PyPK

PyPK is a collection of p-k methods for solving the flutter equation.

The original p-k method is described in Rodden, Aerodynamic lag functions, divergence, and the British flutter method and its non-iterative version is described in van Zyl, Aeroelastic Divergence and Aerodynamic Lag Roots. The mode tracking algorithm is described in van Zyl, Use of eigenvectors in the solution of the flutter equation. The methodology implemented in PyPk is decribed in this technical note.

Install and run

If you only want to use PyPK, you can install it using

python3 -m pip install . [--user]

and then run a case using

python3 path/to/case.py

If you need to develop in PyPK before using it, you do not need to install anything, and you can just run your case from the repo folder using

python3 run.py path/to/case.py

Use

PyPK is initialized through its API init_pypk. Examples can be found under the tests directory. A case file typically contains the following lines

# Initialize
from pypk import init_pypk
cfg = {...}
solver = init_pypk(cfg)
solver.set_matrices(m, k, q)
# Compute flutter solution
solver.compute()
solver.find_flutter()
solver.save(case_name)
solver.plot(case_name, show=True, format=fmt)
# Compute gradients (only available for NIPK)
solver.compute_gradients()

where cfg is a dict defining the configuration of the solution method, m, k and q are the mass, stiffness and aerodynamic force matrices provided as numpy array, and case_name and fmt are str. The variables are stored as public attributes of the solver and are listed in Solution.__init__(). PyPK has also been interfaced with OpenMDAO for performing flutter-constrained optimization, see OMFlut. Within that context, its builder must be imported using from pypk.api_om import PypkBuilder, then initialized with a configuration dictionary and provided to an OMFLut FlutterGroup as FlutterGroup(..., flutter=PypkBuilder(cfg)).

The configuration dictionary contains the following entries

'k_ref': numpy array, # reference reduced frequencies
'l_ref': float, # reference length (usually half root chord)
'mach': float, # freestream Mach number
'n_modes': int, # number of modes
'g_struct': float, # structural damping (complex proportional stiffness)
'rho_ks': float, # aggregation parameter for KS
'method': str, # method type ('pk' or 'nipk')
'vrb': int # verbosity level
'fluid': str, # fluid type ('unmatched' or 'matched_isa')
# IF 'fluid' is 'unmatched'
'rho_inf': float, # freesteam density
'u_idx': numpy array, # velocity index range
'mu': float, # mass ratio
'f_ref': float, # frequency of first torsional mode
# IF 'fluid' is 'mached_isa'
'alt': numpy array, # altitudes range