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Separation and reattachment: why is prediction so hard?

At a sharp edge the separation point is fixed and easy to predict. On a smooth surface the turbulence model decides it — and that is where the error begins.

Separation comes in two kinds, and their difficulty is entirely different.

Geometrically forced separation. At a sharp edge the flow has no choice; the location is fixed by the geometry. Model choice has little effect.

Pressure-gradient separation. On a flat or gently curved surface (a diffuser, a blade suction side, a vehicle rear) where separation begins is set by how well the boundary layer resists the adverse pressure gradient — that is, by the turbulence model. Here the model choice changes the result directly.

Why k-ε sees it late

Standard k-ε overpredicts the turbulent viscosity under an adverse pressure gradient. High viscosity makes the boundary layer look more resilient than it is: the flow stays attached, separation starts late or never appears. The advantage of SST on this problem comes precisely from limiting the shear stress [1]. See the turbulence model note.

Reattachment: the overlooked quantity

Separated flow reattaches to the surface some distance later, and heat transfer peaks at the reattachment point — often several times the undisturbed value. In electronics enclosures, impinging jets and sudden expansions, this is where the hot or cold spot sits.

The mesh must resolve the interior of the separation bubble with enough cells; a mesh that crosses the bubble in three to five cells misses both the reattachment location and the heat transfer peak.

Time dependence

A separation region is rarely steady: the bubble grows and shrinks, the reattachment point oscillates. A steady solution gives an average and often struggles to converge. If the oscillation is being suppressed, the physics is being erased. See the convergence note and the RANS/DES/LES note.

Validation

In a study where separation governs, one model is not enough. Running at least two and reporting how far the separation point moves is the most honest measure of how reliable the result is.

References

  1. Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), 1598–1605. DOI: 10.2514/3.12149
  2. Langtry, R. B. & Menter, F. R. (2009). Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA Journal, 47(12), 2894–2906. DOI: 10.2514/1.42362

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