Same pipe, same physics, four meshes, four different answers. This lesson turns Part 1’s first-cell height into a real inflation-layer mesh, then proves the mesh is good enough with a grid convergence study.
What you will learn
- Why uniform 0.15 mm cells would need 675 cells across the radius
- Growing inflation layers at a 1.2 growth ratio until they meet the core mesh
- Checking the size jump between the last layer and the core cell
- Watching a solver converge: residuals and the velocity profile
- A four-grid study and the Grid Convergence Index (Celik et al. 2008)
- Why mesh independence is not the same as a correct answer
Inflation layers
| Quantity | Value |
|---|---|
| First cell (from Part 1) | 0.15 mm at y+ 50 |
| Growth ratio | 1.2 |
| Layers to reach the core | 19 (last layer 4.00 mm) |
| Core cell | D/50 = 4.05 mm (size jump 1.01, below 1.2) |
| Inflation block thickness | 23.2 mm (23 % of the radius) |
| Cells across the radius | ≈ 38 instead of 675 |
Grid study (bulk velocity, same pressure gradient)
| Grid | Bulk velocity |
|---|---|
| 16 cells | 3.61 m/s |
| 32 cells | 3.93 m/s |
| 64 cells | 4.10 m/s |
| 128 cells | 4.19 m/s |
| Extrapolated (h → 0) | 4.28 m/s |
Finest three grids: observed order p = 0.94, fine-grid GCI = 2.8 %, asymptotic check 1.02 ≈ 1.
Takeaway: the mesh is good to about 3 %, but the result is still 6 % above the 4.02 m/s hand calculation. That gap comes from the turbulence model, not the mesh, which is Lesson 3.
Results come from a 1-D fully developed pipe-flow solver written for this series (Prandtl mixing length, van Driest damping, Cebeci-Chang rough wall).
