Recent Progress in the Calculation of Potential Flows 



□ ■ IMAGINARY PART 

 O • REAL PART 



-•- -•- EXPERIMENTAL DATA 

 — -O D— PRESENT METHOD 



c/2U„ 



c/2Ua 



Fig. 8 - Comparison of calculated and experimental reduced 

 circulatory lift and moment coefficients for a symmetrical 8.4- 

 percent-thick von Mises airfoil oscillating in a simple harmonic 

 manner with an amplitude of 0.06. Cj = lift coefficient (less the 

 added mass terms proportional to accelerations) divided by 

 quarter chord amplitude. C^ = moment coefficient analogous 

 to Ce. 



pass each other. The general level of the lift is low because the airfoils have 

 not moved far enough to develop steady- state lift. As can be seen, the lift is 

 generally consistent with isolated flat-plate theory. When the airfoils are 

 directly over each other (tUo^/c = l.O), the two airfoils have a tendency to 

 be drawn into each other. It would be interesting to see results with a longer 

 run before the airfoils passed each other, in which they would more nearly 

 reach the steady state (Cj/C = l). Expensive computer time has, so far, pre- 

 vented such an experiment. 



An Airfoil with an Oscillating Flap - A second example is given in Fig. 10. 

 In this case the flap of an NACA 23012 airfoil is given a simple-harmonic rota- 

 tional motion (angular range 0° ^ 45°). The flap was moved from its original 

 position (Ax = - 0.047c, Ay = -0.02c) before the motion was initiated (Fig. 10b). 

 Figure 10a shows the wake shed from the main section and the flap at two dif- 

 ferent times. The flap deflection in one case is 45'' and 0° in the other. The 

 pressure distribution over the airfoil and flap system when the flap is at its 

 maximum deflection (45*^) is given in Fig. 10b. The configuration is shown at 

 the upper left in the figure. The flap is shown undeflected beneath the pressure 

 plot. For comparison. Fig. 10b includes the steady-state pressure distribution. 



A Rotor Blade Passing a Stator Blade - As a final example, we consider a 

 rotor blade and a stator blade of a compressor stage, both of chord length c. 



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