def derivatives(self, vec_z):
r"""
Calculate partial derivatives for given equations.
Returns
-------
mat_deriv : ndarray
Matrix of partial derivatives.
"""
######################################################################
# derivatives fluid, mass flow and pressure balance are static
k = self.num_nw_fluids * 2 + 4
######################################################################
# derivatives for energy balance equation
i = 0
for inl in self.inl:
self.mat_deriv[k, i, 0] = inl.h.val_SI
self.mat_deriv[k, i, 2] = inl.m.val_SI
i += 1
j = 0
for outl in self.outl:
self.mat_deriv[k, j + i, 0] = -outl.h.val_SI
self.mat_deriv[k, j + i, 2] = -outl.m.val_SI
j += 1
k += 1
######################################################################
# derivatives of equations for saturated states at outlets
self.mat_deriv[k, 2, 1] = dh_mix_dpQ(self.outl[0].to_flow(), 0)
self.mat_deriv[k, 2, 2] = -1
k += 1
self.mat_deriv[k, 3, 1] = dh_mix_dpQ(self.outl[1].to_flow(), 1)
self.mat_deriv[k, 3, 2] = -1
k += 1
def derivatives(self):
r"""
Calculates matrix of partial derivatives for given equations.
Returns
-------
mat_deriv : ndarray
Matrix of partial derivatives.
"""
mat_deriv = []
######################################################################
# derivatives for fluid balance equations
mat_deriv += self.fl_deriv
######################################################################
# derivatives for mass flow balance equation
mat_deriv += self.m_deriv
######################################################################
# derivatives for pressure eqauations
mat_deriv += self.p_deriv
######################################################################
# derivatives for energy balance equation
deriv = np.zeros((1, 4, self.num_fl + 3))
k = 0
for i in self.inl:
deriv[0, k, 0] = i.h.val_SI
deriv[0, k, 2] = i.m.val_SI
k += 1
j = 0
for o in self.outl:
deriv[0, j + k, 0] = -o.h.val_SI
deriv[0, j + k, 2] = -o.m.val_SI
j += 1
mat_deriv += deriv.tolist()
######################################################################
# derivatives of equations for saturated states at outlets
x_deriv = np.zeros((2, 4, self.num_fl + 3))
x_deriv[0, 2, 1] = dh_mix_dpQ(self.outl[0].to_flow(), 0)
x_deriv[0, 2, 2] = -1
x_deriv[1, 3, 1] = dh_mix_dpQ(self.outl[1].to_flow(), 1)
x_deriv[1, 3, 2] = -1
mat_deriv += x_deriv.tolist()
return np.asarray(mat_deriv)
def outlet_states_deriv(self, increment_filter, k):
r"""
Calculate partial derivatives of outlet states.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
self.jacobian[k, self.num_i, 1] = dh_mix_dpQ(self.outl[0].get_flow(), 0)
self.jacobian[k, self.num_i, 2] = -1
self.jacobian[k + 1, self.num_i + 1, 1] = (
dh_mix_dpQ(self.outl[1].get_flow(), 1))
self.jacobian[k + 1, self.num_i + 1, 2] = -1
def overheating_deriv(self, increment_filter, k):
"""
Calculate partial derivatives for cold side outlet state.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
self.jacobian[k, 5, 1] = -dh_mix_dpQ(self.outl[0].get_flow(), 0)
self.jacobian[k, 5, 2] = 1
def subcooling_deriv(self, increment_filter, k):
"""
Calculate partial derivates of subcooling function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
self.jacobian[k, 2, 1] = -dh_mix_dpQ(self.outl[0].get_flow(), 0)
self.jacobian[k, 2, 2] = 1
def saturated_gas_deriv(self, increment_filter, k):
r"""
Partial derivatives of saturated gas at hot side outlet function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
o1 = self.outl[0].get_flow()
self.jacobian[k, 2, 1] = -dh_mix_dpQ(o1, 1)
self.jacobian[k, 2, 2] = 1
def derivatives(self, increment_filter):
r"""Calculate matrix of partial derivatives for given equations."""
######################################################################
# derivatives fluid and mass balance are static
k = self.num_nw_fluids * 3 + 3
######################################################################
# derivatives for energy balance equation
# mat_deriv += self.energy_deriv()
for i in range(3):
self.jacobian[k, i,
0] = (self.outl[i].h.val_SI - self.inl[i].h.val_SI)
self.jacobian[k, i, 2] = -self.inl[i].m.val_SI
self.jacobian[k, i + 3, 2] = self.inl[i].m.val_SI
k += 1
######################################################################
# derivatives for specified heat transfer
if self.Q.is_set:
self.jacobian[k, 2,
0] = (self.outl[2].h.val_SI - self.inl[2].h.val_SI)
self.jacobian[k, 2, 2] = -self.inl[2].m.val_SI
self.jacobian[k, 5, 2] = self.inl[2].m.val_SI
k += 1
######################################################################
# derivatives for specified pressure ratio at hot side 1
if self.pr1.is_set:
self.jacobian[k, 0, 1] = self.pr1.val
self.jacobian[k, 3, 1] = -1
k += 1
######################################################################
# derivatives for specified pressure ratio at hot side 2
if self.pr2.is_set:
self.jacobian[k, 1, 1] = self.pr2.val
self.jacobian[k, 4, 1] = -1
k += 1
######################################################################
# derivatives for specified pressure ratio at cold side
if self.pr3.is_set:
self.jacobian[k, 2, 1] = self.pr3.val
self.jacobian[k, 5, 1] = -1
k += 1
######################################################################
# derivatives for specified zeta at hot side 1
if self.zeta1.is_set:
f = self.zeta_func
if not increment_filter[0, 0]:
self.jacobian[k, 0, 0] = self.numeric_deriv(f,
'm',
0,
zeta='zeta1',
inconn=0,
outconn=0)
if not increment_filter[0, 1]:
self.jacobian[k, 0, 1] = self.numeric_deriv(f,
'p',
0,
zeta='zeta1',
inconn=0,
outconn=0)
if not increment_filter[0, 2]:
self.jacobian[k, 0, 2] = self.numeric_deriv(f,
'h',
0,
zeta='zeta1',
inconn=0,
outconn=0)
if not increment_filter[3, 1]:
self.jacobian[k, 3, 1] = self.numeric_deriv(f,
'p',
3,
zeta='zeta1',
inconn=0,
outconn=0)
if not increment_filter[3, 2]:
self.jacobian[k, 3, 2] = self.numeric_deriv(f,
'h',
3,
zeta='zeta1',
inconn=0,
outconn=0)
k += 1
######################################################################
# derivatives for specified zeta at hot side 2
if self.zeta2.is_set:
f = self.zeta_func
if not increment_filter[1, 0]:
self.jacobian[k, 1, 0] = self.numeric_deriv(f,
'm',
1,
zeta='zeta2',
inconn=1,
outconn=1)
if not increment_filter[1, 1]:
self.jacobian[k, 1, 1] = self.numeric_deriv(f,
'p',
1,
zeta='zeta2',
inconn=1,
outconn=1)
if not increment_filter[1, 2]:
self.jacobian[k, 1, 2] = self.numeric_deriv(f,
'h',
1,
zeta='zeta2',
inconn=1,
outconn=1)
if not increment_filter[4, 1]:
self.jacobian[k, 4, 1] = self.numeric_deriv(f,
'p',
4,
zeta='zeta2',
inconn=1,
outconn=1)
if not increment_filter[4, 2]:
self.jacobian[k, 4, 2] = self.numeric_deriv(f,
'h',
4,
zeta='zeta2',
inconn=1,
outconn=1)
k += 1
######################################################################
# derivatives for specified zeta at cold side
if self.zeta3.is_set:
f = self.zeta_func
if not increment_filter[2, 0]:
self.jacobian[k, 2, 0] = self.numeric_deriv(f,
'm',
2,
zeta='zeta3',
inconn=2,
outconn=2)
if not increment_filter[2, 1]:
self.jacobian[k, 2, 1] = self.numeric_deriv(f,
'p',
2,
zeta='zeta3',
inconn=2,
outconn=2)
if not increment_filter[2, 2]:
self.jacobian[k, 2, 2] = self.numeric_deriv(f,
'h',
2,
zeta='zeta3',
inconn=2,
outconn=2)
if not increment_filter[5, 1]:
self.jacobian[k, 5, 1] = self.numeric_deriv(f,
'p',
5,
zeta='zeta3',
inconn=2,
outconn=2)
if not increment_filter[5, 2]:
self.jacobian[k, 5, 2] = self.numeric_deriv(f,
'h',
5,
zeta='zeta3',
inconn=2,
outconn=2)
k += 1
######################################################################
# derivatives for saturated liquid at hot side 1 outlet equation
if self.subcooling.val is False:
o1 = self.outl[0].to_flow()
self.jacobian[k, 3, 1] = -dh_mix_dpQ(o1, 0)
self.jacobian[k, 3, 2] = 1
k += 1
######################################################################
# derivatives for saturated gas at cold side outlet 3 equation
if self.overheating.val is False:
o3 = self.outl[2].to_flow()
self.jacobian[k, 5, 1] = -dh_mix_dpQ(o3, 1)
self.jacobian[k, 5, 2] = 1
k += 1