Datenpaket: Dataset for rearrangement of secondary flow over spanwise heterogeneous roughness

These files contain the data used in the publication: “Rearrangement of secondary flow over spanwise heterogeneous roughness” A. Stroh, K. Schäfer, B. Frohnapfel and P. Forooghi published in Journal of Fluid Mechanics, 2019. (DOI: 10.1017/jfm.2019.1030) Abstract: Turbulent flow over a surface with streamwise-elongated rough and smooth stripes is studied by means of direct numerical simulation (DNS) in a periodic plane open channel with fully resolved roughness. The goal is to understand how the mean height of roughness affects the characteristics of the secondary flow formed above a spanwise-heterogeneous rough surface. To this end, while the statistical properties of roughness texture as well as the width and spacing of the rough stripes are kept constant, the elevation of the smooth stripes is systematically varied in different simulation cases. Utilizing this variation three configurations representing protruding, recessed and an intermediate type of roughness are analysed. In all cases secondary flows are present and the skin friction coefficients calculated for all the heterogeneous rough surfaces are meaningfully larger than what would result from the area-weighted average of those of homogeneous smooth and rough surfaces. This drag increase appears to be linked to the strength of the secondary flow. The rotational direction of the secondary motion is shown to depend on the relative surface elevation. The present results suggest that this rearrangement of the secondary flow is linked to the spatial distribution of the spanwise-wall-normal Reynolds stress component which carries opposing signs for protruding and recessed roughness. Numerical Details: The carried out DNS is based on a pseudo-spectral solver for incompressible boundary layer flows developed at KTH/Stockholm. The Navier-Stokes equations are numerically integrated using the velocity-vorticity formulation by a spectral method with Fourier decomposition in the horizontal directions and Chebyshev discretization in the wall-normal direction. For temporal advancement, the convection and viscous terms are discretized using the 3rd order Runge-Kutta and Crank-Nicolson methods, respectively. The simulation domain represents an open turbulent channel flow with periodic boundary conditions applied in streamwise and spanwise directions, while the wall-normal extension of the domain is bounded by no-slip boundary conditions at the lower domain wall (y = 0) and symmetry boundary conditions (v = 0, ∂u/∂y = ∂w/∂y = 0) at the upper boundary (y = δ). The flow is driven by a prescribed constant pressure gradient (CPG). The friction Reynolds number for the present case is fixed to Re_τ = 500. Simulation configuration

• Grid nodes: Nx x Ny x Nz = 768 × 301 × 384
• Domain size: Lx x Ly x Lz = 8δ × δ × 4δ
• Resolution: ∆x+=5.2, ∆y_min+=0.014, ∆y_max+=2.6, ∆z+ = 5.2 The surface structure is introduced through an immersed boundary method (IBM) based on the method proposed by Goldstein et al. (1993) and is essentially a proportional controller which imposes zero velocity in the solid region of the numerical domain. The structure is placed on the lower domain wall in such a way that the surface height H of the largest raised surface elements is given by H/δ = 10.2%. Data Files: The data files are saved and labeled corresponding to the figure in the manuscript in *.mat files. Each file contains MATLAB data consisting of the plotted quantities and corresponding coordinates. The data is non-dimensionalized as shown in the manuscript figures utilizing friction velocity u_τ, viscous lengthscale δ_ν or bulk mean velocity U_b and effective domain height δ_eff. A matlab script “plot_figures.m” provides the code, which loads the data and plots it in the same way as it has been done in the manuscript. “height_distributions.mat” contains the original roughness distributions utilized in the considered simulations. The files can be also loaded and plotted using “plot_figures.m” 3-dimensional instantaneous snapshot and time series of velocity fields is available upon request (alexander.stroh@kit.edu). Reference: Please provide a reference to the article above when using this data. Please direct questions regarding numerical setup/data to Alexander Stroh Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/ November, 2019