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.     

Riblet drag reduction in mild adverse pressure gradients: A numerical investigation

Riblet films are a passive method of turbulent boundary layer control that can reduce viscous drag. They have been studied with great detail for over 30 years. Although common riblet applications include flows with Adverse Pressure Gradients (APG), nearly all research thus far has been performed in channel flows. Recent research has provided motivation to study riblets in more complicated turbulent flows with claims that riblet drag reduction can double in mild APG common to airfoils at moderate angles of attack. Therefore, in this study, we compare drag reduction by scalloped riblet films between riblets in a zero pressure gradient and those in a mild APG using high-resolution large eddy simulations. In order to gain a fundamental understanding of the relationship between drag reduction and pressure gradient, we simulated several different riblet sizes that encompassed a broad range of s⁺ (riblet width in wall units), similarly to many previously published experimental studies. We found that there was only a slight improvement in drag reduction for riblets in the mild APG. We also observed that peak values of streamwise turbulence intensity, turbulent kinetic energy, and streamwise vorticity scale with riblet width. Primary Reynolds shear stresses and turbulence kinetic energy production however scale with the ability of the riblet to reduce skin-friction.     

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re = 13,400 and the nominal size of the roughness was k = 0.44 mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.     

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.     

Turbulent boundary layers over sparsely-spaced rod-roughened walls

Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over sparsely-spaced two-dimensional (2D) rod-roughened walls were performed. The rod elements were periodically arranged along the streamwise direction with pitches of p_x/k = 8, 16, 32, 64 and 128, where p_x is the streamwise spacing of the rods, and k is the roughness height. The Reynolds number based on the momentum thickness was varied from Re_θ = 300–1400, and the height of the roughness element was k = 1.5θ_in, where θ_in is the momentum thickness at the inlet. The characteristics of the TBLs, such as the friction velocity, mean velocity, and Reynolds stresses over the rod-roughened walls, were examined by varying the spacing of the roughness features (8 ⩽ p_x/k ⩽ 128). The outer-layer similarity between the rough and smooth walls was established for the sparsely-distributed rough walls (p_x/k ⩾ 32) based on the profiles of the Reynolds stresses, whereas those are not for p_x/k = 8 and 16. Inspection of the interaction between outer-layer large-scale motions and near-wall small-scale motions using two-point amplitude modulation (AM) covariance showed that modulation effect of large-scale motions on near-wall small-scale motions was strongly disturbed over the rough wall for p_x/k = 8 and 16. For p_x/k ⩾ 32, the flow that passed through the upstream roughness element transitioned to a smooth wall flow between the consecutive rods. The strong influence of the surface roughness in the outer layer for p_x/k = 8 and 16 was attributed to large-scale erupting motions by the surface roughness, creating both upward shift of the near-wall turbulent energy and active energy production in the outer layer with little influence on the near-wall region.     

On the impacts of coarse-scale models of realistic roughness on a forward-facing step turbulent flow

The present work explores the impacts of the coarse-scale models of realistic roughness on the turbulent boundary layers over forward-facing steps. The surface topographies of different scale resolutions were obtained from a novel multi-resolution analysis using discrete wavelet transform. PIV measurements are performed in the streamwise–wall-normal (x–y) planes at two different spanwise positions in turbulent boundary layers at Re_h = 3450 and δ/h = 8, where h is the mean step height and δ is the incoming boundary layer thickness. It was observed that large-scale but low-amplitude roughness scales had small effects on the forward-facing step turbulent flow. For the higher-resolution model of the roughness, the turbulence characteristics within 2h downstream of the steps are observed to be distinct from those over the original realistic rough step at a measurement position where the roughness profile possesses a positive slope immediately after the step’s front. On the other hand, much smaller differences exist in the flow characteristics at the other measurement position whose roughness profile possesses a negative slope following the step’s front.     

Numerical research on micro diesel spray characteristics under ultra-high injection pressure by Large Eddy Simulation (LES)

The Large Eddy Simulation model was introduced to study the micro spray characteristics under ultra-high injection pressure (>220 MPa). EFS8400 spray test platform was set up to verify the accuracy of the numerical model. The mechanisms of micro spray characteristics were studied intensively under different injection pressures (180 MPa, 240 MPa) and nozzle diameters (0.1 mm, 0.16 mm). The results indicated that the micro turbulence vortex structures can be captured, especially in the liquid spray core area. Large Eddy Simulation model combined with the small grid size of 0.25 mm show a huge advantage in studying the micro spray characteristics under ultra-high injection pressure; The turbulence vorticity and spray velocity for injection pressure of 240 MPa are more intensive than that of 180 MPa, and also the ultra-high injection pressure can contribute to strong turbulence disturbance between spray and surrounding air, which is helpful to improve the quality of spray; The spray velocity field extended wider for the diameter of 0.16 mm, and also the values of velocity in the spray center is higher than that of the diameter of 0.1 mm; The entrainment vortex appeared at the edge of the large velocity gradient between spray and surrounding air, and the higher velocity gradient for ultra-high injection pressure (240 MPa) between the spray and air is easier to increase the generation of entrainment vortex in the downstream of the spray, which can significantly increase the quality of spray and atomization.     

Experimental investigation of turbulence modulation in particle-laden coaxial jets by Phase Doppler Anemometry

The effect of solid particles on the flow characteristics of axisymmetric turbulent coaxial jets for two flow conditions was studied. Simultaneous measurements of size and velocity distributions of continuous and dispersed phases in a two-phase flow are presented using a Phase Doppler Anemometry (PDA) technique. Spherical glass particles with a particle diameter range from 102 to 212 μm were used in this two-phase flow, the experimental results indicate a significant influence of the solid particles and the Re on the flow characteristics. The data show that the gas phase has lower mean velocity in the near-injector region and a higher mean velocity at the developed region. Near the injector at low Reynolds number (Re = 2839) the presence of the particles dampens the gas-phase turbulence, while at higher Reynolds number (Re = 11 893) the gas-phase turbulence and the velocity fluctuation of particle-laden jets are increased. The particle velocity at higher Reynolds number (Re = 11 893) and is lower at lower Reynolds number (Re = 2839). The slip velocity between particles and gas phase existed over the flow domain was examined. More importantly, the present experiment results suggest that, consideration of the gas characteristic length scales is insufficient to predict gas-phase turbulence modulation in gas-particle flows.     

Numerical simulation of fully-developed compressible flows over wavy surfaces

Rough surfaces are common on high-speed vehicles, for example on heat shields, but compressibility is not usually taken into account in the flow modelling other than through the mean density. In the present study, supersonic fully-developed turbulent rough wall channel flows are simulated using direct numerical simulation to investigate whether strong compressibility effects significantly alter the mean flow and turbulence properties across the channel. The simulations were run for three different Mach numbers M = 0.3, 1.5 and 3.0 over a range of wall amplitude-to-wavelength ratios from 0.01 to 0.08, corresponding to transitionally and fully rough cases respectively. The velocity deficit values are found to decrease with increasing Mach number. It is also found that at Mach 3.0 significant differences occur in the mean flow and turbulence statistics throughout the channel and not just in a roughness sublayer. These differences are found to be due to the presence of strong shock waves created by the peaks of the roughness elements.     

Air flow aerodynamic on a wall-mounted hemisphere for various turbulent boundary layers

Air flow field around a surface-mounted hemisphere of a fixed height for two different turbulent boundary layers (thin and thick) are investigated experimentally and numerically. Flow measurements are performed in a wind tunnel using hot-wire anemometer and streamwise component of velocity fluctuation are calculated using a special developed program of the hardware system. Mean surface pressure coefficients and velocity field for the same hemisphere are determined by the numerical simulation. Turbulent flow field and intensity are measured for two types of boundary layers and compared at various sections in both streamwise and spanwise directions. Numerical scheme based on finite volume and SIMPLE algorithm is used to treat pressure and velocity coupling. Studies are performed for Reynolds number, Re_H = 32,000. Based on the numerical simulation using RNG k–ε turbulence model, flow pathlines, separation region and recirculation area are determined for the two types of turbulent boundary layer flows and complex flow field and recirculation regions are identified and presented graphically.     

DNS and LES of turbulent flow in a closed channel featuring a pattern of hemispherical roughness elements

Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) were performed for fully-developed turbulent flow in channels with smooth walls and walls featuring hemispherical roughness elements at shear Reynolds numbers Re_τ = 180 and 400, with the goal of studying the effect of these roughness elements on the wall-layer structure and on the friction factor. The LES and DNS approaches were verified first by comparison with existing DNS databases for smooth walls. Then, a parametric study for the hemispherical roughness elements was conducted, including the effects of shear Reynolds number, normalized roughness height (k⁺ = 10–20) and relative roughness spacing (s⁺/k⁺ = 2–6). The sensitivity study also included the effect of distribution pattern (regular square lattice vs. random pattern) of the roughness elements on the walls. The hemispherical roughness elements generate turbulence, thus increasing the friction factor with respect to the smooth-wall case, and causing a downward shift in the mean velocity profiles. The simulations revealed that the friction factor decreases with increasing Reynolds number and roughness spacing, and increases strongly with increasing roughness height. The effect of random element distribution on friction factor and mean velocities is however weak. In all cases, there is a clear cut between the inner layer near the wall, which is affected by the presence of the roughness elements, and the outer layer, which remains relatively unaffected. The study reveals that the presence of roughness elements of this shape promotes locally the instantaneous flow motion in the lateral direction in the wall layer, causing a transfer of energy from the streamwise Reynolds stress to the lateral component. The study indicates also that the coherent structures developing in the wall layer are rather similar to the smooth case but are lifted up by almost a constant wall-unit shift y⁺ (∼10–15), which, interestingly, corresponds to the relative roughness k⁺ = 10.     

Particle image velocimetry investigation on mixing enhancement of non-circular sharp edge nozzles

An experimental study using Particle Image Velocimetry (PIV) on free jets issuing from different orifice plate (OP) nozzles is reported. Mean velocity, turbulence intensity and higher order profiles relevant for large and small scale mixing are considered in the near field and interaction zone (0 < X/D < 20). This is done to determine mixing enhancement due to rectangular, squared, elliptic and triangular nozzles in comparison to circular nozzle results in two orthogonal planes. The effect of Reynolds number on the differences among the nozzle shapes is also considered by performing measurements just after laminar–turbulent transition (Re = 8000) and in the fully turbulent regime (Re = 35,000). The results at low Reynolds number show two classes of jets, i.e. at one side, those closer to axial-symmetric conditions, as circular, square and triangular jets, whereas on the other side those with elongated nozzles as rectangular and elliptic. The reason for the different behavior of the latter is connected to the phenomenon of axis-switching which allows a rearrangement of turbulence over the different velocity components and directions. However, for the highest Reynolds number investigated, all nozzles show similar behavior especially in the jet far field (X/D > 10), thus suggesting a significant Reynolds number dependence of the results.     

The effects of wall roughness on the separated flow over a smoothly contoured ramp

Experimental measurements address the effects on a turbulent boundary layer of wall roughness on a flat plate and a ramp that produces a separation bubble over the ramp trailing edge. A fully rough flow condition is achieved on the upstream flat plate. The main effect of the wall roughness on the outer layer turbulence on a flat plate is to change the friction velocity. The separation region is substantially larger for the rough-wall case. The rough-wall boundary layer turbulence is less sensitive to the onset of an adverse pressure gradient over the ramp, producing substantially smaller Reynolds stress peaks in upstream flat-plate, wall-unit coordinates.     

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.     

Characterizing developing adverse pressure gradient flows subject to surface roughness

An experimental study was conducted to examine the effects of surface roughness and adverse pressure gradient (APG) on the development of a turbulent boundary layer. Hot-wire anemometry measurements were carried out using single and X-wire probes in all regions of a developing APG flow in an open return wind tunnel test section. The same experimental conditions (i.e., T _∞, U _ref, and C _p) were maintained for smooth, k ⁺ = 0, and rough, k ⁺ = 41–60, surfaces with Reynolds number based on momentum thickness, 3,000 < Re _θ < 40,000. The experiment was carefully designed such that the x-dependence in the flow field was known. Despite this fact, only a very small region of the boundary layer showed a balance of the various terms in the integrated boundary layer equation. The skin friction computed from this technique showed up to a 58% increase due to the surface roughness. Various equilibrium parameters were studied and the effect of roughness was investigated. The generated flow was not in equilibrium according to the Clauser (J Aero Sci 21:91–108, 1954) definition due to its developing nature. After a development region, the flow reached the equilibrium condition as defined by Castillo and George (2001), where Λ = const, is the pressure gradient parameter. Moreover, it was found that this equilibrium condition can be used to classify developing APG flows. Furthermore, the Zagarola and Smits (J Fluid Mech 373:33–79, 1998a) scaling of the mean velocity deficit, U _∞δ*/δ, can also be used as a criteria to classify developing APG flows which supports the equilibrium condition of Castillo and George (2001). With this information a ‘full APG region’ was defined.     

Large Eddy Simulations of turbulent particle-laden channel flow

This paper scrutinises the Large Eddy Simulation (LES) approach to simulate the behaviour of inter-acting particles in a turbulent channel flow. A series of simulations that are fully (four-way), two-way and one-way coupled are performed in order to investigate the importance of the individual physical phenomena occurring in particle-laden flows. Moreover, the soft sphere and hard sphere models, which describe the interaction between colliding particles, are compared with each other and the drawbacks and advantages of each algorithm are discussed. Different models to describe the sub-grid scale stresses with LES are compared. Finally, simulations accounting for the rough walls of the channel are compared to simulations with smooth walls. The results of the simulations are discussed with the aid of the experimental data of Kussin J. and Sommerfeld M., 2002, Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness, Exp. in Fluids, 33, pp. 143–159 of Reynolds number 42,000 based on the full channel height. The simulations are carried out in a three-dimensional domain of 0.175 m × 0.035 m  × 0.035 m where the direction of gravity is perpendicular to the flow. The simulation results demonstrate that rough walls and inter-particle collisions have an important effect in redistributing the particles across the channel, even for very dilute flows. A new roughness model is proposed which takes into account the fact that a collision in the soft sphere model is fully resolved and it is shown that the new model is in very good agreement with the available experimental data.     

Flow of drag-reducing surfactant solutions in rough pipes

The paper reports the results of experimental study of the flow of hexadecyltrimethylammonium chloride (CTAC) solutions with addition of sodium salicylate (NaSal) in the rough pipes. Measurements were performed in the range of the surfactant concentration from 200 to 400 ppm at a constant molar ratio CTAC/NaSal of 1:2. Five pipes of the relative roughness k/D varying from 1.2 × 10^?2 to 5.6 × 10^?2, obtained by the covering of inner surface of the pipes with glued silicon carbide particles of different size, were studied. The roughness was observed to increase the drag of flow of CTAC/NaSal solutions already at Reynolds numbers higher than 800. With increasing relative roughness k/D, the critical value of Reynolds number, at which the drag reduction disappears, was found to decrease. However, no influence of the roughness on the critical shear stress was noted. The ratio of the critical Reynolds number for rough pipes to that of hydraulically smooth pipes was independent of the surfactant concentration. The degree of drag reduction by the flow of surfactants was greater in rough pipes than in smooth pipes.     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (∼1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e∼9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.