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Experiments have been performed in a low-speed wind tunnel to determine the detention time of airborne smoke particles that become trapped in the wake vortex (or bubble) region behind flat disks placed perpendicular to the flow. Using a laser transmissometer to detect the smoke, its detention time was obtained from the time-dependent decay of the smoke in the disk bubble during the time immediately following the removal of the source of smoke. The dimensionless groupH, the product of the detention time and the mainstream air velocity divided by the disk diameter, is seen to be a constant equal to 7.44 ± 0.52 for Reynolds numbers in the range 2000–40000. This result is compatible with a simple fluid-mechanical model which describes the transport of fluid-borne scalar entities across the bubble boundary by turbulent diffusion. The investigation suggests thatHshould be unique for the flow about a disk over a wide range of conditions, and further suggests the possibility that similar unique values forHcan exist for flow about other obstacles. The numberHhas potential applications in a number of physical and engineering research areas.

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Experiments reported previously determined the detention time of airborne smoke particles momentarily trapped in the wake bubble behind a flat disk normal to smooth air flow. The dimensionless groupH, the product of the detention timetdand mainstream air velocityUdivided by the disk diameterD, was found to be 7.44 for all combinations ofU, Dand the Reynolds number, a result that was consistent with a suggested physical model for particle transport across the bubble boundary. The work is now extended into the regime of turbulent free-stream flow, whereHis seen to decrease with an increasing level of turbulence while the base pressure coefficient becomes more negative. At the same time, the length of the bubble decreases, as does the bubble shape factor (the ratio of bubble volume to surface area, non-dimensionalized with respect toD). A simple theoretical relationship betweenHand the base pressure coefficient is argued, and is found to be in good agreement with experiment.An important conclusion from this work is that the free-stream turbulence parameter$\Lambda \equiv l_fk^{\frac{1}{2}}_f/DU $(wherelfandkfare the length scale and the kinetic energy of the free-stream turbulence respectively) controls the properties of the flow about the disk.This work has potential applications in several areas of topical technological interest.

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