Bluff-body Aerodynamics

Helical vortex rings in the wake of a disk

(2026) 6, pp. 1-14. (pdf)

Thad S. Morton

Abstract:
The structure of the wake behind a circular disk is examined in numerical solutions for Re = 50, 100, and 120. A slowly reversing helical (swirling) streamline structure was found to exist in the steady numerical solutions at these flow speeds, which are generally regarded as steady and axisymmetric. The nested stream surfaces resemble Reeb-like foliations. The loss in fore-aft symmetry of the pressure field due to the viscous term may be associated with the azimuthal drift seen in the streamlines.

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An estimate of the circulation generated by a bluff body

(2008) 2, pp. 12-19. (pdf)

T. S. Morton
Aerospace & Biomedical Engineering, University of Tennessee Space Institute, 411 B.H. Goethert Parkway, Tullahoma, TN

Abstract:
A loss in circulation is sometimes cited in connection with bluff-body wakes as a result of comparing the circulation actually observed downstream with a well-known theoretical estimate of the total circulation generated by a cylinder. In an effort to better understand this reported loss in circulation, an alternative estimate of the circulation generated by a cylinder is derived by integrating the velocity on a closed loop containing the attached boundary layer. Predictions of the dimensionless circulation for a cylinder in crossflow are less than the previous theoretical estimate and agree with observed values. This suggests that the total circulation generated by bluff bodies may have been overestimated in the past, and that comparison of observed values with this overestimate is the origin of the perceived “loss” in circulation.

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A correlation between drag and an integral property of the wake

(2007) 1, pp. 2-20. (pdf)

T. S. Morton
Department of Mechanical, Aerospace & Biomedical Engineering, University of Tennessee Space Institute, 411 B.H. Goethert Parkway, Tullahoma, TN

Abstract:
An integral quantity is presented that relates the wake of a body in nominally two-dimensional flow to its drag, for Reynolds numbers ranging from 9,000 to 144,000. It is defined as the ratio of the kinetic energy to the vorticity in the fluid boundary and, for the special case of laminar flow, is proportional to the angular momentum in the wake bubble. The new quantity is useful for correlating drag data for cylinders, wedges, v-gutters, and normal flat plates with and without splitter plates. The correlation indicates that the drag force is proportional to the flow speed and the mass flow rate stored in the wake bubble. Order-of-magnitude arguments indicate that, absent any quantization of vortex size, this mass flow rate, and hence the drag force, can become unbounded as the size of the vortices contained in the wake becomes smaller.

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