AeroShapeOpt Demo — Samarjith Biswas

Airfoil Presets

Flight Conditions

Angle of Attack α

−6°3°18°

Reynolds Number

100k3.0M10M

Optimization Objective

CST Shape Weights

Upper Surface (A_u)

Lower Surface (A_l)

Aerodynamic Coefficients

Lift Cl —

Drag Cd —

L/D Ratio —

Cd pressure —

Cd viscous —

Max t/c —

Compute Time —

Shape Optimizer

Gradient-ascent on CST weights (simulates PPO policy steps). Updates shape iteratively to maximize selected objective while satisfying geometric constraints.

Ready — click Start Optimization

Aerodynamic Polar Sweep

Sweep α from −4° to +16° and compute Cl, Cd, L/D at each step using the panel method.

Airfoil Geometry — CST Parameterization

Pressure Coefficient Distribution Cp(x/c)

Thickness & Camber Distributions

Drag Polar — Hess-Smith Panel Method

L/D Ratio & Cl vs Angle of Attack

Optimization Convergence History

AeroShapeOpt — Physics & RL Architecture

CST Weights Bernstein polynomial coefficients (A_u, A_l)

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Airfoil Shape x,z coordinates via class function C(ψ)·S(ψ)

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Panel Solver Hess-Smith source + vortex panels → Cl, Cd, Cp

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Reward / Objective L/D, Cl − constraint penalties

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PPO Update Actor-critic policy gradient on CST space

CST Parameterization (Kulfan, 2008)

z(ψ) = C(ψ)·S(ψ) + ψ·Δz_TE

C(ψ) = ψ^0.5(1−ψ)^1.0 — round nose, sharp TE. S(ψ) = Σ A_i·B_i,n(ψ) where B_i,n are Bernstein basis polynomials. Low-dimensional (5 params/surface) with guaranteed smooth, valid airfoils.

Hess-Smith Panel Method (1967)

Cl = −Σ Cp·Δy, Cd = Σ Cp·Δx

Source + vortex panels with Kutta condition (zero TE velocity). Solves N+1 linear equations for source strengths q_i and circulation γ. Inviscid pressure drag + Schlichting skin friction: Cd = Cd_p + 2C_f.

Schlichting Skin Friction (1979)

C_f = 0.455 / (log₁₀ Re)^2.58

Turbulent flat-plate skin friction coefficient. Multiplied by 2 for both airfoil surfaces. Valid for Re = 10⁵–10⁹. Provides physically consistent viscous drag estimate without boundary-layer solver.

AeroShapeOptCFD Surrogate Explorer