Flow control consists in modifying the flow dynamics by introducing devices, such as pulsating jets or moving walls, in order to improve the aerodynamic performance of systems like bluff-bodies, for which the flow is characterized by a massive detachment. The main difficulty is to find suitable actuator parameters, such as location, frequency and amplitude. In this context, we investigate two main approaches:
- Construction of statistical surrogate models:
Surrogate models based on a flow database, such as kriging, are used to drive the search for optimal control parameters, for a moderate cost.
- Computation of unsteady sensitivity fields:
The continuous sensitivity equation method is employed in an unsteady context to derive either a descent direction in an optimization framework, or a numerical sensor for closed-loop control.
|Perturbation of a boundary layer flow by an oscillating jet actuation.
Robust design methods
A major issue in aerodynamic design for real-life problems is the presence of uncertainty, arising from operational conditions (inflow / outflow conditions), physical models (turbulence), geometry (manufactoring tolerances, neglected details) or even numerical methods (convergence, discretization), that can yield off-design performance losses. To account for uncertainty, we investigate several approaches:
- Optimization based on noisy evaluations:
Statistical models, such as kriging, can include some sources of uncertainty. In this framework, the evaluations are considered as noisy and a statistical criterion (quantile-based) is used to determine the optimum design.
- Optimization with uncertain parameters sampling:
A sampling of the uncertain parameters is achieved to compute the statistical moments of the objective function, such as expectation and variance. Surrogate models can be used to reduce the related CPU cost. A deterministic optimization is then carried out on the basis of the moments of the objective function.
- Sensitivity analysis with respect to uncertain parameters:
The derivatives of the objective function, or possibly the PDE solution, are computed with respect to uncertain parameters (adjoint or direct approaches). Approximations of the statistical moments are then derived from the sensitivity analysis.
|Flow at Mach number 0.85 for a wing optimized at Mach number 0.83 (left) and for a wing optimized in a statistical sense (right).
Isogeometric analysis and design
A major weakness of classical design optimization loops is due to the use of
complex softwares, such as CAD tools, grid generation tools and PDE's solvers,
that rely on different representation bases. The isogeometric paradigm proposes
to employ a unique high-order representation basis, such as NURBS, for all
tools of the design loop. Thus, this approach yields the fusion of CAD and
Finite-Element concepts. We are considering the following research axes:
- Numerical Spline-based schemes :
We develop a prototype of isogeometric solver for heat
conduction problems (Poisson equation) and compressible flows (Euler equations). The use of various Spline bases is studied, in terms of accuracy, robustness and computational efficiency.
- Hierarchical algorithms :
We study various approaches for local refinement of the computational parametric domain. Moreover, in the context of design optimization, we construct hierarchical strategies for both modeling and optimization, to speed-up the design procedure.
- Shape gradients :
Isogeometric analysis is a nice framework to develop shape gradient computations on the basis of a single geometric representation for the shape, the shape gradient and variable fields. Numerical experiments are conducted in linear elasticity.
|Example of bi-cubic NURBS grid and pressure field (Euler equations).