# Interaction Effects on the Drag of Bluff Bodies in Tandem

## Abstract

The objective of this study is to obtain better understanding of the flow over two tandemly positioned bluff bodies in close enough proximity to strongly interact with each other. This interaction is often beneficial in that the drag of the overall system is reduced. Prototypes for this problem come from tractor-trailer and cab-van combinations, and from various add-on devices designed to reduce their drag.

The primary object of the present investigation is an axisymmetric configuration which seems to have first been studied by Saunders (1966). A disc of diameter d_{1} is coaxially placed in front of a flat-faced cylinder of diameter d_{2}. For a given ratio d1/d2, there is a value of gap ratio, g*/d_{2}, for which the drag of the forebody system is a minimum. In the most optimum configuration, d_{1}/d_{2} = 0.75, g*/d_{2} = 0.375, and the corresponding forebody drag coefficient is 0.02, a remarkable reduction from the value of 0.75 for the cylinder alone. For each value of d_{1}/d_{2}, the minimum drag configuration, g*/d_{2}, appears to correspond to a minimum dissipation condition in which the separation stream surface just matches (joins tangentially onto) the rearbody. Support for this idea is furnished by comparison with some results derived from free-streamline theory and from flow visualization experiments. However, when g*/d_{2} exceeds a critical value of about 0.5, the value of C_{Dmin} is almost an order of magnitude higher than for subcritical optimum gap ratios. The increase seems to be connected with the onset of cavity oscillations.

For non-axisymmetric geometry (square cross-sections) the separation surface cannot exactly match the rearbody and the subcritical minimum values of drag are higher than for circular cross-sections.

## Keywords

Shear Layer Drag Coefficient Ring Vortex Bluff Body Cavity Flow## Notation

- A1, A2
frontal area of frontbody and rear body, respectively

- C
_{D} drag coefficient of forebody system based on A

_{2}and freestream dynamic pressure- C
_{Dmin} minimum drag coefficient for fixed A

_{l}/A_{2}- \({{C}_{{{p}_{1}}}}\)
drag coefficient of frontbody based on A

_{l}- \({{C}_{{{D}_{{{1}_{f}}}}}}\)
drag coefficient of frontbody face based on A

_{l}- \({{C}_{{{p}_{2}}}}\)
drag coefficient of rearbody face based on A

_{2}- C
_{p} local rearbody face pressure coefficient

- \({{C}_{{{p}_{s}}}}\)
constant pressure surface or free-streamline pressure coefficient

- C
_{p}* average cavity pressure coefficient at optimum gap

- d
_{l}, d_{2} diameter of frontbody and rearbody, respectively

- (d
_{l}/d_{2})_{cr} frontbody to rearbody diameter ratio at critical g*/D

_{2}- g
gap between frontbody and face of rearbody

- g*
optimum gap for a given d

_{1}/d_{2}- (g*/d
_{2})_{cr} optimum gap ratio of critical geometry

- q
_{∞} freestream dynamic pressure

- r
radius of corner on rearbody face

- r
_{s}(x) radial position of the separation surface

- Re
Reynolds number based on q

_{∞}and d_{2}- τ
_{S} shear stress on separation surface

- U
_{s} flow velocity outside separation surface

- U
_{∞} freestream velocity

- x
coordinate parallel to freestream velocity

- y
radial location on rearbody face

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## References

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