2D axisymmetric compressible-flow simulation of a nozzle with a Bézier-curve wall profile, compared with a conventional De Laval nozzle under the same boundary conditions.
← Baseline study: De Laval nozzle analysis
The study looks at how a smooth Bézier wall contour changes three things compared with a conventional De Laval profile:
- choked flow
- shock structure
- wall loading
Both nozzles use the same boundary conditions, similar mesh densities (≈ 450–500k cells) and the same number of iterations.
| Parameter | Value |
|---|---|
| Geometry | 2D axisymmetric |
| Inlet / outlet diameter | 10 mm / 7.5 mm |
| Fluid | Air, ideal gas |
| Inlet pressure | 200,000 Pa |
| Outlet pressure | 0 Pa (gauge) |
| Solver | Pressure-based, steady |
| Turbulence model | SST k-ω |
| Energy equation | On |
| Mesh | ≈ 460,000 cells |
| Iterations | 2000 |
| Quantity | Value |
|---|---|
| Inlet mass flow rate | 0.0133 kg/s |
| Outlet mass flow rate | 0.0125 kg/s |
| Mass imbalance | ≈ 6.0 % |
| Wall force | ≈ 270 N |
| Inlet mass flow | Outlet mass flow | Wall force |
|---|---|---|
 |
 |
 |
| Pressure | Velocity magnitude |
|---|---|
 |
 |
| Temperature | Density |
|---|---|
 |
 |
Convergence history
- Shock structure: In the Bézier nozzle the shock transitions are more diffuse and less abrupt. The smooth, continuously curved wall spreads the pressure gradients out. The De Laval nozzle, with sharper geometric transitions, shows more distinct shocks and separation zones.
- Wall loading: The Bézier nozzle gives a lower wall force (≈ 270 N vs. ≈ 583 N) because the flow accelerates and decelerates more gently.
- Mass balance: The inlet/outlet imbalance is smaller for the Bézier nozzle (6.0 % vs. 8.7 %).
These first results suggest that the Bézier contour gives smoother flow with weaker shocks. The mass imbalances of both nozzles are still above normal convergence targets (< 0.5 %), so the comparison should be read as qualitative. The next step is a tighter convergence check with a density-based solver.
Burak Yörükçü · GitHub · burakyorukcu@outlook.com