Session H17: Boundary Layers: Roughness Elements II

Prediction of an effective hydraulic length scale for surfaces with heterogeneous roughness

Practical engineering systems which include either external or internal wall-bounded turbulent flow are routinely affected by surface roughness. This causes performance degradation in the form of increased drag or head loss. Often times this roughness exhibits significant spatial heterogenenity.  In this case, it not clear how one 'averages' a number of local roughness conditions to generate a single effective hydraulic length scale for the entire surface.  In the present work, this question is explored.  Boundary layer similarity law analysis of frictional drag is used to predict the influence of roughness variations in both the spanwise and streamwise directions.  It is shown that the arithmetic mean does a poor job of predicting an effective hydraulic length scale for the entire surface due to the nonlinear relationship between the frictional drag increment and the hydraulic length scale.  Alternative averaging approaches are offered which do a much better job.   

DNS and LES of Flow Over Smooth and Rough Wavy Walls

Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent flows over smooth and rough wavy walls has been conducted. The Smooth Wavy Wall is described by a sinusoidal wave in the streamwise direction with amplitude to wavelength ratio of 0.05. Small-amplitude sinusoidal roughness elements are superimposed on to the Smooth Wavy Wall to obtain the Rough Wavy Wall. The smaller undulations on the Rough Wavy Wall represent undulations that LES resolutions do not resolve, and for cases where the roughness elements could still, have an influence on the resolved flow field. Our flow simulations are characterised by Reynolds number of 2390 based on bulk velocity and channel half-height. The budget terms of the Reynolds Stress Transport Equations reveal strong coupling between wall-topography and turbulence dynamics in the near wall region. Flow separation at the crest of the Smooth Wavy Wall and the formation of a persistent recirculation zone near the trough are observed along with a shear layer spanning multiple wavelengths.   

Rough Wall Boundary Layer Development in Response to Changing Pressure Gradients

Experiments were conducted in non-equilibrium turbulent boundary layers on a rough flat wall. The test section included a zero pressure gradient (ZPG) development region, followed by a favorable pressure gradient (FPG) region with constant acceleration parameter K=(ν/U_∞²)(dU_∞/dx), a ZPG recovery, and a constant K adverse pressure gradient (APG) region. Eight cases were documented with three different inlet velocities and K in the FPG ranging from 0.125×10^-6 to 2×10^-6. The K magnitude of the APG in each case was half that of the FPG. Velocity profiles were acquired at 12 streamwise stations using a two component LDV, and PIV was used to document velocity fields at the same stations. Turbulence statistics and two-point correltations of the turbulence quantities were computed. Experiments were completed and documented previously with a smooth wall under these conditions.  In the present work, a wall with mathematically generated stochastic roughness was produced by additive manufacturing, and new experiments were done under the same conditions as in the smooth wall cases.  A subset of the data will be presented to show the response of the rough wall boundary layer to the changing pressure gradient, and similarities and differences from the smooth wall cases will be examined.   

Cross-Stream Stereo PIV Measurements of Turbulent Boundary Layers Overlying Heterogeneous, Oblique Surface Roughness

Streamwise-elongated, spanwise heterogeneous surface roughness can give rise to sustained turbulent secondary flows that can alter mass and momentum transfer relative to smooth-wall and less heterogeneous rough-wall flow. This contribution explores the persistence of these roughness-induced turbulent secondary flows when the mean flow is rotated away from the streamwise-aligned nature of such surfaces. This obliquity reflects the possible varying orientation of the mean flow relative to roughness in practical applications. Streamwise-aligned ridges spaced periodically in the spanwise direction are utilized as the baseline roughness model and this topography is rotated relative to the streamwise direction to introduce obliquity. Models of these roughness scenarios were fabricated, including a transparent roughness tile for each scenario deployed at the measurement position that was cast in urethane to match its refractive index to that of the working fluid (sodium iodide) of the flow facility which yielded an optical continuum between the roughness and the surrounding fluid. High-frame-rate stereo PIV was deployed in the cross-stream plane (wall-normal by spanwise) to explore the impact of obliquity on the turbulent secondary flows and inner-outer interactions.   

Flow-roughness heterogeneity: critical obliquity and salient parameters

Large-scale roughness heterogeneity aligned orthogonal to a prevailing flow forms an internal boundary layer (IBL), while roughness heterogeneity aligned parallel to a prevailing flow induces counter-rotating secondary cells, as has been well established in prior research; little research on flow response to oblique heterogeneity is available. We have used large-eddy simulation to perform comprehensive parametric assessment on the effect of obliquity, element height, and spacing between rows of elements. Results show persistent IBL-like flow patterns, even as the obliquity angle increases significantly from a canonical orthogonal arrangement. The flow patterns in this regime are monotonic, before abruptly collapsing at a critical obliquity. This critical obliquity is caused by successive element sheltering, whereby the frontal area of “leeward” obstacles is sheltered and roughness elements behave as a rough strip. Results of the parametric study are used to record effective roughness length a posteriori and develop of a prognostic roughness model generalized for aggregate roughness, frontal area index, and obliquity angle.   

Comparison of turbulent flow structures over rough permeable and impermeable sediment beds using Direct Numerical Simulation

Pore-resolved direct numerical simulations (DNS) of turbulent flow over a sediment bed are performed to test the hypothesis that the structure and dynamics of turbulence over a porous sediment bed can be significantly different than that over an impermeable rough wall. Simulations are carried out at Re_τ= 180 and roughness Reynolds number of Re_k∼2.56, corresponding to stream flow over a randomly packed permeable gravel bed, and compared to impermeable bed with roughness elements similar to the top layer.

Comparison of flow statistics confirms that bed permeability can significantly increase the skin friction coefficient (~30% greater) due to enhanced flow resistance. Data shows that form-induced/dispersive turbulent stresses induce deeper penetration of turbulence into the sediment (~43% greater).  Results show that a negative streamwise dispersive stress accompanies a positive wall-normal dispersive stress behind bed protrusions, resulting in ejection motions and vice versa in trough regions, causing sweep motions. The stream flow statistics of porous bed as well as surface pressure fluctuations are well captured by half-layer sediment roughness element; however, turbulence penetration and ejection-sweep events are altered in presence of porous bed   

Effect of roughness texture on a transient accelerating channel flow

The topographical effects of wall roughness on the response of a turbulent channel to a very rapid acceleration is studied using direct numerical simulations. Flows over two surfaces with same roughness height, but with different roughness topographies are compared: a sand-grain roughness and a multiscale turbine-blade roughness. The flow is accelerated from a bulk Reynolds Number of 3000 to 12000 over a short time interval. 

During this time, the rough-wall flows change from transitionally rough to fully rough.

It has been shown that, unlike a smooth-wall flow, the rough-wall flows recover to the new equilibrium state quickly without reverse transition, and that roughness geometry affects the rate of such recovery.

In this talk, we show that such roughness effects are attributed to the form-induced turbulent fluctuations, which are intensified by the acceleration. 

First, the form-induced velocities and their strain rates are characterized. Then we show that they significantly affect near-wall pressure fluctuations and Reynolds stress anisotropy, by analyzing various source terms of the pressure Poisson equation.

This work demonstrates that the transient response of rough-wall turbulence to acceleration depends strongly on the texture of the roughness.   

Efficient matrix-free linear analysis for large-scale $n$-periodic systems: Application to spanwise arrays of flow irregularities

This work presents a mathematical framework for the linear analysis of $n$-periodic systems, consisting of $n$ identical units. Such $n$-periodic configurations occur in a variety of applications in fluid dynamics, such as boundary layers over roughness arrays or arrays of injectors. The analysis of these systems as single periodic units is often insufficient as dynamics are likely to span over multiple units. In order to accommodate cross-unit interactions, the roots-of-unity framework is integrated into a large-scale compressible solver and tested on a case of spanwise roughness arrays. The benefit of this approach is the decoupling of the problem from the specific number of units, allowing the analysis of a large range of configurations at a reduced cost. The methodology and its applicability are demonstrated for a model problem of synthetic wakes downstream of roughness elements in subsonic and hypersonic boundary layers. The linear model dynamics are extracted using Dynamic Mode Decomposition.  Finally, capabilities for further non-modal analysis using resolvent modes, linear-adjoint sensitivity analysis and optimization or control are also introduced.   

A priori roughness function from texture-less simulations: the case of slip/no-slip textures

We study the effect of surface texture on an overlying turbulent flow. For very small textures, we have previously discussed that turbulence remains smooth-wall-like, other than experiencing an apparent origin offset for different flow components. For slip/no-slip textures, a common model for superhydrophobic surfaces, this effect reduces to the flow experiencing slip conditions in the streamwise and spanwise directions and zero transpiration at the surface. We have previously reported that these effective boundary conditions for the overlying turbulence persist at least up to texture sizes L⁺ ≈ 50. However, beyond L⁺ ≈ 20 the texture interacts with the overlying turbulence in a non-homogenous fashion, and turbulence is no longer smooth-wall-like. This is the typical effect of surface texture observed in rough surfaces, and results in a degradation of drag. We argue that the texture modifies the overlying turbulence through cross-advective terms between the background turbulence and the flow directly induced by the presence of the texture. To verify this, we introduce additional, forcing terms in the Navier-Stokes equations in homogenous-slip-length simulations that capture the effect of the non-linear interaction on the background turbulence. The interaction can then be accounted for without the need to resolve the surface texture. We show that this captures the changes both in drag and turbulent statistics and spectra up to texture sizes L⁺ ≈ 70.