Add mole reactor science pages

pages/science/reactors/constpresmolereactor.rst

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+.. title: Constant Pressure Reactor
+.. has_math: true
+
+.. jumbotron::
+
+   .. raw:: html
+
+      <h1 class="display-3">Constant Pressure Mole Reactor</h1>
+
+   .. class:: lead
+
+      This page shows the derivation of the governing equations used in
+      Cantera's Constant Pressure Mole Reactor model.
+
+      More information on the Constant Pressure Mole Reactor class can be found `here.
+      <{{% ct_docs doxygen/html/d5/d7d/classCantera_1_1ConstPressureMoleReactor.html %}}>`__
+
+Constant Pressure Mole Reactor
+******************************
+
+For this reactor model, the pressure is held constant. The energy equation is
+defined by the total enthalpy.
+
+A Constant Pressure Reactor is defined by the two state variables:
+
+- :math:`H`, the total enthalpy of the reactor's contents (in J)
+
+- :math:`n_k`, the number of moles for each species (in kmol)
+
+Using the definition of the total enthalpy:
+
+.. math::
+
+   H = U + pV
+
+   \frac{d H}{d t} = \frac{d U}{d t} + p \frac{dV}{dt} + V \frac{dp}{dt}
+
+Noting that :math:`dp/dt = 0` and substituting into the energy equation yields:
+
+.. math::
+
+   \frac{dH}{dt} = \dot{Q} + \sum_{in} \dot{n}_{in} \bar{h}_{in}
+                   - \bar{h} \sum_{out} \dot{n}_{out}
+                   \tag{1}
+
+Where the total specific enthalpy :math:`h` is defined as :math:`h = \sum_k{\bar{h}_k n_k}`.
+The enthalpy terms in equation 2 appear due to enthalpy flowing in and out
+of the reactor.
+The rate of heat transfer :math:`\dot{Q}` can replace :math:`\frac{d U}{d t} + p \frac{dV}{dt}` in the above equation due to the first law
+of thermodynamics, which states :math:`\dot{Q} = \dot{H}` in a closed system where
+no work is done.
+Positive :math:`\dot{Q}` represents heat addition to the system.
+
+The moles of each species in the reactor's contents changes as a result of flow through
+the reactor's inlets and outlets, and production of homogeneous gas phase species and reactions on the reactor :py:class:`Wall`.
+The rate of moles of species :math:`k` generated through homogeneous phase
+reactions is :math:`V \dot{\omega}_k`, and the total rate at which moles of species
+:math:`k` is generated is:
+
+.. math::
+
+   \frac{dn_k}{dt} = V \dot{\omega}_k + \sum_{in} \dot{n}_{in} - \sum_{out} \dot{n}_{out} + \dot{n}_{wall}
+   \tag{2}
+
+Where the subscripts *in* and *out* refer to the sum of the superscripted property
+over all inlets and outlets respectively. A dot above a variable signifies a time
+derivative. Reactor *Walls* are defined `here. <{{% ct_docs sphinx/html/cython/zerodim.html#cantera.Wall %}}>`__
+
+Equations 1-2 are the governing equations for a Constant Pressure Reactor.

pages/science/reactors/idealgasconstpresmolereactor.rst

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+.. title: Ideal Gas Constant Pressure Mole Reactor
+.. has_math: true
+
+.. jumbotron::
+
+   .. raw:: html
+
+      <h1 class="display-3">Ideal Gas Constant Pressure
+      Mole Reactor</h1>
+
+   .. class:: lead
+
+      This page shows the derivation of the governing equations used in
+      Cantera's Ideal Gas Constant Pressure Mole Reactor model.
+
+      More information on the Ideal Gas Constant Pressure Mole Reactor class can
+      be found `here. <{{% ct_docs doxygen/html/de/daa/classCantera_1_1IdealGasConstPressureMoleReactor.html %}}>`__
+
+Ideal Gas Constant Pressure Reactor
+***********************************
+
+An Ideal Gas Constant Pressure Mole Reactor is defined by the two state variables:
+
+- :math:`T`, the temperature (in K)
+
+- :math:`n_k`, the number of moles for each species (in kmol)
+
+The energy equation in terms of temperature is necessary as we replaced enthalpy in the state vector with temperature.
+We develop the equation for temperature by writing the total enthalpy in terms of the molar enthalpy and moles of each species.
+
+.. math::
+
+   H = \sum_k \bar{h}_k(T) n_k(T)
+
+   \frac{dH}{dt} = \frac{dT}{dt}\sum_k n_k \bar{c_{p,k}} + \sum \bar{h}_k \dot{n}_k
+
+After some manipulations yields an equation for the
+temperature:
+
+.. math::
+
+   \frac{dT}{dt} = \frac{\dot{Q} - \sum \bar{h}_k \dot{n}_k}{\sum_k n_k \bar{c}_{p,k} }
+  \tag{1}
+
+The moles of each species in the reactor's contents changes as a result of flow through
+the reactor's inlets and outlets, and production of homogeneous gas phase species and reactions on the reactor :py:class:`Wall`.
+The rate of moles of species :math:`k` generated through homogeneous phase
+reactions is :math:`V \dot{\omega}_k`, and the total rate at which moles of species
+:math:`k` is generated is:
+
+.. math::
+
+   \frac{dn_k}{dt} = V \dot{\omega}_k + \sum_{in} \dot{n}_{in} - \sum_{out} \dot{n}_{out} + \dot{n}_{wall}
+   \tag{2}
+
+Where the subscripts *in* and *out* refer to the sum of the superscripted property
+over all inlets and outlets respectively. A dot above a variable signifies a time
+derivative. Reactor *Walls* are defined `here. <{{% ct_docs sphinx/html/cython/zerodim.html#cantera.Wall %}}>`__
+
+
+Equations 1-2 are the governing equations for an Ideal Gas Constant Pressure
+Reactor.

pages/science/reactors/idealgasmolereactor.rst

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+.. title: Ideal Gas Mole Reactor
+.. has_math: true
+
+.. jumbotron::
+
+   .. raw:: html
+
+      <h1 class="display-3">Ideal Gas Mole Reactor</h1>
+   .. class:: lead
+
+      This page shows the derivation of the governing equations used in
+      Cantera's Ideal Gas Mole Reactor model.
+
+      More information on the Ideal Gas Mole Reactor class can be found `here.
+      <{{% ct_docs doxygen/html/d0/d03/classCantera_1_1IdealGasMoleReactor.html %}}>`__
+
+Ideal Gas Mole Reactor
+**********************
+
+An Ideal Gas Mole Reactor is defined by the three state variables:
+
+- :math:`T`, the temperature (in K)
+
+- :math:`V`, the reactor volume (in m\ :sup:`3`)
+
+- :math:`n_k`, the number of moles for each species (in kmol)
+
+The energy equation in terms of temperature is necessary as we replaced internal energy in the state vector with temperature.
+We develop the equation for temperature by writing the total enthalpy in terms of the molar enthalpy and moles of each species.
+
+.. math::
+
+   U = \sum_k \bar{u}_k(T) n_k(T)
+
+   \frac{dU}{dt} = \frac{dT}{dt}\sum_k n_k \bar{c_{v,k}} + \sum \bar{u}_k \dot{n}_k
+
+After some manipulations yields an equation for the
+temperature:
+
+.. math::
+
+   \frac{dT}{dt} = \frac{\dot{Q} - \sum \bar{u}_k \dot{n}_k}{\sum_k n_k \bar{c}_{p,k} }
+  \tag{1}
+
+The reactor volume changes as a function of time due to the motion of one or
+more walls:
+
+.. math::
+
+   \frac{dV}{dt} = \sum_w f_w A_w v_w(t)
+   \tag{2}
+
+Where :math:`f_w = \pm 1` indicates the facing of the wall (whether moving the wall increases or decreases the volume of the reactor), :math:`A_w` is the surface area of the wall, and :math:`v_w(t)` is the velocity of the wall as a function of time.
+
+Finally, the moles of each species in the reactor's contents changes as a result of flow through the reactor's inlets and outlets, and production of homogeneous gas phase species and reactions on the reactor :py:class:`Wall`.
+The rate of moles of species :math:`k` generated through homogeneous phase
+reactions is :math:`V \dot{\omega}_k`, and the total rate at which moles of species
+:math:`k` is generated is:
+
+.. math::
+
+   \frac{dn_k}{dt} = V \dot{\omega}_k + \sum_{in} \dot{n}_{in} - \sum_{out} \dot{n}_{out} + \dot{n}_{wall}
+   \tag{3}
+
+Equations 1-3 are the governing equations for an Ideal Gas Mole Reactor.

pages/science/reactors/molereactor.rst

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+.. title: Mole Reactor
+.. has_math: true
+
+.. jumbotron::
+
+   .. raw:: html
+
+      <h1 class="display-3">Mole Reactor</h1>
+
+   .. class:: lead
+
+      This page shows the derivation of the governing equations used in
+      Cantera's Mole Reactor model.
+
+      More information on the Mole Reactor class can be found `here.
+      <{{% ct_docs doxygen/html/da/d29/classCantera_1_1MoleReactor.html %}}>`__
+
+Mole Reactor
+************
+
+A homogeneous zero-dimensional reactor. By default, they are closed (no inlets or outlets),
+have fixed volume, and have adiabatic, chemically-inert walls. These properties may all be
+changed by adding appropriate components such as :py:class:`Wall`, :py:class:`MassFlowController`
+and :py:class:`Valve`.
+
+A Mole Reactor is defined by the three state variables:
+
+- :math:`U`, the total internal energy of the reactors contents (in J)
+
+- :math:`V`, the reactor volume (in m\ :sup:`3`)
+
+- :math:`n_k`, the number of moles for each species (in kmol)
+
+The equation for the total internal energy is found by writing the first law
+for an open system:
+
+.. math::
+
+   \frac{dU}{dt} = - p \frac{dV}{dt} + \dot{Q} +
+                    \sum_{in} \dot{n}_{in} \bar{h}_{in} - \bar{h} \sum_{out} \dot{n}_{out}
+   \tag{3}
+
+Where :math:`\dot{Q}` is the net rate of heat addition to the system.
+
+The reactor volume changes as a function of time due to the motion of one or
+more walls:
+
+.. math::
+
+   \frac{dV}{dt} = \sum_w f_w A_w v_w(t)
+   \tag{2}
+
+where :math:`f_w = \pm 1` indicates the facing of the wall (whether moving the wall increases or
+decreases the volume of the reactor), :math:`A_w` is the
+surface area of the wall, and :math:`v_w(t)` is the velocity of the wall as a
+function of time.
+
+The moles of each species in the reactor's contents changes as a result of flow through
+the reactor's inlets and outlets, and production of homogeneous gas phase species and reactions on the reactor :py:class:`Wall`.
+The rate of moles of species :math:`k` generated through homogeneous phase
+reactions is :math:`V \dot{\omega}_k`, and the total rate at which moles of species
+:math:`k` is generated is:
+
+.. math::
+
+   \frac{dn_k}{dt} = V \dot{\omega}_k + \sum_{in} \dot{n}_{in} - \sum_{out} \dot{n}_{out} + \dot{n}_{wall}
+   \tag{3}
+
+Where the subscripts *in* and *out* refer to the sum of the superscripted property
+over all inlets and outlets respectively. A dot above a variable signifies a time
+derivative. Reactor *Walls* are defined `here. <{{% ct_docs sphinx/html/cython/zerodim.html#cantera.Wall %}}>`__
+
+Equations 1-3 are the governing equations for a Mole Reactor.