Backward-facing step
Not yet written up. The set-up and the published reference are recorded; our own results are not. Nothing in this page may be cited until the comparison table is complete.
Case: (to be filled from run) Reference: Armaly B.F., Durst F., Pereira J.C.F., Schönung B., “Experimental and theoretical investigation of backward-facing step flow”, Journal of Fluid Mechanics 127 (1983) 473–496.
Last run: (to be filled from run)
A channel that suddenly gets taller. The flow separates at the step edge and reattaches somewhere downstream, and the distance to that reattachment point is the answer. Armaly et al. measured it with laser-Doppler anemometry over Reynolds numbers from about 70 to 8000, covering laminar, transitional and turbulent flow in one geometry, and the resulting curve of reattachment length against Reynolds number has been the standard separated-flow check ever since.
What this tests, and why it matters
Section titled “What this tests, and why it matters”The lid-driven cavity has a recirculation, but the geometry puts it there. The box is closed, the corners are fixed, and nothing asks the solver to decide anything about where the flow detaches or lands.
Here the separation point is fixed by the geometry — the step edge — and the reattachment point is not. It is an outcome, and a single scalar, and it is sensitive to almost everything that can be wrong with a calculation:
- Numerical diffusion. An upwind-biased convection scheme smears the shear layer and shortens the recirculation. This benchmark is the standard way of catching a scheme that is more diffusive than it claims.
- Mesh resolution across the shear layer, which is thin and does not sit along a mesh line.
- The turbulence model, in the turbulent range. Reattachment length is the classic discriminator between eddy-viscosity models; under-prediction is a well-known k-ε behaviour.
- Whether the case is genuinely two-dimensional. Armaly’s own conclusion is that it stops being so above roughly Re = 400 — see the caution below, which is the single most misused fact about this benchmark.
Nothing on the cavity page exercises any of that.
In SHD Sim CFD
Section titled “In SHD Sim CFD”Derived from docs/solver-map.md and analysis types and solvers.
| Analysis type | Incompressible |
| Time dependency | Steady-state |
| Algorithm | SIMPLE |
| Solver | simpleFoam |
| Turbulence model | Laminar for the Re ≤ 400 cases; a RANS model for the turbulent cases |
| Wall treatment | Not applicable while laminar; Resolved (low-Re) or Wall functions for the turbulent cases |
| Mesher | The step is not a box, so blockMesh only (no body) cannot express it. Either snappyHexMesh (hex-dominant) against an imported step solid, or Import an existing mesh |
| Known blockers | None. simpleFoam carries no blocker in solverPrerequisites |
simpleFoam with the Laminar model is the steady route. The transient route —
pimpleFoam or pisoFoam — reaches the same steady answer and is worth having
if the recirculation will not settle, but the reference quantity is a steady
one.
Which mesh route was used: (to be filled from run)
Set-up
Section titled “Set-up”The geometry Armaly et al. used. These are the numbers that make a run comparable to theirs; a step of different expansion ratio is a different benchmark.
| Step height | S = 4.9 mm |
| Inlet channel height | h = 5.2 mm |
| Downstream channel height | H = h + S = 10.1 mm |
| Expansion ratio | H/h = 1.9423 |
| Aspect ratio (span : downstream height) | 1 : 36 |
| Reynolds number | Re = ū D/ν, on the hydraulic diameter of the inlet channel, D = 2h = 10.4 mm, and the mean inlet velocity ū |
| Reynolds numbers reported | approximately 70 to 8000 |
| Inlet condition | fully developed channel flow entering at the step plane |
| Reported quantity | x₁, the reattachment length on the step-side wall, measured from the step face and normalised by S |
Confirm the geometry figures against the paper when finalising this page. They are widely quoted and quoting them from a secondary source is exactly the habit this section exists to avoid. The reattachment-length values in the table below must come off the source figure regardless.
The expansion ratio and the Reynolds-number definition both have to match. A large fraction of published “disagreement” with Armaly is somebody using Re on the step height, or on the downstream channel height, instead of on 2h. Write the definition out in full in the run notes.
Our set-up, to be recorded when the case is run:
| Domain | (to be filled from run) — inlet length upstream of the step, and outlet length downstream |
| Two-dimensional | (to be filled from run) |
| Mesh | (to be filled from run) |
| Boundary conditions | (to be filled from run) |
| Fluid | (to be filled from run) |
| Run control | (to be filled from run) |
| Result controls | (to be filled from run) |
Convergence: (to be filled from run)
The two-dimensionality caution
Section titled “The two-dimensionality caution”Armaly et al. report that the flow ceases to be two-dimensional above roughly Re = 400, and that two-dimensional predictions depart from their measurements above it. Side-wall effects in a finite-span rig are the cause, and they are not a numerical artefact that a finer mesh removes.
This has two consequences and both belong on this page:
- A 2-D run at Re = 100–400 that matches Armaly is a real result.
- A 2-D run at Re = 800 that does not match Armaly is not necessarily a defect in the software. It is a comparison the reference itself says is invalid.
Do not report a 2-D result above Re ≈ 400 against the experiment without saying this in the same paragraph. Overstating the mismatch is as dishonest as overstating the agreement.
Result — reattachment length
Section titled “Result — reattachment length”x₁/S, the primary reattachment length on the step-side wall.
Reference values are read from Armaly et al. (1983), the figure plotting separation and reattachment lengths against Reynolds number — confirm the figure number against the paper when transcribing, and read the values off the source rather than from any secondary reproduction of it.
| Re (= ū·2h/ν) | Armaly et al. (1983) | SHD Sim CFD | difference |
|---|---|---|---|
| 100 | (read from Armaly et al. 1983, reattachment-length figure) | (to be filled from run) | (to be filled from run) |
| 200 | (read from Armaly et al. 1983, reattachment-length figure) | (to be filled from run) | (to be filled from run) |
| 300 | (read from Armaly et al. 1983, reattachment-length figure) | (to be filled from run) | (to be filled from run) |
| 400 | (read from Armaly et al. 1983, reattachment-length figure) | (to be filled from run) | (to be filled from run) |
Rows above Re = 400 are deliberately absent from the table above. If turbulent cases are run, put them in their own table with the caution restated:
| Re (= ū·2h/ν) | Armaly et al. (1983) | SHD Sim CFD | turbulence model | difference |
|---|---|---|---|---|
| (to be filled from run) | (read from Armaly et al. 1983, reattachment-length figure) | (to be filled from run) | (to be filled from run) | (to be filled from run) |
RMS difference (to be filled from run). Worst point (to be filled from run).
Result — secondary recirculation
Section titled “Result — secondary recirculation”Above roughly Re = 400 a second recirculation appears on the opposite (roof) wall. Armaly et al. report its detachment and reattachment positions, x₄ and x₅, alongside x₁.
Predicting the roof bubble at all is a harder test than predicting x₁, because it exists only if the shear layer has been carried far enough with enough momentum. Record it if the run produces one, and record its absence if it does not.
| Re | Quantity | Armaly et al. (1983) | SHD Sim CFD | difference |
|---|---|---|---|---|
| (to be filled from run) | x₄/S, roof detachment | (read from Armaly et al. 1983) | (to be filled from run) | (to be filled from run) |
| (to be filled from run) | x₅/S, roof reattachment | (read from Armaly et al. 1983) | (to be filled from run) | (to be filled from run) |
Result — velocity profiles
Section titled “Result — velocity profiles”Streamwise velocity across the channel at stations downstream of the step, normalised by the mean inlet velocity ū. Armaly et al. tabulate and plot profiles at several x/S; pick the stations from the paper rather than choosing convenient ones.
| x/S | y/S | Armaly et al. (1983) u/ū | SHD Sim CFD u/ū | difference |
|---|---|---|---|---|
| (to be filled from run) | (to be filled from run) | (read from Armaly et al. 1983) | (to be filled from run) | (to be filled from run) |
What the remaining difference is
Section titled “What the remaining difference is”(to be filled from run)
Candidate attributions, to be chosen between on evidence rather than asserted: mesh resolution across the shear layer; the convection scheme; the inlet profile not being fully developed; three-dimensionality in the experiment; the turbulence model, in the turbulent cases. Establish which by changing one and seeing the number move.
What this benchmark does not cover
Section titled “What this benchmark does not cover”- Unsteadiness. This is a steady separated flow. Nothing here checks a periodic wake, a shedding frequency, or any time-accurate behaviour.
- Near-wall turbulence modelling, in the laminar cases — there is no turbulence model in them at all. The turbulent cases exercise it only as far as reattachment length is sensitive to it, which is not the same as checking a boundary-layer profile.
- Curved or moving separation. The separation point is pinned to a sharp edge. Smooth-body separation, where the solver has to find the detachment point as well as the reattachment point, is a harder problem this does not touch.
- Three-dimensional flow, which is precisely what the reference says is present above Re ≈ 400 and what a 2-D run cannot reproduce.
- Heat, buoyancy, compressibility, multiphase. None involved.
- snappyHexMesh quality on a curved body. A step is flat surfaces and sharp edges; it says nothing about snapping to curvature.
Reproducing this from the application
Section titled “Reproducing this from the application”(to be filled from run) — record the exact steps taken, from the application, with no hand-editing of case files.
Extraction of the reattachment point: (to be filled from run). Record the
method, because it changes the number. Wall shear stress changing sign, the
wallShearStress result control sampled along the step-side wall, and reading
the dividing streamline all give slightly different answers, and a comparison
is only meaningful if the method is stated.
Defects this found
Section titled “Defects this found”(to be filled from run)