Optimization of Subsonic and Transonic Airfoils for Natural Laminar Flow using a Discrete-Adjoint Method

The design of Natural Laminar Flow (NLF) airfoils at subsonic and transonic speeds is demonstrated by high-fidelity multipoint aerodynamic shape optimization capable of efficiently incorporating and exploiting... [ view full abstract ]

The design of Natural Laminar Flow (NLF) airfoils at subsonic and transonic speeds is demonstrated by high-fidelity multipoint aerodynamic shape optimization capable of efficiently incorporating and exploiting laminar-turbulent transition. With the exception of a few more recent works employing Reynolds-averaged Navier-Stokes (RANS) flow solvers [1-3], the majority of research involving transition prediction has employed boundary-layer codes through inviscid-viscous coupling [4-10].

In the authors' previous work [11], a RANS flow solver was extended to incorporate non-local transition prediction criteria, including the compressible form of the Arnal-Habiballah-Delcourt (AHD) criterion [12-15] , and the simplified eN envelope method of Drela and Giles [16]. These criteria are used to predict the natural transition arising due to Tollmien-Schlichting instabilities. The boundary layer properties are obtained directly from the Navier-Stokese flow solution, and the transition region is modeled using an intermittency function in conjunction with the Spalart-Allmaras model [17].

In this work, optimizations are performed using a gradient-based sequential quadratic programming shape optimization framework that makes use of the SNOPT optimization suite [17]. The laminar-turbulent transition criteria are tightly coupled into the objective and gradient evaluations. The gradients are obtained using a new augmented discrete-adjoint formulation proposed for non-local transition criteria. The practical aerodynamic design requirements are cast into a multipoint design optimization problem. A composite objective is defined using a weighted integral of the operating points. The proposed framework is applied to the single and multipoint optimization of subsonic and transonic airfoils, leading to robust and practical natural-laminar-flow designs.

Validation of the transition prediction framework has been carried out by comparison to available experimental transition data, as presented by Rashad and Zingg [11]. NLF airfoils are designed with the objective of minimizing the total drag, while satisfying a specified lift-coefficient constraint (Cl*). Thickness and area constraints are also included. The airfoil geometry is parametrized using B-splines, the details of which may be found in Nemec and Zingg [19]. The design variables are defined as the y-coordinates of the B-spline control points; the control points are free to move in the vertical direction to facilitate shape changes during the optimization cycle. The angle of attack of the airfoil is an additional design variable. A verification of the accuracy of the discrete-adjoint gradient evaluation will be included in the final paper. The verification is performed by comparing the adjoint gradient to the more computationally expensive finite-difference approximation.

While the full paper will include more design examples, here we consider multipoint optimization [20-22] at a range of cruise conditions associated with the Bombardier Dash-8 Q400 aircraft. Nine operating conditions, presented in Table 1, are defined by varying the aircraft weight and Mach number. Table 2 provides a summary of the results comparing the initial and optimized airfoils, along with the various angles of attack. The lift constraint has been satisfied and the drag reduced at each operating point. Figure 1 (a) compares the initial and optimized geometries, and Figure 1 (b) compares the initial and optimized pressure distributions for design point 6. The solid dots represent the transition points. The final paper will quantify the penalty incurred when performing multipoint as compared to single-point optimizations for NLF airfoils. The results demonstrate the optimizer's ability to exploit the transition prediction capabilities of the flow solver in order to extend the regions of favourable pressure gradient, delay the onset of transition, and facilitate the design of new NLF airfoils.

References:

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