Extracting Globally Dominant Parameters of A Realistic Rough Surface Using Continuous Wavelets

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Continuous Morlet and Mexican hat wavelets are used to analyze a highly irregular rough surface replicated from real turbine blades which are roughened by deposition of foreign materials. The globally dominant aspect ratio, length scale, and orientation of the roughness elements are estimated. These parameters extracted from this highly irregular rough surface are important for future studies of their efiects on turbulent ∞ows. Engineering wall-bounded turbulent ∞ows are signiflcantly afiected by the surface roughness conditions. Examples of these ∞ows of practical interest include both external and internal ∞ows such as those over turbine blades, aircrafts, marine vehicles, and through piping systems of heat exchangers. In most cases, the efiects of surface roughness are detrimental. Rough surfaces can increase the skin friction and therefore increase the energy consumption. They can also enhance the heat transfer rate at the wall, which will augment the thermal loading of the system and as a result reduce its lifetime. Thus, a clear and comprehensive understanding of how surface roughness afiects the wall-bounded turbulent ∞ows is imperative for both accurate modeling and successful control of these ∞ows encountered in various engineering applications. A signiflcant amount of efiorts have been devoted to the studies of rough-wall efiects on turbulent ∞ows at a broad range of Reynolds numbers with both laboratory simulated roughness (such as sandgrain, wire meshes, grooves and ordered array of elements) and realistic highly irregular roughness topographies. Review articles of 1,2 provide excellent summaries of the knowledge gleaned in this research fleld. Of particular importance is the substantiation of the classical Townsend’s wall-similarity hypothesis by more and more recent studies in single- and two-point turbulence statistics when the scale separation between the roughness height (either using a characteristic height of the roughness, k, or the equivalent sandgrain height, ks) and the outer length scale of the ∞ow (boundary layer thickness ‐ or diameter of the pipe D) is large. 3{13 As summarized by Raupach (1991) 1 , Townsend’s similarity hypothesis asserts that, at high Reynolds numbers, surface roughness has little efiects on turbulent ∞ows outside the roughness sublayer except in setting the skin friction velocity, u? and the boundary layer thickness, ‐. The roughness sublayer is commonly accepted as the region about 3»5 roughness heights away from the virtual origin of the wall. According to Townsend’s wall-similarity hypothesis, roughness sublayer is more important than the outer layer of the turbulent ∞ows since it is in this layer that the rough surface exerts its strong efiects which is then directly associated with setting the wall shear stress. Past studies 14{19 have observed that turbulent ∞ows within this layer are signiflcantly modifled and the roughness efiects are highly dependent on the details of the local surface conditions, especially on the dominant topographical features. However, there exists a wide parameter space in the roughness topography that could afiect turbulent ∞ows close to the wall. These parameters include roughness heights (average peak-to-valley height, root-mean-square height, maximum peak-to-valley height, and mean elevation, etc.), geometrical shape and aspect ratio of the roughness elements, orientation, distribution, and slope, etc. For a typical rough surface in common engineering ∞ows, it is even more complex since the roughness elements are becoming highly irregular with random distribution and they occupy a wide range of length scales, orientation and slopes.