The near-wall resolution expressed by y⁺ is a fundamental principle in CFD and directly reflects how the boundary layer is represented in a numerical simulation. Because wall shear stress, turbulence production, and flow separation depend on the near-wall treatment, the choice of y⁺ has a decisive influence on the accuracy of pressure prediction in wind simulations. Understanding and controlling y⁺ is, therefore, essential for obtaining reliable surface pressures and load-relevant results. y+ determines where the first computational cell sits inside the boundary layer, and therefore, how wall shear stress and near-wall turbulence are modeled.
That immediately affects:
- Wall shear stress
- Velocity gradient at the wall
- Turbulent viscosity near the wall
- Separation and reattachment behavior
- Pressure recovery and pressure distribution, especially in adverse pressure gradients
Thus, even though pressure is not directly calculated from the wall functions, it is strongly influenced by the modeling of the boundary layer near the wall.
🌬️ How is pressure indirectly affected by y⁺?
The pressure on the surface is governed by the momentum balance in the near-wall region:
The wall functions influence:
- Near-wall velocity profile
- Turbulent stresses
- Separation point location
👉 If the wall shear stress is not calculated accurately, the boundary layer and flow separation are modeled incorrectly, and the resulting surface pressure becomes unreliable.
⚠️ Effect of Incorrect y⁺ by Turbulence Model
The tables below show how pressure results in wind simulations depend on turbulence model choice and y⁺ resolution. They highlight that while mean pressures may appear robust, peak local pressure coefficients are highly sensitive to near-wall modeling, especially when y⁺ requirements are not met. The provided rule-of-thumb ranges help assess the reliability of pressure-based load predictions.
Table 1: Model-Specific Sensitivity Overview
| Turbulence Model | Typical y+ Requirement | Pressure Sensitivity |
|---|---|---|
| Standard k–ε | 30–300 | Low in attached flow, high near separation |
| SST k–ω | ≈1 | High if viscous sublayer not resolved |
| DDES | ≈1 | Moderate to high |
| LES | ≤1 | Very high if violated |
Table 2: Effect of y+ on Mean and Peak Pressure Prediction
| Turbulence model | Recommended y+ | Mean pressure error | Peak local pressure error |
|---|---|---|---|
| Standard k–ε | 30–300 | 2–5% (attached flow) | 5–15% (separation zones) |
| SST k–ω | ≈ 1 | 5–10% (attached flow) | 10–30% (separation zones) |
| DDES | ≈ 1 | 5–15% (separation zones) | 20–40% (near edges and reattachment) |
| LES | ≤ 1 | 10–20% (separation zones) | 30–50% (near edges and reattachment) |
Table 3: Rule-of-Thumb Pressure Error Ranges
| Situation | Expected Pressure Error |
|---|---|
| Correct y | 3–5% |
| y+ off by factor 3 | 5–10% |
| y+ off by factor 10 | 10–25% |
| Separation regions | up to 30–40% |
| Local peak pressure | can exceed 50% |