We conduct a series of large-eddy simulations (LES) to examine the mean flow behaviour within the roughness layer of turbulent boundary layer flow over rough surfaces. We consider several configurations consisting of arrays of rectangular-prism roughness elements with various spacings, aspect ratios and height distributions. The results provide clear evidence for exponential behaviour of the mean flow with respect to the wall normal distance. Such behaviour has been proposed before (see, e.g., Cionco, 1966 Tech. Rep. DTIC document), and is represented asis the spatially/temporally averaged fluid velocity, z is the wall normal distance, h represents the height of the roughness elements and U h is the velocity at z = h. The attenuation factor a depends on the density of the roughness element distribution and details of the roughness distribution on the wall. Once established, the generic velocity profile shape is used to formulate a fully analytical model for the effective drag exerted by turbulent flow on a surface covered with arrays of rectangular-prism roughness elements. The approach is based on the von Karman-Pohlhausen integral method, in which a shape function is assumed for the mean velocity profile and its parameters are determined based on momentum conservation and other fundamental constraints. In order to determine the attenuation parameter a, wake interactions among surface roughness elements are accounted for by using the concept of flow sheltering. The model transitions smoothly between 'k' and 'd' type roughness conditions depending on the surface coverage density and the detailed geometry of roughness elements. Comparisons between model predictions and experimental/numerical data from the existing literature as well as LES data from this study are presented. It is shown that the analytical model provides good predictions of mean velocity and drag forces for the cases considered, thus raising the hope that analytical roughness modelling based on surface geometry is possible, at least for cases when the location of flow separation over surface elements can be easily predicted, as in the case of wall-attached rectangular-prism roughness elements.

A new approach for wall modeling in Large-Eddy-Simulations (LES) is proposed and tested in various applications. To properly include near-wall physics while preserving the basic economy of equilibrium-type wall models, we adopt the classical integral method of von Karman and Pohlhausen (VKP). A velocity profile with various parameters is proposed as an alternative to numerical integration of the boundary layer equations in the near-wall zone. The profile contains a viscous or roughness sublayer and a logarithmic layer with an additional linear term that can account for inertial and pressure gradient effects. Similar to the VKP method, the assumed velocity profile coefficients are determined from appropriate matching conditions and physical constraints. The proposed integral wall-modeled LES (iWMLES) method is tested in the context of a pseudo-spectral code for fully developed channel flow with a dynamic Lagrangian subgrid model as well as in a finite-difference LES code including the immersed boundary method and the dynamic Vreman eddy-viscosity model. Test cases include a fully developed half-channel at various Reynolds numbers, a fully developed channel flow with unresolved roughness, a standard developing turbulent boundary layer flows over smooth plates at various Reynolds numbers, over plates with unresolved roughness, and a case with resolved roughness elements consisting of an array of wall-mounted cubes. The comparisons with data show that the proposed iWMLES method provides accurate predictions of near-wall velocity profiles in LES while, similarly to equilibrium wall models, its cost remains independent of Reynolds number and is thus significantly lower compared to existing zonal or hybrid wall models. A sample application to flow over a surface with truncated cones (representing idealized barnacle-like roughness elements) is also presented, which illustrates effects of subgrid scale roughness when combined with resolved roughness elements. C 2015 AIP Publishing LLC. [http://dx.

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The unsteady flow physics and heat transfer characteristics due to interactions of periodic passing wakes with a separated boundary layer are studied with the help of Large-eddy simulations (LES). A flat plate with a semicircular leading edge is employed to obtain the separated boundary layer. Wake data extracted from precursor LES of flow past a cylinder are used to replicate a moving bar that generates wakes in front of a cascade (in this case an infinite row of flat plates). This setup is a simplified representation of the rotor-stator interaction in turbomachinery. With a uniform inlet, the laminar boundary layer separates near the leading edge, undergoes transition due to amplification of the disturbances, becomes turbulent and finally reattaches forming a bubble. In the presence of oncoming wakes, the characteristics of the separated layer have changed and the impinging wakes are found to be the mechanism affecting the reattachment. Phase averaged results illustrate the periodic behaviour of both flow and heat transfer. Large undulations in the phase-averaged skin friction and Nusselt number distributions can be attributed to the excitation of separated shear layer by convective wakes forming coherent vortices, which are being shed and convect downstream. This interaction also breaks the bubble into multiple bubbles. Further, the transition of the shear layer during the wake-induced path is governed by a mechanism that involves the convection of these vortices followed by increased fluctuations.

In this study, a recently proposed integral wall model 1 and concurrent inflow generation technique 2 are applied in Large-Eddy-Simulation (iWMLES) of developing turbulent boundary layer flow over cuboidal roughness. We examine the performance of this integral wall model at various Reynolds numbers. The integral wall model is based on the vonKarman-Pohlhausen integral method. With several parameters in the proposed functional form of the velocity profile determined from the local flow conditions, the wall model predicts velocity profiles that satisfy the vertically integrated momentum equation. Only an algebraic system must be solved in the wall model which thus preserves the essential economy of equilibrium type models. The rough wall inflow generation technique is proposed based on a new definition of a length scale that is appropriate for the roughness dominated inner layer. It extends the rescaling-recycling method 3 to rough surfaces. The integral wall model and the rough wall rescaling-recycling method are applied in Large Eddy Simulations of turbulent boundary layers over surface with distributed cuboidal roughness. The effect of Reynolds number is studied. A good agreement is found between the roughness function (velocity shift) measured in iWMLES and the Colebrook formula 4 and previous experimental measurements. [5][6][7][8]