Channel Refinement

The Narrow Channels term is conventional and used for the definition of the flow passages of the model in the direction normal to the solid/fluid interface. Regardless of the real solid curvature, the mesh approximation is that the solid boundary is always represented by a set of flat elements, which nodes are the points where the model intersects with the cell edges. Thus, whatever the model geometry, there is always a flat element within a solid-fluid boundary cell and the normal to this element denotes the direction normal to the solid/fluid interface for this solid-fluid boundary cell.

The basic concept of narrow channel refinement is to resolve the narrow channels with a sufficient number of cells to provide a reasonable level of solution accuracy. It is especially important to have narrow channels resolved in analyses of low Reynolds numbers or analyses with long channels, i.e. in such analyses where the boundary layer thickness becomes comparable to the size of the solid-fluid boundary cells where the layer is developed.

There are two ways to specify the channels refinement:

• Number of Cells mode governs the procedure of mesh refining in the model’s narrow channels by specifying the number of mesh cells across model’s flow passages and restricting the refinement level;

• Refinement Level mode allows to define an uniform mesh across each model’s flow passage by specifying the refinement level as a tabular dependency on the channel height.

The narrow channel settings available in the Number of Cells mode are the following:

• Maximum Channel Refinement Level – the maximum level of cells refinement in narrow channels with respect to the basic mesh cell.

• Characteristic Number of Cells Across Channel – the number of cells (including cells lying at the solid/fluid interface) that Flow Simulation will attempt to set across the model flow passages in the direction normal to the solid/fluid interface. If possible, the number of cells across narrow channels will be equal to the specified characteristic number, otherwise it will be as close to it as possible. The Characteristic Number of Cells Across Channel (Nch) and the Maximum Channel Refinement Level (Lch) both influence the mesh in narrow channels in the following manner: the basic mesh in narrow channels will be split to have Nch number per channel, if the resulting cells satisfy the specified Lch. In other words, whatever the specified Nch, the smallest possible cell in a narrow channel is 8L times smaller in volume (or 2L times smaller in each linear dimension) than the basic mesh cell. This is necessary to avoid undesirable mesh splitting in very fine channels that may cause the number of cells to increase to an unreasonable value.

• Minimum Height of Channel, Maximum Height of Channel – the minimum and maximum bounds for the height outside of which a flow passage will not be considered as a narrow channel and thus will not be refined by the narrow channel resolution procedure.

For example, if you specify the minimum and maximum height of narrow channels, the cells will be split only in those fluid regions where the distance between the opposite walls of the flow passage in the direction normal to wall lies between the specified minimum and maximum heights.

The Number of Cells channel refinement mode operates as follows:

1. For each solid-fluid boundary cell Flow Simulation calculates the “local” narrow channel width as the distance between this solid-fluid boundary cell and the next solid-fluid boundary cell found on the line normal to the solid/fluid interface of this cell (i.e. normal to the flat surface element located in the cell).

   Tip

   If the line normal to the solid/fluid interface crosses a local initial mesh area, then the corresponding local narrow channel refinement settings is applied to the cells in this direction.

2. If the distance value falls within the range defined by the Minimum height of channel (Hmin) and Maximum height of channel (Hmax) options, the number of cells per this interval is calculated including both cells lying at the solid/fluid interface and taking into account which portion of each cell is in fluid.

3. More precisely, the number of cells across the channel (i.e. on the interval between the two solid-fluid boundary cells) is calculated as N = Nf + np1 + np2, where Nf is the number of fluid cells on the interval, and np1 and np2 are the fluid portions of the both solid-fluid boundary cells. This value is compared with the specified Characteristic number of cells across a channel (Nch). If N is less than the specified Nch then the cells on this interval are split. For example, on Table 1 (a) Nf = 2, np1 = np2 = 0.4, and N = 2+0.4+0.4 = 2.8 which is less than the criterion Nch = 3. On Table 1 (b) the solid-fluid boundary cells are split, so that the fluid portions of the newly-formed solid-fluid boundary cells are np1 = np2 = 0.9, and the criterion is satisfied (N > Nch).

   Table 1. Examples of the Characteristic Number of Cells Across Channel.

   a) Lch = 2; Nch = 3; N = 2.8 < Nch	b) Lch = 3; Nch = 3; N = 3.8 > Nch

   Note:

   Like in the other refinements, the Maximum channel refinement level (Lch) denotes the maximum level to which the cells can be split to satisfy the Nch criterion. The Lch has higher priority than the Nch, so the refinement will proceed until the Nch criterion is satisfied or all the cells reach the Lch.

   The channel refinement is symmetrical with respect to the midpoint of the interval and proceeds from the both ending solid-fluid boundary cells towards the midpoint. Since the actual number of cells across narrow channels can be greater by 1 than the specified characteristic number.

   Table 2. Examples of the Maximum channel refinement level.

   a) Nch = 5; Lch = 1	b) Nch =  5; Lch = 3

   In Table 2 (a), the specified Characteristic number of cells across a channel (Nch) is 5 but only two cells were generated since the Maximum channel refinement level (Lch) of one allows only basic mesh cells and first-level cells to be generated.

   In Table 2 (b), the specified Maximum channel refinement level (Lch) is high enough to allow 5 cells to be placed across the channel, but there are 6 cells across the channel due to the symmetry requirement of the channel refinement.

   If the channels height is variable along the channel length, pay attention to the Nch criterion and make sure that the proper value of the Nch criterion is satisfied along the entire channel.

   Table 3. Examples of the Characteristic number of cells.

   a) Hmax = 60 mm; Lch = 4; Nch = 10	b) Hmax = 60 mm; Lch = 4; Nch = 25

   In Table 3 (a), the specified Characteristic number of cells across a channel (Nch) is not enough to reach the specified Maximum channel refinement level (Lch) across the entire channel. Only the cells located in the narrowest end of the channel reach the specified Lch.

   In Table 3 (b), the specified Characteristic number of cells across a channel (Nch) is high enough to reach the specified Lch across the entire channel.

   Alternatively, to generate an uniform mesh across a channel, you can specify the refinement level as a tabular dependency on the channel height by using the Refinement Level mode.

   Table 4. Examples of the mesh across a channel.

   a) Number of Cells (Hmax = 80 mm): Lch = 3; Nch = 10	b) Refinement Level: H ≤ 81 mm: Lch = 3

4. Next, for all the fluid cells within the entire computational domain the following Fluid Cell Leveling procedure is applied: if a fluid cell is located between two cells of higher level, it is split to be equalized with the level of neighboring smaller cells.

Although the settings that produce an optimal mesh depends on a particular task, here are some “rule-of-thumb” recommendations for narrow channel settings:

1. Set the number of cells across a channel to a minimum of 5.

2. Use the minimum and maximum heights of narrow channels to concentrate on the regions of interest.

3. If possible, avoid setting high values for the narrow channels refinement level, since it may cause a significant increase in the number of cells where it is not necessary.

   Figure 1. Lssf = 3; Channels refinement is disabled.
   

   

   
   
   Figure 2. Lssf = 3; Channels refinement is on: Nch = 5, Lch = 2.
   

   

   
   
   Figure 3. Lssf = 3; Channels refinement is on: Nch = 5, Lch = 5.