Effects of Strong Irregular Roughness on the Turbulent Boundary Layer

Some recent studies with irregular roughness suggest that the Nikuradse [Nikuradse, J., NACA TM 1292, National Advisory Committee on Aeronautics (1933)] equivalent sand-grain roughness measure gives inconsistent results of the flow characteristics. In situations where the roughness is very strong to stifle or diminish the viscous effects the viscous scaling laws alone will not be very meaningful. The present study aims to find an alternative scaling parameter for such cases. Here, the measured mean and turbulent velocity profiles on a nonuniform roughness surface, simulating a gas turbine blade roughness, are presented. A nonzero wall normal pressure gradient is caused which is believed to contribute to the velocity deficit in the near-wall rough boundary layer velocity profile. The surface pressure variation is also directly influenced by the local roughness. The normal turbulent stresses are increased on the rough surface, the vertical component more than the longitudinal component. A pressure gradient velocity scale (similar to that proposed for adverse pressure gradient boundary layer modeling by Durbin and Belcher [Durbin, P.A. and Belcher, S.E., J. Fluid Mech. 238 (1992), 699-722] is defined to capture the pressure effects induced by such roughness on the inner layer properties.     

Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.     

Turbulence characteristics over k-type rib roughened porous walls

To understand the permeability effects on turbulent rib-roughened porous channel flows, particle image velocimetry measurements are performed at the bulk Reynolds number of 5000–20000. Solid impermeable and porous ribs are considered for the rib-roughness whose geometry is categorised in the k-type roughness whose pitch/rib-height is 10. Three isotropic porous media with nearly the same porosity: 0.8, and different permeabilities (0.004, 0.020, 0.033 mm²) are applied. It is observed that the recirculation between the ribs becomes weak and the recirculation vortex submerges into the porous wall as the wall permeability and Reynolds number increase for both solid and porous rib cases while the recirculation vanishes in high permeable cases. These phenomena result in characteristic difference in turbulence quantities. By fitting the mean velocity profiles to the log-law form, the permeability effects of both rib and bottom wall on the log-law parameters and the equivalent sand-grain roughness are discussed. It is concluded that the zero-plane displacement increases while the von Kármán constant and the equivalent sand-grain roughness decrease as the wall and rib permeability increases.     

Prediction of the interfacial shear-stress in vertical annular flow

Many improvements of the Wallis correlation for the interfacial friction in annular flow have been proposed in the literature. These improvements give in general a better fit to data, however, their physical basis is not always justified. In this work, we present a physical approach to predict the interfacial shear-stress, based on the theory on roughness in single-phase turbulent pipe flows. Using measured interfacial shear-stress data and measured data on roll waves, which provide most of the contribution to the liquid film roughness, we show that the interfacial shear-stress in vertical annular flow is in very close agreement with the theory. We show that the sand-grain roughness of the liquid film is not equal to four times the mean film thickness, as it is assumed in the Wallis correlation. Instead, the sand-grain roughness is proportional to the wave height, and the proportionality constant can be predicted accurately using the roughness density (or solidity). Furthermore, we show that our annular flow, which is in similar conditions to others in the literature, is fully rough. Hence, the bulk Reynolds number should not appear in the prediction of the interfacial friction coefficient, as is often done in the improvements of the Wallis correlation proposed in the literature.     

Some equilibrium turbulent boundary layers

Using the Coles additive law of the wall and law of the wake for the mean velocity profile of a two-dimensional turbulent boundary layer, a differential equation for the friction and wake parameters is derived from the momentum integral equation with a view to finding out the conditions under which the boundary layer can exhibit equilibrium. It is predicted that equilibrium is possible for boundary layers in favorable pressure gradient over smooth as well as k-type rough walls. When the roughness height is allowed to increase linearly with the streamwise distance, equilibrium exists also in zero pressure gradient. For a d-type rough wall, equilibrium is possible for a certain range of pressure gradients, from favorable to adverse. Most of the predictions are verified by evaluating the friction and wake parameters from the available experimental data on mean velocity measurements.     

Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows

Wall-resolved Large Eddy Simulation of fully developed turbulent channel flows over two different rough surfaces is performed to investigate on the effects of irregular 2D and 3D roughness on the turbulence. The two geometries are obtained through the superimposition of sinusoidal functions having random amplitudes and different wave lengths. In the 2D configuration the irregular shape in the longitudinal direction is replicated in the transverse one, while in the 3D case the sinusoidal functions are generated both in streamwise and spanwise directions. Both channel walls are roughened in such a way as to obtain surfaces with statistically equivalent roughness height, but different shapes. In order to compare the turbulence properties over the two rough walls and to analyse the differences with a smooth wall, the simulations are performed at the same Reynolds number Re_τ = 395. The same mean roughness height h = 0.05δ (δ the half channel height) is used for the rough walls.The roughness function obtained with the 3D roughness is larger than in the 2D case, although the two walls share the same mean height. Thus, the considered irregular 3D roughness is more effective in reducing the flow velocity with respect to the 2D roughness, coherently with the literature results that identified a clear dependence of the roughness function on the effective slope (see Napoli et al. (2008)), higher in the generated 3D rough wall. The analysis of higher-order statistics shows that the effects of the roughness, independently on its two- or three-dimensional shape, are mainly confined in the inner region, supporting the Townsend’s wall similarity hypothesis. The tendency towards the isotropization is investigated through the ratio between the resolved Reynolds stress components, putting in light that the 3D irregular rough wall induces an higher reduction of the anisotropy, with respect to the 2D case.     

Distributed Roughness Effects on Transitional and Turbulent Boundary Layers

A numerical investigation is carried out to study the transition of a subsonic boundary layer on a flat plate with roughness elements distributed over the entire surface. Post-transition, the effect of surface roughness on a spatially developing turbulent boundary layer (TBL) is explored. In the transitional regime, the onset of flow transition predicted by the current simulations is in agreement with the experimentally based correlations proposed in the literature. Transition mechanisms are shown to change significantly with the increasing roughness height. Roughness elements that are inside the boundary layer create an elevated shear layer and alternating high and low speed streaks near the wall. Secondary sinuous instabilities on the streaks destabilize the shear layer promoting transition to turbulence. For the roughness topology considered, it is observed that the instability wavelengths are governed by the streamwise and spanwise spacing between the roughness elements. In contrast, the roughness elements that are higher than the boundary layer create turbulent wakes in their lee. The scale of instability is much shorter and transition occurs due to the shedding from the obstacles. Post-transition, in the spatially developing TBL, the velocity defect profiles for both the smooth and rough walls collapsed when non dimensionalized in the outer units. However, when compared to the smooth wall, deviation in the Reynolds stresses are observable in the outer layer; the deviation being higher for the larger roughness elements.     

A Bypass Transition Model Based on the Intermittency Function

An intermittency model that is formulated in local variables is proposed for representing bypass transition in Reynolds-Averaged Navier-Stokes (RANS) computations. No external data correlation is used to fix transition. Transition is initiated by diffusion, and a source term carries it to completion. A sink term is created to predict the laminar region before transition, then it vanishes in the turbulent region. Both the source and sink are functions of a wall-distance Reynolds number and turbulence scale. A modification is introduced to predict transition in separated boundary layers. The transition model is incorporated with the k?ω RANS model. The present model is implemented into a general purpose, computational fluid dynamics (CFD) code. The model is validated with several test cases. Decent agreement with the available data is observed in a range of flows.     

Adverse pressure gradient turbulent flows over rough walls

An experimental study of a fully developed turbulent channel flow and an adverse pressure gradient (APG) turbulent channel flow over smooth and rough walls has been performed using a particle image velocimetry (PIV) technique. The rough walls comprised two-dimensional square ribs of nominal height, k = 3 mm and pitch, p = 2k, 4k and 8k. It was observed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. Similarly, rib roughness significantly increased the level of turbulence production, Reynolds stresses and wall-normal transport of turbulence kinetic energy and Reynolds shear stress well beyond the roughness sublayer. On the contrary, the distributions of the eddy viscosity, mixing length and streamwise transport of turbulence kinetic energy and Reynolds shear stress were reduced by wall roughness, especially in the outer layer. Adverse pressure gradient produced a further reduction in the mean velocity (in comparison to the results obtained in the parallel section) but increased the wall-normal extent across which the mean flow above the ribs is spatially inhomogeneous in the streamwise direction. APG also reinforced wall roughness in augmenting the equivalent sand grain roughness height. The combination of wall roughness and APG significantly increased turbulence production and Reynolds stresses except in the immediate vicinity of the rough walls. The transport velocities of the turbulence kinetic energy and Reynolds shear stress were also augmented by APG across most part of the rough-wall boundary layer. Further, APG enhanced the distributions of the eddy viscosity across most of the boundary layer but reduced the mixing length outside the roughness sublayer.     

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re_θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.     

Drag reducing outer-layer devices in rough wall turbulent boundary layers

The ability of outer-layer devices to reduce wall shear stress over a substantial streamwise distance in rough-wall turbulent boundary layers has been studied experimentally. The devices examined are a pair of thin flat ribbons placed in tandem as well as those having symmetric airfoil sections. The wall conditions examined are smooth, d- and k-type transverse-groove and sandgrain roughnesses. The wall drag is found to be reduced from the respective normal levels in all rough walls. All k-type rough walls exhibit a similar level of relative wall drag reduction which is also smaller than that in a smooth-wall. The d-type rough walls exhibit a transitional behaviour — the relative wall drag reduction drops from the smooth wall level to that of the k-type roughness with increasing roughness Reynolds number. However, the absolute reductions in the local wall shear stress are similar in both the rough and smooth walls. On the other hand, the relative reductions are lower in the rough walls because of a higher reference drag which is caused by the unique presence of a pressure component on which the devices are not as effective.     

A turbulent boundary layer over a two-dimensional rough wall

Particle image velocimetry (PIV) measurements and planar laser induced fluorescence (PLIF) visualizations have been made in a turbulent boundary layer over a rough wall. The wall roughness consisted of square bars placed transversely to the flow at a pitch to height ratio of λ/k = 11 for the PLIF experiments and λ/k = 8 and 16 for the PIV measurements. The ratio between the boundary layer thickness and the roughness height k/δ was about 20 for the PLIF and 38 for the PIV. Both the PLIF and PIV data showed that the near-wall region of the flow was populated by unstable quasi-coherent structures which could be associated to shear layers originating at the trailing edge of the roughness elements. The streamwise mean velocity profile presented a downward shift which varied marginally between the two cases of λ/k, in agreement with previous measurements and DNS results. The data indicated that the Reynolds stresses normalized by the wall units are higher for the case λ/k = 16 than those for λ/k = 8 in the outer region of the flow, suggesting that the roughness density effects could be felt well beyond the near-wall region of the flow. As expected the roughness disturbed dramatically the sublayer which in turn altered the turbulence production mechanism. The turbulence production is maximum at a distance of about 0.5k above the roughness elements. When normalized by the wall units, the turbulence production is found to be smaller than that of a smooth wall. It is argued that the production of turbulence is correlated with the form drag.     

Velocity-defect scaling for turbulent boundary layers with a range of relative roughness

Velocity profile measurements in zero pressure gradient, turbulent boundary layer flow were made on a smooth wall and on two types of rough walls with a wide range of roughness heights. The ratio of the boundary layer thickness (δ) to the roughness height (k) was 16≤δ/k≤110 in the present study, while the ratio of δ to the equivalent sand roughness height (k _s) ranged from 6≤δ/k _s≤91. The results show that the mean velocity profiles for all the test surfaces agree within experimental uncertainty in velocity-defect form in the overlap and outer layer when normalized by the friction velocity obtained using two different methods. The velocity-defect profiles also agree when normalized with the velocity scale proposed by Zagarola and Smits (J Fluid Mech 373:33–70, 1998). The results provide evidence that roughness effects on the mean flow are confined to the inner layer, and outer layer similarity of the mean velocity profile applies even for relatively large roughness.     

Turbulization of the wake behind a single roughness element on a blunted body at a hypersonic Mach number

The influence of a cylinder-shaped single roughness element on the laminar–turbulent transition in the presence of an entropy layer is experimentally studied. The experiments are performed on a blunted cone model at the Mach number M = 5. The roughness element is located on the blunted tip of the model. Information about the mean and fluctuating parameters of the boundary layer in the wake behind the roughness element is obtained by using hot-wire anemometry. It is shown that flow turbulization behind the roughness elements occurs at the local Reynolds number calculated on the basis of the roughness element height and equal to 400–500. It is found that the presence of the roughness element exerts a significant effect on the unsteady characteristics of the boundary layer if the roughness element height is smaller than the effective value.     

The effect of a systematic change in surface roughness skewness on turbulence and drag

Previous work by the authors (Flack and Schultz, 2010) has identified the root-mean-square roughness height, k_rms, and the skewness, Sk, of the surface elevation distribution as important parameters in scaling the skin-friction drag on rough surfaces. In this study, three surfaces are tested in turbulent boundary layer flow at a friction Reynolds number, Re_τ = 1600–2200. All the surfaces have similar root-mean-square roughness height, while the skewness is varied. Measurements are presented using both two-component LDV and PIV. The results show the anticipated trend of increasing skin-friction drag with increasing skewness. The largest increase in drag occurs going from negative skewness to zero skewness with a more modest increase going from zero to positive skewness. Some differences in the mean velocity and Reynolds stress profiles are observed for the three surfaces. However, these differences are confined to a region close to the rough surface, and the mean velocity and Reynolds stress profiles collapse away from the wall when scaled in outer variables. The turbulence structure as documented through two-point spatial correlations of velocity is also observed to be very similar over the three surfaces. These results support Townsend’s (1976) concept of outer-layer similarity that the wall boundary condition exerts no direct influence on the turbulence structure away from the wall except in setting the velocity and length scales for the outer layer.     

Lattice–Boltzmann simulations for analysing the detachment of micron-sized spherical particles from surfaces with large-scale roughness structures

Fully resolved numerical simulations of a micron-sized spherical particle residing on a surface with large-scale roughness are performed by using the Lattice–Boltzmann method. The aim is to investigate the influence of surface roughness on the detachment of fine drug particles from larger carrier particles for transporting fine drug particles in a DPI (dry powder inhaler). Often the carrier surface is modified by mechanical treatments for modifying the surface roughness in order to reduce the adhesion force of drug particles. Therefore, drug particle removal from the carrier surface is equivalent to the detachment of a sphere from a rough plane surface. Here a sphere with a diameter of 5 μm at a particle Reynolds number of 1.0, 3.5 and 10 are considered. The surface roughness is described as regularly spaced semi-cylindrical asperities (with the axes oriented normal to the flow direction) on a smooth surface. The influence of asperity distance and size ratio (i.e. the radius of the semi-cylinder to the particle radius, R_c/R_d) on particle adhesion and detachment are studied. The asperity distance is varied in the range 1.2 < L/R_d < 2 and the semi-cylinder radius between 0.5 < R_c/R_d < 0.75. The required particle resolution and domain size are appropriately selected based on numerical studies, and a parametric analysis is performed to investigate the relationship between the contact distance (i.e. half the distance between the particle contact points on two neighbouring semi-cylinders), the asperity distance, the size ratio, and the height of the particle centroid from the plane wall. The drag, lift and torque acting on the spherical particle are measured for different particle Reynolds numbers, asperity distances and sizes or diameters. The detachment of particles from rough surfaces can occur through lift-off, sliding and rolling, and the corresponding detachment models are constructed for the case of rough surfaces. These studies will be the basis for developing Lagrangian detachment models that eventually should allow the optimisation of dry powder inhaler performance through computational fluid dynamics.     

Turbulent flow over a rough backward-facing step

This work characterizes the impacts of the realistic roughness due to deposition of foreign materials on the turbulent flows at surface transition from elevated rough-wall to smooth-wall. High resolution PIV measurements were performed in the streamwise-wall-normal (x–y) planes at two different spanwise positions in both smooth and rough backward-facing step flows. The experiment conditions were set at a Reynolds number of 3450 based on the free stream velocity U_∞ and the mean step height h, expansion ratio of 1.01, and the ratio of incoming boundary layer thickness to the step height, δ/h, of 8. The mean flow structures are observed to be modified by the roughness and they illustrate three-dimensional features in rough backward-facing step flows. The mean reattachment length X_r is significantly reduced by the roughness at one PIV measurement position while is slightly increased by the different roughness topography at the other measurement position. The mean velocity profiles at the reattachment point indicate that the studied roughness weakens the perturbation of the step to the incoming turbulent flow. Comparisons of Reynolds normal and shear stresses, productions of normal stresses, quadrant analysis of the instantaneous shear-stress contributing events, and mean spanwise vorticity reveal that the turbulence in the separated shear layer is reduced by the studied roughness. The results also indicate an earlier separation of the turbulent boundary layer over the current rough step, probably due to the adverse pressure gradient produced by the roughness topography even before the step.     

Upstream roughness and Reynolds number effects on turbulent flow structure over forward facing step

This paper presents results of experiments conducted to investigate the effects of Reynolds number and upstream wall roughness on the turbulence structure in the recirculation and recovery regions of a smooth forward facing step. A reference smooth upstream wall and a rough upstream wall made from sand gains were studied. For the smooth upstream wall, experiments were conducted at Reynolds number based on the freestream velocity and step height (h), Re_h = 4940, 8400 and 8650. The rough wall experiments was performed at Re_h = 5100, 8200 and 8600 to closely match the corresponding Re_h experiment over the smooth wall. The reattachment lengths in the smooth wall experiments were L_r/h ≈ 2.2, but upstream roughness significantly reduced these values to L_r/h ≈ 1.3. The integral scales within the recirculation bubbles were independent of upstream roughness and Reynolds number; however, upstream roughness significantly increased the spatial coherence and integral scales outside the recirculation bubbles and in the recovery region. Irrespective of the upstream wall condition, the redeveloping boundary layer recovered at 25h from reattachment.     

Predicting crossflow induced transition with laminar kinetic energy transition model

The hypersonic laminar kinetic energy transition model is developed to be appropriate for crossflow induced boundary layer transition prediction. A crossflow timescale is constructed and incorporated in the k_T-k_L-ω transition model to reflect crossflow effect during three-dimensional boundary layer transition. The stream-wise vorticity is selected as the indicator of crossflow strength. Regarding the inviscid unstable characteristic of crossflow instability, the crossflow timescale is constructed by reference to the second mode timescale. To eliminate inappropriate development of the crossflow timescale where the effective length scale is large enough while the crossflow strength remains at a quite low level, a crossflow velocity limit function is proposed. The revised k_T-k_L-ω transition model has been applied to HIFiRE-5 and blunt cone with 1°angle of attack test cases. Results show good correspondence with the experimental data and DNS data, which demonstrates that the constructed crossflow timescale makes the revised transition model capable of reproducing crossflow induced transition behavior with a reasonable degree of accuracy.