From d48152139bed4ff38d4c2420d821d3ea493416e9 Mon Sep 17 00:00:00 2001 From: decaluwe Date: Tue, 22 Mar 2022 14:35:29 +1100 Subject: [PATCH 1/6] Initial restructure of Science section. --- pages/science/index.rst | 32 ++++++++--------- pages/science/thermodynamics.rst | 60 ++++++++++++++++++++++++++++++++ pages/science/transport.rst | 13 +++++++ 3 files changed, 88 insertions(+), 17 deletions(-) create mode 100644 pages/science/thermodynamics.rst create mode 100644 pages/science/transport.rst diff --git a/pages/science/index.rst b/pages/science/index.rst index 678029f7f..29e399119 100644 --- a/pages/science/index.rst +++ b/pages/science/index.rst @@ -21,12 +21,11 @@

Chemical Kinetic Theory

-These sections describe some of the theory underpinning the various ways that Cantera models phases +These sections describe some of the basic scientific theory underpinning the various ways that Cantera models phases of matter. This involves calculations for thermodynamic and transport properties and chemical reaction rates. The above information gives some insight into the basic constitutive models -available in Cantera: capabilities for calculating the basic properties of -phases of matter, which can be extended to model a wide range of science and -technology applications. +available in Cantera: capabilities for calculating the basic thermodynamic, chemical kinetic, and transport properties of phases of matter, which can be +extended to model a wide range of science and technology applications. .. container:: container :tagname: section @@ -37,56 +36,55 @@ technology applications. .. container:: :tagname: a - :attributes: href=phases.html - title=Phases + :attributes: href=thermodynamics.html + title=Thermodynamics .. container:: card-header section-card :tagname: div - Phases + Thermodynamics .. container:: card-body .. container:: card-text - The theory behind some of Cantera's phase models. + The theory behind how Cantera calculates species and phase thermodynamic properties. .. container:: card .. container:: :tagname: a - :attributes: href=science-species.html - title=Species + :attributes: href=reactions.html + title=Reactions .. container:: card-header section-card :tagname: div - Species + Reactions .. container:: card-body .. container:: card-text - The models Cantera uses to calculate species properties (thermodynamic and - transport). + The models and equations that Cantera uses to calculate chemical reaction rates. .. container:: card .. container:: :tagname: a - :attributes: href=reactions.html - title=Reactions + :attributes: href=transport.html + title=Transport .. container:: card-header section-card :tagname: div - Reactions + Transport .. container:: card-body .. container:: card-text - The models that Cantera uses to calculate chemical reaction rates. + The models that Cantera uses to calculate transport properties and rates. .. raw:: html diff --git a/pages/science/thermodynamics.rst b/pages/science/thermodynamics.rst new file mode 100644 index 000000000..69e09e80e --- /dev/null +++ b/pages/science/thermodynamics.rst @@ -0,0 +1,60 @@ +.. slug: thermodynamics +.. has_math: true +.. title: Calculating phase and species thermodynamics + +.. jumbotron:: + + .. raw:: html + +

Calculating thermodynamic properties in Cantera

+ + .. class:: lead + + Here, we describe how Cantera uses species and phase information to calculate thermodynamic properties. Thermodynamic properties typically depend on information at both the species and phase levels. + + - The user must specify a thermodynamic model for each species and provide inputs that inform how species-specific properties are calculated (e.g. as a function of temperature). + - The user also selects a phase model. This model describes how the species interact with one another to determine overall phase properties. This includes general :math:`P-v-T` behavior, as well as how species-specific properties are used to calculate phase-average properties such as internal energy, entropy, etc. + + +.. container:: container + :tagname: section + + .. container:: card-deck + + .. container:: card + + .. container:: + :tagname: a + :attributes: href=species.html + title=Species + + .. container:: card-header section-card + :tagname: div + + Species + + .. container:: card-body + + .. container:: card-text + + The models and equations that Cantera uses to calculate species thermdynamic properties. + + .. container:: card + + .. container:: + :tagname: a + :attributes: href=phases.html + title=Phases + + .. container:: card-header section-card + :tagname: div + + Phases + + .. container:: card-body + + .. container:: card-text + + The theory behind some of Cantera's phase models. + + \ No newline at end of file diff --git a/pages/science/transport.rst b/pages/science/transport.rst new file mode 100644 index 000000000..4c434269b --- /dev/null +++ b/pages/science/transport.rst @@ -0,0 +1,13 @@ +.. slug: transport +.. has_math: true +.. title: Calculating phase and species transport properties and rates + +.. jumbotron:: + + .. raw:: html + +

Calculating transport properties and rates in Cantera

+ + .. class:: lead + + Here, we describe how Cantera uses species and phase information to calculate transport properties and rates. From e6513a5e08658f953ded0809acf47f00df29a3a3 Mon Sep 17 00:00:00 2001 From: decaluwe Date: Thu, 24 Mar 2022 12:30:20 +1100 Subject: [PATCH 2/6] Additional `Science` Fixes -Slightly more detail on the `Thermodynamics` landing page. -A few small typo fixes - Correcting inconsistencies in the `Species` page with when the `hat` over molar property variables was used. - Replaced the number 0 with `^\circ` to indicate reference properties. --- pages/science/index.rst | 2 +- pages/science/species.rst | 44 ++++++++++++++++---------------- pages/science/thermodynamics.rst | 37 ++++++++++++++++++++++++--- 3 files changed, 56 insertions(+), 27 deletions(-) diff --git a/pages/science/index.rst b/pages/science/index.rst index 29e399119..e30c3b485 100644 --- a/pages/science/index.rst +++ b/pages/science/index.rst @@ -21,7 +21,7 @@

Chemical Kinetic Theory

-These sections describe some of the basic scientific theory underpinning the various ways that Cantera models phases +These sections describe some of the fundamental scientific theory underpinning the ways that Cantera models phases of matter. This involves calculations for thermodynamic and transport properties and chemical reaction rates. The above information gives some insight into the basic constitutive models available in Cantera: capabilities for calculating the basic thermodynamic, chemical kinetic, and transport properties of phases of matter, which can be diff --git a/pages/science/species.rst b/pages/science/species.rst index e3d91dc09..f6b0da9c5 100644 --- a/pages/science/species.rst +++ b/pages/science/species.rst @@ -80,11 +80,11 @@ expressions to compute the properties, they all require thermodynamic property information for the individual species. For the phase types implemented at present, the properties needed are: -1. the molar heat capacity at constant pressure :math:`\hat{c}^0_p(T)` for a - range of temperatures and a reference pressure :math:`P_0`; -2. the molar enthalpy :math:`\hat{h}(T_0, P_0)` at :math:`P_0` and a reference - temperature :math:`T_0`; -3. the absolute molar entropy :math:`\hat{s}(T_0, P_0)` at :math:`(T_0, P_0)`. +1. the molar heat capacity at constant pressure :math:`\hat{c}^\circ_p(T)` for a + range of temperatures and a reference pressure :math:`p^\circ`; +2. the molar enthalpy :math:`\hat{h}(T^\circ, p^\circ)` at :math:`p^\circ` and a reference + temperature :math:`T^\circ`; +3. the absolute molar entropy :math:`\hat{s}(T^\circ, p^\circ)` at :math:`(T^\circ, p^\circ)`. See: :ref:`the Thermodynamic Models section ` @@ -119,20 +119,20 @@ The NASA 7-Coefficient Polynomial Parameterization -------------------------------------------------- The NASA 7-coefficient polynomial parameterization is used to compute the -species reference-state thermodynamic properties :math:`\hat{c}^0_p(T)`, -:math:`\hat{h}^0(T)`, and :math:`\hat{s}^0(T)`. +species reference-state thermodynamic properties :math:`\hat{c}^\circ_p(T)`, +:math:`\hat{h}^\circ(T)`, and :math:`\hat{s}^\circ(T)`. -The NASA parameterization represents :math:`\hat{c}^0_p(T)` with a fourth-order +The NASA parameterization represents :math:`\hat{c}^\circ_p(T)` with a fourth-order polynomial: .. math:: - \frac{c_p^0(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4 + \frac{\hat{c}_p^\circ(T)}{\overline{R}} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4 - \frac{h^0 (T)}{R T} = a_0 + \frac{a_1}{2} T + \frac{a_2}{3} T^2 + + \frac{\hat{h}^\circ (T)}{\overline{R} T} = a_0 + \frac{a_1}{2} T + \frac{a_2}{3} T^2 + \frac{a_3}{4} T^3 + \frac{a_4}{5} T^4 + \frac{a_5}{T} - \frac{s^0(T)}{R} = a_0 \ln T + a_1 T + \frac{a_2}{2} T^2 + \frac{a_3}{3} T^3 + + \frac{\hat{s}^\circ(T)}{\overline{R}} = a_0 \ln T + a_1 T + \frac{a_2}{2} T^2 + \frac{a_3}{3} T^3 + \frac{a_4}{4} T^4 + a_6 Note that this is the "old" NASA polynomial form, used in the original NASA @@ -160,14 +160,14 @@ the following equations: .. math:: - \frac{C_p^0(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T + \frac{\hat{c}_p^\circ(T)}{\overline{R}} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T + a_4 T^2 + a_5 T^3 + a_6 T^4 - \frac{H^0(T)}{R T} = - a_0 T^{-2} + a_1 \frac{\ln T}{T} + a_2 + \frac{\hat{h}^\circ(T)}{\overline{R} T} = - a_0 T^{-2} + a_1 \frac{\ln T}{T} + a_2 + \frac{a_3}{2} T + \frac{a_4}{3} T^2 + \frac{a_5}{4} T^3 + \frac{a_6}{5} T^4 + \frac{a_7}{T} - \frac{s^0(T)}{R} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln T + \frac{\hat{s}^\circ(T)}{\overline{R}} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln T + a_3 T + \frac{a_4}{2} T^2 + \frac{a_5}{3} T^3 + \frac{a_6}{4} T^4 + a_8 A common source for species data in the NASA9 format is the @@ -184,12 +184,12 @@ The Shomate parameterization is: .. math:: - \hat{c}_p^0(T) = A + Bt + Ct^2 + Dt^3 + \frac{E}{t^2} + \hat{c}_p^\circ(T) = A + Bt + Ct^2 + Dt^3 + \frac{E}{t^2} - \hat{h}^0(T) = At + \frac{Bt^2}{2} + \frac{Ct^3}{3} + \frac{Dt^4}{4} - + \hat{h}^\circ(T) = At + \frac{Bt^2}{2} + \frac{Ct^3}{3} + \frac{Dt^4}{4} - \frac{E}{t} + F - \hat{s}^0(T) = A \ln t + B t + \frac{Ct^2}{2} + \frac{Dt^3}{3} - + \hat{s}^\circ(T) = A \ln t + B t + \frac{Ct^2}{2} + \frac{Dt^3}{3} - \frac{E}{2t^2} + G where :math:`t = T / 1000 K`. It requires 7 coefficients :math:`A`, :math:`B`, :math:`C`, :math:`D`, @@ -213,14 +213,14 @@ thermodynamic properties: .. math:: - \hat{c}_p^0(T) = \hat{c}_p^0(T_0) + \hat{c}_p^\circ(T) = \hat{c}_p^\circ(T^\circ) - \hat{h}^0(T) = \hat{h}^0(T_0) + \hat{c}_p^0\cdot(T-T_0) + \hat{h}^\circ(T) = \hat{h}^\circ(T_0) + \hat{c}_p^\circ\cdot(T-T^\circ) - \hat{s}^0(T) = \hat{s}^0(T_0) + \hat{c}_p^0 \ln (T/T_0) + \hat{s}^\circ(T) = \hat{s}^\circ(T_0) + \hat{c}_p^\circ \ln (T/T^\circ) -The parameterization uses four constants: :math:`T_0, \hat{c}_p^0(T_0), -\hat{h}^0(T_0), \hat{s}^0(T)`. The default value of :math:`T_0` is 298.15 K; the +The parameterization uses four constants: :math:`T^\circ, \hat{c}_p^\circ(T^\circ), +\hat{h}^\circ(T^\circ), \hat{s}^\circ(T)`. The default value of :math:`T^\circ` is 298.15 K; the default value for the other parameters is 0.0. A constant heat capacity parameterization can be defined in the CTI format using diff --git a/pages/science/thermodynamics.rst b/pages/science/thermodynamics.rst index 69e09e80e..63b1eb390 100644 --- a/pages/science/thermodynamics.rst +++ b/pages/science/thermodynamics.rst @@ -10,11 +10,40 @@ .. class:: lead - Here, we describe how Cantera uses species and phase information to calculate thermodynamic properties. Thermodynamic properties typically depend on information at both the species and phase levels. + Here, we describe how Cantera uses species and phase information to calculate thermodynamic properties. + + Thermodynamic properties typically depend on information at both the species and phase levels. The user must specify thermodynamic models for both levels, and these selections must be compatible with one another. For instance: one cannot pair a non-ideal species thermodyamic model with an ideal phase model. - - The user must specify a thermodynamic model for each species and provide inputs that inform how species-specific properties are calculated (e.g. as a function of temperature). - - The user also selects a phase model. This model describes how the species interact with one another to determine overall phase properties. This includes general :math:`P-v-T` behavior, as well as how species-specific properties are used to calculate phase-average properties such as internal energy, entropy, etc. + - The user must specify a thermodynamic model for each species and provide inputs that inform how species-specific properties are calculated. For example, the user specifies how the reference enthalpy and entropy values for each species are calcualted, as a function of temperature. + - The user also selects a phase model. This model describes how the species interact with one another to determine phase properties and species specific properties, for a given thermodynamic state. This includes general :math:`P-\hat{v}-T` behavior (for example, calculate the phase pressure for a given molar volume, temperature, and chemical composition), as well as how species-specific properties, such as internal energy, entropy, and others depend on the state variables +Example: The Ideal Gas Model +============================ +For a simple example: in the Ideal Gas model, one might use 7-parameter NASA polynomials to specify the species thermodynamics. These would be used to calculate the reference molar enthalpy :math:`\hat{h}_k^\circ(T)` and entropy :math:`\hat{s}_k^\circ(T)` for a given species :math:`k` as a function of temperature :math:`T`: + +.. math:: + + \frac{\hat{h}^\circ_k (T)}{\overline{R} T} = a_0 + \frac{a_1}{2} T + \frac{a_2}{3} T^2 + + \frac{a_3}{4} T^3 + \frac{a_4}{5} T^4 + \frac{a_5}{T} + + \frac{\hat{s}^\circ_k(T)}{\overline{R}} = a_0 \ln T + a_1 T + \frac{a_2}{2} T^2 + \frac{a_3}{3} T^3 + + \frac{a_4}{4} T^4 + a_6 + +At the phase level, the Ideal Gas Law determines the state, for example the pressure as a function of molar volume :math:`\hat{v}`, and temperature :math:`T`: + +.. math:: + p = \frac{\overline{R}T}{v} + +where :math:`\overline{R}` is the Universal Gas Constant. The phase model also dictates how the state variables influence the species thermodynamic quantities at a given state. For a species :math:`k`, for example, the Ideal Gas Model specifies that the specific molar internal energy :math:`\hat{u}_k` and entropy :math:`s_k` will be: + +.. math:: + \hat{u}_k = \hat{h}^\circ_k(T) - p\hat{v}X_k + + \hat{s}_k = \hat{s}^\circ_k(T) - \overline{R}T\ln\left(\frac{pX_k}{p^\circ}\right) + +where :math:`X_k` is the mole fraction of species :math:`k`, and where :math:`p^\circ` is the reference pressure at which the properties :math:`\hat{h}_k^\circ(T)` and :math:`\hat{s}_k^\circ(T)` are known. + +Please click either of the cards below for details on specific species and phase models available in Cantera: .. container:: container :tagname: section @@ -37,7 +66,7 @@ .. container:: card-text - The models and equations that Cantera uses to calculate species thermdynamic properties. + The models and equations that Cantera uses to calculate species thermodynamic properties. .. container:: card From 5f7028846c5c6d7c94aa8e3d9be12ef0bd1f56e8 Mon Sep 17 00:00:00 2001 From: decaluwe Date: Thu, 24 Mar 2022 14:17:21 +1100 Subject: [PATCH 3/6] Copyediting thermodynamics page. --- pages/science/index.rst | 6 ++-- pages/science/{reactions.rst => kinetics.rst} | 0 pages/science/thermodynamics.rst | 28 +++++++------------ 3 files changed, 13 insertions(+), 21 deletions(-) rename pages/science/{reactions.rst => kinetics.rst} (100%) diff --git a/pages/science/index.rst b/pages/science/index.rst index e30c3b485..977e79311 100644 --- a/pages/science/index.rst +++ b/pages/science/index.rst @@ -54,13 +54,13 @@ extended to model a wide range of science and technology applications. .. container:: :tagname: a - :attributes: href=reactions.html - title=Reactions + :attributes: href=kinetics.html + title=Kinetics .. container:: card-header section-card :tagname: div - Reactions + Kinetics and Reaction Rates .. container:: card-body diff --git a/pages/science/reactions.rst b/pages/science/kinetics.rst similarity index 100% rename from pages/science/reactions.rst rename to pages/science/kinetics.rst diff --git a/pages/science/thermodynamics.rst b/pages/science/thermodynamics.rst index 63b1eb390..ce9cb6609 100644 --- a/pages/science/thermodynamics.rst +++ b/pages/science/thermodynamics.rst @@ -12,38 +12,30 @@ Here, we describe how Cantera uses species and phase information to calculate thermodynamic properties. - Thermodynamic properties typically depend on information at both the species and phase levels. The user must specify thermodynamic models for both levels, and these selections must be compatible with one another. For instance: one cannot pair a non-ideal species thermodyamic model with an ideal phase model. + Thermodynamic properties typically depend on information at both the species and phase levels. The user must specify thermodynamic models for both levels, and these selections must be compatible with one another. For instance: one cannot pair certain non-ideal species thermodyamic models with an ideal phase model. - - The user must specify a thermodynamic model for each species and provide inputs that inform how species-specific properties are calculated. For example, the user specifies how the reference enthalpy and entropy values for each species are calcualted, as a function of temperature. + - The user must specify a thermodynamic model for each species and provide inputs that inform how species properties are calculated. For example, the user specifies how the reference enthalpy and entropy values for each species are calcualted, as a function of temperature. - The user also selects a phase model. This model describes how the species interact with one another to determine phase properties and species specific properties, for a given thermodynamic state. This includes general :math:`P-\hat{v}-T` behavior (for example, calculate the phase pressure for a given molar volume, temperature, and chemical composition), as well as how species-specific properties, such as internal energy, entropy, and others depend on the state variables Example: The Ideal Gas Model ============================ -For a simple example: in the Ideal Gas model, one might use 7-parameter NASA polynomials to specify the species thermodynamics. These would be used to calculate the reference molar enthalpy :math:`\hat{h}_k^\circ(T)` and entropy :math:`\hat{s}_k^\circ(T)` for a given species :math:`k` as a function of temperature :math:`T`: +For a simple example: in the Ideal Gas model, one might use 7-parameter NASA polynomials to specify the species reference thermodynamic quantities. These would be used to calculate the reference molar enthalpy :math:`\hat{h}_k^\circ(T)` and entropy :math:`\hat{s}_k^\circ(T)` for a given species :math:`k` as a function of temperature :math:`T`. See the `NASA Polynomials Species Thermo entry `__ for more information. -.. math:: - - \frac{\hat{h}^\circ_k (T)}{\overline{R} T} = a_0 + \frac{a_1}{2} T + \frac{a_2}{3} T^2 + - \frac{a_3}{4} T^3 + \frac{a_4}{5} T^4 + \frac{a_5}{T} - - \frac{\hat{s}^\circ_k(T)}{\overline{R}} = a_0 \ln T + a_1 T + \frac{a_2}{2} T^2 + \frac{a_3}{3} T^3 + - \frac{a_4}{4} T^4 + a_6 - -At the phase level, the Ideal Gas Law determines the state, for example the pressure as a function of molar volume :math:`\hat{v}`, and temperature :math:`T`: +At the phase level, the Ideal Gas Law provides the P-v-T relationship, called an equation of state. This is used, for example, to calculate the pressure as a function of molar volume :math:`\hat{v}` and temperature :math:`T`: .. math:: - p = \frac{\overline{R}T}{v} + p = \frac{\overline{R}T}{\hat{v}} -where :math:`\overline{R}` is the Universal Gas Constant. The phase model also dictates how the state variables influence the species thermodynamic quantities at a given state. For a species :math:`k`, for example, the Ideal Gas Model specifies that the specific molar internal energy :math:`\hat{u}_k` and entropy :math:`s_k` will be: +where :math:`\overline{R}` is the Universal Gas Constant. Maxwell's relations are used to derive other thermodynamic properties from the equation of state. With the Ideal Gas phase model, these reduce to rather simple forms. For example, for a species :math:`k`, the Ideal Gas molar internal energy :math:`\hat{u}_k` and entropy :math:`\hat{s}_k` are: .. math:: - \hat{u}_k = \hat{h}^\circ_k(T) - p\hat{v}X_k + \hat{u}_k = \hat{h}^\circ_k(T) - p\hat{v} - \hat{s}_k = \hat{s}^\circ_k(T) - \overline{R}T\ln\left(\frac{pX_k}{p^\circ}\right) + \hat{s}_k = \hat{s}^\circ_k(T) - \overline{R}\ln\left(\frac{pX_k}{p^\circ}\right) where :math:`X_k` is the mole fraction of species :math:`k`, and where :math:`p^\circ` is the reference pressure at which the properties :math:`\hat{h}_k^\circ(T)` and :math:`\hat{s}_k^\circ(T)` are known. -Please click either of the cards below for details on specific species and phase models available in Cantera: +Please click either of the cards below for details on the species and phase models available in Cantera: .. container:: container :tagname: section @@ -54,7 +46,7 @@ Please click either of the cards below for details on specific species and phase .. container:: :tagname: a - :attributes: href=species.html + :attributes: href=science-species.html title=Species .. container:: card-header section-card From 5798b732e08fe7183c92d6d6f9242c808b8bb6d3 Mon Sep 17 00:00:00 2001 From: decaluwe Date: Thu, 24 Mar 2022 14:21:00 +1100 Subject: [PATCH 4/6] Change Reactions page title. --- pages/science/kinetics.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pages/science/kinetics.rst b/pages/science/kinetics.rst index a28717854..e79c22bb3 100644 --- a/pages/science/kinetics.rst +++ b/pages/science/kinetics.rst @@ -1,4 +1,4 @@ -.. slug: reactions +.. slug: kinetics .. has_math: true .. title: Modeling Chemical Reactions From fd071f32f927b08871ef892e17322199466e76f0 Mon Sep 17 00:00:00 2001 From: decaluwe Date: Wed, 6 Apr 2022 14:17:55 +1000 Subject: [PATCH 5/6] Complete re-formatting of Science section. Moves transport property information from the `species` and `phases` pages to the `Transport` landing page. The information on the `Transport` landing page is still insufficient (imho), but as the current changes fully reproduce the information currently on the website, I will address this in a future PR. --- .../science/{phases.rst => phase-thermo.rst} | 20 ++--------- .../{species.rst => species-thermo.rst} | 15 ++------ pages/science/thermodynamics.rst | 4 +-- pages/science/transport.rst | 36 +++++++++++++++++++ pages/tutorials/cti/phases.rst | 2 +- pages/tutorials/yaml/phases.rst | 2 +- pages/tutorials/yaml/species.rst | 2 +- 7 files changed, 45 insertions(+), 36 deletions(-) rename pages/science/{phases.rst => phase-thermo.rst} (78%) rename pages/science/{species.rst => species-thermo.rst} (94%) diff --git a/pages/science/phases.rst b/pages/science/phase-thermo.rst similarity index 78% rename from pages/science/phases.rst rename to pages/science/phase-thermo.rst index d2f929948..69cc5ad35 100644 --- a/pages/science/phases.rst +++ b/pages/science/phase-thermo.rst @@ -1,4 +1,4 @@ -.. slug: phases +.. slug: phase-thermo .. has_math: true .. title: Modeling Phases @@ -6,7 +6,7 @@ .. raw:: html -

Modeling Phases in Cantera

+

Modeling Phase Thermodynamics in Cantera

.. class:: lead @@ -29,15 +29,6 @@ Ideal gas mixtures can be defined in the CTI format using the :cti:class:`ideal_gas` entry, or in the YAML format by specifying :ref:`ideal-gas ` in the ``thermo`` field. -.. _sec-transport-models: - -Transport Models -^^^^^^^^^^^^^^^^ - -Two transport models are available for use with ideal gas mixtures. The first is a multicomponent -transport model that is based on the model described by Dixon-Lewis [#dl68]_ (see also Kee et al. -[#Kee2017]_). The second is a model that uses the mixture-averaged rule. - Stoichiometric Solid -------------------- @@ -82,10 +73,3 @@ field. .. [#Kee1989] R. J. Kee, F. M. Rupley, and J. A. Miller. Chemkin-II: A Fortran chemical kinetics package for the analysis of gasphase chemical kinetics. Technical Report SAND89-8009, Sandia National Laboratories, 1989. - -.. [#dl68] G. Dixon-Lewis. Flame structure and flame reaction kinetics, - II: Transport phenomena in multicomponent systems. *Proc. Roy. Soc. A*, - 307:111--135, 1968. - -.. [#Kee2017] R. J. Kee, M. E. Coltrin, P. Glarborg, and H. Zhu. *Chemically Reacting Flow: - Theory and Practice*. 2nd Ed. John Wiley and Sons, 2017. diff --git a/pages/science/species.rst b/pages/science/species-thermo.rst similarity index 94% rename from pages/science/species.rst rename to pages/science/species-thermo.rst index f6b0da9c5..e605313fe 100644 --- a/pages/science/species.rst +++ b/pages/science/species-thermo.rst @@ -1,4 +1,4 @@ -.. slug: science-species +.. slug: species-thermo .. has_math: true .. title: Elements and Species @@ -6,7 +6,7 @@ .. raw:: html -

Elements and Species

+

Elements and Species Thermodynamics

.. class:: lead @@ -88,17 +88,6 @@ present, the properties needed are: See: :ref:`the Thermodynamic Models section ` -Species Transport Coefficients ------------------------------- - -Transport property models in general require coefficients that express the -effect of each species on the transport properties of the phase. Currently, -ideal-gas transport property models are implemented. - -Transport properties can be defined in the CTI format using the -:cti:class:`gas_transport` entry, or in the YAML format using the -:ref:`transport ` field of a ``species`` entry. - .. _sec-thermo-models: Thermodynamic Property Models diff --git a/pages/science/thermodynamics.rst b/pages/science/thermodynamics.rst index ce9cb6609..589e2e097 100644 --- a/pages/science/thermodynamics.rst +++ b/pages/science/thermodynamics.rst @@ -46,7 +46,7 @@ Please click either of the cards below for details on the species and phase mode .. container:: :tagname: a - :attributes: href=science-species.html + :attributes: href=species-thermo.html title=Species .. container:: card-header section-card @@ -64,7 +64,7 @@ Please click either of the cards below for details on the species and phase mode .. container:: :tagname: a - :attributes: href=phases.html + :attributes: href=phase-thermo.html title=Phases .. container:: card-header section-card diff --git a/pages/science/transport.rst b/pages/science/transport.rst index 4c434269b..37ce1ac98 100644 --- a/pages/science/transport.rst +++ b/pages/science/transport.rst @@ -11,3 +11,39 @@ .. class:: lead Here, we describe how Cantera uses species and phase information to calculate transport properties and rates. + + Similar to Cantera's approach to `thermodynamic properties `__, transport property calcualtions in Cantera depend on information at both the species and phase levels. The user must specify transport models for both levels, and these selections must be compatible with one another. + + - The user must specify a transport model for each species and provide inputs that inform how species properties are calculated. For example, the user provides inputs that allow Cantera to calculate species collision integrals based on species-specific Lennard-Jones parameters. + - The user also selects a phase model. This model describes how the species interact with one another to determine phase-averaged properties (such viscosity or thermal conductivity) and species specific properties (such as diffusion coefficients), for a given thermodynamic state. + +Species Transport Coefficients +------------------------------ + +Transport property models in general require coefficients that express the +effect of each species on the transport properties of the phase. Currently, +ideal-gas transport property models are implemented. + +Transport properties can be defined in the CTI format using the +:cti:class:`gas_transport` entry, or in the YAML format using the +:ref:`transport ` field of a ``species`` entry. + +.. _sec-phase-transport-models: + +Phase Transport Models +---------------------- + +Two transport models are available for use with ideal gas mixtures. The first is a multicomponent +transport model that is based on the model described by Dixon-Lewis [#dl68]_ (see also Kee et al. +[#Kee2017]_). The second is a model that uses the mixture-averaged rule. + + + +.. rubric:: References + +.. [#dl68] G. Dixon-Lewis. Flame structure and flame reaction kinetics, + II: Transport phenomena in multicomponent systems. *Proc. Roy. Soc. A*, + 307:111--135, 1968. + +.. [#Kee2017] R. J. Kee, M. E. Coltrin, P. Glarborg, and H. Zhu. *Chemically Reacting Flow: + Theory and Practice*. 2nd Ed. John Wiley and Sons, 2017. \ No newline at end of file diff --git a/pages/tutorials/cti/phases.rst b/pages/tutorials/cti/phases.rst index f922ea648..79814797e 100644 --- a/pages/tutorials/cti/phases.rst +++ b/pages/tutorials/cti/phases.rst @@ -215,7 +215,7 @@ The Transport Model A *transport model* is a set of equations used to compute transport properties. For :cti:class:`ideal_gas` phases, multiple transport models are available; the one desired can be selected by assigning a string to this -field. See :ref:`Transport Models ` for more details. +field. See :ref:`Transport Models ` for more details. The Initial State ^^^^^^^^^^^^^^^^^ diff --git a/pages/tutorials/yaml/phases.rst b/pages/tutorials/yaml/phases.rst index 8a545d1aa..045d89f67 100644 --- a/pages/tutorials/yaml/phases.rst +++ b/pages/tutorials/yaml/phases.rst @@ -5,7 +5,7 @@ .. raw:: html -

Phases and their Interfaces

+

Phases and their Interfaces in YAML

.. class:: lead diff --git a/pages/tutorials/yaml/species.rst b/pages/tutorials/yaml/species.rst index 0abed7313..23c57f7ad 100644 --- a/pages/tutorials/yaml/species.rst +++ b/pages/tutorials/yaml/species.rst @@ -6,7 +6,7 @@ .. raw:: html -

Elements and Species

+

Elements and Species in YAML

.. class:: lead From 44e1fb483d4d39c5f9f57086d1fe6d0d5abd2af9 Mon Sep 17 00:00:00 2001 From: "Steven C. DeCaluwe" Date: Fri, 8 Apr 2022 07:38:09 +1000 Subject: [PATCH 6/6] Final edits - typos, clarity, formatting, etc. Update pages/science/thermodynamics.rst Explaining the ideal gas law. - Fix math formatting. - Link to info on Maxwell relations. Update pages/science/species-thermo.rst - Grammar - Fix math formatting. Typo fix on pages/science/transport.rst --- pages/science/species-thermo.rst | 10 +++++----- pages/science/thermodynamics.rst | 10 +++++----- pages/science/transport.rst | 2 +- 3 files changed, 11 insertions(+), 11 deletions(-) diff --git a/pages/science/species-thermo.rst b/pages/science/species-thermo.rst index e605313fe..f674a3ed9 100644 --- a/pages/science/species-thermo.rst +++ b/pages/science/species-thermo.rst @@ -73,7 +73,7 @@ defined to be composed solely of electrons. Thermodynamic Properties ------------------------ -The phase models discussed in the `Phases section `__ +The phase models discussed in the `Phases section `__ implement specific models for the thermodynamic properties appropriate for the type of phase or interface they represent. Although each one may use different expressions to compute the properties, they all require thermodynamic property @@ -86,7 +86,7 @@ present, the properties needed are: temperature :math:`T^\circ`; 3. the absolute molar entropy :math:`\hat{s}(T^\circ, p^\circ)` at :math:`(T^\circ, p^\circ)`. -See: :ref:`the Thermodynamic Models section ` +The superscript :math:`^\circ` here represents the *reference state*--a specified state (i.e. set of conditions :math:`T^\circ` and :math:`p^\circ` and fixed chemical composition) at which thermodynamic properties are known. .. _sec-thermo-models: @@ -204,12 +204,12 @@ thermodynamic properties: \hat{c}_p^\circ(T) = \hat{c}_p^\circ(T^\circ) - \hat{h}^\circ(T) = \hat{h}^\circ(T_0) + \hat{c}_p^\circ\cdot(T-T^\circ) + \hat{h}^\circ(T) = \hat{h}^\circ\left(T_0\right) + \hat{c}_p^\circ \left(T-T^\circ\right) - \hat{s}^\circ(T) = \hat{s}^\circ(T_0) + \hat{c}_p^\circ \ln (T/T^\circ) + \hat{s}^\circ(T) = \hat{s}^\circ(T_0) + \hat{c}_p^\circ \ln{\left(\frac{T}{T^\circ}\right)} The parameterization uses four constants: :math:`T^\circ, \hat{c}_p^\circ(T^\circ), -\hat{h}^\circ(T^\circ), \hat{s}^\circ(T)`. The default value of :math:`T^\circ` is 298.15 K; the +\hat{h}^\circ(T^\circ), and \hat{s}^\circ(T)`. The default value of :math:`T^\circ` is 298.15 K; the default value for the other parameters is 0.0. A constant heat capacity parameterization can be defined in the CTI format using diff --git a/pages/science/thermodynamics.rst b/pages/science/thermodynamics.rst index 589e2e097..2d76fb2a4 100644 --- a/pages/science/thermodynamics.rst +++ b/pages/science/thermodynamics.rst @@ -15,18 +15,18 @@ Thermodynamic properties typically depend on information at both the species and phase levels. The user must specify thermodynamic models for both levels, and these selections must be compatible with one another. For instance: one cannot pair certain non-ideal species thermodyamic models with an ideal phase model. - The user must specify a thermodynamic model for each species and provide inputs that inform how species properties are calculated. For example, the user specifies how the reference enthalpy and entropy values for each species are calcualted, as a function of temperature. - - The user also selects a phase model. This model describes how the species interact with one another to determine phase properties and species specific properties, for a given thermodynamic state. This includes general :math:`P-\hat{v}-T` behavior (for example, calculate the phase pressure for a given molar volume, temperature, and chemical composition), as well as how species-specific properties, such as internal energy, entropy, and others depend on the state variables + - The user also selects a phase model. This model describes how the species interact with one another to determine phase properties and species specific properties, for a given thermodynamic state. This includes general :math:`p`-:math:`\hat{v}`-:math:`T` behavior (for example, calculate the phase pressure for a given molar volume, temperature, and chemical composition), as well as how species-specific properties, such as internal energy, entropy, and others depend on the state variables Example: The Ideal Gas Model ============================ For a simple example: in the Ideal Gas model, one might use 7-parameter NASA polynomials to specify the species reference thermodynamic quantities. These would be used to calculate the reference molar enthalpy :math:`\hat{h}_k^\circ(T)` and entropy :math:`\hat{s}_k^\circ(T)` for a given species :math:`k` as a function of temperature :math:`T`. See the `NASA Polynomials Species Thermo entry `__ for more information. -At the phase level, the Ideal Gas Law provides the P-v-T relationship, called an equation of state. This is used, for example, to calculate the pressure as a function of molar volume :math:`\hat{v}` and temperature :math:`T`: +At the phase level, the Ideal Gas Law provides the :math:`P`-:math:`\hat{v}`-:math:`T` relationship. The ideal gas law is an example of an equation of state. This is used, for example, to calculate the pressure as a function of molar volume :math:`\hat{v}`, and temperature, :math:`T`: .. math:: p = \frac{\overline{R}T}{\hat{v}} -where :math:`\overline{R}` is the Universal Gas Constant. Maxwell's relations are used to derive other thermodynamic properties from the equation of state. With the Ideal Gas phase model, these reduce to rather simple forms. For example, for a species :math:`k`, the Ideal Gas molar internal energy :math:`\hat{u}_k` and entropy :math:`\hat{s}_k` are: +where :math:`\overline{R}` is the Universal Gas Constant. The `Maxwell relations `__ are used to derive other thermodynamic properties from the equation of state. With the Ideal Gas phase model, these reduce to rather simple forms. For example, for a species :math:`k`, the Ideal Gas molar internal energy :math:`\hat{u}_k` and entropy :math:`\hat{s}_k` are: .. math:: \hat{u}_k = \hat{h}^\circ_k(T) - p\hat{v} @@ -58,7 +58,7 @@ Please click either of the cards below for details on the species and phase mode .. container:: card-text - The models and equations that Cantera uses to calculate species thermodynamic properties. + The models and equations that Cantera uses to calculate species thermodynamic properties, such as the NASA 7-parameter polynomial form. .. container:: card @@ -76,6 +76,6 @@ Please click either of the cards below for details on the species and phase mode .. container:: card-text - The theory behind some of Cantera's phase models. + The theory behind some of Cantera's phase models, such as the Ideal Gas Law. \ No newline at end of file diff --git a/pages/science/transport.rst b/pages/science/transport.rst index 37ce1ac98..3571e7fdb 100644 --- a/pages/science/transport.rst +++ b/pages/science/transport.rst @@ -12,7 +12,7 @@ Here, we describe how Cantera uses species and phase information to calculate transport properties and rates. - Similar to Cantera's approach to `thermodynamic properties `__, transport property calcualtions in Cantera depend on information at both the species and phase levels. The user must specify transport models for both levels, and these selections must be compatible with one another. + Similar to Cantera's approach to `thermodynamic properties `__, transport property calculations in Cantera depend on information at both the species and phase levels. The user must specify transport models for both levels, and these selections must be compatible with one another. - The user must specify a transport model for each species and provide inputs that inform how species properties are calculated. For example, the user provides inputs that allow Cantera to calculate species collision integrals based on species-specific Lennard-Jones parameters. - The user also selects a phase model. This model describes how the species interact with one another to determine phase-averaged properties (such viscosity or thermal conductivity) and species specific properties (such as diffusion coefficients), for a given thermodynamic state.