def run_wagner(self, Nsurf, integr_ord, RemovePred, UseSparse, RollNodes):
"""
see test_wagner
"""
### ----- set reference solution
self.setUp_from_params(Nsurf, integr_ord, RemovePred, UseSparse,
RollNodes)
tsaero0 = self.tsaero0
ws = self.ws
M = self.M
N = self.N
Mstar_fact = self.Mstar_fact
Uinf0 = self.Uinf0
### ----- linearisation
uvlm = linuvlm.Dynamic(tsaero0,
dynamic_settings=ws.config['LinearUvlm'])
uvlm.assemble_ss()
zeta_pole = np.array([0., 0., 0.])
uvlm.get_total_forces_gain(zeta_pole=zeta_pole)
uvlm.get_rigid_motion_gains(zeta_rotation=zeta_pole)
uvlm.get_sect_forces_gain()
### ----- Scale gains
Fref_tot = self.Fref_tot
Fref_span = self.Fref_span
uvlm.Kftot = uvlm.Kftot / Fref_tot
uvlm.Kmtot = uvlm.Kmtot / Fref_tot / ws.c_ref
uvlm.Kfsec /= Fref_span
uvlm.Kmsec /= (Fref_span * ws.c_ref)
### ----- step input
# rotate incoming flow, wing lattice and wing lattice speed about
# the (rolled) wing elastic axis to create an effective angle of attack.
# Rotation is expressed through a CRV.
delta_AlphaEffDeg = 1e-2
delta_AlphaEffRad = 1e-2 * np.pi / 180.
Roll0Rad = self.Roll0Deg / 180. * np.pi
dcrv = -delta_AlphaEffRad * np.array(
[0., np.cos(Roll0Rad), np.sin(Roll0Rad)])
uvec0 = np.array([Uinf0, 0, 0])
uvec = np.dot(algebra.crv2rotation(dcrv), uvec0)
duvec = uvec - uvec0
dzeta = np.zeros((Nsurf, 3, M + 1, N // Nsurf + 1))
dzeta_dot = np.zeros((Nsurf, 3, M + 1, N // Nsurf + 1))
du_ext = np.zeros((Nsurf, 3, M + 1, N // Nsurf + 1))
for ss in range(Nsurf):
for mm in range(M + 1):
for nn in range(N // Nsurf + 1):
dzeta_dot[ss, :, mm, nn] = -1. / 3 * duvec
du_ext[ss, :, mm, nn] = +1. / 3 * duvec
dzeta = 1. / 3 * np.dot(uvlm.Krot, dcrv)
Uaero = np.concatenate(
(dzeta.reshape(-1), dzeta_dot.reshape(-1), du_ext.reshape(-1)))
### ----- Steady state solution
xste, yste = uvlm.solve_steady(Uaero)
Ftot_ste = np.dot(uvlm.Kftot, yste)
Mtot_ste = np.dot(uvlm.Kmtot, yste)
# first check of gain matrices...
Ftot_ste_ref = np.zeros((3, ))
Mtot_ste_ref = np.zeros((3, ))
fnodes = yste.reshape((Nsurf, 3, M + 1, N // Nsurf + 1))
for ss in range(Nsurf):
for nn in range(N // Nsurf + 1):
for mm in range(M + 1):
Ftot_ste_ref += fnodes[ss, :, mm, nn]
Mtot_ste_ref += np.cross(uvlm.MS.Surfs[ss].zeta[:, mm, nn],
fnodes[ss, :, mm, nn])
Ftot_ste_ref /= Fref_tot
Mtot_ste_ref /= (Fref_tot * ws.c_ref)
Fmag = np.linalg.norm(Ftot_ste_ref)
er_f = np.max(np.abs(Ftot_ste - Ftot_ste_ref)) / Fmag
er_m = np.max(np.abs(Mtot_ste - Mtot_ste_ref)) / Fmag / ws.c_ref
assert (er_f < 1e-8 and er_m < 1e-8), \
'Error of total forces (%.2e) and moment (%.2e) too large!' % (er_f, er_m) + \
'Verify gains produced by linuvlm.Dynamic.get_total_forces_gain.'
# then compare against analytical ...
Cl_inf = delta_AlphaEffRad * np.pi * 2.
Cfvec_inf = Cl_inf * np.array(
[0., -np.sin(Roll0Rad), np.cos(Roll0Rad)])
er_f = np.abs(np.linalg.norm(Ftot_ste) / Cl_inf - 1.)
assert (er_f < 1e-2), \
'Error of total lift coefficient (%.2e) too large!' % (er_f,) + \
'Verify linuvlm.Dynamic.'
er_f = np.abs(np.linalg.norm(Ftot_ste - Cfvec_inf) / Cl_inf)
assert (er_f < 1e-2), \
'Error of total aero force (%.2e) too large!' % (er_f,) + \
'Verify linuvlm.Dynamic.'
# ... and finally compare against non-linear UVLM
# ps: here we roll the wing and rotate the incoming flow to generate an effective
# angle of attack
case_pert = 'wagner_r%.4daeff%.2d_rnodes%s_Nsurf%.2dM%.2dN%.2dwk%.2d' \
% (int(np.round(100 * self.Roll0Deg)),
int(np.round(100 * delta_AlphaEffDeg)),
RollNodes,
Nsurf, M, N, Mstar_fact)
ws_pert = flying_wings.QuasiInfinite(M=M,
N=N,
Mstar_fact=Mstar_fact,
n_surfaces=Nsurf,
u_inf=Uinf0,
alpha=self.Alpha0Deg,
roll=self.Roll0Deg,
aspect_ratio=1e5,
route=self.route_main,
case_name=case_pert,
RollNodes=RollNodes)
ws_pert.u_inf_direction = uvec / Uinf0
ws_pert.main_ea = ws.main_ea
ws_pert.clean_test_files()
ws_pert.update_derived_params()
ws_pert.generate_fem_file()
ws_pert.generate_aero_file()
# solution flow
ws_pert.set_default_config_dict()
ws_pert.config['SHARPy']['flow'] = ws.config['SHARPy']['flow']
ws_pert.config['SHARPy']['write_screen'] = 'off'
ws_pert.config['SHARPy']['write_log'] = 'off'
ws_pert.config['SHARPy'][
'log_folder'] = self.route_test_dir + '/output/' + self.case_code + '/'
ws_pert.config.write()
# solve at perturbed point
data_pert = sharpy.sharpy_main.main(
['...', self.route_main + case_pert + '.sharpy'])
tsaero = data_pert.aero.timestep_info[0]
self.start_writer()
# get total forces
Ftot_ste_pert = np.zeros((3, ))
Mtot_ste_pert = np.zeros((3, ))
for ss in range(Nsurf):
for nn in range(N // Nsurf + 1):
for mm in range(M + 1):
Ftot_ste_pert += tsaero.forces[ss][:3, mm, nn]
Mtot_ste_pert += np.cross(
uvlm.MS.Surfs[ss].zeta[:, mm, nn],
tsaero.forces[ss][:3, mm, nn])
Ftot_ste_pert /= Fref_tot
Mtot_ste_pert /= (Fref_tot * ws.c_ref)
Fmag = np.linalg.norm(Ftot_ste_pert)
er_f = np.max(np.abs(Ftot_ste - Ftot_ste_pert)) / Fmag
er_m = np.max(np.abs(Mtot_ste - Mtot_ste_pert)) / Fmag / ws.c_ref
assert (er_f < 2e-4 and er_m < 2e-4), \
'Error of total forces (%.2e) and moment (%.2e) ' % (er_f, er_m) + \
'with respect to geometrically-exact UVLM too large!'
# and check non-linear uvlm against analytical solution
er_f = np.abs(np.linalg.norm(Ftot_ste_pert - Cfvec_inf) / Cl_inf)
assert (er_f <= 1.5e-2), \
'Error of total aero force components (%.2e) too large!' % (er_f,) + \
'Verify StaticUvlm'
### ----- Analytical step response (Wagner solution)
NT = 251
tv = np.linspace(0., uvlm.dt * (NT - 1), NT)
Clv_an = an.wagner_imp_start(delta_AlphaEffRad, Uinf0, ws.c_ref, tv)
assert np.abs(Clv_an[-1] / Cl_inf - 1.) < 1e-2, \
'Did someone modify this test case?! The time should be enough to reach ' \
'the steady-state CL with a 1 perc. tolerance...'
Cfvec_an = np.zeros((NT, 3))
Cfvec_an[:, 1] = -np.sin(Roll0Rad) * Clv_an
Cfvec_an[:, 2] = np.cos(Roll0Rad) * Clv_an
### ----- Dynamic step response
Fsect = np.zeros((NT, Nsurf, 3, N // Nsurf + 1))
# Fbeam=np.zeros((NT,6,N//Nsurf+1))
Ftot = np.zeros((NT, 3))
Er_f_tot = np.zeros((NT, ))
# Ybeam=[]
gamma = np.zeros((NT, Nsurf, M, N // Nsurf))
gamma_dot = np.zeros((NT, Nsurf, M, N // Nsurf))
gamma_star = np.zeros((NT, Nsurf, int(M * Mstar_fact), N // Nsurf))
xold = np.zeros((uvlm.SS.A.shape[0], ))
for tt in range(1, NT):
xnew, ynew = uvlm.solve_step(xold, Uaero)
change = np.linalg.norm(xnew - xold)
xold = xnew
# record state ?
if uvlm.remove_predictor is False:
gv, gvstar, gvdot = uvlm.unpack_state(xnew)
gamma[tt, :, :, :] = gv.reshape((Nsurf, M, N // Nsurf))
gamma_dot[tt, :, :, :] = gvdot.reshape((Nsurf, M, N // Nsurf))
gamma_star[tt, :, :, :] = gvstar.reshape(
(Nsurf, int(M * Mstar_fact), N // Nsurf))
# calculate forces (and error)
Ftot[tt, :3] = np.dot(uvlm.Kftot, ynew)
Er_f_tot[tt] = np.linalg.norm(Ftot[tt, :] -
Cfvec_an[tt, :]) / Clv_an[tt]
Fsect[tt, :, :, :] = np.dot(uvlm.Kfsec, ynew).reshape(
(Nsurf, 3, N // Nsurf + 1))
# ### beam forces
# Ybeam.append(np.dot(Sol.Kforces[:-10,:],ynew))
# Fdummy=Ybeam[-1].reshape((N//Nsurf,6)).T
# Fbeam[tt,:,:N//Nsurf]=Fdummy[:,:N//Nsurf]
# Fbeam[tt,:,N//Nsurf+1:]=Fdummy[:,N//Nsurf:]
if RemovePred:
ts2perc, ts1perc = 6, 6
else:
ts2perc, ts1perc = 16, 36
er_th_2perc = np.max(Er_f_tot[ts2perc:])
er_th_1perc = np.max(Er_f_tot[ts1perc:])
### ----- generate plot
if self.ProducePlots:
# sections to plot
if Nsurf == 1:
Nplot = [0, N // 2, N]
labs = [r'tip', r'root', r'tip']
elif Nsurf == 2:
Nplot = [0, N // 2 - 1]
labs = [r'tip', r'near root', r'tip', r'near root']
axtitle = [r'$C_{F_y}$', r'$C_{F_z}$']
# non-dimensional time
sv = 2.0 * Uinf0 * tv / ws.c_ref
# generate figure
clist = ['#003366', '#CC3333', '#336633', '#FF6600'] * 4
fontlabel = 12
std_params = {
'legend.fontsize': 10,
'font.size': fontlabel,
'xtick.labelsize': fontlabel - 2,
'ytick.labelsize': fontlabel - 2,
'figure.autolayout': True,
'legend.numpoints': 1
}
# plt.rcParams.update(std_params)
# fig = plt.figure('Lift time-history', (12, 6))
# axvec = fig.subplots(1, 2)
# for aa in [0, 1]:
# comp = aa + 1
# axvec[aa].set_title(axtitle[aa])
# axvec[aa].plot(sv, Cfvec_an[:, comp] / Cl_inf, lw=4, ls='-',
# alpha=0.5, color='r', label=r'Wagner')
# axvec[aa].plot(sv, Ftot[:, comp] / Cl_inf, lw=5, ls=':',
# alpha=0.7, color='k', label=r'Total')
# cc = 0
# for ss in range(Nsurf):
# for nn in Nplot:
# axvec[aa].plot(sv, Fsect[:, ss, comp, nn] / Cl_inf,
# lw=4 - cc, ls='--', alpha=0.7, color=clist[cc],
# label=r'Surf. %.1d, n=%.2d (%s)' % (ss, nn, labs[cc]))
# cc += 1
# axvec[aa].grid(color='0.8', ls='-')
# axvec[aa].grid(color='0.85', ls='-', which='minor')
# axvec[aa].set_xlabel(r'normalised time $t=2 U_\infty \tilde{t}/c$')
# axvec[aa].set_ylabel(axtitle[aa] + r'$/C_{l_\infty}$')
# axvec[aa].set_xlim(0, sv[-1])
# if Cfvec_inf[comp] > 0.:
# axvec[aa].set_ylim(0, 1.1)
# else:
# axvec[aa].set_ylim(-1.1, 0)
# plt.legend(ncol=1)
# # plt.show()
# fig.savefig(self.figfold + self.case_main + '.png')
# fig.savefig(self.figfold + self.case_main + '.pdf')
# plt.close()
assert er_th_2perc < 2e-2 and er_th_1perc < 1e-2, \
'Error of dynamic step response at time-steps 16 and 36 ' + \
'(%.2e and %.2e) too large. Verify Linear UVLM.' % (er_th_2perc, er_th_1perc)
def __init__(self,
data,
custom_settings_linear=None,
uvlm_block=False,
chosen_ts=None):
self.data = data
if custom_settings_linear is None:
settings_here = data.settings['LinearUvlm']
else:
settings_here = custom_settings_linear
sharpy.utils.settings.to_custom_types(settings_here,
linuvlm.settings_types_dynamic,
linuvlm.settings_default_dynamic)
if chosen_ts is None:
self.chosen_ts = self.data.ts
else:
self.chosen_ts = chosen_ts
## TEMPORARY - NEED TO INCLUDE PROPER INTEGRATION OF SETTINGS
try:
self.rigid_body_motions = settings_here['rigid_body_motion']
except KeyError:
self.rigid_body_motions = False
try:
self.use_euler = settings_here['use_euler']
except KeyError:
self.use_euler = False
if self.rigid_body_motions and settings_here['track_body']:
self.track_body = True
else:
self.track_body = False
## -------
### extract aeroelastic info
self.dt = settings_here['dt'].value
### reference to timestep_info
# aero
aero = data.aero
self.tsaero = aero.timestep_info[self.chosen_ts]
# structure
structure = data.structure
self.tsstr = structure.timestep_info[self.chosen_ts]
# --- backward compatibility
try:
rho = settings_here['density'].value
except KeyError:
warnings.warn(
"Key 'density' not found in 'LinearUvlm' solver settings. '\
'Trying to read it from 'StaticCoupled'."
)
rho = data.settings['StaticCoupled']['aero_solver_settings']['rho']
if type(rho) == str:
rho = np.float(rho)
if hasattr(rho, 'value'):
rho = rho.value
self.tsaero.rho = rho
# --- backward compatibility
### gebm
if self.use_euler:
self.num_dof_rig = 9
else:
self.num_dof_rig = 10
self.num_dof_flex = np.sum(self.data.structure.vdof >= 0) * 6
self.num_dof_str = self.num_dof_flex + self.num_dof_rig
self.reshape_struct_input()
try:
beam_settings = settings_here['beam_settings']
except KeyError:
beam_settings = dict()
self.lingebm_str = lingebm.FlexDynamic(self.tsstr, structure,
beam_settings)
cga = algebra.quat2rotation(self.tsstr.quat)
### uvlm
if uvlm_block:
self.linuvlm = linuvlm.DynamicBlock(
self.tsaero,
dt=settings_here['dt'].value,
dynamic_settings=settings_here,
RemovePredictor=settings_here['remove_predictor'].value,
UseSparse=settings_here['use_sparse'].value,
integr_order=settings_here['integr_order'].value,
ScalingDict=settings_here['ScalingDict'],
for_vel=np.hstack((cga.dot(self.tsstr.for_vel[:3]),
cga.dot(self.tsstr.for_vel[3:]))))
else:
self.linuvlm = linuvlm.Dynamic(
self.tsaero,
dt=settings_here['dt'].value,
dynamic_settings=settings_here,
RemovePredictor=settings_here['remove_predictor'].value,
UseSparse=settings_here['use_sparse'].value,
integr_order=settings_here['integr_order'].value,
ScalingDict=settings_here['ScalingDict'],
for_vel=np.hstack((cga.dot(self.tsstr.for_vel[:3]),
cga.dot(self.tsstr.for_vel[3:]))))
def initialise(self, data, custom_settings=None):
if custom_settings:
self.settings = custom_settings
else:
try:
self.settings = data.settings['LinearAssembler'][
'linear_system_settings'] # Load settings, the settings should be stored in data.linear.settings
except KeyError:
pass
settings.to_custom_types(self.settings,
self.settings_types,
self.settings_default,
self.settings_options,
no_ctype=True)
settings.to_custom_types(self.settings['ScalingDict'],
self.scaling_settings_types,
self.scaling_settings_default,
no_ctype=True)
data.linear.tsaero0.rho = float(self.settings['density'])
self.scaled = not all(
scale == 1.0 for scale in self.settings['ScalingDict'].values())
for_vel = data.linear.tsstruct0.for_vel
cga = data.linear.tsstruct0.cga()
uvlm = linuvlm.Dynamic(data.linear.tsaero0,
dt=None,
dynamic_settings=self.settings,
for_vel=np.hstack((cga.dot(for_vel[:3]),
cga.dot(for_vel[3:]))))
self.tsaero0 = data.linear.tsaero0
self.sys = uvlm
input_variables_database = {
'zeta': [0, 3 * self.sys.Kzeta],
'zeta_dot': [3 * self.sys.Kzeta, 6 * self.sys.Kzeta],
'u_gust': [6 * self.sys.Kzeta, 9 * self.sys.Kzeta]
}
state_variables_database = {
'gamma': [0, self.sys.K],
'gamma_w': [self.sys.K, self.sys.K_star],
'dtgamma_dot':
[self.sys.K + self.sys.K_star, 2 * self.sys.K + self.sys.K_star],
'gamma_m1': [
2 * self.sys.K + self.sys.K_star,
3 * self.sys.K + self.sys.K_star
]
}
self.linearisation_vectors['zeta'] = np.concatenate([
self.tsaero0.zeta[i_surf].reshape(-1, order='C')
for i_surf in range(self.tsaero0.n_surf)
])
self.linearisation_vectors['zeta_dot'] = np.concatenate([
self.tsaero0.zeta_dot[i_surf].reshape(-1, order='C')
for i_surf in range(self.tsaero0.n_surf)
])
self.linearisation_vectors['u_ext'] = np.concatenate([
self.tsaero0.u_ext[i_surf].reshape(-1, order='C')
for i_surf in range(self.tsaero0.n_surf)
])
self.linearisation_vectors['forces_aero'] = np.concatenate([
self.tsaero0.forces[i_surf][:3].reshape(-1, order='C')
for i_surf in range(self.tsaero0.n_surf)
])
self.input_variables = ss_interface.LinearVector(
input_variables_database, self.sys_id)
self.state_variables = ss_interface.LinearVector(
state_variables_database, self.sys_id)
if data.aero.n_control_surfaces >= 1:
import sharpy.linear.assembler.lincontrolsurfacedeflector as lincontrolsurfacedeflector
self.control_surface = lincontrolsurfacedeflector.LinControlSurfaceDeflector(
)
self.control_surface.initialise(data, uvlm)
if self.settings['rom_method'] != '':
# Initialise ROM
self.rom = dict()
for rom_name in self.settings['rom_method']:
self.rom[rom_name] = rom_interface.initialise_rom(rom_name)
self.rom[rom_name].initialise(
self.settings['rom_method_settings'][rom_name])
if 'u_gust' not in self.settings['remove_inputs'] and self.settings[
'gust_assembler'] == 'leading_edge':
import sharpy.linear.assembler.lineargustassembler as lineargust
self.gust_assembler = lineargust.LinearGustGenerator()
self.gust_assembler.initialise(data.aero)