Cavity-flow wall effects and correction rules
Authors: Wu T. Yao-Tsu , Whitney Arthur K. , Brennen Christopher 
Published: March 2006

This paper is intended to evaluate the wall effects in the pure-drag case of plane cavity flow past an arbitrary body held in a closed tunnel, and to establish an accurate correction rule. The three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant-jet models, are employed to provide solutions in the form of some functional equations. From these theoretical solutions several different rules for the correction of wall effects are derived for symmetric wedges. These simple correction rules are found to be accurate, as compared with their corresponding exact numerical solutions, for all wedge angles and for small to moderate ‘tunnel-spacing ratio’ (the ratio of body frontal width to tunnel spacing). According to these correction rules, conversion of a drag coefficient, measured experimentally in a closed tunnel, to the corresponding unbounded flow case requires only the data of the conventional cavitation number and the tunnel-spacing ratio if based on the open-wake model, though using the Riabouchinsky model it requires an additional measurement of the minimum pressure along the tunnel wall.

The numerical results for symmetric wedges show that the wall effects in-variably result in a lower drag coefficient than in an unbounded flow at the same cavitation number, and that this percentage drag reduction increases with decreasing wedge angle and/or with decreasing tunnel spacing relative to the body frontal width. This indicates that the wall effects axe generally more significant for thinner bodies in cavity flows, and they become exceedingly small for sufficiently blunt bodies. Physical explanations for these remarkable features of cavity-flow wall effects are sought; they are supported by the present experimental investigation of the pressure distribution on the wetted body surface as the flow parameters are varied. It is also found that the theoretical drag coefficient based on the Riabouchinsky model is smaller than that predicted by the open-wake model, all the flow parameters being equal, except when the flow approaches the choked state (with the cavity becoming infinitely long in a closed tunnel), which is the limiting case common to all theoretical models. This difference between the two flow models becomes especially pronounced for smaller wedge angles, shorter cavities, and with tunnel walls farther apart.

In order to gauge the degree of accuracy of these theoretical models in approximating the real flows, and t o ascertain the validity of the correction rules, a series of definitive experiments was carefully designed to complement the theory, and then carried out in a high-speed water tunnel. The measurements on a series of fully cavitating wedges at zero incidence suggest that, of the theoretical models, that due to Riabouchinsky is superior throughout the range tested. The accuracy of the correction rule based on that model has also been firmly established. Although the experimental investigation has been limited to symmetric wedges only, this correction rule (equations (85), (86) of the text) is expected to possess a general validity, at least for symmetric bodies without too large curvatures, since the geometry of the body profile is only implicitly involved in the correction formula. This experimental study is perhaps one of a very few with the particular objective of scrutinizing various theoretical cavity-flow models.