342 



DISTANCE FROM 

 SURFACE. 2 



R linchesl 



O WITHOUT UPSTT^EAM STT^UTS 

 WITHOUT SCREEN 

 WITHOUT ROTOR 



WITHOUT UPSTREAM STRUTS 

 WITHOUT SCREEN 

 DESIGN FLOW COEFFICIENT 

 IBASIC FLOW NO, II 



CALCULATED PROFILE 



WITHOUT UPSTREAM STRUTS 

 WITHOUT SCREEN 

 DESIGN FLOW COEFFICIENT 

 IBASIC FLOW NO. II 



CALCULATED PROFILES 



0.2 0.4 0.6 0.8 1.0 1.2 

 AXIAL VELOCI?!' RATIO, V /V„ 



a o 



0.2' O.'l 0.6 0.8 1.0 1.2 1.4 

 VELOCITY RATIOS, -t-ANDtt" 



FIGURE 3. Comparison between velocity profile with/ 

 without rotor. 



FIGURE 5. Tangential and axial velocity profiles 

 at cap. 



through the rotor with the first streamline being 

 at the inner wall and the last streamline going 

 through the rotor tip. The streamlines were spaced 

 more closely near the inner wall because the second- 

 ary flow calculations are most important near the 

 wall. Also, the streamline curvature equations are 

 inviscid so that there is a finite velocity at the 

 inner wall streamline. 



A sample of the calculations for the flow field 

 is given in Figures 3,4, and 5 for the flow config- 

 uration called Basic Flow No. 1. For. Basic Flow 

 No. 1, the boundaiy layer entering the rotor is 

 axisymmetric with no upstream distribution such as 

 screens or struts forward of the rotor which is 

 operating at its design flow coefficient. In Figure 

 3, the calculated axial velocity profile in the 

 plane of the rotor without the rotor and the calcu- 

 lated axial velocity profile in front of the rotor 

 with the rotor operating on design is shown. In 

 addition, experimental data measured in the 48- inch 



WITHOUT UPSTREAM SHOUTS 

 WITHOUT SCREEN 

 DESIGN FLOW COEFFICIENT 

 IBASIC FLOW NO. 1) 



0.2 0.4 0.6 0.8 1.0 1.2 1.4 



FIGURE 4. Rotor outlet velocity profiles for basic 

 flow no. 1. 



water tunnel by a LDA system are given for a com- 

 parison. In Figure 4, the calculated outlet velocity 

 profiles are shown with coirparison to measured data. 

 Finally, Figure 5 shows the calculated and measured 

 tangential velocity, component, Vg , downstream of the 

 rotor plane where cavitation occurs under certain 

 flow conditions. In general, the flow field calcu- 

 lations show very good agreement with the experi- 

 mental data. 



Secondary Flow Field 



The major equations used in the streamline curvature 

 method for calculation of the flow field were derived 

 from the principles of conservation of mass, momentum, 

 and energy. The fluid was assumed to be incompress- 

 ible, inviscid, and steady. In addition, the flow 

 field was assiomed to be axisymmetric. 



The resultant equations allow for streamline 

 curvature and for vorticity in the flow. However, 

 it is important to realize that the solution to the 

 flow field does not contain all of the vorticity. 

 In particular, only the circumferential vorticity 

 is totally included. The other components of 

 vorticity contain derivatives with respect to the 

 circumferential direction which are assumed to he 

 zero. As discussed by Hawthorne and Novak (1969) , 

 the neglected vorticity terms can be related to the 

 secondary flows that occur in the blade passage 

 along the inner wall. 



Using the generalized vorticity equations, Lak- 

 shminarayana and Horlock (1973) derived a set of 

 incompressible vorticity equations valid for a 

 rotor operating with an incoming velocity gradient. 

 Their expressions for the absolute vorticities, 

 '^s' ' '^n' • defined along relative streamlines, s', 

 n' , were modified for the boundary conditions imposed 

 by this problem and were integrated. The resulting 

 equations are 



u ' = 0) • • (3) 



"2 "1 W2 aja^ 



and 



