05 / case-study

Regional 28m wing — aerostructural CD-min

E190-class regional jet wing, vortex-lattice aero coupled with a tube FEM structural model. Minimize drag at a fixed lift coefficient, with a realistic structural-mass cap. Run end-to-end through the hangar-omd Lane B plan pipeline.

plan: reg28m-opt-refined v1 / run: run-20260414T145425-65b0174e / factory: oas/AerostructPoint
0.500
CL (lift constraint)
0.02213
CD (objective)
22.60
L/D
3000 kg
struct mass (cap active)
28
SLSQP iterations
converged
status
formulation

MDO problem setup.

Operating conditions, wing geometry, DVs, and constraints. Aluminum 7075-T6 tube FEM structural model coupled with vortex-lattice aero via OpenAeroStruct.

operating conditions

Mach0.78
velocity230.15 m/s
altitude density0.3639 kg/m³
Reynolds number5.5 × 10&sup6;
alpha (initial)5.0 deg
gross weight (W0)40,000 kg
design range3,704 km (2,000 nmi)
load factor1.0

wing geometry

span28.0 m
root chord4.2 m
taper ratio0.32
sweep24.0 deg
dihedral5.0 deg
mesh (ny × nx)21 × 3
FEM modeltube
materialAl 7075-T6
safety factor1.5

design variables (3)

  • twist_cp [-10, +15] deg, 5 stations
  • thickness_cp [0.002, 0.05] m, 5 stations
  • alpha [-5, +10] deg

objective & constraints

  • minimize CD (drag coefficient)
  • CL = 0.5 equality
  • failure ≤ 0 von Mises stress, KS aggregated
  • struct_mass ≤ 3000 kg realistic E190-class cap
optimizerSLSQP
maxiter200
tol (ftol)1e-9
timeout600 s
decisions

Design decisions.

Formulation choices that moved the problem from a coarse proof-of-concept to a production-quality run.

formulation3 decisions
dec-ref-01
Refined mesh: num_y=21, num_x=3 for production-quality results
The coarse mesh (ny=7) proved the formulation worked. 21 spanwise panels provide adequate resolution of spanwise lift and structural loads; 3 chordwise panels capture camber effects. Run cost roughly 3x the coarse mesh, still well under a minute.
dec-ref-02
CD objective with CL=0.5 and structural mass ≤ 3000 kg constraints
Fuelburn objective with L=W constraint was numerically unstable with SLSQP (oscillating L_equals_W, singular matrices). CD minimization with a CL equality constraint is much better conditioned. The mass cap prevents thickness from hitting upper bounds and produces realistic structural sizing. The coarse mesh converged in 35 iterations with this formulation; the refined mesh converges in 28.
dec-ref-03
Structural-mass upper bound set to 3000 kg
E190-class wing structural weight is approximately 3000 to 4000 kg. Upper bound of 3000 kg forces the optimizer to trade structural stiffness against aerodynamic performance, producing meaningful thickness distributions. Looser bounds let the optimizer pad thickness without regard to weight.
run plots

Analysis plots.

All plots generated by omd-cli plot <run_id> --type all from the converged optimization case in the OpenMDAO recorder.

Convergence history
convergenceCD objective and constraint histories vs SLSQP iteration (28 iters to converge)
DV evolution
dv_evolutiontwist_cp, thickness_cp, alpha values across iterations
Spanwise lift distribution
liftspanwise lift distribution vs elliptical reference — induced-drag/struct tradeoff
Wing planform
planformLE/TE outline; optimized vs initial overlay if deformed
Von Mises stress
vonmisesvon Mises stress vs Al 7075-T6 yield with 1.5x safety factor
Failure index
failureKS-aggregated failure index (satisfied when ≤ 0)
Tube thickness
thicknessoptimized tube wall thickness; thicker at root, tapered outboard
Thickness-to-chord
t_over_ct/c ratio input to the aerodynamic model
Structural overview
structtube FEM element sizing and load paths through the wingbox
3D mesh
mesh_3d3D aero mesh with structural FEM overlay (21 x 3 panels)
Twist and chord
twistspanwise twist and chord distributions; washout to tip
model

OpenMDAO model structure.

Interactive N2 matrix and problem graph. Blue cells indicate feedforward connections, red cells indicate feedback. Both are static renders of the live omd viewer.

N2 diagram

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problem graph

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provenance

W3C PROV-Agent graph & plan detail.

The provenance graph shows plan entities, decisions, run activities, and result assessments. The plan detail page renders the YAML plan with cross-links into provenance.

provenance graph

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plan detail

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