Gradient-based control and optimization of boundary layer transition

In flow past bodies, small amounts of surface suction can delay the transition from laminar to turbulent flow. Suction therefore has significant potential to reduce the drag and hence the operating costs of aircraft. To obtain best results the suction distribution must be optimized, and, if necessary, should be adjusted to take account of changing conditions. Here distributed suction is used through a number of independently controlled discrete suction panels, with transition maintained at a desired location while an automatic adaptive control feedback loop regulates the suction flowrates. The combination of minimum suction effort with constant transition position is expressed as a constrained optimization problem. A gradient-based algorithm is used to perform the control and optimization. Up to six suction panels are used, and flows both with and without an imposed pressure gradient are considered. In simple cases the method converges rapidly, but in other situations there is no single optimum solution within the numerical tolerance of the method. There are also cases in which an optimum solution exists but cannot be achieved as it occurs at a discontinuity in the relationship between the transition position and the suction flowrates. Similar problems could occur with other cost functions and formulations, and when using different solution algorithms.