3-D Axisymmetric Transonic Shock Solutions of the Full Euler System in Divergent Nozzles

We establish the stability of 3-D axisymmetric transonic shock solutions of the steady full Euler system in divergent nozzles under small perturbations of an incoming radial supersonic flow and a constant pressure at the exit of the nozzles. To study 3-D axisymmetric transonic shock solutions of the full Euler system, we use a stream function formulation of the full Euler system for a 3-D axisymmetric flow. We resolve the singularity issue arising in stream function formulations of the full Euler system for a 3-D axisymmetric flow. We develop a new scheme to determine a shock location of a transonic shock solution of the steady full Euler system based on the stream function formulation.

Review of Adaptive Shock Control Systems

Drag reduction plays a major role in future aircraft design in order to lower emissions in aviation. In transonic flight, the transonic shock induces wave drag and thus increases the overall aircraft drag and hence emissions. In the past decades, shock control has been investigated intensively from an aerodynamic point of view and has proven its efficacy in terms of reducing wave drag. Furthermore, a number of concepts for shock control bumps (SCBs) that can adapt their position and height have been introduced. The implementation of adaptive SCBs requires a trade-off between aerodynamic benefits, system complexity and overall robustness. The challenge is to find a system with low complexity which still generates sufficient aerodynamic improvement to attain an overall system benefit. The objectives of this paper are to summarize adaptive concepts for shock control, and to evaluate and compare them in terms of their advantages and challenges of their system integrity so as to offer a basis for robust comparisons. The investigated concepts include different actuation systems as conventional spoiler actuators, shape memory alloys (SMAs) or pressurized elements. Near-term applications are seen for spoiler actuator concepts while highest controllability is identified for concepts several with smaller actuators such as SMAs.