Quantities#

This part of the documentation presents notations for all multipy quantities.

Composition#

Species mole fractions#

Notation

Unit

Code

Type

Shape

\(\mathbf{X}_i\)

\([-]\)

Composition.species_mole_fractions

scalar numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{X}_i = \begin{bmatrix} \cdots & X_1 & \cdots \\ \cdots & X_2 & \cdots \\ & \vdots & \\ \cdots & X_n & \cdots \\ \end{bmatrix}\end{split}\]

Species mole fractions gradients#

Notation

Unit

Code

Type

Shape

\(\nabla \mathbf{X}_i\)

\([-]\)

Composition.grad_species_mole_fractions

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\nabla \mathbf{X}_i = \begin{bmatrix} \cdots & \nabla X_1 & \cdots \\ \cdots & \nabla X_2 & \cdots \\ & \vdots & \\ \cdots & \nabla X_n & \cdots \\ \end{bmatrix}\end{split}\]

Species mass fractions#

Notation

Unit

Code

Type

Shape

\(\mathbf{Y}_i\)

\([-]\)

Composition.species_mass_fractions

scalar numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{Y}_i = \begin{bmatrix} \cdots & Y_1 & \cdots \\ \cdots & Y_2 & \cdots \\ & \vdots & \\ \cdots & Y_n & \cdots \\ \end{bmatrix}\end{split}\]

Species mass fractions gradients#

Notation

Unit

Code

Type

Shape

\(\nabla \mathbf{Y}_i\)

\([-]\)

Composition.grad_species_mass_fractions

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\nabla \mathbf{Y}_i = \begin{bmatrix} \cdots & \nabla Y_1 & \cdots \\ \cdots & \nabla Y_2 & \cdots \\ & \vdots & \\ \cdots & \nabla Y_n & \cdots \\ \end{bmatrix}\end{split}\]

Species volume fractions#

Notation

Unit

Code

Type

Shape

\(\mathbf{V}_i\)

\([-]\)

Composition.species_volume_fractions

scalar numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{V}_i = \begin{bmatrix} \cdots & V_1 & \cdots \\ \cdots & V_2 & \cdots \\ & \vdots & \\ \cdots & V_n & \cdots \\ \end{bmatrix}\end{split}\]

Species volume fractions gradients#

Notation

Unit

Code

Type

Shape

\(\nabla \mathbf{V}_i\)

\([-]\)

Composition.grad_species_volume_fractions

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\nabla \mathbf{V}_i = \begin{bmatrix} \cdots & \nabla V_1 & \cdots \\ \cdots & \nabla V_2 & \cdots \\ & \vdots & \\ \cdots & \nabla V_n & \cdots \\ \end{bmatrix}\end{split}\]

Species molar densities#

Notation

Unit

Code

Type

Shape

\(\mathbf{c}_i\)

\([mole/m^3]\)

Composition.species_molar_densities

scalar numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{c}_i = \begin{bmatrix} \cdots & c_1 & \cdots \\ \cdots & c_2 & \cdots \\ & \vdots & \\ \cdots & c_n & \cdots \\ \end{bmatrix}\end{split}\]

Species mass densities#

Notation

Unit

Code

Type

Shape

\(\pmb{\rho}_i\)

\([kg/m^3]\)

Composition.species_mass_densities

scalar numpy.ndarray

(n_species,n_observations)
\[\begin{split}\pmb{\rho}_i = \begin{bmatrix} \cdots & \rho_1 & \cdots \\ \cdots & \rho_2 & \cdots \\ & \vdots & \\ \cdots & \rho_n & \cdots \\ \end{bmatrix}\end{split}\]

Species molar masses#

Notation

Unit

Code

Type

Shape

\(\pmb{M}_i\)

\([kg/mole]\)

Composition.species_molar_masses

scalar numpy.ndarray

(n_species,1)
\[\begin{split}\pmb{M}_i = \begin{bmatrix} M_1 \\ M_2 \\ \vdots \\ M_n \\ \end{bmatrix}\end{split}\]

Species molar production rates#

Notation

Unit

Code

Type

Shape

\(\mathbf{s}_i\)

\([mole/(m^3s)]\)

Composition.get_species_molar_production_rates

scalar numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{s}_i = \begin{bmatrix} \cdots & s_1 & \cdots \\ \cdots & s_2 & \cdots \\ & \vdots & \\ \cdots & s_n & \cdots \\ \end{bmatrix}\end{split}\]

Species mass production rates#

Notation

Unit

Code

Type

Shape

\(\pmb{\omega}_i\)

\([kg/(m^3s)]\)

Composition.get_species_mass_production_rates

scalar numpy.ndarray

(n_species,n_observations)
\[\begin{split}\pmb{\omega}_i = \begin{bmatrix} \cdots & \omega_1 & \cdots \\ \cdots & \omega_2 & \cdots \\ & \vdots & \\ \cdots & \omega_n & \cdots \\ \end{bmatrix}\end{split}\]

Mixture molar density#

Notation

Unit

Code

Type

Shape

\(c\)

\([mole/m^3]\)

Composition.mixture_molar_density

scalar float

N/A

Mixture molar volume#

Notation

Unit

Code

Type

Shape

\(\bar{V}\)

\([m^3/mole]\)

Composition.mixture_molar_volume

scalar float

N/A

Mixture mass density#

Notation

Unit

Code

Type

Shape

\(\pmb{\rho}\)

\([kg/m^3]\)

Composition.mixture_mass_density

scalar numpy.ndarray

(1,n_observations)
\[\begin{split}\pmb{\rho} = \begin{bmatrix} \cdots & \rho & \cdots \\ \end{bmatrix}\end{split}\]

Mixture molar mass#

Notation

Unit

Code

Type

Shape

\(\pmb{M}\)

\([kg/mole]\)

Composition.mixture_molar_mass

scalar numpy.ndarray

(1,n_observations)
\[\begin{split}\pmb{M} = \begin{bmatrix} \cdots & M & \cdots \\ \end{bmatrix}\end{split}\]

Velocity#

Species velocities#

Notation

Unit

Code

Type

Shape

\(\mathbf{u}_i\)

\([m/s]\)

Velocity.species_velocities

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{u}_i = \begin{bmatrix} \cdots & \mathbf{u}_1 & \cdots \\ \cdots & \mathbf{u}_2 & \cdots \\ & \vdots & \\ \cdots & \mathbf{u}_n & \cdots \\ \end{bmatrix}\end{split}\]

Molar-averaged mixture velocity#

Notation

Unit

Code

Type

Shape

\(\mathbf{u}\)

\([m/s]\)

Velocity.molar_averaged

vector numpy.ndarray

(1,n_observations)
\[\begin{split}\mathbf{u} = \begin{bmatrix} \cdots & \mathbf{u} & \cdots \\ \end{bmatrix}\end{split}\]

Mass-averaged mixture velocity#

Notation

Unit

Code

Type

Shape

\(\mathbf{v}\)

\([m/s]\)

Velocity.mass_averaged

vector numpy.ndarray

(1,n_observations)
\[\begin{split}\mathbf{v} = \begin{bmatrix} \cdots & \mathbf{v} & \cdots \\ \end{bmatrix}\end{split}\]

Volume-averaged mixture velocity#

Notation

Unit

Code

Type

Shape

\(\mathbf{u}^V\)

\([m/s]\)

Velocity.volume_averaged

vector numpy.ndarray

(1,n_observations)
\[\begin{split}\mathbf{u}^V = \begin{bmatrix} \cdots & \mathbf{u}^V & \cdots \\ \end{bmatrix}\end{split}\]

Arbitrarily-averaged mixture velocity#

Notation

Unit

Code

Type

Shape

\(\mathbf{u}^a\)

\([m/s]\)

Velocity.arbitrarily_averaged

vector numpy.ndarray

(1,n_observations)
\[\begin{split}\mathbf{u}^a = \begin{bmatrix} \cdots & \mathbf{u}^a & \cdots \\ \end{bmatrix}\end{split}\]

Flux#

Total molar flux#

Notation

Unit

Code

Type

Shape

\(\mathbf{N}_i\)

\([mole/(m^2 s)]\)

Flux.total_molar_flux

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{N}_i = \begin{bmatrix} \cdots & \mathbf{N}_1 & \cdots \\ \cdots & \mathbf{N}_2 & \cdots \\ & \vdots & \\ \cdots & \mathbf{N}_n & \cdots \\ \end{bmatrix}\end{split}\]

Total mass flux#

Notation

Unit

Code

Type

Shape

\(\mathbf{n}_i\)

\([kg/(m^2 s)]\)

Flux.total_mass_flux

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{n}_i = \begin{bmatrix} \cdots & \mathbf{n}_1 & \cdots \\ \cdots & \mathbf{n}_2 & \cdots \\ & \vdots & \\ \cdots & \mathbf{n}_n & \cdots \\ \end{bmatrix}\end{split}\]

Molar diffusive flux relative to a molar-averaged velocity#

Notation

Unit

Code

Type

Shape

\(\mathbf{J}_i\)

\([mole/(m^2 s)]\)

Flux.diffusive_molar_molar

vector numpy.ndarray

(n_species,n_observations)

\(\mathbf{J}_i\)

\([mole/(m^2 s)]\)

Diffusion.diffusive_flux_molar_molar

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{J}_i = \begin{bmatrix} \cdots & \mathbf{J}_1 & \cdots \\ \cdots & \mathbf{J}_2 & \cdots \\ & \vdots & \\ \cdots & \mathbf{J}_n & \cdots \\ \end{bmatrix}\end{split}\]

Molar diffusive flux relative to a mass-averaged velocity#

Notation

Unit

Code

Type

Shape

\(\mathbf{J}_i^v\)

\([mole/(m^2 s)]\)

Flux.diffusive_molar_mass

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{J}_i^v = \begin{bmatrix} \cdots & \mathbf{J}_1^v & \cdots \\ \cdots & \mathbf{J}_2^v & \cdots \\ & \vdots & \\ \cdots & \mathbf{J}_n^v & \cdots \\ \end{bmatrix}\end{split}\]

Mass diffusive flux relative to a molar-averaged velocity#

Notation

Unit

Code

Type

Shape

\(\mathbf{j}_i^u\)

\([kg/(m^2 s)]\)

Flux.diffusive_mass_molar

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{j}_i^u = \begin{bmatrix} \cdots & \mathbf{j}_1^u & \cdots \\ \cdots & \mathbf{j}_2^u & \cdots \\ & \vdots & \\ \cdots & \mathbf{j}_{n}^u & \cdots \\ \end{bmatrix}\end{split}\]

Mass diffusive flux relative to a mass-averaged velocity#

Notation

Unit

Code

Type

Shape

\(\mathbf{j}_i\)

\([kg/(m^2 s)]\)

Flux.diffusive_mass_mass

vector numpy.ndarray

(n_species,n_observations)

\(\mathbf{j}_i\)

\([kg/(m^2 s)]\)

Diffusion.diffusive_flux_mass_mass

vector numpy.ndarray

(n_species,n_observations)
\[\begin{split}\mathbf{j}_i = \begin{bmatrix} \cdots & \mathbf{j}_1 & \cdots \\ \cdots & \mathbf{j}_2 & \cdots \\ & \vdots & \\ \cdots & \mathbf{j}_{n} & \cdots \\ \end{bmatrix}\end{split}\]

Diffusion#

Binary diffusion coefficients#

Notation

Unit

Code

Type

Shape

\(\pmb{\mathcal{D}}\)

\([m^2/s]\)

Diffusion.get_binary_diffusion_coefficients

scalar numpy.ndarray

(n_species,n_species)
\[\begin{split}\pmb{\mathcal{D}} = \begin{bmatrix} - & \mathcal{D}_{1,2} & \dots & \mathcal{D}_{1,n} \\ \mathcal{D}_{2,1} & - & \dots & \mathcal{D}_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ \mathcal{D}_{n,1} & \mathcal{D}_{n,2} & \dots & - \\ \end{bmatrix}\end{split}\]

where \(\mathcal{D}_{i,j} = \mathcal{D}_{j,i} \,\,\, \forall_{i \neq j}\).

Molar Fickian diffusion coefficients#

Notation

Unit

Code

Type

Shape

\(\mathbf{D}\)

\([m^2/s]\)

Diffusion.fickian_diffusion_coefficients_molar_molar

scalar numpy.ndarray

(n_species-1,n_species-1,n_observations)
\[\begin{split}\mathbf{D} = \begin{bmatrix} D_{1,1} & D_{1,2} & \dots & D_{1,n-1} \\ D_{2,1} & D_{2,2} & \dots & D_{2,n-1} \\ \vdots & \vdots & \ddots & \vdots \\ D_{n-1,1} & D_{n-1,2} & \dots & D_{n-1,n-1} \\ \end{bmatrix}\end{split}\]

where, in general, \(D_{i,j} \neq D_{j,i}\) and \(D_{i,j} \neq 0 \,\,\, \forall_{i, j}\).