def compute_partials(self, inputs, J):
# rename
rho = inputs['rho']
U = inputs['U']
d = inputs['d']
mu = inputs['mu']
beta = inputs['beta']
# dynamic pressure
q = 0.5 * rho * U**2
# Reynolds number and drag
if float(inputs['cd_usr']) < 0.:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = inputs['cd_usr']
Re = 1.0
dcd_dRe = 0.0
# derivatives
dq_dU = rho * U
const = (dq_dU * cd + q * dcd_dRe * rho * d / mu) * d
dPx_dU = const * cosd(beta)
dPy_dU = const * sind(beta)
const = (cd + dcd_dRe * Re) * q
dPx_dd = const * cosd(beta)
dPy_dd = const * sind(beta)
n = len(inputs['z'])
zeron = np.zeros((n, n))
J['windLoads_Px', 'U'] = np.diag(dPx_dU)
J['windLoads_Px', 'z'] = zeron
J['windLoads_Px', 'd'] = np.diag(dPx_dd)
J['windLoads_Py', 'U'] = np.diag(dPy_dU)
J['windLoads_Py', 'z'] = zeron
J['windLoads_Py', 'd'] = np.diag(dPy_dd)
J['windLoads_Pz', 'U'] = zeron
J['windLoads_Pz', 'z'] = zeron
J['windLoads_Pz', 'd'] = zeron
J['windLoads_qdyn', 'U'] = np.diag(dq_dU)
J['windLoads_qdyn', 'z'] = zeron
J['windLoads_qdyn', 'd'] = zeron
J['windLoads_z', 'U'] = zeron
J['windLoads_z', 'z'] = np.eye(n)
J['windLoads_z', 'd'] = zeron
def compute(self, inputs, outputs):
rho = inputs["rho_air"]
U = inputs["U"]
d = inputs["d"]
mu = inputs["mu_air"]
beta = inputs["beta_wind"]
# dynamic pressure
q = 0.5 * rho * U**2
# Reynolds number and drag
if float(inputs["cd_usr"]) < 0.0:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = inputs["cd_usr"]
Re = 1.0
dcd_dRe = 0.0
Fp = q * cd * d
# components of distributed loads
Px = Fp * cosd(beta)
Py = Fp * sind(beta)
Pz = 0 * Fp
# pack data
outputs["windLoads_Px"] = Px
outputs["windLoads_Py"] = Py
outputs["windLoads_Pz"] = Pz
outputs["windLoads_qdyn"] = q
outputs["windLoads_z"] = inputs["z"]
outputs["windLoads_beta"] = beta
def compute(self, inputs, outputs):
rho = inputs['rho_air']
U = inputs['U']
d = inputs['d']
mu = inputs['mu_air']
beta = inputs['beta_wind']
# dynamic pressure
q = 0.5 * rho * U**2
# Reynolds number and drag
if float(inputs['cd_usr']) < 0.:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = inputs['cd_usr']
Re = 1.0
dcd_dRe = 0.0
Fp = q * cd * d
# components of distributed loads
Px = Fp * cosd(beta)
Py = Fp * sind(beta)
Pz = 0 * Fp
# pack data
outputs['windLoads_Px'] = Px
outputs['windLoads_Py'] = Py
outputs['windLoads_Pz'] = Pz
outputs['windLoads_qdyn'] = q
outputs['windLoads_z'] = inputs['z']
outputs['windLoads_beta'] = beta
def compute_partials(self, inputs, J):
# wlevel = inputs['wlevel']
# if wlevel > 0.0: wlevel *= -1.0
rho = inputs["rho_water"]
U = inputs["U"]
# U0 = inputs['U0']
d = inputs["d"]
# zrel= inputs['z']-wlevel
mu = inputs["mu_water"]
beta = inputs["beta_wave"]
# beta0 = inputs['beta0']
# dynamic pressure
q = 0.5 * rho * U**2
# q0= 0.5*rho*U0**2
# Reynolds number and drag
if float(inputs["cd_usr"]) < 0.0:
cd = inputs["cd_usr"] * np.ones_like(d)
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
# derivatives
dq_dU = rho * U
const = (dq_dU * cd + q * dcd_dRe * rho * d / mu) * d
dPx_dU = const * cosd(beta)
dPy_dU = const * sind(beta)
const = (cd + dcd_dRe * Re) * q + rho * inputs[
"cm"] * math.pi / 4.0 * 2 * d * inputs["A"]
dPx_dd = const * cosd(beta)
dPy_dd = const * sind(beta)
const = rho * inputs["cm"] * math.pi / 4.0 * d**2
dPx_dA = const * cosd(beta)
dPy_dA = const * sind(beta)
J["waveLoads_Px", "A"] = dPx_dA
J["waveLoads_Py", "A"] = dPy_dA
J["waveLoads_qdyn", "U"] = dq_dU
J["waveLoads_pt", "U"] = dq_dU
def compute_partials(self, inputs, J):
# rename
rho = inputs["rho_air"]
U = inputs["U"]
d = inputs["d"]
mu = inputs["mu_air"]
beta = inputs["beta_wind"]
# dynamic pressure
q = 0.5 * rho * U**2
# Reynolds number and drag
if float(inputs["cd_usr"]) < 0.0:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = inputs["cd_usr"]
Re = 1.0
dcd_dRe = 0.0
# derivatives
dq_dU = rho * U
const = (dq_dU * cd + q * dcd_dRe * rho * d / mu) * d
dPx_dU = const * cosd(beta)
dPy_dU = const * sind(beta)
const = (cd + dcd_dRe * Re) * q
dPx_dd = const * cosd(beta)
dPy_dd = const * sind(beta)
J["windLoads_Px", "U"] = dPx_dU
J["windLoads_Px", "d"] = dPx_dd
J["windLoads_Py", "U"] = dPy_dU
J["windLoads_Py", "d"] = dPy_dd
J["windLoads_qdyn", "U"] = dq_dU
def compute_partials(self, inputs, J):
# rename
rho = inputs['rho_air']
U = inputs['U']
d = inputs['d']
mu = inputs['mu_air']
beta = inputs['beta_wind']
# dynamic pressure
q = 0.5 * rho * U**2
# Reynolds number and drag
if float(inputs['cd_usr']) < 0.:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = inputs['cd_usr']
Re = 1.0
dcd_dRe = 0.0
# derivatives
dq_dU = rho * U
const = (dq_dU * cd + q * dcd_dRe * rho * d / mu) * d
dPx_dU = const * cosd(beta)
dPy_dU = const * sind(beta)
const = (cd + dcd_dRe * Re) * q
dPx_dd = const * cosd(beta)
dPy_dd = const * sind(beta)
J['windLoads_Px', 'U'] = dPx_dU
J['windLoads_Px', 'd'] = dPx_dd
J['windLoads_Py', 'U'] = dPy_dU
J['windLoads_Py', 'd'] = dPy_dd
J['windLoads_qdyn', 'U'] = dq_dU
def compute(self, inputs, outputs):
# wlevel = inputs['wlevel']
# if wlevel > 0.0: wlevel *= -1.0
rho = inputs["rho_water"]
U = inputs["U"]
# U0 = inputs['U0']
d = inputs["d"]
# zrel= inputs['z']-wlevel
mu = inputs["mu_water"]
beta = inputs["beta_wave"]
# beta0 = inputs['beta0']
# dynamic pressure
q = 0.5 * rho * U * np.abs(U)
# q0= 0.5*rho*U0**2
# Reynolds number and drag
if float(inputs["cd_usr"]) < 0.0:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = inputs["cd_usr"] * np.ones_like(d)
Re = 1.0
dcd_dRe = 0.0
# inertial and drag forces
Fi = rho * inputs["cm"] * math.pi / 4.0 * d**2 * inputs[
"A"] # Morrison's equation
Fd = q * cd * d
Fp = Fi + Fd
# components of distributed loads
Px = Fp * cosd(beta)
Py = Fp * sind(beta)
Pz = 0.0 * Fp
# FORCES [N/m] AT z=0 m
# idx0 = np.abs(zrel).argmin() # closest index to z=0, used to find d at z=0
# d0 = d[idx0] # initialize
# cd0 = cd[idx0] # initialize
# if (zrel[idx0]<0.) and (idx0< (zrel.size-1)): # point below water
# d0 = np.mean(d[idx0:idx0+2])
# cd0 = np.mean(cd[idx0:idx0+2])
# elif (zrel[idx0]>0.) and (idx0>0): # point above water
# d0 = np.mean(d[idx0-1:idx0+1])
# cd0 = np.mean(cd[idx0-1:idx0+1])
# Fi0 = rho*inputs['cm']*math.pi/4.0*d0**2*inputs['A0'] # Morrison's equation
# Fd0 = q0*cd0*d0
# Fp0 = Fi0 + Fd0
# Px0 = Fp0*cosd(beta0)
# Py0 = Fp0*sind(beta0)
# Pz0 = 0.*Fp0
# Store qties at z=0 MSL
# outputs['waveLoads_Px0'] = Px0
# outputs['waveLoads_Py0'] = Py0
# outputs['waveLoads_Pz0'] = Pz0
# outputs['waveLoads_qdyn0'] = q0
# outputs['waveLoads_beta0'] = beta0
# pack data
outputs["waveLoads_Px"] = Px
outputs["waveLoads_Py"] = Py
outputs["waveLoads_Pz"] = Pz
outputs["waveLoads_qdyn"] = q
outputs["waveLoads_pt"] = q + inputs["p"]
outputs["waveLoads_z"] = inputs["z"]
outputs["waveLoads_beta"] = beta
def compute_partials(self, inputs, J):
#wlevel = inputs['wlevel']
#if wlevel > 0.0: wlevel *= -1.0
rho = inputs['rho']
U = inputs['U']
#U0 = inputs['U0']
d = inputs['d']
#zrel= inputs['z']-wlevel
mu = inputs['mu']
beta = inputs['beta']
#beta0 = inputs['beta0']
# dynamic pressure
q = 0.5 * rho * U**2
#q0= 0.5*rho*U0**2
# Reynolds number and drag
if float(inputs['cd_usr']) < 0.:
cd = inputs['cd_usr'] * np.ones_like(d)
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
# derivatives
dq_dU = rho * U
const = (dq_dU * cd + q * dcd_dRe * rho * d / mu) * d
dPx_dU = const * cosd(beta)
dPy_dU = const * sind(beta)
const = (cd + dcd_dRe * Re) * q + rho * inputs[
'cm'] * math.pi / 4.0 * 2 * d * inputs['A']
dPx_dd = const * cosd(beta)
dPy_dd = const * sind(beta)
const = rho * inputs['cm'] * math.pi / 4.0 * d**2
dPx_dA = const * cosd(beta)
dPy_dA = const * sind(beta)
n = len(inputs['z'])
zeron = np.zeros((n, n))
J['waveLoads.Px', 'U'] = np.diag(dPx_dU)
J['waveLoads.Px', 'A'] = np.diag(dPx_dA)
J['waveLoads.Px', 'z'] = zeron
J['waveLoads.Px', 'd'] = np.diag(dPx_dd)
J['waveLoads.Px', 'p'] = zeron
J['waveLoads.Py', 'U'] = np.diag(dPy_dU)
J['waveLoads.Py', 'A'] = np.diag(dPy_dA)
J['waveLoads.Py', 'z'] = zeron
J['waveLoads.Py', 'd'] = np.diag(dPy_dd)
J['waveLoads.Py', 'p'] = zeron
J['waveLoads.Pz', 'U'] = zeron
J['waveLoads.Pz', 'A'] = zeron
J['waveLoads.Pz', 'z'] = zeron
J['waveLoads.Pz', 'd'] = zeron
J['waveLoads.Pz', 'p'] = zeron
J['waveLoads.qdyn', 'U'] = np.diag(dq_dU)
J['waveLoads.qdyn', 'A'] = zeron
J['waveLoads.qdyn', 'z'] = zeron
J['waveLoads.qdyn', 'd'] = zeron
J['waveLoads.qdyn', 'p'] = zeron
J['waveLoads.pt', 'U'] = np.diag(dq_dU)
J['waveLoads.pt', 'A'] = zeron
J['waveLoads.pt', 'z'] = zeron
J['waveLoads.pt', 'd'] = zeron
J['waveLoads.pt', 'p'] = 1.0
J['waveLoads.z', 'U'] = zeron
J['waveLoads.z', 'A'] = zeron
J['waveLoads.z', 'z'] = np.eye(n)
J['waveLoads.z', 'd'] = zeron
J['waveLoads.z', 'p'] = zeron