Study of Transonic Cascade Airfoils by a Panel Method

A panel method was applied to transonic flow problems of obtaining shock-free airfoils in turbomachine cascades. With introduction of Sovieczky's fictitious gas concept, the panel method succeeded in treating both subsonic and supersonic flow regions in a unified fashion. It was shown that the location of a sonic line was not necessary for the formulation of the panel method. In the process of calculation the sonic line was determined automatically under given fictitious gas conditions. But the supersonic flow region thus obtained was recalculated to meet the actual gas conditions and to find out how much modification of the airfoil shape was required. At higher Mach numbers a limit line was often encountered, and valid shock-free solutions were destroyed. Numerical results show that the shock-free solutions are obtainable even at higher Mach numbers under such conditions as follows: high inlet flow angles, high pitch-chord ratio, and rear-loaded airfoil shapes.