def char_map_eta_s_func_doc(self, label):
r"""
Get LaTeX equation for isentropic efficiency from characteristic map.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}'
r'X = &\sqrt{\frac{T_\mathrm{in,design}}{T_\mathrm{in}}}\\'
'\n'
r'Y = &\frac{\dot{m}_\mathrm{in} \cdot p_\mathrm{in,design}}'
r'{\dot{m}_\mathrm{in,design} \cdot p_\mathrm{in} \cdot X}\\'
'\n'
r'\vec{Y} = &f\left(X,Y\right)\cdot\left(1-\frac{igva}{100}\right)'
r'\\' + '\n'
r'\vec{Z} = &'
r'f\left(X,Y\right)\cdot\left(1-\frac{igva^2}{10000}\right)\\'
'\n'
r'0 = &\frac{\eta_\mathrm{s}}{\eta_\mathrm{s,design}} -'
r'f\left(Y,\vec{Y},\vec{Z}\right)' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, label)
def darcy_func_doc(self, label):
r"""
Equation for pressure drop calculation from darcy friction factor.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0 = &p_\mathrm{in}-p_\mathrm{out}-'
r'\frac{8\cdot|\dot{m}_\mathrm{in}| \cdot\dot{m}_\mathrm{in}'
r'\cdot \frac{v_\mathrm{in}+v_\mathrm{out}}{2} \cdot L \cdot'
r'\lambda\left(Re, ks, D\right)}{\pi^2 \cdot D^5}\\' + '\n'
r'Re =&\frac{4 \cdot |\dot{m}_\mathrm{in}|}{\pi \cdot D \cdot'
r'\frac{\eta_\mathrm{in}+\eta_\mathrm{out}}{2}}\\' + '\n'
r'\end{split}'
)
return generate_latex_eq(self, latex, label)
def dp_char_func_doc(self, label):
r"""
Equation for characteristic line of difference pressure to mass flow.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
p = self.dp_char.param
expr = self.get_char_expr_doc(p, **self.dp_char.char_params)
if not expr:
msg = ('Please choose a valid parameter, you want to link the '
'pressure drop to at component ' + self.label + '.')
logging.error(msg)
raise ValueError(msg)
latex = (
r'0=p_\mathrm{in}-p_\mathrm{out}-f\left(' + expr +
r'\right)')
return generate_latex_eq(self, latex, label)
def energy_balance_func_doc(self, label):
r"""
Equation for heat exchanger energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0 = &' + '\n'
r'\dot{m}_\mathrm{in,1}\cdot\left(h_\mathrm{out,1}-'
r'h_\mathrm{in,1}\right) \\' + '\n'
r'&+ \dot{m}_\mathrm{in,2} \cdot \left(h_\mathrm{out,2} - '
r'h_\mathrm{in,2} \right)\\' + '\n'
r'&+ \dot{m}_\mathrm{in,3} \cdot \left(h_\mathrm{out,3} - '
r'h_\mathrm{in,3} \right)' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, latex)
def energy_group_func_doc(self, label):
r"""
Equation for solar collector energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0 = & \dot{m}_\mathrm{in} \cdot \left( h_\mathrm{out} - '
r'h_\mathrm{in} \right)\\' + '\n'
r'& - A \cdot \left[E \cdot \eta_\mathrm{opt} - \alpha_1 \cdot'
r'\left(T_\mathrm{m} - T_\mathrm{amb} \right) - \alpha_2 \cdot'
r'\left(T_\mathrm{m} -T_\mathrm{amb}\right)^2 \right]\\' + '\n'
r'T_\mathrm{m}=&\frac{T_\mathrm{out}+T_\mathrm{in}}{2}\\' +
'\n'
r'\end{split}'
)
return generate_latex_eq(self, latex, label)
def energy_group_func_doc(self, label):
r"""
Equation for solar collector energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'\begin{split}' + '\n'
r'0 = & \dot{m}_\mathrm{in} \cdot \left( h_\mathrm{out} - '
r'h_\mathrm{in} \right)\\' + '\n'
r'& - A \cdot \left[E \cdot \eta_\mathrm{opt} \cdot doc^{1.5}'
r'\cdot iam \right. \\' + '\n'
r'&\left. -c_1\cdot\left(T_\mathrm{m}-T_\mathrm{amb}\right) -'
r'c_2 \cdot \left(T_\mathrm{m} - T_\mathrm{amb}\right)^2'
r'\vphantom{\eta_\mathrm{opt}\cdot doc^{1.5}}\right]\\' + '\n'
r'T_\mathrm{m}=&\frac{T_\mathrm{out}+T_\mathrm{in}}{2}\\' +
'\n'
r'iam = & 1 - iam_1 \cdot |aoi| - iam_2 \cdot aoi^2\\' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, label)
def energy_balance_func_doc(self, label):
r"""
Calculate the residual in energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'\begin{split}' + '\n'
r'0=&P + \dot{m}_\mathrm{in,2}\cdot\left(h_\mathrm{in,2}-'
r'h_\mathrm{in,2,ref}\right)\\' + '\n'
r'&-\dot{m}_\mathrm{in,1}\cdot\left( h_\mathrm{out,1} -'
r'h_\mathrm{in,1} \right)\\' + '\n'
r'& - \dot{m}_\mathrm{out,2} \cdot \left( h_\mathrm{out,2} -'
r'h_\mathrm{out,2,ref} \right)\\' + '\n'
r'& + \dot{m}_\mathrm{out,3} \cdot \left( h_\mathrm{out,3} -'
r'h_\mathrm{out,3,ref} + e_0\right)\\' + '\n'
r'&p_\mathrm{ref}=\unit[1]{bar},'
r'\;T_\mathrm{ref}=\unit[25]{^\circ C}\\' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, label)
def combustion_pressure_func_doc(self, label):
r"""
Equations for reactor pressure balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
inl = self.inl[::-1][:2][::-1]
outl = self.outl[::-1][0]
idx_out = outl.source_id[:3] + ',' + outl.source_id[3:]
idx_in1 = inl[0].target_id[:2] + ',' + inl[0].target_id[2:]
idx_in2 = inl[1].target_id[:2] + ',' + inl[1].target_id[2:]
latex = (r'\begin{split}' + '\n'
r'0 = & p_\mathrm{' + idx_in1 + r'} - p_\mathrm{' + idx_out +
r'}\\' + '\n'
r'0 = & p_\mathrm{' + idx_in1 + r'} - p_\mathrm{' + idx_in2 +
r'}\\' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, label)
def energy_balance_func_doc(self, label):
r"""
Calculate the energy balance of the adiabatic combustion chamber.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0 = & \sum_i \dot{m}_{\mathrm{in,}i} \cdot\left( '
r'h_{\mathrm{in,}i} - h_{\mathrm{in,}i\mathrm{,ref}} \right) -'
r'\dot{m}_\mathrm{out,1}\cdot\left( h_\mathrm{out,1}'
r' - h_\mathrm{out,1,ref}\right)\\' + '\n'
r'& + LHV_{fuel} \cdot \left(\sum_i \dot{m}_{\mathrm{in,}i} '
r'\cdot x_{fuel\mathrm{,in,}i} - \dot{m}_\mathrm{out,1} '
r'\cdot x_{fuel\mathrm{,out,1}} \right)\\' + '\n'
r'& \forall i \in \text{inlets}\\'
r'& T_\mathrm{ref}=\unit[298.15]{K}'
r'\;p_\mathrm{ref}=\unit[10^5]{Pa}\\'
'\n' + r'\end{split}')
return generate_latex_eq(self, latex, label)
def zeta_func_doc(self, label, zeta='', inconn=0, outconn=0):
r"""
Calculate residual value of :math:`\zeta`-function.
Parameters
----------
zeta : str
Component parameter to evaluate the zeta_func on, e.g.
:code:`zeta1`.
inconn : int
Connection index of inlet.
outconn : int
Connection index of outlet.
Returns
-------
residual : float
Residual value of function.
"""
inl = r'_\mathrm{in,' + str(inconn + 1) + r'}'
outl = r'_\mathrm{out,' + str(outconn + 1) + r'}'
latex = (
r'0 = \begin{cases}' + '\n' +
r'p' + inl + r'- p' + outl + r' & |\dot{m}' + inl +
r'| < \unitfrac[0.0001]{kg}{s} \\' + '\n' +
r'\frac{\zeta}{D^4}-\frac{(p' + inl + r'-p' + outl + r')'
r'\cdot\pi^2}{8\cdot\dot{m}' + inl + r'\cdot|\dot{m}' + inl +
r'|\cdot\frac{v' + inl + r' + v' + outl + r'}{2}}' +
r'& |\dot{m}' + inl + r'| \geq \unitfrac[0.0001]{kg}{s}' + '\n'
r'\end{cases}'
)
return generate_latex_eq(self, latex, label)
def eta_char_func_doc(self, label):
r"""
Equation for given efficiency characteristic of a water electrolyzer.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
p = self.eta_char.param
expr = self.get_char_expr_doc(p, **self.eta_char.char_params)
if not expr:
msg = ('Please choose a valid parameter, you want to link the '
'efficiency to at component ' + self.label + '.')
logging.error(msg)
raise ValueError(msg)
latex = (r'0=P-\dot{m}_\mathrm{H_2,out,3}\cdot\frac{e_0}'
r'{\eta_\mathrm{design}\cdot f\left(X\right)}')
return generate_latex_eq(self, latex, label)
def pr_func_doc(self, label, pr='', inconn=0, outconn=0):
r"""
Calculate residual value of pressure ratio function.
Parameters
----------
pr : str
Component parameter to evaluate the pr_func on, e.g.
:code:`pr1`.
inconn : int
Connection index of inlet.
outconn : int
Connection index of outlet.
Returns
-------
residual : float
Residual value of function.
"""
latex = (
r'0=p_\mathrm{in,' + str(inconn + 1) + r'}\cdot ' + pr +
r' - p_\mathrm{out,' + str(outconn + 1) + r'}'
)
return generate_latex_eq(self, latex, label)
def fluid_func_doc(self, label):
r"""
Equations for fluid composition.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'\begin{split}' + '\n'
r'0 = &x_\mathrm{i,in,1} - x_\mathrm{i,out,1}\\' + '\n'
r'0 = &\begin{cases}' + '\n'
r'1 - x_\mathrm{i,in2} & \text{i=}H_{2}O\\' + '\n'
r'x_\mathrm{i,in2} & \text{else}\\' + '\n'
r'\end{cases}\\' + '\n'
r'0 =&\begin{cases}' + '\n'
r'1 - x_\mathrm{i,out,2} & \text{i=}O_{2}\\' + '\n'
r'x_\mathrm{i,out,2} & \text{else}\\' + '\n'
r'\end{cases}\\' + '\n'
r'0 =&\begin{cases}' + '\n'
r'1 - x_\mathrm{i,out,3} & \text{i=}H_{2}\\' + '\n'
r'x_\mathrm{i,out,3} & \text{else}\\' + '\n'
r'\end{cases}\\' + '\n'
r'&\forall i \in \text{network fluids}' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, label)
def kA_char_func_doc(self, label):
r"""
Calculate heat transfer from heat transfer coefficient characteristic.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0 = & \dot{m}_\mathrm{in,1} \cdot \left( h_\mathrm{out,1} - '
r'h_\mathrm{in,1}\right)\\' + '\n'
r'&+kA_\mathrm{design} \cdot '
r'f_\mathrm{kA} \cdot \frac{T_\mathrm{out,1} - T_\mathrm{in,2}'
r' - T_\mathrm{in,1} + T_\mathrm{out,2}}{\ln{'
r'\frac{T_\mathrm{out,1} - T_\mathrm{in,2}}{T_\mathrm{in,1} -'
r' T_\mathrm{out,2}}}}\\' + '\n'
r'f_\mathrm{kA}=&\frac{2}{\frac{1}{f\left(X_1\right)}+'
r'\frac{1}{f\left(X_2\right)}}\\' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, label)
def kA_char_group_func_doc(self, label):
r"""
Calculate heat transfer from heat transfer coefficient characteristic.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0=&\dot{m}_\mathrm{in}\cdot\left(h_\mathrm{out}-'
r'h_\mathrm{in}\right)+kA_\mathrm{design} \cdot f_\mathrm{kA}'
r' \cdot \Delta T_\mathrm{log}\\' + '\n'
r'\Delta T_\mathrm{log} = &\begin{cases}' + '\n'
r'\frac{T_\mathrm{in}-T_\mathrm{out}}{\ln{\frac{T_\mathrm{in}-'
r'T_\mathrm{amb}}{T_\mathrm{out}-T_\mathrm{amb}}}} &'
r' T_\mathrm{in} > T_\mathrm{out} \\' + '\n'
r'\frac{T_\mathrm{out}-T_\mathrm{in}}{\ln{\frac{'
r'T_\mathrm{out}-T_\mathrm{amb}}{T_\mathrm{in}-'
r'T_\mathrm{amb}}}} & T_\mathrm{in} < T_\mathrm{out}\\' + '\n'
r'0 & T_\mathrm{in} = T_\mathrm{out}' + '\n'
r'\end{cases}\\' + '\n'
r'f_{kA}=&\frac{2}{1 + \frac{1}{f\left(X\right)}}\\' + '\n'
r'T_\mathrm{amb} =& \text{ambient temperature}' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, label)
def overheating_func_doc(self, label):
r"""
Equation for cold side outlet state.
Parameters
----------
label : str
Label for equation.
"""
latex = r'0=h_\mathrm{out,3} -h\left(p_\mathrm{out,3}, x=1 \right)'
return generate_latex_eq(self, latex, label)
def energy_balance_func_doc(self, label):
r"""
Calculate energy balance.
Parameters
----------
label : str
Label for equation.
"""
latex = r'0=h_{in}-h_{\mathrm{out,}j}\;\forall j \in\text{outlets}'
return generate_latex_eq(self, latex, label)
def flow_char_func_doc(self, label):
r"""
Equation for given flow characteristic of a pump.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'0=p_\mathrm{out}-p_\mathrm{in}-f\left(X\right)')
return generate_latex_eq(self, latex, label)
def subcooling_func_doc(self, label):
r"""
Equation for steam side outlet state.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0=h_\mathrm{out,1} -h\left(p_\mathrm{out,1}, x=0 \right)'
return generate_latex_eq(self, latex, label)
def saturated_gas_func_doc(self, label):
r"""
Calculate hot side outlet state.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0=h_\mathrm{out,1}-h\left(p_\mathrm{out,1}, x=1 \right)'
return generate_latex_eq(self, latex, label)
def specific_energy_consumption_func_doc(self, label):
r"""
Equation for specific energy consumption.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0=P - \dot{m}_\mathrm{H_2,out3} \cdot e'
return generate_latex_eq(self, latex, label)
def eta_func_doc(self, label):
r"""
Equation for electrolysis efficiency.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0 = P \cdot \eta - \dot{m}_\mathrm{H_2,out,3} \cdot e_0'
return generate_latex_eq(self, latex, label)
def gas_temperature_func_doc(self, label):
r"""
Equation for temperature equality of product gases.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0 = T_\mathrm{out,2} - T_\mathrm{out,3}'
return generate_latex_eq(self, latex, label)
def ttd_l_func_doc(self, label):
r"""
Equation for upper terminal temperature difference.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0 = ttd_\mathrm{l} - T_\mathrm{out,1} + T_\mathrm{in,2}'
return generate_latex_eq(self, latex, label)
def energy_balance_func_doc(self, label):
r"""
Equation for pressure drop calculation.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'0 = \dot{m}_\mathrm{in} \cdot \left(h_\mathrm{out} - '
r'h_\mathrm{in} \right) -\dot{Q}')
return generate_latex_eq(self, latex, label)
def energy_balance_func_doc(self, label):
r"""
Calculate energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'0= T_\mathrm{in} - T_{\mathrm{out,}j}'
r'\; \forall j \in \text{outlets}')
return generate_latex_eq(self, latex, label)
def mass_flow_func_doc(self, label):
r"""
Calculate the residual value for component's mass flow balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'0=\dot{m}_\mathrm{in,1} + \dot{m}_\mathrm{in,2} - '
r'\dot{m}_\mathrm{out,1}')
return generate_latex_eq(self, latex, label)
def eta_s_func_doc(self, label):
r"""
Equation for given isentropic efficiency of a turbine.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'0=-\left(h_\mathrm{out}-h_\mathrm{in}\right)+\left('
r'h_\mathrm{out,s}-h_\mathrm{in}\right)\cdot\eta_\mathrm{s}')
return generate_latex_eq(self, latex, label)
def heat_func_doc(self, label):
r"""
Equation for heat output.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'0=\dot{Q}-\dot{m}_\mathrm{in,1}\cdot\left(h_\mathrm{in,1}-'
r'h_\mathrm{out,1}\right)')
return generate_latex_eq(self, latex, label)
def energy_balance_hot_func_doc(self, label):
r"""
Equation for hot side heat exchanger energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (r'0 =\dot{m}_{in,1} \cdot \left(h_{out,1}-'
r'h_{in,1}\right)-\dot{Q}')
return generate_latex_eq(self, latex, label)