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.