Morgan and Caster 



flow field. Satisfactory, unsatisfactory, and marginal will be defined in a simi- 

 lar manner to that for the pressure distribution on the surface of the annular 

 airfoil. 



Knowledge of the forces and moments is necessary: [1] for estimating the 

 system performance, [2] for design of a system to produce a given force, [3] for 

 determination of the stability of a particular craft, and [4] for making structural 

 analyses. Satisfactory will be taken to mean that the particular force or mo- 

 ment being discussed is, in general, within experimental accuracy, and unsatis- 

 factory will be taken to mean that it is not within experimental accuracy. When 

 discussing the thrust, or drag, on the duct of a ducted propeller however, the 

 adequacy will be based on a comparison of the total thrust of the system, since 

 the total force is the important parameter. 



These criteria serve as a basis for making comparisons, however, the estab- 

 lishment of the experimental accuracy of the various tests is not straightforward. 

 If no information is available on the experimental accuracy of a particular set of 

 data, the following accuracy will be assumed: (1) for the pressure, or velocity, 

 coefficients ±5 percent, and (2) for force and moment coefficients ±2 percent. 

 The accuracy of the pressure measurements may very well be less than ± 5 per- 

 cent and more than ±10 percent for small values of the pressure coefficient. 



Annular Airfoil Pressure Distributions 



Experimental and theoretical pressure distributions are presented for sev- 

 eral annular airfoils (ducts) which typify some of the duct shapes used for ducted 

 propeller systems. Two ducts were tested in a wind tunnel at NSRDC and re- 

 ported in Ref. (33). Duct I typifies a shape used for accelerating velocities at 

 the propeller (Kort nozzle type). This duct has a NACA 0010 thickness distribu- 

 tion, a NACA 250 mean line with a camber-chord ratio of -0.0375, a chord- 

 diameter ratio of 0.8, and a section angle of attack a, of 6°. 



The measured pressure coefficients c , along with the theoretical predicted 

 values from linearized theory with a nonlinear approximation (33) are plotted in 

 Fig. 1 for this duct at a zero angle of incidence(ar = 0). The symbols used are 

 described in the Notation Section of this paper. Two sets of theoretical curves 

 are shown on this figure; one using the linearized Bernoulli equation (shown by a 

 solid line) and the other using the Bernoulli equation without linearization (shown 

 by a dashed line). Figure 1 shows that the theoretical prediction of the pressure 

 distribution on the inside of the duct is satisfactory. While on the outside of the 

 duct boundary layer separation* occurs near the leading edge of this duct and 



-Two regions of separation may occur on an annular airfoil; one is laminar 

 separation near the leading edge and the other is turbulent separation near the 

 trailing edge. The occurrence of separation depends on the gradient of the 

 chordwise pressure distribution and will always occur if the annular airfoil has 

 a sufficiently high angle of incidence. For ducts which are very thick, it would 

 be expected that turbulent separation would occur near the duct trailing edge at 

 angles of incidence lower than for which laminar separation would occur near 

 the leading edge. For ducts of conventional thickness , laminar separation would 

 be expected at lower angles of incidence than for which turbulent separation 

 would occur. At high angles of incidence, both regions of separation would be 

 expected to be present and at sufficiently high angles, the regions merge and 

 stall of the annular airfoil occurs. These various flow regions on annular air- 

 foils have been investigated in detail by Eichelbrenner et al. (34). 



1316 



