def test_linVnln(self):
"""Test ss UVLM output equations against full nonlinear calcs."""
# Init steady problem at 1 deg AoA
aoa = 1 * np.pi / 180.0
V = 1
m = 2
n = 2
mW = 3
delS = 1
chords = np.linspace(-1.0, 0.0, m + 1, True)
chordsW = np.linspace(0.0, 10000.0, mW + 1, True)
spans = np.linspace(-10000, 10000, n + 1, True)
zeta0 = np.zeros(3 * len(chords) * len(spans))
zetaW0 = np.zeros(3 * len(chordsW) * len(spans))
kk = 0
for c in chords:
for s in spans:
zeta0[3 * kk] = np.cos(aoa) * c
zeta0[3 * kk + 1] = s
zeta0[3 * kk + 2] = -np.sin(aoa) * c
kk = kk + 1
# end for s
# end for c
kk = 0
for c in chordsW:
for s in spans:
zetaW0[3 * kk] = c
zetaW0[3 * kk + 1] = s
kk = kk + 1
# end for s
# end for c
zetaPri0 = np.zeros((3 * len(chords) * len(spans)))
gamPri0 = np.zeros((m * n))
nu = np.zeros((3 * len(chords) * len(spans))) # atmospheric velocity
nu[0::3] = V
# to be solved
gam0 = np.zeros((m * n))
gamW0 = np.zeros((mW * n))
f0 = np.zeros((3 * len(chords) * len(spans))) # forces
# initialise nonlinear options
VMOPTS = VMopts(
m,
n,
False, # image methods
mW,
True, # steady
True, # KJ is true
True,
delS,
False,
1) #numCores
# solve nonlinear
Cpp_Solver_VLM(zeta0, zetaPri0, nu, zetaW0, VMOPTS, f0, gam0, gamW0)
# generate linear output eqs at x0, u0
foo1, foo2, foo3, C, D = genSSuvlm(gam0, gamW0, gamPri0, zeta0, zetaW0,
zetaPri0, nu, m, n, mW, delS)
del foo1, foo2, foo3
# init delta vectors for testing
dX = np.zeros((2 * m * n + mW * n))
dU = np.zeros((9 * len(chords) * len(spans)))
# variations in gamma--------------------------------------------------
for i in range(m * n):
dX[i] = 0.00002 / (m * n) * (i + 1)
gamPdX = gam0 + dX[0:m * n]
f = np.zeros_like(f0)
gam_tm1 = gam0 - delS * gamPri0
Cpp_KJForces(zeta0, gamPdX, zetaW0, gamW0, zetaPri0, nu, VMOPTS,
gam_tm1, f)
f_dGamma = f - f0
dfApprox = np.dot(C, dX) + np.dot(D, dU)
# lift
dLexact = sum(f_dGamma[2::3])
dLapprox = sum(dfApprox[2::3])
self.assertLess(np.abs((dLapprox - dLexact) / dLexact), 0.001)
# drag
dDexact = sum(f_dGamma[0::3])
dDapprox = sum(dfApprox[0::3])
self.assertLess(np.abs((dDapprox - dDexact) / dDexact), 0.001)
# side force
dSexact = sum(f_dGamma[1::3])
dSapprox = sum(dfApprox[1::3])
self.assertLess(dSexact, 1e-7)
self.assertLess(dSapprox, 1e-7)
# variations in gamma w ------------------------------------------------
f[:] = 0.0
dX[:] = 0.0
for i in range(m * n, mW * n):
dX[i] = 0.00002 / (mW * n) * (i + 1)
gamWpDx = gamW0 + dX[m * n:m * n + mW * n]
Cpp_KJForces(zeta0, gam0, zetaW0, gamWpDx, zetaPri0, nu, VMOPTS,
gam_tm1, f)
f_dGammaW = f - f0
dfApprox = np.dot(C, dX) + np.dot(D, dU)
# lift
dLexact = sum(f_dGammaW[2::3])
dLapprox = sum(dfApprox[2::3])
self.assertLess(np.abs((dLapprox - dLexact) / dLexact), 0.001)
# drag
dDexact = sum(f_dGammaW[0::3])
dDapprox = sum(dfApprox[0::3])
self.assertLess(np.abs((dDapprox - dDexact) / dDexact), 0.001)
# side force
dSexact = sum(f_dGammaW[1::3])
dSapprox = sum(dfApprox[1::3])
self.assertLess(dSexact, 1e-7)
self.assertLess(dSapprox, 1e-7)
# variations in gamPri ------------------------------------------------
f[:] = 0.0
dX[:] = 0.0
for i in range(m * n + mW * n, 2 * m * n + mW * n):
dX[i] = 0.002 / (m * n) * (i + 1)
gam_tm1pDx = gam0 - 2.0 * delS * dX[m * n + mW * n:]
VMOPTS.Steady = ct.c_bool(False)
Cpp_KJForces(zeta0, gam0, zetaW0, gamW0, zetaPri0, nu, VMOPTS,
gam_tm1pDx, f)
f_dGamPri = f - f0
dfApprox = np.dot(C, dX) + np.dot(D, dU)
# lift
dLexact = sum(f_dGamPri[2::3])
dLapprox = sum(dfApprox[2::3])
self.assertLess(np.abs((dLapprox - dLexact) / dLexact), 0.001)
# drag
dDexact = sum(f_dGamPri[0::3])
dDapprox = sum(dfApprox[0::3])
self.assertLess(np.abs((dDapprox - dDexact) / dDexact), 0.001)
# side force
dSexact = sum(f_dGamPri[1::3])
dSapprox = sum(dfApprox[1::3])
self.assertLess(dSexact, 1e-7)
self.assertLess(dSapprox, 1e-7)
# variations in zetaPri ------------------------------------------------
f[:] = 0.0
dX[:] = 0.0
for i in range(3 * (m + 1) * (n + 1)):
dU[i] = 0.002 / (3 * (m + 1) * (n + 1) * (i + 1))
zetaPriPdX = zetaPri0 + dU[0:3 * (m + 1) * (n + 1)]
VMOPTS.Steady = ct.c_bool(True)
Cpp_KJForces(zeta0, gam0, zetaW0, gamW0, zetaPriPdX, nu, VMOPTS,
gam_tm1, f)
f_dZetaPri = f - f0
dfApprox = np.dot(C, dX) + np.dot(D, dU)
# lift
dLexact = sum(f_dZetaPri[2::3])
dLapprox = sum(dfApprox[2::3])
self.assertLess(np.abs((dLapprox - dLexact) / dLexact), 0.001)
# drag
dDexact = sum(f_dZetaPri[0::3])
dDapprox = sum(dfApprox[0::3])
self.assertLess(np.abs((dDapprox - dDexact) / dDexact), 0.001)
# side force
dSexact = sum(f_dZetaPri[1::3])
dSapprox = sum(dfApprox[1::3])
self.assertLess(np.abs((dSapprox - dSexact) / dSexact), 0.001)
# variations in nu -----------------------------------------------------
f[:] = 0.0
dU[:] = 0.0
for i in range(6 * (m + 1) * (n + 1), 9 * (m + 1) * (n + 1)):
dU[i] = 0.002 / (3 * (m + 1) * (n + 1) * (i + 1))
nuPdX = nu + dU[6 * (m + 1) * (n + 1):]
Cpp_KJForces(zeta0, gam0, zetaW0, gamW0, zetaPri0, nuPdX, VMOPTS,
gam_tm1, f)
f_dNu = f - f0
dfApprox = np.dot(C, dX) + np.dot(D, dU)
# lift
dLexact = sum(f_dNu[2::3])
dLapprox = sum(dfApprox[2::3])
self.assertLess(np.abs((dLapprox - dLexact) / dLexact), 0.001)
# drag
dDexact = sum(f_dNu[0::3])
dDapprox = sum(dfApprox[0::3])
self.assertLess(np.abs((dDapprox - dDexact) / dDexact), 0.001)
# side force
dSexact = sum(f_dNu[1::3])
dSapprox = sum(dfApprox[1::3])
self.assertLess(np.abs((dSapprox - dSexact) / dSexact), 0.001)
def test_nlnVsolver(self):
"""Test nln force calcs against full solver solution on aerofoil
problem."""
# Init steady problem at 1 deg AoA
aoa = 1 * np.pi / 180.0
V = 1
m = 2
n = 2
mW = 3
delS = 1
chords = np.linspace(-1.0, 0.0, m + 1, True)
chordsW = np.linspace(0.0, 10000.0, mW + 1, True)
spans = np.linspace(-10000, 10000, n + 1, True)
zeta0 = np.zeros(3 * len(chords) * len(spans))
zetaW0 = np.zeros(3 * len(chordsW) * len(spans))
kk = 0
for c in chords:
for s in spans:
zeta0[3 * kk] = np.cos(aoa) * c
zeta0[3 * kk + 1] = s
zeta0[3 * kk + 2] = -np.sin(aoa) * c
kk = kk + 1
# end for s
# end for c
kk = 0
for c in chordsW:
for s in spans:
zetaW0[3 * kk] = c
zetaW0[3 * kk + 1] = s
kk = kk + 1
# end for s
# end for c
zetaPri0 = np.zeros((3 * len(chords) * len(spans)))
nu = np.zeros((3 * len(chords) * len(spans))) # atmospheric velocity
nu[0::3] = V
# to be solved
gam0 = np.zeros((m * n))
gamW0 = np.zeros((mW * n))
f0 = np.zeros((3 * len(chords) * len(spans))) # forces
# initialise nonlinear options
VMOPTS = VMopts(
m,
n,
False, # image methods
mW,
True, # steady
True, # KJ is true
True,
delS,
False,
1) #numCores
# solve nonlinear
Cpp_Solver_VLM(zeta0, zetaPri0, nu, zetaW0, VMOPTS, f0, gam0, gamW0)
# check lift curve slope
self.assertAlmostEqual((sum((f0[2::3]) / 10000.0)) / aoa, 2 * np.pi, 1)
# test independent force calculation
f0i = np.zeros((3 * len(chords) * len(spans)))
gamPri0 = np.zeros((m * n))
gam_tm1 = gam0 - gamPri0
Cpp_KJForces(zeta0, gam0, zetaW0, gamW0, zetaPri0, nu, VMOPTS, gam_tm1,
f0i)
self.assertAlmostEqual((sum((f0i[2::3]) / 10000.0)) / aoa, 2 * np.pi,
1)
self.assertTrue(sum(f0i[2::3]) == sum(f0[2::3]))
def test_linVnln_dZeta(self):
"""Test ss UVLM output equations against full nonlinear calcs."""
# Init steady problem at 1 deg AoA
aoa = 1.0 * np.pi / 180.0
V = 1
m = 4
n = 3
mW = 11
delS = 1
chords = np.linspace(-1.0, 0.0, m + 1, True)
chordsW = np.linspace(0.0, 10000.0, mW + 1, True)
spans = np.linspace(-10000, 10000, n + 1, True)
zeta0 = np.zeros(3 * len(chords) * len(spans))
zetaW0 = np.zeros(3 * len(chordsW) * len(spans))
kk = 0
for c in chords:
for s in spans:
zeta0[3 * kk] = np.cos(aoa) * c
zeta0[3 * kk + 1] = s
zeta0[3 * kk + 2] = -np.sin(aoa) * c
kk = kk + 1
# end for s
# end for c
kk = 0
for c in chordsW:
for s in spans:
zetaW0[3 * kk] = c
zetaW0[3 * kk + 1] = s
kk = kk + 1
# end for s
# end for c
zetaPri0 = np.zeros((3 * len(chords) * len(spans)))
gamPri0 = np.zeros((m * n))
nu = np.zeros((3 * len(chords) * len(spans))) # atmospheric velocity
nu[0::3] = V
# to be solved
gam0 = np.zeros((m * n))
gamW0 = np.zeros((mW * n))
f0 = np.zeros((3 * len(chords) * len(spans))) # forces
# initialise nonlinear options
VMOPTS = VMopts(
m,
n,
False, # image methods
mW,
True, # steady
True, # KJ is true
True,
delS,
False,
1) #numCores
# solve nonlinear
Cpp_Solver_VLM(zeta0, zetaPri0, nu, zetaW0, VMOPTS, f0, gam0, gamW0)
# set to unsteady mode and calculate with zetaPri0
f0[:] = 0.0
VMOPTS.Steady = ct.c_bool(False)
gamPri0 = 0.01 * np.ones_like(gamPri0)
gam_tm1 = gam0 - 2.0 * delS * gamPri0
Cpp_KJForces(zeta0, gam0, zetaW0, gamW0, zetaPri0, nu, VMOPTS, gam_tm1,
f0)
# generate linear output eqs at x0, u0
foo1, foo2, foo3, C, D = genSSuvlm(gam0, gamW0, gamPri0, zeta0, zetaW0,
zetaPri0, nu, m, n, mW, delS)
del foo1, foo2, foo3
# init delta vectors for testing
dX = np.zeros((2 * m * n + mW * n))
dU = np.zeros((9 * len(chords) * len(spans)))
# variations in zeta -----------------------------------------------------
f = np.zeros_like(f0)
for i in range(3 * (m + 1) * (n + 1), 6 * (m + 1) * (n + 1)):
if isodd(i):
dU[i] = 0.1 / (m * 3 * (m + 1) * (n + 1) * (i + 1))
else:
dU[i] = -0.1 / (m * 3 * (m + 1) * (n + 1) * (i + 1))
zetaPdX = zeta0 + dU[3 * (m + 1) * (n + 1):6 * (m + 1) * (n + 1)]
gam_tm1 = gam0 - 2.0 * delS * gamPri0
Cpp_KJForces(zetaPdX, gam0, zetaW0, gamW0, zetaPri0, nu, VMOPTS,
gam_tm1, f)
# calculate diffs
f_dZeta = f - f0
dfApprox = np.dot(C, dX) + np.dot(D, dU)
# lift
dLexact = sum(f_dZeta[2::3])
dLapprox = sum(dfApprox[2::3])
self.assertLess(np.abs((dLapprox - dLexact) / dLexact), 0.01)
# drag
dDexact = sum(f_dZeta[0::3])
dDapprox = sum(dfApprox[0::3])
self.assertLess(np.abs((dDapprox - dDexact) / dDexact), 0.01)
# side force
dSexact = sum(f_dZeta[1::3])
dSapprox = sum(dfApprox[1::3])
self.assertLess(np.abs((dSapprox - dSexact) / dSexact), 0.01)
def test_AIC3s(self):
"""Run on AR4 wing to generate basis for interpolation."""
# Init steady problem at 1 deg AoA
aoa = 0.01 * np.pi / 180.0
V = 100
factor = 1
m = factor * 2
n = factor * 4
mW = 1
delS = 1.0
chords = np.linspace(-1.0, 0.0, m + 1, True)
chordsW = np.linspace(0.0, 10000.0, mW + 1, True)
spans = np.linspace(-2, 2, n + 1, True)
zeta0 = np.zeros(3 * len(chords) * len(spans))
zetaW0 = np.zeros(3 * len(chordsW) * len(spans))
kk = 0
for c in chords:
for s in spans:
zeta0[3 * kk] = np.cos(aoa) * c
zeta0[3 * kk + 1] = s
zeta0[3 * kk + 2] = -np.sin(aoa) * c
kk = kk + 1
# end for s
# end for c
kk = 0
for c in chordsW:
for s in spans:
zetaW0[3 * kk] = c
zetaW0[3 * kk + 1] = s
kk = kk + 1
# end for s
# end for c
zetaPri0 = np.zeros((3 * len(chords) * len(spans)))
nu = np.zeros((3 * len(chords) * len(spans))) # atmospheric velocity
nu[0::3] = V
# to be solved
gam0 = np.zeros((m * n))
gamW0 = np.zeros((mW * n))
f0 = np.zeros((3 * len(chords) * len(spans))) # forces
VMOPTS = VMopts(
m,
n,
False, # image methods
mW,
True, # steady
True, # KJ is true
True,
delS,
False,
1) #numCores
# solve for gamma
Cpp_Solver_VLM(zeta0, zetaPri0, nu, zetaW0, VMOPTS, f0, gam0, gamW0)
# call AIC matrix function
AIC3 = np.zeros((3 * m * n, m * n))
AIC3s = np.zeros((12 * m * n, m * n))
Cpp_AIC3(zeta0, m, n, zeta0, m, n, AIC3)
Cpp_AIC3s(zeta0, m, n, zeta0, m, n, AIC3s)
# unit gamma
colVel = np.dot(AIC3, gam0)
midVel = np.dot(AIC3s, gam0)
#get geometry
zetaC = self.getCollocs(zeta0, m, n)
zetaM = self.getMidpoints(zeta0, m, n)
# list midpoints and eliminate coincident ones
zetaMarr = np.reshape(zetaM, (4 * m * n, 3), 'C')
zetaMarr, I = unique_rows(zetaMarr)
zetaMnr = np.reshape(zetaMarr, (3 * len(zetaMarr)))
midVelnr = np.zeros_like(zetaMnr)
sNr = 0
for s in I:
midVelnr[3 * sNr:3 * sNr + 3] = midVel[3 * s:3 * s + 3]
sNr = sNr + 1
# end for s
# interpolate onto fine grid
grid_x, grid_y = np.mgrid[min(chords) * np.cos(aoa):max(chords):100j,
min(spans):max(spans):200j]
wGrid = griddata(np.transpose(np.array([zetaMnr[0::3],
zetaMnr[1::3]])),
midVelnr[2::3], (grid_x, grid_y),
method='cubic')
plt.subplot(211)
plt.imshow(wGrid.T, extent=(-1, 0, -2, 2))
plt.plot(zetaMnr[0::3], zetaMnr[1::3], 'ks', ms=4)
plt.title('Midpoint velocity field [v_z]')
# collocation vels
wGridc = griddata(np.transpose(np.array([zetaC[0::3], zetaC[1::3]])),
colVel[2::3], (grid_x, grid_y),
method='cubic')
plt.subplot(212)
plt.imshow(wGridc.T, extent=(-1, 0, -2, 2))
plt.plot(zetaC[0::3], zetaC[1::3], 'ko', ms=4)
plt.title('Collocation velocity field [v_z]')
if False:
plt.show()
# save data to matlab
savemat(Settings.OutputDir + ' AICinterp', {
'm': m,
'n': n,
'zetaC': zetaC,
'colVel': colVel,
'zetaM': zetaMnr,
'midVel': midVelnr,
'wGridC': wGridc,
'wGridM': wGrid,
'gridX': grid_x,
'gridY': grid_y
},
appendmat=True)
