def test_flat_rotation_about_zero(self):
'''
Calculate steady case / very short wake can be used. A flat plate at
at zero angle of attack is taken as reference condition. The state is
perturbed of an angle dalpha.
'''
MList = [1, 8, 16]
DAlphaList = [0.1, 0.5, 1., 2., 4., 6., 8., 10., 12., 14.] # degs
Nm = len(MList)
Na = len(DAlphaList)
CDlin, CLlin = np.zeros((Na, Nm)), np.zeros((Na, Nm))
CDnnl, CLnnl = np.zeros((Na, Nm)), np.zeros((Na, Nm))
for mm in range(len(MList)):
# input: reference condition: flat plate at zero angle
Mw = 2
M = MList[mm]
alpha = 0. * np.pi / 180.
chord = 3.
b = 0.5 * chord
Uinf = np.array([20., 0.])
rho = 1.225
S0 = uvlm.solver(M, Mw, b, Uinf, alpha, rho=1.225)
S0.build_flat_plate()
S0.solve_static_Gamma2d()
print('Testing steady aerofoil for M=%d...' % M)
for aa in range(len(DAlphaList)):
# Perturbation
dalpha = np.pi / 180. * DAlphaList[aa] # angle [rad]
dUinf = 0.0 # velocity [m/s]
qinf_tot = 0.5 * rho * (S0.Uabs + dUinf)**2
print('\talpha==%.2f deg' % DAlphaList[aa])
### Linearised solution
# Perturb reference state
ZetaRot = geo.rotate_aerofoil(S0.Zeta, dalpha)
dZeta = ZetaRot - S0.Zeta
Slin = linuvlm.solver(S0)
Slin.Zeta = dZeta
# solve
Slin.solve_static_Gamma2d()
# store data
CDlin[aa,mm],CLlin[aa,mm]=np.sum(Slin.Faero,0)/\
(qinf_tot*Slin.S0.chord*(alpha+dalpha))
### Reference nonlinear solution
Sref = uvlm.solver(M, Mw, b, Uinf, alpha + dalpha, rho)
Sref.build_flat_plate()
# solve
Sref.solve_static_Gamma2d()
# store
CDnnl[aa,mm],CLnnl[aa,mm]=np.sum(Sref.Faero,0)/\
(qinf_tot*Sref.chord*(alpha+dalpha))
clist = [
'k',
'r',
'b',
'0.6',
]
fig = plt.figure('Aerodynamic coefficients', (12, 4))
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)
for mm in range(Nm):
#
ax1.plot(DAlphaList,
CDlin[:, mm],
clist[mm],
lw=Nm - mm,
ls='--',
label=r'M=%.2d lin' % MList[mm])
ax1.plot(DAlphaList,
CDnnl[:, mm],
clist[mm],
lw=Nm - mm,
label=r'M=%.2d nnl' % MList[mm])
#
ax2.plot(DAlphaList,
CLlin[:, mm],
clist[mm],
lw=Nm - mm,
ls='--',
label=r'M=%.2d lin' % MList[mm])
ax2.plot(DAlphaList,
CLnnl[:, mm],
clist[mm],
lw=Nm - mm,
label=r'M=%.2d nnl' % MList[mm])
ax1.set_xlabel(r'\alpha [deg]')
ax1.set_title(r'CD')
ax1.legend()
ax2.set_xlabel(r'\alpha [deg]')
ax2.set_title(r'CL')
ax2.legend()
if self.SHOW_PLOT: plt.show()
else: plt.close()
def test_impulse(self):
'''
Impulsive start (with/out Hall's correction) against Wagner solution
'''
print('Testing aerofoil impulsive start...')
# set-up
M = 20
WakeFact = 20
c = 3.
b = 0.5 * c
uinf = 20.0
aeff = 0.1 * np.pi / 180.
T = 8.0
### reference static solution - at zero - Hall's correction
S0 = uvlm2d_sta.solver(M=M,
Mw=M * WakeFact,
b=b,
Uinf=np.array([uinf, 0.]),
alpha=0.0,
rho=1.225)
S0.build_flat_plate()
S0.solve_static_Gamma2d()
Ftot0 = np.sum(S0.Faero, 0)
Slin1 = lin_uvlm2d_dyn.solver(S0, T=T)
ZetaRot = geo.rotate_aerofoil(S0.Zeta, aeff)
dZeta = ZetaRot - S0.Zeta
Slin1.Zeta = dZeta
for tt in range(Slin1.NT):
Slin1.THZeta[tt, :, :] = dZeta
Slin1._imp_start = True
Slin1.eps_Hall = 0.003
Slin1.solve_dyn_Gamma2d()
### reference static solution - at zero - no Hall's correction
S0 = uvlm2d_sta.solver(M=M,
Mw=M * WakeFact,
b=b,
Uinf=np.array([uinf, 0.]),
alpha=0.0,
rho=1.225)
S0.build_flat_plate()
S0.eps_Hall = 1.0
S0.solve_static_Gamma2d()
Slin2 = lin_uvlm2d_dyn.solver(S0, T=T)
Slin2.Zeta = dZeta
for tt in range(Slin2.NT):
Slin2.THZeta[tt, :, :] = dZeta
Slin2._imp_start = True
Slin2.eps_Hall = 1.0
Slin2.solve_dyn_Gamma2d()
### Analytical solution
CLv_an = an.wagner_imp_start(aeff, uinf, c, Slin1.time)
##### Post-process numerical solution - Hall's correction
THFtot1 = 0.0 * Slin1.THFaero
for tt in range(Slin1.NT):
THFtot1[tt, :] = Slin1.THFaero[tt, :] + Ftot0
THCFtot1 = THFtot1 / S0.qinf / S0.chord
# Mass and circulatory contribution
THCFmass1 = Slin1.THFaero_m / S0.qinf / S0.chord
THCFcirc1 = THCFtot1 - THCFmass1
##### Post-process numerical solution - no Hall's correction
THFtot2 = 0.0 * Slin2.THFaero
for tt in range(Slin2.NT):
THFtot2[tt, :] = Slin2.THFaero[tt, :] + Ftot0
THCFtot2 = THFtot2 / S0.qinf / S0.chord
# Mass and circulatory contribution
THCFmass2 = Slin2.THFaero_m / S0.qinf / S0.chord
THCFcirc2 = THCFtot2 - THCFmass2
plt.close('all')
# non-dimensional time
sv = 2.0 * S0.Uabs * Slin1.time / S0.chord
fig = plt.figure('Lift coefficient', (10, 6))
ax = fig.add_subplot(111)
# Wagner
ax.plot(0.5 * sv, CLv_an, '0.6', lw=3, label='An Tot')
# numerical
ax.plot(0.5 * sv, THCFtot1[:, 1], 'k', lw=1, label='Num Tot - Hall')
ax.plot(0.5 * sv, THCFmass1[:, 1], 'b', lw=1, label='Num Mass - Hall')
ax.plot(0.5 * sv, THCFcirc1[:, 1], 'r', lw=1, label='Num Jouk - Hall')
# numerical
ax.plot(0.5 * sv, THCFtot2[:, 1], 'k--', lw=2, label='Num Tot')
ax.plot(0.5 * sv, THCFmass2[:, 1], 'b--', lw=2, label='Num Mass')
ax.plot(0.5 * sv, THCFcirc2[:, 1], 'r--', lw=2, label='Num Jouk')
ax.set_xlabel(r'$s/2=U_\infty t/c$')
ax.set_ylabel('force')
ax.set_title('Lift')
ax.legend()
fig2 = plt.figure('Lift coefficient - zoom', (10, 6))
ax = fig2.add_subplot(111)
# Wagner
ax.plot(0.5 * sv, CLv_an, '0.6', lw=3, label='An Tot')
# numerical
ax.plot(0.5 * sv, THCFtot1[:, 1], 'k', lw=1, label='Num Tot - Hall')
ax.plot(0.5 * sv, THCFmass1[:, 1], 'b', lw=1, label='Num Mass - Hall')
ax.plot(0.5 * sv, THCFcirc1[:, 1], 'r', lw=1, label='Num Jouk - Hall')
# numerical
ax.plot(0.5 * sv, THCFtot2[:, 1], 'k--', lw=2, label='Num Tot')
ax.plot(0.5 * sv, THCFmass2[:, 1], 'b--', lw=2, label='Num Mass')
ax.plot(0.5 * sv, THCFcirc2[:, 1], 'r--', lw=2, label='Num Jouk')
ax.set_xlabel(r'$s/2=U_\infty t/c$')
ax.set_ylabel('force')
ax.set_title('Lift')
ax.legend()
ax.set_xlim(0., 6.)
fig3 = plt.figure("Lift coefficient - Hall's correction effect",
(10, 6))
ax = fig3.add_subplot(111)
# Wagner
ax.plot(0.5 * sv, CLv_an, '0.6', lw=3, label='An Tot')
# numerical
ax.plot(0.5 * sv, THCFtot1[:, 1], 'k', lw=1, label='Num Tot - Hall')
ax.plot(0.5 * sv, THCFmass1[:, 1], 'b', lw=1, label='Num Mass - Hall')
ax.plot(0.5 * sv, THCFcirc1[:, 1], 'r', lw=1, label='Num Jouk - Hall')
# numerical
ax.plot(0.5 * sv, THCFtot2[:, 1], 'k--', lw=2, label='Num Tot')
ax.plot(0.5 * sv, THCFmass2[:, 1], 'b--', lw=2, label='Num Mass')
ax.plot(0.5 * sv, THCFcirc2[:, 1], 'r--', lw=2, label='Num Jouk')
ax.set_xlabel(r'$s/2=U_\infty t/c$')
ax.set_ylabel('force')
ax.set_title('Lift')
ax.legend()
ax.set_xlim(15., 0.5 * sv[-1])
ax.set_ylim(0.10, 0.116)
fig = plt.figure('Drag coefficient', (10, 6))
ax = fig.add_subplot(111)
ax.plot(Slin1.time, THCFtot1[:, 0], 'k', label='Num Tot')
ax.plot(Slin1.time, THCFmass1[:, 0], 'b', label='Num Mass')
ax.plot(Slin1.time, THCFcirc1[:, 0], 'r', label='Num Jouk')
ax.plot(Slin1.time, THCFtot2[:, 0], 'k', label='Num Tot')
ax.plot(Slin1.time, THCFmass2[:, 0], 'b', label='Num Mass')
ax.plot(Slin1.time, THCFcirc2[:, 0], 'r', label='Num Jouk')
ax.set_xlabel('time')
ax.set_ylabel('force')
ax.set_title('Drag')
ax.legend()
fig = plt.figure('Vortex rings circulation time history', (10, 6))
ax = fig.add_subplot(111)
clist = ['0.2', '0.4', '0.6']
Mlist = [0, int(S0.M / 2), S0.M - 1]
for kk in range(len(Mlist)):
mm = Mlist[kk]
ax.plot(Slin1.time,
Slin1.THGamma[:, mm],
color=clist[kk],
label='M=%.2d - Hall' % (mm))
clist = ['r', 'y', 'b']
MWlist = [0, int(S0.Mw / 2), S0.Mw - 1]
for kk in range(len(MWlist)):
mm = Mlist[kk]
ax.plot(Slin1.time,
Slin1.THGammaW[:, mm],
color=clist[kk],
label='Mw=%.2d - Hall' % (mm))
clist = ['0.2', '0.4', '0.6']
Mlist = [0, int(S0.M / 2), S0.M - 1]
for kk in range(len(Mlist)):
mm = Mlist[kk]
ax.plot(Slin2.time,
Slin2.THGamma[:, mm],
color=clist[kk],
linestyle='--',
label='M=%.2d' % (mm))
clist = ['r', 'y', 'b']
MWlist = [0, int(S0.Mw / 2), S0.Mw - 1]
for kk in range(len(MWlist)):
mm = Mlist[kk]
ax.plot(Slin2.time,
Slin2.THGammaW[:, mm],
color=clist[kk],
linestyle='--',
label='Mw=%.2dl' % (mm))
ax.set_xlabel('time')
ax.set_ylabel('Gamma')
ax.legend(ncol=2)
if self.SHOW_PLOT: plt.show()
else: plt.close()
# Final error
ErCDend = np.abs(THCFtot1[-1, 0])
ErCDend2 = np.abs(THCFtot2[-1, 0])
ErCLend = np.abs(THCFtot1[-1, 1] - CLv_an[-1]) / CLv_an[-1]
ErCLend2 = np.abs(THCFtot2[-1, 1] - CLv_an[-1]) / CLv_an[-1]
# Expected values
CLexp = 0.010914578545119
CLexp2 = 0.010964883644861
changeCLnum = np.abs(THCFtot1[-1, 1] - CLexp)
changeCLnum2 = np.abs(THCFtot2[-1, 1] - CLexp2)
# Check/raise error
self.assertTrue(
ErCDend < 1e-15,
msg=
'Final CD %.2e (with Hall correction) above limit value of %.2e!' %
(ErCDend, self.TOL_analytical))
self.assertTrue(
ErCDend2 < 1e-15,
msg=
'Final CD %.2e (without Hall correction) above limit value of %.2e!'
% (ErCDend2, self.TOL_analytical))
tolCL, tolCL2 = 0.4e-2, 0.2e-2
self.assertTrue(ErCLend<tolCL,msg='Relative CL error %.2e '\
'(with Hall correction) above tolerance %.2e!' %(ErCLend,tolCL))
self.assertTrue(ErCLend2<tolCL2,msg='Relative CL error %.2e '\
'(without Hall correction) above tolerance %.2e!'%(ErCLend2,tolCL2))
if changeCLnum > self.TOL_numerical:
warnings.warn('Relative change in CL numerical solution '\
'(with Hall correction) of %.2e !!!'%changeCLnum)
if changeCLnum2 > self.TOL_numerical:
warnings.warn('Relative change in CL numerical solution '\
'(without Hall correction) of %.2e !!!'%changeCLnum2)
def test_camber_rotation(self):
'''
Calculate steady case / very short wake can be used. A cambered aerofoil
is tested at different angles of attack. Two linearisations, about zero
and 10deg are used.
'''
DAlphaList = [
0.0, 0.1, 0.2, 0.3, 0.5, 1., 2., 4., 6., 8., 9.5, 9.7, 9.8, 9.9,
10., 10.1, 10.2, 10.3, 10.5, 12., 14., 16., 18.
] # degs
MList = [20]
Nm, mm = 1, 0
Na = len(DAlphaList)
Llin01, Dlin01 = np.zeros((Na, Nm)), np.zeros((Na, Nm))
Llin02, Dlin02 = np.zeros((Na, Nm)), np.zeros((Na, Nm))
Lnnl, Dnnl = np.zeros((Na, Nm)), np.zeros((Na, Nm))
# input:
Mw = 2
M = MList[mm]
chord = 3.
b = 0.5 * chord
Uinf = np.array([20., 0.])
rho = 1.225
# reference condition 1: aerofoil at 0 deg angle
alpha01 = 0. * np.pi / 180.
S01 = uvlm.solver(M, Mw, b, Uinf, alpha01, rho=1.225)
S01.build_camber_plate(Mcamb=10, Pcamb=4)
S01.solve_static_Gamma2d()
Fref01 = np.sum(S01.Faero, 0)
# reference condition 2: aerofoil at 10 deg angle
alpha02 = 10. * np.pi / 180.
S02 = uvlm.solver(M, Mw, b, Uinf, alpha02, rho=1.225)
S02.build_camber_plate(Mcamb=10, Pcamb=4)
S02.solve_static_Gamma2d()
Fref02 = np.sum(S02.Faero, 0)
print('Testing steady aerofoil for M=%d...' % M)
for aa in range(len(DAlphaList)):
# Perturbation
alpha_tot = np.pi / 180. * DAlphaList[aa]
dUinf = 0.0 # velocity [m/s]
qinf_tot = 0.5 * rho * (S01.Uabs + dUinf)**2
print('\talpha==%.2f deg' % DAlphaList[aa])
### Linearised solution 01:
# Perturb reference state
dalpha01 = alpha_tot - alpha01 # angle [rad]
ZetaRot = geo.rotate_aerofoil(S01.Zeta, dalpha01)
dZeta = ZetaRot - S01.Zeta
Slin01 = linuvlm.solver(S01)
Slin01.Zeta = dZeta
# solve
Slin01.solve_static_Gamma2d()
# store data
dFtot01 = np.sum(Slin01.Faero, 0)
Dlin01[aa, mm], Llin01[aa, mm] = dFtot01 + Fref01
### Linearised solution 02:
# Perturb reference state
dalpha02 = alpha_tot - alpha02 # angle [rad]
ZetaRot = geo.rotate_aerofoil(S02.Zeta, dalpha02)
dZeta = ZetaRot - S02.Zeta
Slin02 = linuvlm.solver(S02)
Slin02.Zeta = dZeta
# solve
Slin02.solve_static_Gamma2d()
# store data
dFtot02 = np.sum(Slin02.Faero, 0)
Dlin02[aa, mm], Llin02[aa, mm] = dFtot02 + Fref02
### Reference nonlinear solution
Sref = uvlm.solver(M, Mw, b, Uinf, alpha_tot, rho)
Sref.build_camber_plate(Mcamb=10, Pcamb=4)
# solve
Sref.solve_static_Gamma2d()
# store
Dnnl[aa, mm], Lnnl[aa, mm] = np.sum(Sref.Faero, 0)
clist = [
'k',
'r',
'b',
'0.6',
]
### Aerodynamic forces
fig1 = plt.figure('Drag', (12, 4))
fig2 = plt.figure('Lift', (12, 4))
ax1 = fig1.add_subplot(111)
ax2 = fig2.add_subplot(111)
ax1.plot(DAlphaList,
Dnnl[:, mm],
'r',
lw=Nm - mm,
label=r'M=%.2d nnl' % MList[mm])
ax1.plot(DAlphaList,
Dlin01[:, mm],
'k',
lw=2,
ls='--',
label=r'M=%.2d lin 0 deg' % MList[mm])
ax1.plot(DAlphaList,
Dlin02[:, mm],
'b',
lw=2,
ls=':',
label=r'M=%.2d lin 10 deg' % MList[mm])
#
ax2.plot(DAlphaList,
Lnnl[:, mm],
'r',
lw=2,
label=r'M=%.2d nnl' % MList[mm])
ax2.plot(DAlphaList,
Llin01[:, mm],
'k',
lw=2,
ls='--',
label=r'M=%.2d lin 0 deg' % MList[mm])
ax2.plot(DAlphaList,
Llin02[:, mm],
'b',
lw=Nm - mm,
ls=':',
label=r'M=%.2d lin 10 deg' % MList[mm])
ax1.set_xlabel(r'\alpha [deg]')
ax1.set_title(r'Drag')
ax1.legend()
ax2.set_xlabel(r'\alpha [deg]')
ax2.set_title(r'Lift')
ax2.legend()
fig1 = plt.figure('Relative error lift', (12, 4))
ax1 = fig1.add_subplot(111)
ax1.plot(DAlphaList,
Llin01[:, mm] / Lnnl[:, mm] - 1.,
'k',
lw=2,
ls='--',
label=r'M=%.2d lin 0 deg' % MList[mm])
ax1.plot(DAlphaList,
Llin02[:, mm] / Lnnl[:, mm] - 1.,
'b',
lw=2,
ls=':',
label=r'M=%.2d lin 10 deg' % MList[mm])
ax1.set_xlabel(r'$\alpha$ [deg]')
ax1.set_ylabel(r'relative error')
ax1.set_title(r'Lift error w.r.t. exact solution')
ax1.legend()
ax2.legend()
if self.SHOW_PLOT: plt.show()
else: plt.close()
def test_steady(self):
'''
Calculate steady case / very short wake can be used.
'''
### random geometry
c = 3.
b = 0.5 * c
uinf = 20.0
T = 1.0
WakeFact = 2
alpha0 = 1.00 * np.pi / 180.
dalpha = 2.00 * np.pi / 180.
alpha_tot = alpha0 + dalpha
TimeList = []
THCFList = []
MList = [4, 8, 16]
for mm in range(len(MList)):
M = MList[mm]
print('Testing steady aerofoil M=%d...' % M)
### reference solution (static)
S0 = uvlm2d_sta.solver(M=M,
Mw=M * WakeFact,
b=b,
Uinf=np.array([uinf, 0.]),
alpha=alpha0,
rho=1.225)
S0.build_flat_plate()
S0.eps_Hall = 1.0 # no correction
S0.solve_static_Gamma2d()
Ftot0 = np.sum(S0.Faero, 0)
### linearisation
Slin = lin_uvlm2d_dyn.solver(S0, T)
# perturb reference state
ZetaRot = geo.rotate_aerofoil(S0.Zeta, dalpha)
dZeta = ZetaRot - S0.Zeta
Slin.Zeta = dZeta
for tt in range(Slin.NT):
Slin.THZeta[tt, :, :] = dZeta
# solve
Slin.solve_dyn_Gamma2d()
# total force
THFtot = 0.0 * Slin.THFaero
for tt in range(Slin.NT):
THFtot[tt, :] = Slin.THFaero[tt, :] + Ftot0
TimeList.append(Slin.time)
THCFList.append(THFtot / S0.qinf / S0.chord)
clist = [
'k',
'r',
'b',
'0.6',
]
fig = plt.figure('Aerodynamic forces', (12, 4))
ax = fig.add_subplot(131)
for mm in range(len(MList)):
ax.plot(TimeList[mm],
THCFList[mm][:, 1],
clist[mm],
label=r'M=%.2d' % MList[mm])
ax.set_xlabel('time [s]')
ax.set_title('Lift coefficient')
ax.legend()
ax = fig.add_subplot(132)
for mm in range(len(MList)):
ax.plot(TimeList[mm],
THCFList[mm][:, 1] / alpha_tot,
clist[mm],
label=r'M=%.2d' % MList[mm])
ax.set_xlabel('time [s]')
ax.set_title('CL alpha')
ax.legend()
ax = fig.add_subplot(133)
for mm in range(len(MList)):
ax.plot(TimeList[mm],
THCFList[mm][:, 0],
clist[mm],
label=r'M=%.2d' % MList[mm])
ax.set_xlabel('time [s]')
ax.set_title('Drag coefficient')
ax.legend()
if self.SHOW_PLOT: plt.show()
else: plt.close()
### Testing
maxDrag = 0.0
ClaExpected = 2. * np.pi
ClaError = 0.0
for mm in range(len(MList)):
# zero drag
maxDragHere = np.max(np.abs(THCFList[mm][:, 0]))
if maxDragHere > maxDrag: maxDrag = maxDragHere
# Cla relative error
maxClaErrorHere = np.max(
np.abs(THCFList[mm][:, 1] / alpha_tot / ClaExpected - 1.0))
if maxClaErrorHere > ClaError: ClaError = maxClaErrorHere
self.assertTrue(maxDragHere<self.TOL_zero,msg=\
'Max Drag %.2e above tolerance %.2e!' %(maxDragHere,self.TOL_zero))
self.assertTrue(maxClaErrorHere < self.TOL_analytical,
msg='Cla error %.2e'
' above tolerance %.2e!' %
(maxClaErrorHere, self.TOL_analytical))