model. 2 typically works well.
rotor – The geometry of the rotor this inflow model is modeling.
dt – The timestep of the simulation.

inflow_at()

Computes the rotor induced flow at the requested location.

Parameters

x – A chunk of x positions to compute the induced velocity at.
y – A chunk of y positions to compute the induced velocity at.
z – A chunk of z positions to compute the induced velocity at.
x_e – A chunk of x_e positions to compute the induced velocity at. Unused in this inflow model.
angle_of_attack – Current angle of attack of the rotor. Unused in this inflow model.

Returns

A chunk of z induced velocities.

update()

Updates the inflow model by one timestep

Parameters

C_T – Current rotor thrust coefficient. This does nothing for this inflow model.
rotor – The current input state for the rotor.
rotor_state – The current rotor state.
advance_ratio – The current advance ratio for the rotor.
axial_advance_ratio – The current axial advance ratio for the rotor.
dt – The current timestep size.

wake_skew()

Returns: The current wake skew angle of the rotor in radians.

Wake

Classes

class libmurosim.WakeHistory

Top level structure for holding the wake and its history

history: An array of Wake s, one for each timestep

class libmurosim.Wake

rotor_wakes: An array of RotorWake

class libmurosim.RotorWake

shed_vortices: An array of ShedVortex

tip_vortices: An array of VortexFilament

class libmurosim.ShedVortex

shed_filaments: An array of VortexFilament

class libmurosim.VortexFilament

chunks: An array of FilamentChunk

class libmurosim.FilamentChunk

gamma: A chunk of circulation strengths along the filament

r_c: A chunk of vortex core size along the filament

v_z: A chunk of induced velocities along the filament

x: A chunk of x positions along the filament

y: A chunk of y positions along the filament

z: A chunk of z positions along the filament

Functions

libmurosim.get_wake_x_component(votex_filament)

Extract filament x position component to a linear array.

Parameters: votex_filament – the VortexFilament to extract the x position component from
Returns: List of filament x positions

libmurosim.get_wake_y_component(votex_filament)

Extract filament y position component to a linear array.

Parameters: votex_filament – the VortexFilament to extract the y position component from
Returns: List of filament y positions

libmurosim.get_wake_z_component(votex_filament)

Extract filament z position component to a linear array.

Parameters: votex_filament – the VortexFilament to extract the z position component from
Returns: List of filament z positions

libmurosim.get_wake_gamma_component(votex_filament)

Extract filament cirulation strength (\(\Gamma\)) to a linear array.

Parameters: votex_filament – the VortexFilament to extract \(\Gamma\) from
Returns: List of filament \(\Gamma\)

libmurosim.get_wake_r_c_component(votex_filament)

Extract filament vortex core size (\(r_c\)) to a linear array.

Parameters: votex_filament – the VortexFilament to extract \(r_c\) from
Returns: List of filament core sizes

libmurosim.get_wake_v_z_component(votex_filament)

Extract induced velocity (\(v_z\)) acting upon the filament to a linear array.

Parameters: votex_filament – the VortexFilament to extract \(v_z\) from
Returns: List of induced velocities

Vtk integration

Classes

class libmurosim.VtkWake: This is an opaque type that holds all the relevant data for writing out a vtu file that holds the wake geometric data as well as various data in a filament.

Attention

Do not instantiate one of these yourself. Instead use build_base_vtu_wake()

class libmurosim.VtkRotor: This is an opaque type that holds all the relevant data for writing out a vtu file that holds the rotor geometric data as well as various spanwise data.

Attention

Do not instantiate one of these yourself. Instead use build_base_vtu_rotor()

Functions

libmurosim.build_base_vtu_rotor(rotor)

Construct and allocate all required data for a VtkRotor.

Parameters: rotor – An instance of a RotorGeometry object
Returns: An initialized VtkRotor object

libmurosim.write_rotor_vtu(base_filename, iteration, rotor_idx, vtk_rotor, rotor_state, rotor_input_state)

Takes the RotorState and RotorInput data, converts it a VtkRotor, and saves it to a vtu file.

The filaname that the data is saved to is constructed by the function such that:

filename = base_filename + "_" + rotor_idx + "_" + iteration + ".vtu"

This ensures that timeseries files can be iterpreted by paraview correctly

Caution

This function has a relatively high runtime cost, use sparingly

Parameters

base_filename – The filename to save the data to
iteration – The iteration of the saved data
rotor_idx – The index of the rotor being saved
vtk_rotor – The VtkRotor object to save out
rotor_state – The RotorState object containing the rotor state data to save
rotor_input – the RotorInput object containing the rotor position data

libmurosim.build_base_vtu_wake(wake)

Construct and allocate all required data for a VtkWake.

Parameters: wake – An instance of a Wake object
Returns: An initialized VtkWake object

libmurosim.write_wake_vtu(base_filename, iteration, vtk_wake, wake)

Takes the Wake data, converts it a VtkWake, and saves it to several vtu files. One file is saved per blade tip vortex filament, and one file is saved per blade shed wake.

The filanames that the data is saved to is constructed by the function such that:

tip_vortex_filename = base_filename + "_" + rotor_idx + "_" + blade_idx + iteration + ".vtu"

shed_wake_filename = base_filename + "_shed_" + rotor_idx + "_" + blade_idx + iteration + ".vtu"

This ensures that timeseries files can be iterpreted by paraview correctly

Caution

This function has a very high runtime cost, use sparingly

Parameters

base_filename – The filename to save the data to
iteration – The iteration of the saved data
vtk_wake – The VtkWake object to save out
wake – The Wake object containing the wake data