130 



from the supporting strut. One half of the model 

 length protruded from the closed-jet working sec- 

 tion of the wind tunnel into the open- jet test 

 section. The ambient static pressure coefficients 

 across and along the entire open- jet chamber (7.16 

 X 7.16 X 6.4 m) were found to vary less than 0.3 

 percent of dynamic pressure. The tunnel blockage 

 and the longitudinal pressure gradient along the 

 tunnel length were almost completely removed by 

 testing the afterbody in the open- jet test section. 



The location of boundary-layer transition from 

 laminar to turbulent flow was artifically induced 

 by a 0.61 mm diameter trip wire located at X/L = 

 0.05. When the flow was probed with a hot-wire, 

 the trip wire was found to effectively stimulate 

 the flow at a location 1 cm downstream from the 

 wire. As a result of the parasitic drag of the 

 wire , the boundary layer can be theoretically con- 

 sidered to become turbulent at a virtual origin 

 upstream of the trip wire. This virtual origin for 

 the turbulent flow is defined such that the sum of 

 the laminar frictional drag from the body nose to 

 the trip wire, the parasitic drag of the trip wire, 

 and the turbulent frictional drag after the trip 

 wire equals the sum of the laminar frictional drag 

 from the nose to the virtual origin and the turbu- 

 lent frictional drag from the virtual origin to 

 the after end of the model [McCarthy et al . (1976)]. 

 The location of the virtual origin on the forebody 

 with a 0.61 ram trip wire at X/L = 0.05 was found 

 to be at X/L = 0.015 for a length Reynolds number 



of 5.9 X lO*: 



The location of transition in the 



mathematical model for the present boundary-layer 

 calculation is specified at this virtual origin. 

 The length Reynolds number based on the distance 

 from the trip wire to the end of the parallel middle 

 body is larger than for 4 x lo^ for the two after- 

 bodies. It can be assumed that a fully established 

 axisymmetric turbulent boundary layer exists at the 

 beginning of the afterbody and that the trip wire 

 has no peculiar effect on the boundary- layer char- 

 acteristics of the stern. 



3. INSTRUMENTATION 



A 1.83-cm Preston tube was taped to the stern at 

 successively further aft locations in order to 

 measure the shear stress distribution along the 

 upper meridian of each stern. The Preston tube 

 used was calibrated in a 2.54-cm water pipe flow 

 facility described by Huang and von Kerczek (1972) . 

 Pressure taps (0.8 mm diameter) were used to mea- 

 sure steady pressures at the same locations as the 

 Preston tubes. The taps were connected by "Tygon" 

 plastic tubes to a scanning valve located inside 

 the model. The output tube from the scanning valve 

 was run from the model through the supporting strut 

 to a precision pressure transducer located on the 

 quiescent floor of the open- jet chamber. The pres- 

 sure transducer was a Validyne Model DP 15-560 de- 

 signed for measuring low pressure up to ± 1.4 x 10^ 

 dyn/cm^ (±0.2 psi) . The zero-drift, linearity, and 

 hysteresis of this transducer system were carefully 

 checked and the overall accuracy was found to be 

 within 0.5 percent of the dynamic pressure. 



A Prandtl type pitot-static pressure probe of 

 3.125-mm diameter with four equally spaced holes 

 located at three diameters aft of the nose was used 

 to measure static pressure across the boundary 

 layer. The yaw sensitivity of the static pressure 



probe was examined by yawing the probe in the free- 

 stream. It was found that the measured static pres- 

 sure was insensitive to the probe angle up to 5° 

 yaw. The response of measured static pressure to 

 probe angle was nearly a cosine function of yaw 

 angle for yaw angles less than 15°. The static 

 pressure probe was aligned parallel to the model 

 axis for all of the static pressure measurements. 

 The local angles between the resultant velocity of 

 the boundary-layer flow and probe axis were found 

 to be less than 15° (5° for most cases) . The maxi- 

 mum static pressure coefficient in the boundary 

 layer was less than 0.2. Thus, the error in the 

 measured static pressure caused by not aligning the 

 probe with the local flow was less than 0.8 percent 

 of the dynamic pressure. 



The mean axial and radial velocity components 

 and the Reynolds stress were measured by a TSI, Inc. 

 Model 1241 "X" wire. The probe elements were 0.05 

 mm in diameter with a sensing length of 1.0 mm. 

 The spacing between the two cross elements is 1.0 

 mm. A two-channel TSI Model 1050-1 hot-wire ane- 

 mometer and linearizer were used. The "X" wire, 

 together with temperature compensated probes, were 

 calibrated at the factory and supplied with their 

 individual linearization polynomial coefficients. 

 This eliminated the time-consuming linearization 

 process. The frequency response of the anemometer 

 system claimed by the manufacturer is dc to 200 kHz. 

 Calibration of the "X" wire was made before and after 

 each set of measurements. It was found that this 

 hot-wire anemometer system had a ±0.5 percent ac- 

 curacy (io.l5 m/s accuracy at the free stream ve- 

 locity of 30.5 m/sec) during the entire experiment. 

 The accuracy of cross-flow velocity measurements 

 by the cross wire was estimated by yawing the cross- 

 wire in the free stream. It was found that the ac- 

 curacy of the measured cross-flow velocities was 

 about one percent of the free stream velocity. 



The linearized signals were fed into a Time/Data 

 Model 1923-C Real-Time analyzer. Both channels of 

 analog signal were digitized at a rate of 80 points 

 per second for ten seconds. These data were imme- 

 diametely analyzed by a computer code to obtain the 

 individual components of mean velocity, turbulence 

 fluctuation, and Reynolds stress on a real time 

 basis. 



A traversing system enclosed in a 15 cm chord, 

 streamlined strut was used to support both the 

 static pressure probe and the cross-wire probe. The 

 traversing system was mounted either on an I-beam 

 along the axis of the lower floor of the open- jet 

 chamber or on the ceiling of the closed-jet section. 

 The combination of these two mounting arrangements 

 allowed the measurements to be made at any axial 

 location along the stern and up to 50 percent of 

 the body length downstream from the aft end of the 

 body. Positioning of the traversing system was 

 achieved by manual adjustment in the axial direction 

 and by remote control in the radial direction. The 

 total radial traverse of the probe was 25 cm. The 

 radial position of the probe was monitored by a 

 potentiometer to with a +0.01 mm accuracy. 



4. COMPARISON OF EXPERIMENTAL AND THEORETICAL 

 RESULTS 



In the following, the experimental results for the 

 thick stern boundary layers are presented and com- 

 pared with theoretical results. The theories used 



