Flow over a Magnetically Suspended Cylinder in an Axial Free Stream

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1.00 0.95 L/D = 4.13 L/D = 6.13 L/D = 8.13 CD 0.90 0.85 0.80 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Reynolds number (million) Fig. 8 Drag coefficient versus Reynolds number at 3 large fineness ratios. Figure 8 shows that the measured drag coefficients for 3 fineness ratios are nearly constant over the range of Reynolds number between 60,000 and 100,000. On the other hand, the fineness ratio has shown a clear influence on the drag coefficient as shown at the top of Fig. 9. In order to estimate the contributions to the total drag from the front face pressure, the base pressure and the boundary layer drag, Fig. 9 shows the total drag, the momentum loss based on the boundary layer measurement (see Fig 7), and the estimated skin friction drag. The skin friction drag was simply estimated from the empirical formula for the flat plate turbulent boundary layer (1/5 th power to the Reynolds number based on the length.) Here, the separated flow at the front corner is considered to attach at 1.5 diameter downstream, based on the oil flow visualization, which is consistent with Ota’s observation 5 . The differences among the three lines are, in effect, estimates of the front pressure and the base pressure, respectively, and they are nearly independent of the fineness ratio. 1.0 total drag (measured) CD based on momentaum thickness friction drag 0.8 C D = 0.0182(L/D) + 0.7809 base drag 0.6 C D 0.4 C D = 0.0197(L/D) + 0.4331 forebody pressure drag 0.2 0.0 Fig. 9. C D = 0.0167 (L/D) - 0.0071 friction drag 0 1 2 3 4 5 6 7 8 L/D Drag coefficient based on momentum thickness versus fineness ratio (simple line fit is also given.) 9 Figure 10 summarizes the present measurements and historical as well as classical data. The first experiment by Eiffel 5 was conducted by dropping the test models from the Eiffel tower along a guide cable. The second Eiffel data 3 were collected in his wind tunnel with models cable-mounted in the test section. Apparently Hoerner used Eiffel’s second data (not as listed in his book) and subtracted the estimated skin friction and presented the data. It is of interest that these Hoerner’s data have been quoted for many decades in many articles, reference books and textbooks, not necessarily after critical evaluation. Robertson et al. 7 carried out new wind tunnel measurements to study the effect of - 6 – American Institute of Aeronautics and Astronautics
1.2 1.1 1.0 Eiffel 1913 (30cm Dia.) Eiffel 1913 (15cm Dia.) Roberson JAXA/NAL(45Dia) JAXA(85Dia) JAXA(110Dia) Cd 0.9 0.8 0.7 0.6 0 1 2 3 4 5 6 7 8 9 L/D Fig. 10. Drag coefficient variations with fineness ratio (The present data are all at Re D =1x10 5 ) the free stream turbulence on the flow reattachment and the drag at small fineness ratios. Original technical results are given, for example in Ref. 7, but summary of data is listed in Roberson and Crowe’s textbook 8 for Re D >10 4 are used in this figure. The present series of experiment are expected to provide modern, more definitive results on how the flowfield and drag vary with the wide range of fineness ratio. D. Discussion of results and additional flowfield measurement in water. The lower drag coefficients obtained in the fineness ratio L/D=1-2 is expected to represent flow reattachment on the side surface. Oil flow visualization was conducted on the long magnetic suspended model of the 45 mm diameter. The reattachment line was located near 1.6-1.7 diameters downstream of the leading edge. In order to obtain better ascertain the flowfield, an additional set of experiment was conducted in a Syracuse University water channel. In lieu of the magnetic suspension system, the model was sting-mounted from downstream. The sting diameter was kept small (635mm) compared to the model diameter of 77mm. The cross-flow strut was also kept sufficiently far downstream. The velocity vector field was measured using a DANTEC particle image velocimeter (PIV) system at reduced Reynolds number between 10,000 and 30,000. Seeding was provided by 20µm PSP particles uniformly mixed in the flow. Figure 11 shows the mean velocity vector field together with a short model of the fineness ratio of 0.67. One can clearly see that the separating shear layer remains separated forming a large reverse flow region in the wake. Figure 12 on the other hand shows the mean velocity vector past a long cylinder of L/D=3. The separating and reattaching shear layer and the recirculating flow within the separation bubble are clearly seen in the measurement. Even though Ota used the hot wire anemometer on a rear-mounted cylindrical model and its use in the vicinity of this type of separating flow may be of suspect, the deduced streamlines and the location of the flow reattachment are in very good agreement with the current PIV measurement. The behavior of the boundary layer development subsequent to the flow reattachment and the drag variation with the fineness ratio are in accordance with the velocity profile measurement in Fig. 7 and Fig. 10, respectively. At an intermediate fineness, L/D=1.5, the time averaged separated shear layer attached in the immediate vicinity of the trailing edge as shown in Fig. 13. At higher Reynods number of 20,000 and 30,000, the shear layer was found to attach slightly upstream, indicating the higher sensitivity to the Reynolds number. This is close to the region where the drag coefficient reaches its minimum with respect to the fineness ration as shown in Fig. - 7 – American Institute of Aeronautics and Astronautics
Page 1 and 2: Flow over a Magnetically Suspended
Page 3 and 4: Fig. 2(a) A magnetically supported
Page 5: (y - D/2)/delta 2.0 1.5 1.0 0.5 L/D
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Flow over a Magnetically Suspended Cylinder in an Axial Free Stream

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