Large Scale Interfaces

The large scale interface detection model is implemented within the multiple flow regime framework to enable the detection of a group of cells that contain a large interface.

Interface Detection

This model is based on the LIM method of Coste [443].

The interface detection for a pair of primary ( $p$ ) and secondary ( $s$ ) phases is achieved in two steps:

Identifying the cells that contain the interface to derive a raw interface.
Reducing the raw interface to a one-cell-thick interface.

Step 1: Identifying the cells that contain the interface

A sharp gradient of volume fraction for both the phases is calculated as:

Figure 1. EQUATION_DISPLAY

\nabla α_{c} = \frac{1}{Δ v} \sum_{f} α_{c, f} Δ s_{f}

(2309)

where:

Subscript $c$ is for the phase.
Subscript $f$ is for the cell-face.
$Δ v$ represents the volume of the cell.
$Δ s$ represents the surface area of the cell.

To evaluate Eqn. (2309), the volume-fraction value at the cell-face for neighboring cells A and B is calculated as follows:

Figure 2. EQUATION_DISPLAY

\begin{matrix} i f & α_{A} + α_{B} < 1 & \frac{2}{α_{f}} = \frac{1}{α_{A}} + \frac{1}{α_{B}} \\ i f & α_{A} + α_{B} = 1 & α_{f} = 0.5 \\ i f & α_{A} + α_{B} > 1 & \frac{2}{1 - α_{f}} = \frac{1}{1 - α_{A}} + \frac{1}{1 - α_{B}} \end{matrix}

(2310)

This selective use of harmonic averaging is necessary to achieve a sharp gradient.

Once the sharp gradient of the volume fraction has been calculated for each phase of the phase interaction, the sharp gradient of the volume fraction for the phase interaction ( $p s$ ) is calculated by taking the harmonic average of the absolute value of the individual components ( $i$ ) of phase as:

Figure 3. EQUATION_DISPLAY

\nabla α_{p s} = \partial_{x_{i}} α_{p s} = \frac{2 | \partial_{x_{i}} α_{p} | | \partial_{x_{i}} α_{s} |}{| \partial_{x_{i}} α_{p} | + | \partial_{x_{i}} α_{s} |}

(2311)

This sharp gradient of the volume fraction for the phase interaction is compared to a maximum value of the sharp gradient of the volume fraction in each direction, which is calculated as:

Figure 4. EQUATION_DISPLAY

{(\nabla α_{p s})}_{\max} = \frac{0.5}{Δ v} \sum_{f} Δ s_{f}

(2312)

The interface exists in a cell when at least one component satisfies:

Figure 5. EQUATION_DISPLAY

\partial_{x_{i}} α_{p s} > \frac{{(\partial_{x_{i}} α_{p s})}_{\max}}{C_{1}}

(2313)

All of the cells that satisfy Eqn. (2313) are considered to be a raw representation of the interface, which is then refined to obtain a single cell thick interface.

Step 2: Constructing a one-cell-thick interface

To reduce the raw interface to a one-cell-thick interface, it is necessary to select between two neighboring cells that belong to the raw interface and are also parallel to the interface. For each pair of such cells ( $A$ , $B$ ) with $\vec{A B}$ representing the line joining the centroids of the two cells, if the following condition is satisfied, the cell in which the volume fraction of the primary phase is less is removed from the raw interface to obtain the final interface:

Figure 6. EQUATION_DISPLAY

| (\nabla α_{p s, A} + \nabla α_{p s, B}) \cdot \vec{A B} | > C_{2} ‖ \nabla α_{p s, A} + \nabla α_{p s, B} ‖ ‖ \vec{A B} ‖

(2314)

where:

$| x |$ is the absolute value of a scalar $x$ .
$‖ \vec{x} ‖$ is the magnitude of vector $\vec{x}$ .

Adaptive Interface Sharpening (ADIS) Scheme for Volume Fraction

The Multiple Flow Regime model lets you model dispersed and segregated two-phase flows within a single framework. If an interface sharpening scheme for volume fraction is used for the entire domain, the result is good in the regions where a sharp interface exists naturally but can exhibit artificial sharpening in naturally smooth regions. Similarly, if a standard TVD scheme is used for the entire domain, the result can show artificial diffusion in sharp regions while preserving naturally smooth regions.

The Adaptive Interface Sharpening (ADIS) scheme addresses this problem by using an interface sharpening scheme (the High-Resolution Interface Capturing (HRIC) scheme) in the vicinity of a large scale interface and using the standard TVD scheme (a first order or second order scheme) away from the sharp interface.

The Large Scale Interface Detection model provides a "Large Interface Marker Band" which represents the large interface. To avoid sharp changes that are due to the use of different advection schemes, a blending function is built upon this Large Interface Marker Band. The blending function goes from 1 to 0 across a specified number of cells. You specify the number of cells in the Number of Cell Layers for Smoothing property of the Adaptive Interface Sharpening model.

The face value of the volume fraction is calculated as:

Figure 7. EQUATION_DISPLAY

α_{f} = f_{b l e n d i n g} (n) α_{f^{H R I C}} + [1 - f_{b l e n d i n g} (n)] α_{f^{T V D}}

(2315)

with:

Figure 8. EQUATION_DISPLAY

f_{b l e n d i n g} (n) = \frac{1}{1 + e^{B [n - 0.5 n_{s}]}}

(2316)

where:

$n$ is the $n$ -th cell from the Large Interface Marker Band.
$B$ is the blending constant.
$n_{s}$ is the number of cell layers for smoothing.

Interface Distance Specification

The large interface distance $l_{d}$ can be calculated by approximating the interface distance to the cell volume ( $l_{d} = \sqrt[3]{Δ v}$ ) or by performing geometric reconstruction of the interface.

The interface reconstruction procedure (following Rider and Kothe, [[535]) is summarized as follows:

The interface shape within the cell is approximated as a line-segment. For this line-segment interface, Simcenter STAR-CCM+ calculates its orientation and position within the cell. The orientation of the interface is approximated as the unit interface normal.

Once the orientation of the interface is known, the line-segment is positioned within the cell such that the enclosed volume represented by the reconstructed interface is the same as the actual volume of a phase in that cell. The large interface distance is the distance between the interface and the cell centroid, normal to the interface.