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UAV Trip-Strip Optimizer

Low-Re Aerodynamics · Boundary Layers · Finite-Wing Modelling · Design Optimisation

Extended a low-Reynolds-number aerofoil solver into a UAV trip-strip design study, combining panel methods, integral boundary-layer modelling, finite-wing analysis and physical trip-drag modelling to determine whether forced transition actually improved performance.

MATLABPanel MethodsBoundary LayersTransitionLifting-Line TheoryAerodynamic OptimisationModel Validation
Design Workflow

From section to mission decision

Aerofoil
Panel Method
Boundary Layer
Predict Separation
Place Trip
Force Transition
Add Trip Drag
Propagate to Finite Wing
Compare Mission Performance
Clean Wing Wins
01 — The Design Question

Should the wing use a trip at all?

Can a passive trip strip force transition early enough to reduce low-Reynolds-number separation losses without adding more drag than it saves? At low Re, laminar separation and transition dominate drag. A trip can trigger transition earlier to reduce separation — but the strip is itself a source of drag. So the study compares three cases:

Clean aerofoil
Forced-transition aerofoil
Physical trip strip incl. device drag
02 — 2D Solver

Panel method + integral boundary layer

The solver couples a vortex-sheet panel method with an integral boundary-layer model. Geometry is spline-refined and repanelled before the potential-flow system is solved. I refactored the original interactive solver into a reusable solve_case() workflow so angle-of-attack and design sweeps could be automated.

Surface vortex strengthPressure coefficient CpCirculationLiftSurface velocityStagnation point
Predicted surface pressure (Cp) comparison.
Predicted surface pressure (Cp) comparison.
03 — Boundary-Layer Model

Marching from the stagnation point

The viscous solver marches independently along the upper and lower surfaces from the stagnation point, using Thwaites' integral laminar method followed by numerical integration of the turbulent layer.

StagnationLaminar BLTransition / SeparationTurbulent BLTrailing Edge
Computes
  • Momentum thickness
  • Displacement thickness
  • Shape factor
  • Energy shape factor
  • Pressure-gradient effects
Detects
  • Natural transition
  • Laminar separation
  • Turbulent reattachment
  • Turbulent separation
Pressure distributions across angle of attack.
Pressure distributions across angle of attack.
04 — Forced Transition

Tripping the boundary layer

I extended the solver so a trip can force transition at a chosen position, switching between natural and forced transition, with explicit tracking of the forced-transition location for later optimisation.

A trip only takes effect if it occurs before natural transition or laminar separation. Downstream of either, it becomes a no-op.

05 — Trip-Location Sweep

Automated across aerofoils and conditions

Aerofoils
  • E387
  • NACA 6412
  • Final low-Re design
Conditions
  • Re = 1×10⁵ – 5×10⁵
  • α = 0°, 2°, 4°, 6°
Per clean case
  • Locate natural transition / laminar separation
  • Place candidate trips ahead of separation
  • Coarse sweep
  • Refine around the best location
Successful 2D cases558
ClCdL/DTransition locationLaminar separationReattachmentTurbulent separationBL thicknessConvergence status
06 — Clean Aerofoil Design

The baseline the study is built on

NACA 6412 · Re 5×10⁵ · best L/D98.56
Final low-Re · Re 5×10⁵ · best L/D110.73
Final high-Re · best L/D153.81
L/D — low-Reynolds-number designs.
L/D — low-Reynolds-number designs.
L/D — high-Reynolds-number designs.
L/D — high-Reynolds-number designs.
07 — 2D → 3D

Coupling the section to a finite wing

A 2D section is not enough for a UAV wing, so the 2D aerodynamic database is coupled to a Prandtl lifting-line model:

Why 2D is not enough
  • Chord changes across the span
  • Local Reynolds number changes
  • Induced angle changes
  • Span loading changes
Finite-wing solver computes
  • Local Reynolds number
  • Effective incidence
  • Induced angle
  • Circulation
  • Local Cl
  • Wing CL
  • Induced drag
  • Profile drag
  • Total L/D
Span1.50 m
Root chord0.25 m
Tip chord0.15 m
Area0.30 m²
Aspect ratio7.5
Taper ratio0.60
08 — Finite-Wing Campaign

Full 3D sweep

Speeds
  • 8 m/s
  • 12 m/s
  • 16 m/s
Root incidences
  • 0°
  • 2°
  • 4°
  • 6°
Mission weighting
  • 8 m/s → 25%
  • 12 m/s → 50%
  • 16 m/s → 25%
Span stations25
Wing configurations108
Span-station results2,700
09 — Trip Strategy Optimisation

Comparing whole strategies, not one position

Strategies

  • Clean
  • Uniform trip — one x/c across the span
  • Three-zone adaptive — root / mid / tip rules
  • Continuous ideal — chosen per span station

Objective

Mission-weighted L/DL/D consistencySeparation penaltiesUnreliable-interpolation penaltiesConvergence penaltiesTrip complexity
J = weighted L/D − variability − penalties

The nominal idealised ranking put E387, 2° root incidence, uniform trip near x/c = 0.45 as the highest-scoring strategy under that objective.

Still an ideal forced-transition result — no physical trip drag yet.

10 — Sensitivity Analysis

Was the optimum robust?

Rather than trusting one optimisation setup, I varied its assumptions — mission-speed weighting, span-station count, separation-location shift and trip penalty. Across 81 sensitivity cases the winning strategy was not fixed:

Sensitivity cases81
Uniform trip wins45
Continuous ideal wins36
11 — Physical Trip Model

Making the trip pay for itself

The ideal trip was deliberately not the final answer. A real strip must actually trigger transition and pay its own drag. I added a physical-trip model using roughness Reynolds number Re_k and trip height / momentum thickness k / θ, only counting a strip as effective when its local state exceeds the configured thresholds. Its drag is kept separate from the profile drag:

Cd,total = Cd,profile + Cd,trip
12 — Trip Shape & Height

Screening real strips

Shapes
  • 2D strip
  • Zigzag
Heights
  • 0.1 mm
  • 0.2 mm
  • 0.3 mm
  • 0.5 mm
Reference chord
  • 0.20 m

The physical-trip calibration is a screening model, not a measured hardware calibration — the code labels its threshold / drag coefficients as heuristic or fallback where appropriate.

13 — Physical Screening

144 real configurations

Grid
  • 3 aerofoils
  • 3 Reynolds numbers
  • 2 incidences
  • 2 trip shapes
  • 4 trip heights
Configurations144
Forced transition138 / 144

The strips generally did trigger transition — so the finding is not simply “the strips did not work.”

14 — Main Result

The trips worked, and still lost

144configurations tested
138forced transition
0improved L/D over clean

The strongest average physical candidate — final low-Re design, 0.1 mm zigzag — still came in at roughly ΔL/D = −5.86 relative to the clean aerofoil. The strips generally worked as transition devices, but their added drag outweighed the benefit from reduced separation.

Clean aerofoil selected. The study asked “should we use a trip?” — and the evidence answered no.

15 — External Validation

Against NASA TM-4062

E387 predictions were compared with digitised experimental data from NASA TM-4062 across multiple Reynolds numbers and angles of attack. Lift trends reproduced more reliably than drag in the most low-Re / separation-bubble-sensitive cases.

Mean abs Cl error≈ 0.108
Mean abs Cd error≈ 0.0068
E387 predictions vs NASA TM-4062 experimental data.
E387 predictions vs NASA TM-4062 experimental data.

The project also generates XFOIL and AVL input decks for independent follow-up, but those external binaries were not available in the recorded environment, so those comparisons were not run.

16 — Testing & Verification

Regression and behaviour tests

NACA0012 symmetryNACA4412 reference behaviourBaseline L/D reproductionForced transitionTrips after natural transitionTrips before / after laminar separationPanel-grid convergenceUpper / lower symmetry

A separate Python verification port cross-checked forced-transition behaviour when MATLAB was unavailable.

NACA 0012 — Cl vs α, predicted vs experimental.
NACA 0012 — Cl vs α, predicted vs experimental.
NACA 4412 — Cd vs Cl, predicted vs experimental.
NACA 4412 — Cd vs Cl, predicted vs experimental.
Skills Developed

What the project built up

Aerodynamic Modelling

Vortex-Sheet Panel MethodsPressure-Coefficient CalculationCirculationLift / Drag PredictionLow-Re Aerodynamics

Boundary Layers

Thwaites MethodMomentum ThicknessDisplacement ThicknessNatural TransitionForced TransitionLaminar SeparationTurbulent ReattachmentTurbulent Separation

Wing Analysis

Prandtl Lifting-Line TheorySpanwise LoadingInduced DragLocal Reynolds Number2D → 3D Aerodynamic Coupling

Numerical / Computational

MATLABNumerical IntegrationLinear-System SolvesInterpolationAutomated Parameter SweepsSensitivity AnalysisData Processing

Design & Optimisation

Mission-Weighted ObjectivesMulti-Condition OptimisationPenalty FunctionsDesign Trade-OffsStrategy Comparison

Validation

Experimental Data ComparisonRegression TestingGrid-Convergence TestingReproducible BaselinesModel-Limitation Analysis

Engineering Judgement

Ideal vs Physical ModelsDevice-Drag Trade-OffsNegative ResultsUncertainty / Sensitivity Analysis