Passive Scalars Transport

Passive scalars are called passive, because they do not affect the physical properties of the simulation. You can use more than one passive scalar in a simulation.

The following situations are examples where passive scalars can be useful:

Choosing the best position for a sensor while designing a part with multiple inlet pipes and an exhaust pipe.
You can use the passive scalars to check the scalar values at discrete points in the computational domain. Then you can determine which of the scalars sends the strongest signal to the sensor.
Analyzing the mixing of two fluid streams that have the same properties.
The fluid is represented as single-phase, but you can use multiple passive scalars to examine the effect of mixing.
Tracing how smoke or any other vapor would convect and diffuse in a room or any fluid domain.
More specifically, you can model the dissolution of a gas in a liquid.

The transport equation for the passive scalar component $ϕ_{i}$ is:

Figure 1. EQUATION_DISPLAY

\frac{\partial}{\partial t} \int_{V} ρ ϕ_{i} d V + \oint_{A} ρ ϕ_{i} v \cdot d a = \oint_{A} j_{i} \cdot d a + \int_{V} S_{ϕ_{i}} d V

(1899)

where:

$i$ is the component index.
$V$ is the volume.
$j_{i}$ is the diffusion flux.
$a$ is the area vector.
$S_{ϕ_{i}}$ is a source term for the passive scalar component $i$ .
$ϕ_{i}$ is assumed to be positive-definite.

If passive scalars are part of a Lagrangian Multiphase, a Dispersed Multiphase, or a porous media simulation using the physical velocity approach, Eqn. (1899) is scaled to account for a reduction in available volume through the presence of a dispersed phase or a solid porous phase. For more information on how these phases affect the transport equation, see Volume Partitioning.

Linear Eddy-Diffusivity

In the linear eddy-diffusivity model, the diffusion flux is:

Figure 2. EQUATION_DISPLAY

j_{i} = (\frac{μ}{σ} + \frac{μ_{t}}{σ_{t}}) \nabla ϕ_{i}

(1900)

where:

$μ$ is the viscosity.
$μ_{t}$ is the turbulent viscosity.
$σ$ is molecular Schmidt number—a material property.
$σ_{t}$ is the turbulent Schmidt number.

Generalized Gradient Diffusion Hypothesis (GGDH)

The Generalized Gradient Diffusion Hypothesis model (GGDH) provides improved prediction for passive scalar diffusion in highly anisotropic turbulent flows. This hypothesis models the passive scalar diffusion flux as a tensor quantity proportional to the Reynolds stresses:

Figure 3. EQUATION_DISPLAY

j_{i} = \frac{μ}{σ} \nabla ϕ_{i} + \frac{C_{s}}{σ_{t}} \frac{k}{ϵ} R \cdot \nabla ϕ_{i}

(1901)

where:

$ϕ_{i}$ is the value of the passive scalar component $i$ .
$C_{s} = 0.2$ is a model constant.
$k$ is kinetic energy.

$ϵ$ is the dissipation rate.
$R$ is the Reynolds stress tensor.

Passive Diffusion in Porous Media

In porous media, the passive scalar diffusion flux

j_{i}

is multiplied by the porosity/tortuosity ratio

χ / τ