26072017  Original Article  Issue 2/2018 Open Access
Parametric design velocity computation for CADbased design optimization using adjoint methods
 Journal:
 Engineering with Computers > Issue 2/2018
1 Introduction
2 Theory
2.1 Adjoint methods
2.2 Design velocity
3 Methodology
3.1 The projection test
3.2 Determining which facet in the perturbed model to test first
3.3 Determining which facet in the perturbed model to test next

\( \zeta < 0 \) the adjacent facet which shares the points \( F_{1} \) and \( F_{3} \) should be tested next,

\( \eta < 0 \) the adjacent facet which shares the points \( F_{1} \) and \( F_{2} \) should be tested next,

\( \zeta + \eta > 1 \) the adjacent facet which shares the points \( F_{2} \) and \( F_{3} \) should be tested next.
3.4 Computing design velocity
4 Results
4.1 Validation of design velocity
4.2 Validation of performance gradients
4.3 Optimization test case

Freestream temperature = 288.15 K

Freestream mach number = 0.8395

Angle of attack (AoA) = \( 3.06^{ \circ } \)

Objective function = \( { \hbox{min} }(C_{D} ) \)

No. of design variables = 27
5 Discussion
6 Conclusion

An efficient procedure to calculate performance gradients with respect to CAD parameters, using adjoint methods, was presented.

The gradients obtained using this approach can be used in an optimization framework to produce an optimized CAD model geometry in a featurebased CAD system.

The projection methodology using a surface tessellation of CAD geometries overcomes several limitations of alternative approaches, such as the persistent naming problem or changes in the model’s topology.