Scalar Transport of Multiple Species

AcuSolve has the capability to track multiple species in a fluid flow by using the scalar transport equations for each of them individually.

The species transport equation is similar to the generalized governing equations for the fluid flow and it is expressed as: (1)

ρ \frac{\partial φ_{i}}{\partial t} + (ρ \to u \cdot \nabla) φ_{i} = \nabla \cdot Ψ_{i} + ρ σ_{i}

$ρ \frac{\partial φ_{i}}{\partial t} + (ρ \vec{u} \cdot \nabla) φ_{i} = \nabla \cdot Ψ_{i} + ρ σ_{i}$

where

$φ_{i}$ $φ_{i}$ represents the i^th scalar species.
$Ψ_{i}$ $Ψ_{i}$ is the diffusion flux vector for species $φ_{i}$ $φ_{i}$ .
$σ_{i}$ $σ_{i}$ is the source per unit mass for species $φ_{i}$ $φ_{i}$ .

The diffusivity flux vector is expressed as: (2)

Ψ = d \nabla φ

$Ψ = d \nabla φ$

where $d$ $d$ is the diffusivity for species $φ$ $φ$ . The diffusivity can be modeled as constant, ramped against time step or customized using variable property and user functions.

The material properties can be set to be functions of species concentration. This models a ‘miscible’ property relative to mixing of multiple fluids.