# Characterizing developing adverse pressure gradient flows subject to surface roughness

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## Abstract

An experimental study was conducted to examine the effects of surface roughness and adverse pressure gradient (APG) on the development of a turbulent boundary layer. Hot-wire anemometry measurements were carried out using single and *X*-wire probes in all regions of a developing APG flow in an open return wind tunnel test section. The same experimental conditions (i.e., *T* _{∞}, *U* _{ref}, and *C* _{p}) were maintained for smooth, *k* ^{+} = 0, and rough, *k* ^{+} = 41–60, surfaces with Reynolds number based on momentum thickness, 3,000 < *Re* _{θ} < 40,000. The experiment was carefully designed such that the *x*-dependence in the flow field was known. Despite this fact, only a very small region of the boundary layer showed a balance of the various terms in the integrated boundary layer equation. The skin friction computed from this technique showed up to a 58% increase due to the surface roughness. Various equilibrium parameters were studied and the effect of roughness was investigated. The generated flow was not in equilibrium according to the Clauser (J Aero Sci 21:91–108, 1954) definition due to its developing nature. After a development region, the flow reached the equilibrium condition as defined by Castillo and George (2001), where Λ = const, is the pressure gradient parameter. Moreover, it was found that this equilibrium condition can be used to classify developing APG flows. Furthermore, the Zagarola and Smits (J Fluid Mech 373:33–79, 1998a) scaling of the mean velocity deficit, *U* _{∞}δ*/δ, can also be used as a criteria to classify developing APG flows which supports the equilibrium condition of Castillo and George (2001). With this information a ‘full APG region’ was defined.

## Keywords

Wall Shear Stress Skin Friction Reynolds Stress Turbulent Boundary Layer Reynolds Shear Stress## Notes

### Acknowledgments

A special thanks to Victoria University and Dr. Turan for the use of their facility and Dr. Roosevelt Johnson from NSF-AGEP for making this international collaboration possible. And finally to Dr. Ronald Joslin from the Office of Naval Research for continuously funding this project.

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