Metacomp’s Adjoint solver in action — Aerodynamic shape optimization

Metacomp’s Adjoint solver is used to optimize the shape of the 3D wing of the common research model (CRM). A decrement of about 5% in drag is realized while maintaining the lift coefficient at 0.5 for fight conditions of Mach 0.85 and Re/m of 5 million. A platform integrating Metacomp’s software suite (MIME® and CFD++®), OpenMDAO and pyGeo is built in the process.

**Figure 1**: NASA Common Research model (CRM) wing geometry

This work was presented at the 8th National Conference on Multidisciplinary Design, Analysis, and Optimization (NCMDAO) held at Ramiah University of Applied Sciences (RUAS), Bengaluru, India, on 3^rd – 5^th December 2025. Please contact Metacomp support if you wish to read the full paper.

Figure 2: Tasks performed by the software suites and the data flow across them

Freeform deformation (FFD) volumes are defined at six span locations. Each FFD has 14 control points with 7 points above and 7 points below the wing surface. These FFDs are employed to bring global (twist) and local changes to the wing’s shape.

**Figure 3**: Control points (red dots) define a FFD volume

Including angle of attack and anchoring control points of the FFD volume at the wing’s root, a total of 76 design variables are considered in the optimization exercise. The movement of control points in transverse direction that brings in local changes to wing’s shape is constrained such that the distance between the corresponding top and bottom control points for a FFD volume is greater than 25% of initial wing thickness.

A total of 86 design point evaluation with gradients evaluated at 17 of these design points were required in order to converge to the optimized wing shape.

**Figure 4**: Outer contour of baseline and optimised wings when viewed in the x-direction (yz plane).

A summary of changes in Cd is given in the table below.

	Baseline	Optimized	Change (%)
Cd	0.0212	0.0202	-4.74
Cd_inviscid	0.0146	0.0134	-8.06
Cd_viscous	0.0066	0.0068	+2.52

A near 8% decrease in inviscid drag (Cd_inviscid) is noted. While the pressure contour has not changed significantly on the windward side of the wing, its recovery has improved for the optimised shape contributing primarily to the decrement in the inviscid drag

**Figure 5a**: Windward (+X) side pressure distribution for baseline (top) and optimized (bottom) wing shapes

**Figure 5b**: Leeward (-X) side pressure distribution for baseline (top) and optimized (bottom) wing shapes

The shape change has weakened the transonic shock strength contributing to the noted pressure distribution on the windward and leeward sides of the wing:

**Figure 6**: Mach number contours of the baseline wing (left) and optimized wing (right) on the z = 1.12m cut-plane.

However, this comes at the expense of increased viscous drag (+2.5%), resulting in an overall decrease in drag by 4.7% (see skin friction contours below):