Independent numerical study on a Mach 3 double-wedge model — RANS/SST k–ω, ANSYS Fluent
This project investigates how surface roughness on an aerodynamic body changes the oblique shock angle it produces in supersonic flow — a question with direct relevance to supersonic intakes, control surfaces, and vehicle forebodies that operate with eroded, ablated, or manufacturing-rough surfaces rather than idealized smooth ones.
A two-dimensional double-wedge model (5.3° half-angle, Mach 3 freestream) was chosen because it produces the full compression–expansion–recompression wave sequence in one simple geometry: an attached oblique shock at the leading edge, a Prandtl–Meyer expansion fan at the shoulder, and a recompression shock on the trailing surface. This gives multiple points of comparison between analytical theory and CFD in a single simulation, rather than validating only one shock relation.
The study combines:
- Classical compressible-flow theory (oblique shock relations + Prandtl–Meyer theory) to establish an inviscid smooth-wall baseline
- CFD (ANSYS Fluent) solving the compressible RANS equations with the SST k–ω turbulence model, first validated against a benchmark rough-wall supersonic flat-plate case, then applied to the double-wedge geometry at multiple equivalent sand-grain roughness heights
The complete project report (PBL Lab Report, Gas Dynamics AS362IA) is available in
report/PBL-Report-Roughness-Effects-Oblique-Shock.pdf.
Geometry: Symmetric double wedge, 70 mm total length, 5.3° wedge surface angle, shoulder at mid-chord (35 mm), ~6.5 mm max thickness.
Freestream conditions: M∞ = 2.73–3.0, p₀ = 3.581 bar, T₀ = 455 K, air modelled as an ideal gas.
Methodology: solver validation on a benchmark rough flat-plate case → grid independence study → smooth-wall double-wedge baseline → parametric sweep over equivalent sand-grain roughness height (kₛ = 0, 0.6, 0.8, 0.9 mm) → shock-angle extraction and comparison.
Shock–boundary-layer interaction is sensitive to near-wall turbulence modelling, and rough-wall treatment specifically depends on how the roughness height is translated into a wall boundary condition for ω (specific dissipation rate) in the SST k–ω model. Running the double-wedge roughness sweep without first checking that the solver reproduces a known rough-wall result would leave no way to distinguish real roughness physics from a solver or mesh artifact — so the solver setup was validated first, against a published rough-wall supersonic flat-plate skin-friction benchmark (Latin & Bowersox, M∞ = 2.73, equivalent sand-grain roughness kₛ = 1.09 mm).
A grid-independence sweep on first-layer height was run in parallel, monitoring skin-friction coefficient against the experimental reference value (Cf = 0.0038):
The selected mesh (1.2×10⁻³ mm first-layer height) predicted Cf = 0.00382, a 0.57% error against experiment. Interestingly, the finest tested mesh (4×10⁻⁴ mm) did not improve on this — its error was actually slightly higher (0.89%), a reminder that grid refinement doesn't monotonically reduce error against experimental data once discretization error is already small relative to turbulence-model uncertainty. The mid-resolution mesh was kept as the better cost/accuracy tradeoff, and the same solver settings, turbulence model, and roughness treatment were carried forward to the double-wedge case with confidence.
Both the leading-edge wall (first compression surface, where the primary shock forms) and the trailing-edge wall (downstream of the expansion fan, where recompression occurs) were monitored independently, since they sit under different local pressure gradients and could in principle converge at different mesh densities.
First-layer height was swept from 1×10⁻¹ mm down to 1×10⁻⁵ mm, tracking skin-friction coefficient, wall shear stress, and y⁺ (to confirm compatibility with the SST k–ω near-wall treatment) at both walls:
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Full convergence data (Cf, wall shear stress, y⁺, iteration count per grid level):
From 1×10⁻³ mm onward, leading-edge average Cf changed by only 0.62% between 1×10⁻³ mm and 1×10⁻⁴ mm, and 0.38% between 1×10⁻⁴ mm and 1×10⁻⁵ mm — the trailing-edge wall showed the same stabilization. The 1×10⁻⁴ mm first-layer mesh was selected as the production grid for all runs: the 1×10⁻⁵ mm grid gave only marginal additional accuracy (sub-0.4% change) while taking roughly 4× more iterations to converge — not worth the cost for a sweep that needed to run at four separate roughness levels.
The classical oblique-shock + Prandtl–Meyer relations give the smooth-wall reference shock structure:
| Region | Mach number | Pressure (Pa) | Event |
|---|---|---|---|
| 0 — Freestream | 2.73 | 9,750 | — |
| 1 — Post first shock | 2.735 | 14,485 | Oblique shock, β₁ = 23.37° |
| 2 — Post expansion | 3.286 | 6,351 | Prandtl–Meyer fan |
| 3 — Post recompression | 2.991 | 9,746 | Recompression shock, β₂ = 21.56° |
The smooth-wall CFD result reproduces the correct qualitative wave structure — attached leading shock, supersonic expansion, and recompression — and agrees with the analytical thermodynamic state to well under 1% on pressure, temperature, and Mach number. The one larger discrepancy is the measured shock angle itself (24.83° CFD vs 23.37° analytical, ~6% difference), which is expected: the analytical solution assumes an inviscid slip wall and a sharp corner, while CFD includes a real boundary layer whose displacement thickness slightly changes the effective body contour seen by the outer flow.
Surface roughness was represented using the equivalent sand-grain roughness height (kₛ) approach rather than resolving individual roughness elements geometrically — standard practice for RANS-based rough-wall modelling. In Fluent this enters the SST k–ω model through a modified wall boundary condition for ω, scaled by the roughness Reynolds number k⁺ₛ = kₛ·u_τ/ν. Four cases were run: smooth wall (kₛ = 0, baseline) and kₛ = 0.6, 0.8, 0.9 mm, chosen to sit in the aerodynamically relevant transitionally-rough-to-fully-rough regime for the given freestream Reynolds number.
Sweeping roughness height shows a clear, monotonic trend on the near-wall quantities: rougher walls increase near-wall momentum loss, and raise skin friction and wall shear stress consistently.
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The measured shock angle, however, does not move monotonically with roughness — and this is the most important result to read carefully. At kₛ = 0.8 mm, the measured shock angle (23.88°) actually landed closer to the inviscid analytical prediction than the smooth-wall CFD value did.
This isn't a bug or a fluke. The shock angle read off a contour is not a direct output of the roughness boundary condition — it's measured geometrically off the wave pattern in post-processing, and depends on three separate things at once: (1) the boundary-layer displacement effect, where a thicker boundary layer presents a slightly different effective wedge angle to the outer inviscid flow than the true geometric angle; (2) exactly where the shock line is sampled, since the shock has finite numerical thickness in a finite-volume solution and the two-point angle measurement is sensitive to which contour points are picked; and (3) the combined effect of shock compression and viscous dissipation on local total-pressure loss, which changes how sharply the pressure gradient reads on the contour. A rougher wall doesn't simply "push the shock angle further from theory" — it changes the boundary-layer state that all three of these depend on, and the net effect at a given kₛ can go either direction. The clean takeaway is that surface condition is a real, non-negligible parameter for shock-angle prediction on small supersonic geometries, but the relationship isn't a single trend line without accounting for the boundary-layer state at each condition.
- The study is 2D only; real roughness is a 3D, often random, distribution rather than a uniform equivalent sand-grain height.
- Angle of attack: all cases here were run at zero incidence. A natural extension is to sweep the double-wedge model through a range of angles of attack — the leading and trailing wedge surfaces would then see different effective deflection angles, and the roughness effect on shock angle may not stay symmetric between them.
- Higher roughness heights: roughness height was only tested up to kₛ = 0.9 mm (transitionally-rough to fully-rough regime). Pushing further would clarify whether the non-monotonic shock-angle trend continues or settles into a clearer fully-rough asymptote.
- Only one freestream Mach number was swept; extending to a Mach number sweep would clarify whether the roughness–shock-angle relationship holds at other speeds.
- The recompression shock (second wedge surface) was characterized analytically and in the smooth-wall CFD case, but the rough-wall parametric sweep focused primarily on the leading shock; extending full recompression-shock tracking to all roughness cases is a natural next step.
- ANSYS Fluent 2024/2026 R1 — density-based compressible RANS solver, SST k–ω turbulence model, Roe flux-difference splitting
- Pointwise — structured mesh generation for both the flat-plate validation case and the double-wedge model
- SolidWorks — double-wedge and flat-plate geometry
- Classical compressible-flow theory (oblique shock relations, Prandtl–Meyer expansion) for the analytical baseline
Independent research project (Project Based Learning report, Gas Dynamics AS362IA), Department of Aerospace Engineering, RV College of Engineering, 2025–26.
- Akula Uday Kiran
- Shanthosh K V
- Tejas L
- Vishnu Raghavendra Mannapur
Assistant Professor · Faculty Mentor: Mukesh M, Assistant Professor*