# Numerical calculation of rough turbulent boundary layer for incompressible fluids

2018
Atay, Görkem
In this thesis, a numerical code for calculating turbulent boundary layer parameters is developed. Two-dimensional turbulent flow over a rough flat plate with zero pressure gradient is numerically solved by using the integral method. Fluid mechanics formulations, such as momentum integral equation are coupled with the results of Nikuradse’s experiment. Throughout the calculation, turbulent boundary layer parameters, such as boundary layer thickness, displacement thickness, momentum thickness, local skin-friction coefficient etc. are obtained. Development of turbulent boundary layer (TBL) is taken into consideration in the present study. This notion is quite important in terms of accuracy of the calculation of TBL parameters. Because, flow conditions may change from fully-rough flow to hydraulically smooth flow, and this may reduce the drag force severely. For a precise TBL solution, the calculation method considers the relative size of the TBL sublayers thicknesses and the surface roughness height with respect to each other at every computation step along the developing TBL. Furthermore, one of the parameters of TBL is the wake parameter and has a vital importance in the calculations. It is at the same time a function of TBL thickness, local skin-friction coefficient and surface roughness. By using a method developed during this study, wake parameter is computed and embedded into the relevant equations at every solution-point on the calculation domain. The developed code is tested against experimental data, a numerical study in the literature and Schlichting skin-friction formula. Generally, the full flow conditions are not detailed in the experimental cases found in the literature. Hence, the comparisons are reliable much more on the cases for which full details were available. The developed code shows very good agreement within its range. For the fully-rough flow regime, the present study’s relative mean discretization error in Cf is 0.6% whereas it is 2.1% for the numerical study in the literature. For the transition flow regime, the relative mean discretization error in Cf is found to be 1.9% in the present work and it is 8.0% for the numerical study in the literature.

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Citation Formats
G. Atay, “Numerical calculation of rough turbulent boundary layer for incompressible fluids,” M.S. - Master of Science, Middle East Technical University, 2018. 