spelling fix

Author: Cristopher-Morales

_tutorials/incompressible_flow/Inc_Species_Transport_Composition_Dependent_Model/Inc_Species_Transport_Composition_Dependent_Model.md

@@ -15,7 +15,7 @@ follows: Inc_Species_Transport
 
 ## Goals
 
-In this tutorial, the user will be familiarized with the composition-dependent model in SU2 based on the Ideal Gas law for a gas mixture. The necessary steps and configuration options for the aforementioned model will be explained through a 3D simulation in the incompressible regime for a kenics static mixer for a methane-air mixture.
+In this tutorial, the user will be familiarized with the composition-dependent model in SU2 based on the Ideal Gas law for a gas mixture. The necessary steps and configuration options for the aforementioned model will be explained through a 3D incompressible kenics static mixer for a methane-air mixture.
 
 ## Resources
 
@@ -32,7 +32,7 @@ The following tutorial assumes you have already compiled `SU2_CFD` in serial or
 
 ## Background
 
-The geometry consists on a Static Kenics mixer with three blades, each blade starts at 90 degrees perpendicular to the previous blades and they are being twisted 180 degrees along the z-axis in order to enhance the mixing. Furthermore, two inlets are considered where pure air and pure methane are injected in each inlet. Finally, one oulet is considered at the end of the mixer device in order to study the pressure drop and the variance of the mass fraction, which is a measure of the mixing performance of the mixing device.
+The geometry consists on a Static Kenics mixer with three blades, each blade starts at 90 degrees perpendicular to the previous blades and they are being twisted 180 degrees along the z-axis in order to enhance the mixing. Furthermore, two inlets are considered where pure air and pure methane are injected at each inlet. Finally, one oulet is considered at the end of the mixer device in order to study the pressure drop and the variance of the mass fraction, which is a measure of the mixing performance of the mixing device.
 
 
 ## Problem Setup
@@ -58,7 +58,7 @@ The thermochemical properties for each gas are given below:
     - Heat capacity at constant pressure: 1009.39 [J/(kg K)]
     - Thermal Conductivity: 0.0258 [W /(m K)]
 
-The species mass fractions at each inlet are given below:
+The species mass fractions at each inlet are the following:
 
 - Inlet_1: mass fractions methane, Y_CH4 = 1.0 (pure methane, Y_air=0.0)
 - Inlet_2: mass fractions methane, Y_CH4 = 0.0 (pure air, Y_air=1.0)
@@ -67,15 +67,19 @@ It must be noticed that inside SU2, for a mixture of N species, N-1 species tran
 
 ## Configuration File Options
 
-All available options concerning species transport are listed in the [config_template.cfg](https://github.com/su2code/SU2/blob/master/config_template.cfg).Here, we are going to focus in the compostion-dependent options.
+All available options concerning species transport are listed in the [config_template.cfg](https://github.com/su2code/SU2/blob/master/config_template.cfg).Here, we are going to focus in the composition-dependent options.
 
 For activating the composition-dependent model, the fluid model must be chosen as `FLUID_MODEL= FLUID_MIXTURE`. It must be noted that this model is only compatible with `INC_DENSITY_MODEL= VARIABLE`. Otherwise, an error will be shown at run-time.
-For incompressible flows, a low-mach Number approximation allow to decompose the pressure into dynamics and thermodynamics (operating) pressure (see [Theory]/docs_v7/Theory/). The operating pressure is used for computing the mixture density using the Ideal gas law. The thermodynamic pressure might strongly affects the density at the inlets causing unphysical results. Therefore, the thermodynamic pressure must be provided for the user for the `FLUID_MIXTURE` model and it is not longer computed from the free-stream conditions as it is donde in the other fluid models. As in mixing and combustion processes, the operating pressure is often assumed as 101325 pa, then this is the default value considered inside SU2 if the thermodynamics pressure is not given in the .cfg file. The thermodynamics pressure is given in the .cfg file as follow: `THERMODYNAMIC_PRESSURE= 101325.0`.
-Subsequently, The molecular weights and Heat capacities at constant pressure must be provided as a list as follow: `MOLECULAR_WEIGHT= W_1, W_2,...., W_N` ,  `SPECIFIC_HEAT_CP = Cp_1, Cp_2,..., Cp_N`. The length of the list must match the number of the N species in the mixture. Moreover, the mean molecular weight is computed as a mole fraction average and the mixture heat capacity is computes as a mass fraction average. For more information, please see $^{1},^{3}$. 
+
+For incompressible flows, a low-mach Number approximation allows to decompose the pressure into dynamics and thermodynamics (operating) pressure (see [Theory]/docs_v7/Theory/). The operating pressure is used for computing the mixture density using the Ideal gas law. The thermodynamic pressure might strongly affects the density at the inlets causing unphysical results. Therefore, the thermodynamic pressure must be provided for the user for the `FLUID_MIXTURE` model and it is not longer computed from the free-stream conditions as it is done in the other fluid models. As in mixing and combustion processes, the operating pressure is often assumed as 101325 pa, then this is the default value considered inside SU2 if the thermodynamics pressure is not given in the .cfg file. The thermodynamics pressure is given in the .cfg file as follow: `THERMODYNAMIC_PRESSURE= 101325.0`.
+
+Subsequently, The molecular weights and Heat capacities at constant pressure must be provided as a list as follow: `MOLECULAR_WEIGHT= W_1, W_2,...., W_N` ,  `SPECIFIC_HEAT_CP = Cp_1, Cp_2,..., Cp_N`. The length of the list must match the number of the N species in the mixture. Moreover, the mean molecular weight is computed as a mole fraction average and the mixture heat capacity is computed as a mass fraction average. For more information, please see $^{1},^{3}$.
+
 For the conductivity model, the following options are available: `CONDUCTIVITY_MODEL= CONSTANT_CONDUCTIVITY, CONSTANT_PRANDTL, POLYNOMIAL_CONDUCTIVITY `. In this tutorial, the option `CONSTANT_CONDUCTIVITY` is used. For this option, a constant conductivity for each species must be provided as follow: `THERMAL_CONDUCTIVITY_CONSTANT= k_1, k_2,...., k_N`. 
 Currently, the only mixing law available in SU2 for computing the mixture thermal conductivity is based on the Wilke mixing law. Therefore, this is the default option and it is hardcoded for the `FLUID_MIXTURE` option. For more information regarding this mixing model, please see $^{1},^{2}$.
 
 Similar treatment is done for the Laminar Prandtl numbers: `PRANDTL_LAM= Pr_1, Pr_2,....,Pr_N`. Finally, for turbulence simulations, the option of turbulent Prandlt number can be enabled as `TURBULENT_CONDUCTIVITY_MODEL= CONSTANT_PRANDTL_TURB`. If this option is enabled, the turbulent Prandtl numbers must follow the same structure as the Laminar Prandtl numbers: `PRANDTL_TURB= Pr_Turb_1, Pr_Turb_2, ..., Pr_Turb_N`. For more information about laminar and turbulent Prandlt Number, please see [Theory](/docs_v7/Theory/).
+
 For the present tutorial, the options are given below:
 
 ```
@@ -98,7 +102,7 @@ TURBULENT_CONDUCTIVITY_MODEL= CONSTANT_PRANDTL_TURB
 PRANDTL_TURB= 0.90, 0.90
 ```
 
-Regarding the viscosity model, the following options are available `VISCOSITY_MODEL= SUTHERLAND, CONSTANT_VISCOSITY, POLYNOMIAL_VISCOSITY`. In the case of `CONSTANT_VISCOSITY`, the viscosities must be provided as a list as follow: `MU_CONSTANT= mu_1, mu_2, ..., mu_N`. Similarly, if `SUTHERLAND` model is chosen, the sutherland parameters must be given as a list for each species in the mixture. For completeness, an example for SUTHERLAND option is given below:
+Regarding the viscosity model, the following options are available `VISCOSITY_MODEL= SUTHERLAND, CONSTANT_VISCOSITY, POLYNOMIAL_VISCOSITY`. In the case of `CONSTANT_VISCOSITY`, the viscosities must be provided as a list as follow: `MU_CONSTANT= mu_1, mu_2, ..., mu_N`. Similarly, if `SUTHERLAND` model is chosen, the sutherland parameters must be given as a list for each species in the mixture. For completeness, an example for SUTHERLAND option is given below for a mixture of two species:
 
 ```
 % --------------------------- VISCOSITY MODEL ---------------------------------%
@@ -127,7 +131,7 @@ MIXING_VISCOSITY_MODEL = WILKE
 
 The Species transport is switched on by setting `KIND_SCALAR_MODEL= SPECIES_TRANSPORT`. For the mass diffusivity, the following models are available `DIFFUSIVITY_MODEL= CONSTANT_DIFFUSIVITY, CONSTANT_SCHMIDT, UNITY_LEWIS, CONSTANT_LEWIS` , where `CONSTANT_DIFFUSIVITY` is the default model. For the two first, a constant value for all species must be given in the .cfg file, as it is done in the species transport tutorial [Inc_Species_Transport](/tutorials/Inc_Species_Transport/). For the UNITY_LEWIS, no values must be provided because the diffusivity is computed using the mixture thermal conductivity, density and heat capacity at constant pressure, for more information please see $^{3}$. For highly diffusive gases, such as hydrogen, the `CONSTANT_LEWIS` option could be used. For this option, the Lewis numbers of the N-1 species which a transport equation is being solved must be provided as a list using the following option `CONSTANT_LEWIS_NUMBER= Le_1, Le_2, ..., Le_N_1`. Finally, for turbulent simulations, the turbulent diffusivity is computed based on the `SCHMIDT_NUMBER_TURBULENT`. For reference, please consult [the respective theory](/docs_v7/Theory/#species-transport).
 
-Finally, for the SST model, it is possible to provide the intensity and turbulent-to-laminar viscosity ratios per inlet. For this option, we use the following structure `ARKER_INLET_TURBULENT= (inlet_1, TurbIntensity_1, TurbLamViscRatio_1, inlet_2, TurbIntensity_2, TurbLamViscRatio_2, ...)`. The other species transport options can be found in the species transpor 
+Finally, for the SST model, it is possible to provide the intensity and turbulent-to-laminar viscosity ratios per inlet. For this option, we use the following structure `MARKER_INLET_TURBULENT= (inlet_1, TurbIntensity_1, TurbLamViscRatio_1, inlet_2, TurbIntensity_2, TurbLamViscRatio_2, ...)`. The other species transport options can be found in the species transport. 
 
 The number of species transport equations is not set individually but deduced from the number of values given in the respective lists for species options. SU2 checks whether the same amount of values is given in each option and solves the appropriate amount of equations. `MARKER_INLET_SPECIES` is one of these options and has to be used alongside a usual `MARKER_INLET`. For outlets, symmetries or walls this is not necessary. 
 
@@ -236,8 +240,11 @@ Figure (4): Velocity Magnitude in the domain.
 
 ### References
 $^{1}$ B. Poling, J. Prausnitz, J. O’Connell, The Properties of Gases and Liquids, 5th Edition, McGraw-Hill Education,2000.(URL https://books.google.nl/books?id=9tGclC3ZRX0C)
+
 $^{2}$ C. R. Wilke, A viscosity equation for gas mixtures, The Journal of Chemical Physics 18 (4) (1950),517–519.(https:doi:10.1063/1.1747673).
+
 $^{3}$ T. Poinsot, D. Veynante, Theoretical and Numerical Combustion, Ch. 1, 2012.
+
 $^{4}$ T. A. Davidson, A simple and accurate method for calculating viscosity of gaseous mixtures. (URL https://www.osti.gov/biblio/6129940)