Turbulent drag reduction by oblique wavy wall undulations

Abstract

The turbulent flow past a horizontal wavy wall, positioned at an angle to the main flow direction, is investigated by means of Direct Numerical Simulations with the purpose of reducing the drag.

The concept aims to emulate the active control by spanwise wall oscillations---known for its high drag-reducing effectiveness---by use of a passive device. The latter takes advantage of the large characteristic spatial wavelength of the active method, which is a crucial aspect for the potential practical implementation on commercial aircraft.

Imparting wall oscillations in the form of a standing wave $w_w = A_\textrm{SSL} \sin\left(\frac{2\pi}{\lambda_x}x\right)$ gives rise to a so-called Spatial Stokes Layer (SSL), resulting in a shear-strain layer, which induces a strong suppression of the near-wall turbulence, thereby leading to drag reduction. A skewed wavy wall described by $h_w = A_w \sin\left(\frac{2\pi}{\lambda_x}x + \frac{2\pi}{\lambda_z}z\right)$ is considered, so as to produce a shear-strain layer that is similar to that of the SSL in featuring the same streamwise wavelength $\lambda_x$. The main points of resemblance between the wavy wall and SSL are investigated, and then contrasted through the identification of significant differences.

A reduced-order model is formulated to aid the DNS exploration of the parameter space (wave height, flow angle and wavelength) in the search for the optimal flow configuration. The validity of the assumptions made in the model, as well as its ability to predict the main flow properties, are examined by comparison to the DNS results.

Arising from a DNS exploration of the 3D parameter space, a configuration yielding approximately 1\% drag reduction is identified. The response of the flow properties and the drag to variations in the wave height, flow angle and wavelength on the flow properties is reported and analysed. Major emphasis is placed on quantifying the influence of numerical accuracy on the predicted drag-reduction margin and on the computational efforts required to achieve this margin.