Three-dimensional wall-bounded laminar boundary layer with span-wise cross free stream and moving boundary |
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Authors: | Tiegang Fang Chia-fon F Lee |
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Affiliation: | 1. Department of Mechanical and Aerospace Engineering, North Carolina State University, 3182 Broughton Hall-Campus Box 7910, 2601 Stinson Drive, Raleigh, NC, 27695, USA 2. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 158 Mechanical Engineering Building, MC-244, 1206 West Green Street, Urbana, IL, 61801, USA
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Abstract: | In the current work, the 3D boundary layers of wall-bounded flow configurations were extended to the situations with span-wise cross moving boundary and free stream. The unsteady boundary layer is also addressed for the Falkner–Skan wedge flow with a span-wise oscillating wall or oscillating free stream. The span-wise secondary boundary layer equation is obtained using similarity transformation technique and solved analytically in terms of the primary stream-wise boundary layer flow solutions. Different fluid motion behaviors are found for these new solutions. It is found that for the span-wise secondary boundary layer flow there is no flow separation for any wall cross moving velocity, which is different from the primary stream-wise boundary layers with a reverse flow. For the unsteady boundary layer with an oscillating wall or free stream, it is seen that the solution is different from the Stokes oscillating plate or free stream problem. The unsteady wall drag increases with the increase in the oscillating frequency and decreases with increasing the primary span-wise free stream magnitude. The velocity overshooting near the wall is also seen for an oscillating free stream for a large oscillating frequency or a lower primary stream-wise free stream magnitude. |
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