Fictitious gas for a flow control concept

Bom from originally a mathematically motivated mampulatum to solve the mixed type differen­tial equations modelling shock-free transonic flow, the definition of modified gas properties may be considered as a physical equivalent to this theoretical approach. Rhcograph models for 2D flow for an analytical extension of the subsonic (elliptic type) problem into the supersonic do­main in order to pose and solve a boundary value problem for shock-free airfoil flow results in a modified equation of state as part of the Euler or Navier Stokes equations. Solving such mod­ified equations in direct 2D or 3D space for airfoils, wings or full aircraft configurations will therefore result in supercritical shock-free flow where the domain with velocities higher than the critical value is of a subsonic nature with locally “fictitious” properties, i. e. no practical realiza­tion of this flow is proposed so far

Before this approach is explained as just the first part of a systematic and practical design method, it may be noted (Figure 41), that an interpretation of the fictitious gas as an ideal gas with pressure-controlled energy removal within the local supercritical domain lays ground for an interpretation as a thermodynamic flow control method for obtaining higher aerodynamic efficiency of given configurations. This Figure illustrates this for a thick wing section in tran­sonic flow: Entropy contours and wake profiles at a control surface behind the airfoil allow to compare drag for these flows. Including viscous drag, aerodynamic efficiency (lift over drag) of the controlled airfoil flow is about 50% higher than for an uncontrolled flow. The remaining problem, of course, is the need to remove energy depending on the local pressure p < p* within the supercritical domain, as indicated in Figure 41 by the region w ith local entropy s < 0. rela­tive to upstream values.