1. and 40 give details for a 14 percent circular arc airfoil. Related information regarding the interaction of unsteady airloads caused by transitional boundary layers with structural oscillations i s given by Mabey et al." Another class of separation-induced periodic flow problems, vortex shedding about rigid cylinders and airfoils at high angle-of-attack, has been studied using NS codes for a variety of Reynolds numbers i n Refs. 42-44.
2. Unsteady aerodynamics has been the theme of four recent AGARD conference^^'-^^ whose proceedings contain a wealth of information. Survey papers focusing upon computational requirements and resources are given by peterson 4' and McCroskey et al. '. Summary papers of the 1984 and 1985 AGARD conferences are g i v f by k t o w ' and by Mabey and Chambers . The latter
3. It w i l l be helpful t o distinguish the main features of steady transonic flow i n order t o organize the discussion of unsteady aerodynamics. Figure 2, from Ref. 4, indicates various regions of transonic flow development for the NLR 7301 airfoi 1, a 16-percent cambered supercritical -type section. With increasing Mach number and moderate angle-of-attack, the upper surface becomes critical between M = 0.4-0.7 with the f i r s t shock forming at an increase of a proximately 0.1 i n Mach number. Pearcy et a1 have classified several types of flow separation which may occur. For conventional airfoi 1s the typical pattern, termed type A, involves the growth of a local separation bubble induced by boundary layer separation at the shock foot, spreading rapidly t o the trailing edge as Mach number increases. This condition i s often accompanied by unsteady phenomena such as buffet and aileron buzz 4. The steep a f t pressure gradients of modern airfoils, such as the NLR 7301, can lead to an alternate pattern, termed type B, i n which separation progresses from the trailing edge towards the shock. Figure 2 illustrates this type R separation, with fully separated flow a f t of the shock occuring along the line of maximum lift. Note the small "shock free" design condition occuring over a small isolated range of lift coefficient and Mach number just prior to the onset of t r a i1ing edge separation. i jdeman 4 notes that flow conditions i n the region between the onset of trailing edge separation and fully separated flow are very sensitive t o Reynolds number and the location of transition from laminar to turbulent flow.
4. Tests of rigid circular arc airfoils have been reported by McDevitt et a1.35, M D e v i t t , a b e 38 and Mabey et a1. 39 References 35 and 36 give details of tests of an 18 percent thick airfoil for Reynolds numbers of 1 million t o 17 mi 11ion, covering laminar t o fully developed turbulent flows. The wind tunnel walls were contoured t o approximate the inviscid stream-lines over an airfoil at M = 0.775. Periodic unsteady airflows were observed over a narrow Mach range whose extent depended upon whether Mach number was increasing or decreasing. Forincreasing Mach numbers, oscillations occurred for 0.76 < M < 0.78 while for decreasing Mach number the range was wider, 0.73 < M < 0.78. The frequency of the oscillations was 188 '3 Hz (reduced fre uency k = 0.48 based upon semi-chord). Mabey'' studied similar periodic flows for a series of circular arc airfoils ranging i n thickness from 10 t o 20 percent at Reynolds numbers of 0.4-0.6 mi 11ion. I n Ref. 39, further investigations on a larger 14 percent thick biconvex wing at Reynolds numbers of 1-7 million i s reported. Two necessary criteria evident from the experimental results for the existence of the periodic unsteady flow are given: thickness/chord ratio greater than 12 percent and local Mach number upstream of the terminal shock wave i n the range c e v i t t 36 identifies the predominant shock motion for the 18 percent thick airfoil as type C whereas Mabey et a1.39 argue that it i s type B motion.