Per-Åge Krogstad

An experimental and numerical study of channel flow with rough walls

Direct numerical simulation has been performed in order to study ressure-driven turbulent flow in a rod-roughened channel at Reynolds number Reτ = 400 (based on the mean pressure gradient). Square rods were attached to both channel walls and protruded only 0.034 of the channel’s half-height into the flow. Roughness elements were spaced at 7 heights, which corresponded to the so-called “k–type” laboratory roughness.The classical logarithmic variation of the mean velocity was found to be maintained in the rough-wall channel flow. The only effect roughness had was to shift the log-profile downwards, the magnitude of which was about 7.1. This, corresponded to the upper limit of the transitionally rough region, based on the associated equivalent sand-grain roughness height. Within the layer of thickness about 3-5 times roughness height (roughness sublayer ), the dependency of the mean velocity and turbulence properties on the streamwise location with respect to the rods was revealed.Instead of viscous sublayer, an intensive shear layer was formed emanated from the crest of roughness elements. It was observed that the wall-ward transport of the kinetic energy was substantially increased very close to the wall while the transport of the kinetic energy away from the wall was relatively reduced at just about the edge of the roughness sublayer. Visualizations of the fluctuating velocities and vortices in this region revealed the presence of elongated streaky structures very similar to those routinely observed in the structure of the smooth-wall turbulence, with much shorter coherence in the streamwise direction and less organization in the spanwise direction. The intensity of the vorticity fluctuations in the roughness sublayer were increased whereas in the outer layer, they remained unaffected. The anisotropy invariant maps for the smooth and rough cases clearly showed that the state of the near-wall turbulence for the two cases were substantially different, whereas in the regions away from the wall, the two cases exhibited similarities. Generally, the results obtained from this study supported the classical wall similarity hypothesis.

Turbulence structure in boundary layers over different types of surface roughness

The classical treatment of rough wall turbulent boundary layers consists in determining the effect the roughness has on the mean velocity profile. This effect is usually described in terms of the roughness function ΔU+. The general implication is that different roughness geometries with the same ΔU+ will have similar turbulence characteristics, at least at a sufficient distance from the roughness elements. Measurements over two different surface geometries (a mesh roughness and spanwise circular rods regularly spaced in the streamwise direction) with nominally the same ΔU+ indicate significant differences in the Reynolds stresses, especially those involving the wall-normal velocity fluctuation, over the outer region. The differences are such that the Reynolds stress anisotropy is smaller over the mesh roughness than the rod roughness. The Reynolds stress anisotropy is largest for a smooth wall. The small-scale anisotropy and intermittency exhibit much smaller differences when the Taylor microscale Reynolds number and the Kolmogorov-normalized mean shear are nominally the same. There is nonetheless evidence that the small-scale structure over the three-dimensional mesh roughness conforms more closely with isotropy than that over the rod-roughened and smooth walls.

Reynolds number effects in the outer layer of the turbulent flow in a channel with rough walls

Turbulent channel flow measurements for two different rough surfaces have been compared with a smooth reference case. A range of Reynolds numbers, Reτ∊⟨360,6000⟩, has been investigated using hot-wire anemometry. Reynolds stresses and third-order moments are shown to be very little affected by the substantially different wall conditions outside 5k, where k is the characteristic length scale of the roughness. In this region, a reasonably good collapse with Reynolds number is demonstrated when scaling with friction velocity is used. This contrasts some of the rough-wall investigations previously published for boundary layers and channels with only one rough wall. It is believed that the differences observed are due to the differences in boundary conditions and that symmetrically roughened channel flows and flows in rough-wall pipes may be better candidates for the Townsend’s wall similarity hypothesis than asymmetrical flows.

Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall

Direct numerical simulation (DNS) of a spatially developing turbulent boundary layer (TBL) over a wall roughened with regularly arrayed cubes was performed to investigate the effects of three-dimensional (3-D) surface elements on the properties of the TBL. The cubes were staggered in the downstream direction and periodically arranged in the streamwise and spanwise directions with pitches of p x / k = 8 and p z / k = 2, where p x and p z are the streamwise and spanwise spacings of the cubes and k is the roughness height. The Reynolds number based on the momentum thickness was varied in the range Re θ = 300−1300, and the roughness height was k = 1.5θ in , where θ in is the momentum thickness at the inlet, which corresponds to k /δ = 0.052–0.174 from the inlet to the outlet; δ is the boundary layer thickness. The characteristics of the TBL over the 3-D cube-roughened wall were compared with the results from a DNS of the TBL over a two-dimensional (2-D) rod-roughened wall. The introduction of cube roughness affected the turbulent Reynolds stresses not only in the roughness sublayer but also in the outer layer. The present instantaneous flow field and linear stochastic estimations of the conditional averaging showed that the streaky structures in the near-wall region and the low-momentum regions and hairpin packets in the outer layer are dominant features in the TBLs over the 2-D and 3-D rough walls and that these features are significantly affected by the surface roughness throughout the entire boundary layer. In the outer layer, however, it was shown that the large-scale structures over the 2-D and 3-D roughened walls have similar characteristics, which indicates that the dimensional difference between the surfaces with 2-D and 3-D roughness has a negligible effect on the turbulence statistics and coherent structures of the TBLs.

Freely decaying, homogeneous turbulence generated by multi-scale grids

We investigate wind-tunnel turbulence generated by both conventional and multi-scale grids. Measurements were made in a tunnel which has a large test section, so that possible side wall effects are very small and the length ensures that the turbulence has time to settle down to a homogeneous shear-free state. The conventional and multi-scale grids were all designed to produce turbulence with the same integral scale, so that a direct comparison could be made between the different flows. Our primary finding is that the behaviour of the turbulence behind our multi-scale grids is virtually identical to that behind the equivalent conventional grid. In particular, all flows exhibit a power-law decay of energy, u 2 ~ t − n , where n is very close to the classical Saffman exponent of n = 6/5. Moreover, all spectra exhibit classical Kolmogorov scaling, with the spectra collapsing on the integral scales at small k , and on the Kolmogorov microscales at large k . Our results are at odds with some other experiments performed on similar multi-scale grids, where significantly higher energy decay exponents and turbulence levels have been reported.

Delayed correlation between turbulent energy injection and dissipation

The dimensionless kinetic energy dissipation rate C_epsilon is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number Re_lambda range is 20<Re_lambda<220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re_lambda dependence of C_epsilon abates when Re_lambda approx. 100 after which C_epsilon slowly approaches approx 0.5 a value slightly different to previously reported simulations but in good agreement with experimental results. If C_epsilon is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to +-30%. This may explain the spread in results from previously published estimates of C_epsilon.

Near-field investigation of turbulence produced by multi-scale grids

We investigate grid turbulence behind two multi-scale grids and one conventional one, with particular emphasis on the properties of the near-field turbulence. All three grids are designed to produce the same integral scale, l0, at a downstream distance of two meters (x = 2 m). We find that the turbulence is highly inhomogeneous for x 50l0. The structure of the near-field turbulence for the present grids is dependent on the type of grid used, exhibiting a number of curious properties, which is consistent with earlier studies [D. Hurst and J. C. Vassilicos, “Scalings and decay of fractal-generated turbulence,” Phys. Fluids 19, 035103 (2007)]. However, the far-field is remarkably similar for all three grids. For example, the far-field energy decay rate is virtually identical for all three grids, as was shown by Krogstad and Davidson [“Freely-decaying, homogeneous turbulence generated by multiscale grids,” J. Fluid Mech. 680, 417 (2011)]. Thi...

Some Measurements of Surface Drag in Urban-Type Boundary Layers at Various Wind Angles

Using experimental data obtained in naturally grown boundary layers over a generic urban-type roughness (height h) it is shown that the surface drag is strongly dependent on the flow direction with respect to the roughness orientation. The variations with wind direction are accompanied by corresponding changes in the parameters contained in the usual logarithmic description of the flow in the near-wall inertial layer,

Rough Wall Skin Friction Measurements Using a High Resolution Surface Balance

{U/u_\tau=\frac{1}{\kappa}\ln[(z-d)/z_{\rm o}]}