Sevik 



The conclusions which may be drawn from this analysis can be summarized 

 as follows: 



1. The rms thrust coefficient is directly proportional to the turbulence 

 level u/u. 



2. The rms thrust coefficient depends on the ratios b/M and R M, namely, 

 the ratio of chord to grid mesh size and radius to grid mesh size. 



3. The dependence on the advance ratio J is not very pronounced. - 



4. The spectrum tensor n/Rc Gi^(r) varies as r-3/2 for large values of the 

 frequency parameter r = wM/U. Most of the energy is concentrated at the low- 

 frequency end of the spectrum. 



EXPERIMENTAL INVESTIGATIONS 



To verify the theory experiments were conducted in the water tunnel of the 

 Ordnance Research Laboratory at the Pennsylvania State University (8). This 

 tunnel has a test section 4 feet in diameter and 14 feet long. Velocities as high 

 as 80 ft/sec can be achieved, and the static pressure can be varied from 3 psia 

 to 60 psia. A honeycomb of large ratio of length to diameter in the settling sec- 

 tion of the tunnel reduces the turbulence level in the test section to about 0.1%. 



The propeller used for this investigation had ten blades with a constant 

 chord length of 1 inch and a radius of 4 inches. By means of hub inserts the 

 number of blades can be changed and the propeller can be operated with two or 

 five blades. The design static thrust coefficient based on propeller disk area is 

 0.183, and the advance ratio at the design thrust coefficient is 1.17. The pro- 

 peller, and its installation in the water tvmnel, is shown in Fig. 6. 



A special balance was designed for measuring the unsteady propeller thrust 

 force. These measurements require an instrument having a high sensitivity, a 

 low noise level, and a natural frequency much greater than the range of frequen- 

 cies of interest. Figure 7 illustrates the arrangement used. A piezoelectric 

 crystal is mounted in a steel cup at the end of the propeller shaft. After assem- 

 bly the cup is positioned by set screws until the hemispherical ball bonded to the 

 crystal lies exactly on the centerline of the shaft, thus minimizing the crystal's 

 response to bending distortions of the shaft caused by hydrodynamic moments 

 acting on the propeller. 



The frequency response and the linearity of the balance are shown in Fig. 8. 

 These measurements, made in air, indicate that the useful range of the balance 

 is approximately 600 Hz in water. As shown in Fig. 8 the frequency response 

 was measured by means of an electromagnetic exciter whose force output was 

 monitored by a calibrated force gage. The propeller was driven by a 20-hp dc 

 motor housed in a streamlined enclosure. It was mounted as far downstream as 

 possible in the test section and was carefully aligned so that the propeller shaft 

 was concentric with the center line of the tunnel. 



302 



