Friction drag resulting from the simultaneous imposed motions of a freestream and its bounding surface

The problem of laminar fluid flow which results from the simultaneous motions of a freestream and its bounding surface in the same direction has been investigated numerically. A special focus was to establish thresholds demarking the degree of interaction between the two imposed motions. For the case in which the freestream velocity, U_∞, is greater than the surface velocity, U_S, it was found that surface velocities as great as 0.183U_∞ could be tolerated without causing an appreciable effect on the drag force. On the other hand, in the case where the surface velocity exceeds the freestream velocity, the drag is significantly affected by freestream velocities ≥0.0686U_S. The validity of the so-called relative-velocity model was investigated. In that model, the relative velocity between the two media is used in conjunction with the drag-force formula for the dominant of the two motions acting alone. The results of exact solutions demonstrate that this model is flawed and underpredicts the drag force. Finally, a new model, termed the similarity-based, relativevelocity model was devised by which exact similarity solutions were obtained. The drag results provided by this model may be considered to be the definitive information for application.