■ ./ ' Smith 



The stator blade is an 8.4-percent-thick von Mises symmetrical airfoil and the 

 rotor blade is a cambered 11.4-percent-thick airfoil obtained by conformal 

 transformation. When the trailing edge of the rotor blade is immediately in 

 front of the leading edge of the stator blade, the gap is 0.412c. The stator blade 

 is aligned with the remote onset flow U^. The problem is illustrated in Fig. 11a. 

 The figure includes wake shapes shortly after the rotor blade has passed in 

 front of the stator blade. The rotor wake opens up to pass around the stator as 

 it is carried downstream by the general flow U„. Figure lib shows a very highly 

 loaded blade. Here the deflections of the wakes are much greater. The vorticity 

 shed from the rotor is so great that roUing-up instability is developing. Refer- 

 ence 5 presents pressure-distribution and time-history information on the blade 

 force coefficients that is not repeated here. It is interesting to note that the 

 present method can solve exactly a two-dimensional simplification of a Voith- 

 Schneider propeller having either one or two blades. 



FLOW-FIELD CHARTS 



Charts of flow fields are a rarity; that is why they are mentioned here, even 

 though they represent no advance in basic capability. Reference 8 has been 

 written with the primary objective of providing a set of charts and formulas by 

 which one may conveniently estimate perturbation velocities at any point in the 

 field around some arbitrary shape. In many problems of design, such informa- 

 tion is needed. Both two-dimensional flows and flows about bodies of revolution 

 are treated. , , : ■ 



Two-Dimensional Flows T'"^- ' " . ' 



A two-dimensional lifting flow can be resolved into three subflows: a uni- 

 form onset flow parallel to a chord line, a uniform onset flow perpendicular to 

 a chord line, and a purely circulatory flow (Fig. 12). If there is no lift, of 

 course, the third flow is zero. Now for each flow the body induces perturba- 

 tions that can be resolved into components parallel and perpendicular to the 

 chord line. Hence to cover all cases of a lifting two-dimensional flow, six 

 charts are needed, which present the following quantities, all of which are 

 perturbations: 



v„ v„ v.. V^ V^ Vy 



V„ ^ ' V„ ' VC, ' V ' V ■^' 



v„c. 



The first line is the set of v^ perturbations, and the second the set of Vy pertur- 

 bations. The velocity v„ is the entire onset velocity, which equals (V<^^ + viy)^/^. 

 By reading the charts, v^ and Vy perturbations can be figured quickly by means 

 of the following formulas, if the surface is at an angle of attack a: 





v.. \ /v. 



1 1 COS a + 



V /V\ /V \ /V 



yp / y \ / y ^ ' - 



V V / V \ V C 



(14) 



1 sin a+ -— Cl . (15) 



>'a)'-L 



338 



