KAUST Grant NumberURF/1/1394-01
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AbstractA semi-empirical model is presented that describes the development of a fully developed turbulent boundary layer in the presence of surface roughness with length scale ks that varies with streamwise distance x . Interest is centred on flows for which all terms of the von Kármán integral relation, including the ratio of outer velocity to friction velocity U+∞≡U∞/uτ , are streamwise constant. For Rex assumed large, use is made of a simple log-wake model of the local turbulent mean-velocity profile that contains a standard mean-velocity correction for the asymptotic fully rough regime and with assumed constant parameter values. It is then shown that, for a general power-law external velocity variation U∞∼xm , all measures of the boundary-layer thickness must be proportional to x and that the surface sand-grain roughness scale variation must be the linear form ks(x)=αx , where x is the distance from the boundary layer of zero thickness and α is a dimensionless constant. This is shown to give a two-parameter (m,α) family of solutions, for which U+∞ (or equivalently Cf ) and boundary-layer thicknesses can be simply calculated. These correspond to perfectly self-similar boundary-layer growth in the streamwise direction with similarity variable z/(αx) , where z is the wall-normal coordinate. Results from this model over a range of α are discussed for several cases, including the zero-pressure-gradient ( m=0 ) and sink-flow ( m=−1 ) boundary layers. Trends observed in the model are supported by wall-modelled large-eddy simulation of the zero-pressure-gradient case for Rex in the range 108−1010 and for four values of α . Linear streamwise growth of the displacement, momentum and nominal boundary-layer thicknesses is confirmed, while, for each α , the mean-velocity profiles and streamwise turbulent variances are found to collapse reasonably well onto z/(αx) . For given α , calculations of U+∞ obtained from large-eddy simulations are streamwise constant and independent of Rex when this is large. The present results suggest that, in the sense that U+∞(α,m) is constant, these flows can be interpreted as the fully rough limit for boundary layers in the presence of small-scale linear roughness.
CitationSridhar A, Pullin DI, Cheng W (2017) Rough-wall turbulent boundary layers with constant skin friction. Journal of Fluid Mechanics 818: 26–45. Available: http://dx.doi.org/10.1017/jfm.2017.132.
SponsorsA.S. and D.I.P. were partially supported by the KAUST Office of Competitive Research Funds (OCRF) under award no. URF/1/1394-01 and partially by NSF award CBET 1235605. W.C. was supported by the KAUST OCRF under award no. URF/1/1394-01. The authors acknowledge helpful conversations with R. A. Antonia.
PublisherCambridge University Press (CUP)
JournalJournal of Fluid Mechanics