An adjoint-based methodology for calculating manufacturing tolerances for natural laminar flow airfoils susceptible to smooth surface waviness

• Published in: Theoretical and computational fluid dynamics 2024-02, Vol.38 (1), p.15-37
• Main Authors: Moniripiri, Mohammad, Brito, Pedro P. C., Cavalieri, André V. G., Sêcco, Ney R., Hanifi, Ardeshir
• Format: Article
• Language: English
• Subjects: Accuracy; Adjoints; Angle of attack; Approximation; Boundary layer stability; Boundary layers; Classical and Continuum Physics; Computation; Computational Science and Engineering; Disturbances; Engineering; Engineering Fluid Dynamics; Flight; Flight conditions; Fluid flow; Kinetic energy; Laminar flow; Laminar flow airfoils; Mach number; Manufacturing; Mathematical analysis; Methods; Original Article; Parabolized stability equations; Reynolds number; Surface waviness; Tolerances; Tolerances (dimensional); Wavelengths
• ISSN: 0935-4964; 1432-2250
• DOI: 10.1007/s00162-023-00681-y

An adjoint-based method is presented for determining manufacturing tolerances for aerodynamic surfaces with natural laminar flow subjected to wavy excrescences. The growth of convective unstable disturbances is computed by solving Euler, boundary layer, and parabolized stability equations. The gradient of the kinetic energy of disturbances in the boundary layer ( E ) with respect to surface grid points is calculated by solving adjoints of the governing equations. The accuracy of approximations of Δ E , using gradients obtained from adjoint, is investigated for several waviness heights. It is also shown how second-order derivatives increase the accuracy of approximations of Δ E when surface deformations are large. Then, for specific flight conditions, using the steepest ascent and the sequential least squares programming methodologies, the waviness profile with minimum L 2 - norm that causes a specific increase in the maximum value of N - factor, Δ N , is found. Finally, numerical tests are performed using the NLF(2)-0415 airfoil to specify tolerance levels for Δ N up to 2.0 for different flight conditions. Most simulations are carried out for a Mach number and angle of attack equal to 0.5 and 1 . 25 ∘ , respectively, and with Reynolds numbers between 9 × 10 6 and 15 × 10 6 and for waviness profiles with different ranges of wavelengths. Finally, some additional studies are presented for different angles of attack and Mach numbers to show their effects on the computed tolerances. Graphic abstract