Experiments on the flow past a circular cylinder at very high Reynolds number

Experiments on the flow past a circular cylinder at very high Reynolds number

15 November 1960 | ANATOL ROSHKO
Experiments on flow past a circular cylinder at very high Reynolds numbers (R) were conducted in a pressurized wind tunnel, achieving R up to ~10⁷. The drag coefficient (Cd) increased from a low supercritical value to ~0.7 at R = 3.5×10⁶, then became constant. Vortex shedding occurred at R > 3.5×10⁶ with a Strouhal number (S) of ~0.27. Previous studies showed discrepancies in Cd at supercritical R, with values between 0.2 and 0.4. Measurements by Delany & Sorensen (1953) showed S between 0.35 and 0.45 at R up to 2×10⁶. The present experiments aimed to extend these measurements to higher R and investigate the flow behavior. The experiments were conducted in a subsonic wind tunnel with a 8.5 ft height and 11 ft width, pressurized to 4 atm. A seamless steel cylinder with diameter 18 in. was used, with wall interference corrected using formulas by Allen & Vincenti. The corrected drag coefficient (Cd) increased from ~0.3 to ~0.7 as R increased from 10⁶ to 3.5×10⁶, then stabilized. Dryden & Hill (1930) measured Cd at R ~3–5×10⁶, finding a mean Cd of 0.67 ± 0.04, consistent with the present results. The base pressure coefficient (Cpb) showed similar trends, with a decrease at R > 3.5×10⁶. Pressure distributions at high R (8.4×10⁶) showed a base pressure coefficient closer to subcritical values, with separation point further back. The Strouhal number S increased with R, reaching 0.267 at R = 3.5×10⁶. Vortex shedding was first observed at R = 3.5×10⁶, with a strong spectral peak. The splitter plate suppressed shedding and slightly reduced Cd at R > 3.5×10⁶. The flow was classified into subcritical (Cd = 1.2), supercritical (Cd = 0.3), and transcritical (Cd = 0.7) regimes. The transcritical regime showed a wake width (dw) less than the cylinder diameter (d), with S = 0.27. The free-streamline model suggested a universal Strouhal number S* = 0.16, consistent with experimental results. The presence of a laminar separation bubble in the supercritical range was noted, but its disappearance marked the transition to the transcritical regime. The experiments suggest that the flowExperiments on flow past a circular cylinder at very high Reynolds numbers (R) were conducted in a pressurized wind tunnel, achieving R up to ~10⁷. The drag coefficient (Cd) increased from a low supercritical value to ~0.7 at R = 3.5×10⁶, then became constant. Vortex shedding occurred at R > 3.5×10⁶ with a Strouhal number (S) of ~0.27. Previous studies showed discrepancies in Cd at supercritical R, with values between 0.2 and 0.4. Measurements by Delany & Sorensen (1953) showed S between 0.35 and 0.45 at R up to 2×10⁶. The present experiments aimed to extend these measurements to higher R and investigate the flow behavior. The experiments were conducted in a subsonic wind tunnel with a 8.5 ft height and 11 ft width, pressurized to 4 atm. A seamless steel cylinder with diameter 18 in. was used, with wall interference corrected using formulas by Allen & Vincenti. The corrected drag coefficient (Cd) increased from ~0.3 to ~0.7 as R increased from 10⁶ to 3.5×10⁶, then stabilized. Dryden & Hill (1930) measured Cd at R ~3–5×10⁶, finding a mean Cd of 0.67 ± 0.04, consistent with the present results. The base pressure coefficient (Cpb) showed similar trends, with a decrease at R > 3.5×10⁶. Pressure distributions at high R (8.4×10⁶) showed a base pressure coefficient closer to subcritical values, with separation point further back. The Strouhal number S increased with R, reaching 0.267 at R = 3.5×10⁶. Vortex shedding was first observed at R = 3.5×10⁶, with a strong spectral peak. The splitter plate suppressed shedding and slightly reduced Cd at R > 3.5×10⁶. The flow was classified into subcritical (Cd = 1.2), supercritical (Cd = 0.3), and transcritical (Cd = 0.7) regimes. The transcritical regime showed a wake width (dw) less than the cylinder diameter (d), with S = 0.27. The free-streamline model suggested a universal Strouhal number S* = 0.16, consistent with experimental results. The presence of a laminar separation bubble in the supercritical range was noted, but its disappearance marked the transition to the transcritical regime. The experiments suggest that the flow
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