A Mesh Sensitivity Study, also known as a Grid Independence Study, Mesh study and Mesh convergence study is a fundamental step in CFD simulations to ensure the reliability and accuracy of results. In other words, without performing a mesh sensitivity study, you cannot trust the results. This process involves consecutive refining the grid used in the simulation and analyzing how key parameters of interest change with increasing mesh resolution. Typically, the study starts with a coarse mesh and progressively refines it, and comparing the results. This convergence indicates that further mesh refinement would not significantly change the results. Needless to say, the solution is then independent of the mesh.
Tip: It’s important to note that absolute convergence is often not achievable. Thus, you should define an acceptable level of change (e.g., less than 1% difference between successive refinements).
As an example, check out Table 1. The graph shows the grid independence study done the project entitled “ Non-newtonian Blood In Artery CFD Simulation, ANSYS Fluent Training”. The table represents the impact of cell number on the key performance metrics of the system: wall shear stress at five different times. As cell number increases, there’s an increment in wall shear stress in all five time steps. Given 3%>Error difference between the results, the mesh #3 with 570571 cell number is selected.
| Cell Number | t=0.2s | Error | t=0.4s | Error | t=0.6s | Error | t=0.8s | Error | t=1s | Error |
| 126657 | 1.74E | – | 8.62E-01 | – | 6.12E | – | 9.12E-01 | – | 8.53E-01 | – |
| 280566 | 1.79E | 2.69 | 8.88E-01 | 3 | 6.21 | 1.39 | 9.33E-01 | 2.33 | 8.78E-01 | 3.01 |
| 570571 | 1.84E | 2.83 | 9.14E-01 | 2 | 6.26E | 8.99E-01 | 9.53E-01 | 2.13 | 9.05E-01 | 3.06 |
| 938352 | 1.88E | 2.42 | 9.39E-01 | 2 | 6.29E | 3.69E-01 | 9.74E-01 | 2.19 | 9.31E-01 | 2.80 |
Table 1: Grid independence study on Prototype Francis Turbine, DOI:10.3390/ijtpp4030021
Grid Size Independency in Discrete Phase Model (DPM)
The explanation given above about grid sensitivity analysis is the fundamentals of CFD simulation. However, the problem is somehow different when it comes to the Discrete Phase Model (DPM). In most CFD cases, the continuous phase fills the cells, but in DPM simulation, the dispersed phase is not large enough to cover all volumes of a single cell. It is actually one of the biggest concerns of DPM simulation. The DPM model becomes grid-dependent if the cell size is too small or big. Hopefully, ANSYS tutorials suggest a rule of thumb for grid size in DPM simulations:
- Volume fraction of particle should be less than 10% of the cell volume
Let`s continue with an example. Imagine 1*1m cross-section for injection of 1mm particles. According to the rule of thumb, the suitable cell size is: 10mm. So, the particle would fill 10% of the cell volume at maximum.
Figure 1: Grid size independence for Discrete Phase Model (DPM)
DPM Particle Diameter and Mesh Cell Size-Using the Dynamic Interaction Range
In many DPM cases, due to the presence of particles with various diameters ranging from small to large, some particle diameters may be too large compared to the local mesh cell size. ANSYS Fluent provides an option in the Discrete Phase Model (DPM) panel, down the Numerics tab (see Fig. 2), which can be used to get around this problem.
When the Dynamic Interaction Range option is enabled, all the laws regarding the discrete phase (such as drag, physical models, and others) for such large particles are formulated based on freestream conditions of coarser (or agglomerated) mesh elements. The DPM source terms are distributed over these coarser mesh elements, thus providing more realistic fluid conditions.
You can get access to DPM CFD
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