Session HA: Turbulent Boundary Layers: Roughness Effects

Turbulent boundary layer over a small, 2-D, $k$-type roughness

Previous results (Volino, Schultz \& Flack $JFM$ to appear) indicate that 2-D, $k$-type roughness gives rise to significant changes in the turbulence structure well into the outer layer. This stands in contrast to the similarity that has been observed between flows over smooth walls and 3-D roughness outside the roughness sublayer and seems to indicate that there is a fundamental difference in the response of boundary layers to 2-D and 3-D roughness. In the previous study, however, the relative roughness height was fairly large ($k/\delta$ = 0.03; $k_s/\delta$ = 0.42) leaving open the possibility that the observed effect was simply due to the strength of the wall perturbation. In the present paper, experimental results are presented for a zero pressure gradient boundary layer over a surface with 2-D, $k$-type roughness. The roughness consisted of transverse bars of square cross section with a pitch of 8$k$ like the previous 2-D rough wall but with $k$ reduced by a factor of 7. The relative roughness height was significantly reduced ($k/\delta$ = 0.007; $k_s/\delta$ = 0.055) in the present case. The results were qualitatively similar to those over the larger roughness. Specifically, the Reynolds stresses were significantly larger over the 2-D roughness than over a smooth wall, and length scales based on two-point spatial correlations were longer for the 2-D roughness.   

Boundary Layer Measurements over 2/3-D Roughness

Boundary layer flows over three-dimensional roughness show remarkable similarity to smooth-wall flows outside a region near the roughness elements. In contrast, the turbulence statistics for flows over two-dimensional bar roughness have exhibited significant differences in the outer layer compared to smooth-wall flows. It is not clear whether the difference is due to the larger scales imposed on the flow due to the spanwise extent of the roughness, or if the boundary layer is strongly perturbed by, in essence, being repeatedly tripped by the spanwise elements. To address this question, measurements have been made over spanwise rows of cubes with a spanwise spacing of one roughness height and a streamwise spacing of seven roughness heights. Results are compared to bars of the same height and streamwise spacing.   

Turbulence Statistics Over 3D Roughness in a Turbulent Channel Flow

This study focuses on the near-wall flow field within a turbulent channel flow over a rough surface. Performing experiments in a facility containing a fluid with the same refractive index as the acrylic rough plate facilitates PIV measurements very near the wall. Presently, the flow in the vicinity of uniformly distributed 0.45mm high pyramids at Re$_{\tau }$=3400-5418 is resolved at a vector spacing of 63um, $\sim $9 wall units. Data in a streamwise-wall-normal plane shows that below one roughness height, there is an upsurge of $<$u'u'$>$, and there are substantial spatial variations in $<$u'u'$>$, $<$u'v'$>$ and $<$v'v'$>$, which rapidly diminish father from the wall. All Reynolds stress components peak above the forward face of roughness, with $<$v'v'$>$ peaked slightly downstream of the others. The in-plane turbulent kinetic energy (TKE) production peaks deep in the roughness sublayer, especially near the pyramid crest. Both $<$u'u'$>\partial $U/$\partial $x and -$<$u'v'$>\partial $U/$\partial $y are significant contributors. Measurements in a streamwise-spanwise plane located within the roughness sublayer show spatial variability of $<$w'w'$>$ and $<$u'w'$>$, and their contributions to TKE production.   

Flow of Turbulent Boundary Layers Over Low-Order Representations of Irregular Surface Roughness

The relative impact of various topographical scales present within irregular surface roughness on a turbulent boundary layer is explored. Low-order representations of roughness replicated from a turbine blade damaged by deposition of foreign materials are generated using singular value decomposition (SVD) to decompose the surface into a set of topographical basis functions (383 total) of decreasing importance to the original (``full'') surface character. The low-order surface models are then formed by truncating the full set of basis functions at the first 5 and 16 modes (containing approximately 65\% and 95\% of the full surface content, respectively), so that only the most dominant, and large-scale, topographical features are included in the models. Physical replications of the full surface and the two models are created by rapid prototyping and PIV is used to acquire ensembles of velocity fields for all cases. Comparison of single-point statistics indicates that a 16-mode model of the full surface generally reproduces the statistical character of flow over the full surface. In the outer region, both the 5- and 16-mode models reproduce the characteristics for flow over the full surface in accordance with Townsend's wall similarity hypothesis. However, both surface representations fail to reproduce important details of the Reynolds-shear-stress-producing events within the roughness sublayer.   

A Shape-Hessian based analysis of roughness effects on turbulence

One of the difficulties with evaluating the effects of roughness on wall-bounded flows is that the commonly used metric for roughness effects, the equivalent sand-grain roughness height, is determined not from the topography of the roughness, but from the measured effect of the roughness on the flow. It would be much more useful if the effects of roughness could be predicted directly from the roughness topography. To do this, we characterize the mapping from roughness topography to fluid dynamics impact (in this case the drag) by examining its shape gradient and shape Hessian. The eigenfunctions and eigenvalues of the shape Hessian are studied as they describe how the fluid dynamics impact changes with the roughness. For flat boundaries, the Fourier modes can be proven to be the eigenfunctions of the shape Hessian. Further, the flat boundary is a stationary point (a minimum) of this mapping and the eigenvalues depend on the wavenumber and the Reynolds number. A priori knowledge of the eigenfunctions allows the entire shape Hessian operator to be determined from a single solution of state, incremental state, adjoint and incremental adjoint equations, making determination of the adjoint feasible, even for turbulent flows. For transient Navier Stokes flow (i.e. turbulence), DNS will be used to find the Hessian in this way. The adjoint equations are solved backwards in time, requiring the complete time history of the state solution. The algorithmic and computational challenges of these calculations are discussed.   

Continuous Wavelet Analysis of a Highly Irregular Roughness Topography for Turbulence Studies

The realistic surfaces encountered in engineering wall-bounded turbulent flows have complex roughness topographies and occupy a wide range of various roughness parameters such as length scales, aspect ratios, and orientation angles, etc. In order to quantify the effects of those roughness parameters of a highly irregular rough surface on the turbulent boundary layers, the present study used continuous Mexican hat and Morlet wavelets to extract the dominant aspect ratio, length scale and orientation of the surface's random roughness elements. The roughness under the current study is replicated from a turbine blade damaged by deposition of foreign materials. For this particular roughness topography, the continuous wavelet analysis reveals that the dominant aspect ratio, length scale and orientation angle are 1/5, 24 mm and 4$^{\circ}$, respectively.   

Internal Layer Hierarchy in Rough-Wall Turbulent Boundary

The existence of an internal layer hierarchy is centric to the characteristic properties of wall-bounded turbulent flows. Its presence, which is revealed through an analysis of the mean momentum balance (MMB), accounts for the dynamics undergoing a continuous self-similar variation over a length scale range spanning the viscous length scale to the outer scale, $\nu/u_\tau \le \ell \le \delta$. Surface roughness introduces multiple new length scales which are often reduced (for simplification and comparison) to a single ``working'' scale given by the equivalent sandgrain roughness $k_s^+$. We report on our continuing efforts to study how this imposition modifies the continuous hierarchy of scaling layers admitted by the MMB. The establishment of log-like behavior closer to the wall in rough-wall flows is one such effect. It is speculated to be the direct consequence of the roughness causing the vorticity field to three-dimensionalize more rapidly compared to a smooth-wall. Data sets comprising of experiments being performed at UNH and high quality data sets available in the literature are being used for this combined roughness--Reynolds number study. The current experiments are conducted in a 8m long boundary layer wind-tunnel. Roughness is introduced in the form of sandpaper attached to the entire lower wall and profiles are taken using hot-wires and two-dimensional laser velocimetry.   

Perturbation of a Turbulent Boundary Layer by Spatially Impulsive Dynamic Roughness

The effect of a spatially impulsive patch of dynamic roughness on a zero pressure gradient, turbulent boundary layer is experimentally studied. The roughness patch is mechanically actuated at a range of frequencies on the order of the boundary layer burst frequency.The downstream evolution of the perturbed boundary layer is then measured by hot-wire anemometry and particle image velocimetry. Velocity profiles and spectral characteristics of the dynamic roughness case are compared with those in the spatially impulsive static roughness case, over a range of roughness amplitudes in the inner region of the boundary layer. The impact of the dynamic roughness on the near-wall turbulence in close proximity to the roughness as well as the recovery of the outer layer farther from the impulse are explored. The additional timescale introduced by the dynamic roughness provides a potential tool for the manipulation of the structure of boundary layers and, by extension, flow control.   

Relating turbulent friction and energy spectrum in rough-pipe flows

The classical experiments on turbulent flows over rough walls date back to Nikuradse in 1933. Nikuradse reported measurements of friction factor ($f$), or non-dimensional wall shear stress, as a function of the Reynolds number (Re) of the flow for pipes of six different values of roughness. A recent theory makes a mathematical link between the turbulent energy spectrum and the functional dependence of $f$ on Re (PRL, 044502, 96, 2006). Here we perform experiments on rough pipes to test this mathematical link. To that end, we measure $f$ vs Re as well as the attendant turbulent energy spectrum. Our experimental results are in good with the mathematical link predicted by the theory.   

Experimental Investigation of Flow Structures in the Boundary Layer over a Moving Rough Wall

Understanding turbulent flows over a moving surface has overarching implications in understanding rotary machinery and buffer-layer dynamics. We investigate effects imposed by such a boundary on flow structures and further elucidate its role to near wall dynamics. The wind-tunnel experiments are conducted over a 1.5x0.9m belt moving in the spanwise direction to impose crossflow wall stresses to a flat-plate turbulent boundary layer. Stream-wise roughness stripes (h=1mm) are patterned over the entire surface at the spacing of 1cm to imitate transverse waveform. The belt rotates at 10-50 rpm to generate effective wave speeds of 0.25-1.27 m/s. The free stream velocities are 5-20 m/s resulting in \textit{Re}$_{x}=(0.5-2)$x$10^{6}$, and \textit{Re}$_{h}$\textit{=500-2000} based on the roughness height. PIV is used to measure mean velocity profiles and fluctuation fields in three $x-y$ planes located at leading, mid, and trailing edges of the belt. Measurements on two $x-z$ planes located at $y=h$ and \textit{50$\delta $}$_{v}$ are also performed to assess effects of moving roughness on near wall structures. Turbulence statistics, i.e. distributions of Reynolds stress, turbulent kinetic energy, budgets and dissipation, are provided.