Mean Streamwise Velocity Profiles Research Articles

A generalized wall-pressure spectral model for non-equilibrium boundary layers

This study uses high-fidelity simulations (direct numerical simulation or large-eddy simulation) and experimental datasets to analyse the effect of non-equilibrium streamwise mean pressure gradients (adverse or favourable), including attached and separated flows, on the statistics of boundary-layer wall-pressure fluctuations. The datasets collected span a wide range of Reynolds numbers ( $Re_\theta$ from 300 to 23 400) and pressure gradients (Clauser parameter from $-0.5$ to 200). The datasets are used to identify an optimal set of variables to scale the wall-pressure spectrum: edge velocity, boundary layer thickness and the peak magnitude of Reynolds shear stress. Using the present datasets, existing semi-empirical models of the wall-pressure spectrum are shown unable to capture effects of strong, non-equilibrium adverse pressure gradients, due to inappropriate scaling of the wall pressure using the wall shear stress, calibration with limited types of flows and dependency on model parameters based on the friction velocity, which reduces to zero at the detachment point. To address these shortcomings, a generalized wall-pressure spectral model is developed with parameters that characterize the extent of the logarithmic layer and the strength of the wake. Derived from the local mean streamwise velocity profile, these two parameters inherently carry the effect of the Reynolds number, as well as those of the non-equilibrium pressure gradient and its history. Comparison with existing models shows that the proposed model behaves well and is more accurate in strong-pressure-gradient flows and in separated-flow regions.

Direct numerical simulation of fully-developed supersonic turbulent channel flows with dense vapors

This work aims to investigate the impact of the molecule-complexity effect and the non-ideal effect on wall-bounded turbulent flows by applying direct numerical simulation (DNS) to fully-developed channel flows of two typical organic vapors: R1233zd(E) and octamethyltrisiloxane (MDM). For each vapor, three thermodynamic states are analyzed: one in the dilute-gas region, one near the saturation line, and one in the supercritical region. For mean flow fields, it is found that, due to smaller Prandtl and Eckert numbers, both the molecule-complexity effect and the non-ideal effect reduce the mean temperature rise from the cold wall to the channel center. Meanwhile, the molecule-complexity effect weakens the mean density drop, while the non-ideal effect strengthens the drop. Furthermore, once the density and viscosity variations are considered, the mean streamwise velocity profiles of dense vapors are practically the same as the ideal gas. For turbulent fluctuations, it is found that the correlations between T′, p′, and ρ′ in dense vapors are more complicated than the ideal gas: for the ideal gas, fluctuations are dominated by “vorticity mode”; hence, ρ′ and T′ are strongly related to u′ but independent of p′; however, for dense vapors, “acoustic mode” can also play an important role. A newly derived equation illustrates that, through the “acoustic mode,” the molecule-complexity effect obviously enhances the positive correlation between ρ′ and p′, while the non-ideal effect can enhance the positive correlation between T′ and p′. Further analysis of instantaneous flow fields shows that p′ is isotropic. The isotropic character affects fluctuation magnitudes but has limited effect on the specified wall-direction turbulent transport. Consequently, Walz's equation and Reynolds analogy in terms of enthalpy are still valid. Finally, a comparison between the DNS energy budget and k equation of Reynolds-averaged Navier–Stokes (RANS) model has been carried out. Results show that obvious deviation happens on the production term in spite of the careful selection of eddy viscosity model.

Compressibility effect on flow characteristics over a circular cylinder at Reynolds number of 3900

The compressibility effect of flow over a circular cylinder has been investigated using wall-resolved large eddy simulation. The Reynolds number in terms of the freestream quantities and the cylinder diameter is fixed at 3900 while varying the freestream Mach number from 0.01 to 0.5. Mesh quality, numerical scheme, and subgrid-scale model are carefully verified prior to the detailed flow study. Results such as Mach number effects on the drag coefficient, the shape of the mean streamwise velocity profile in the near-wake, the length of the recirculation zone, and shear layer instability are provided. Although compressibility suppresses the Kelvin–Helmholtz instability and mixing process within the shear layer, it increases the velocity fluctuation in the boundary layer and the pressure difference between the freestream and recirculation zone, which intensifies the wake oscillation, shedding amplitude, thus shortens the recirculation zone significantly with the Mach number up to 0.5. This phenomenon is different from that found in lower Reynolds number cases where the length of the recirculation zone elongates as the Mach number increases. The deficit of the velocity profile shape in the near-wake depends on the length of the recirculation zone. Furthermore, inside the wake zone and near the cylinder back wall, two pairs of recirculation bubbles emerge as the Mach number increases.

Direct numerical simulation of channel flow with real surface roughness using a ghost cell immersed boundary method

This paper investigates the impact of real surface roughness on channel flow using direct numerical simulation assisted by a ghost cell immersed boundary method (DNS-GCIBM). The principles and implementations of DNS-GCIBM are first introduced. Two test cases, including the two-dimensional flow around a cylinder and the three-dimensional flow in a sinusoidal roughness channel are employed to demonstrate the practicability and accuracy of the proposed approach, especially in numerical studies on the rough wall-bounded flow. Using DNS-GCIBM, channel flows under conditions of Ma = 0.3 and Reτ≈300, with both the real-world and regular roughness surfaces are studied. The results are statistically analyzed using the triple decomposition technique. The outer layer similarity in the streamwise mean velocity and Reynolds stress profiles indicate that the impact of roughness on the boundary layer primarily localizes within roughness sub-layer. In the streamwise mean velocity profile, both regular and real-world roughness surfaces induce obvious increase to the roughness function ΔU+ as roughness height Ra increases, while discrepancy of ΔU+ between the two types of roughness can be found. Furthermore, turbulence statistics are sensitive to the variations of Ra. As Ra increases, it becomes challenging to organize coherent structures near the wall, resulting in the reduction of streamwise Reynolds stress intensity. In addition, although the skin friction coefficient and ΔU+ are almost the same, the real-world roughness and the corresponding equivalent regular roughness manifest different flow structures near the wall. The real-world roughness contributes greater spatial inhomogeneity but lower turbulence intensity.

Comparison of flow characteristics of plane jet impingement on a solid plate and on a sand bed

As compared to the well-researched case of a plane jet impinging on a solid plate, relatively rare attention was paid to the impingent on an erodible sand bed, which induces continuous bed transformations and interactively affects the jet development. The present study measured the flow of an impinging plane jet on a solid plate and on an erodible sand bed, respectively, by using particle image velocimetry technology, and then comparatively investigated the flow structure, main jet development and downstream wall jet development for the two cases. The results revealed that the jet impingement on the sand bed has a longer free jet region than that on the solid plate due to enlarged separation distance induced by localized scouring. The width of the plane jet impinging on the sand bed is larger than that on the plate by as high as five times the nozzle width, due to intensified interactions with the complex vortical structures in the concave scour hole. The impinging angle even decreases to negative values near the sand bed due to upward deflection of flow induced by bedform transformation. For both cases, however, the normalized streamwise mean velocity profiles exhibit universal self-similarity at different zones of jet development: specifically, the main jet and the wall jet satisfy exactly the same exponential function and the power law function, respectively.

Flow past two rotationally oscillating cylinders

Wake interaction of two rotationally oscillating cylinders in side-by-side configuration is studied experimentally at a Reynolds number of 150. Five spacing ratios, $T/D$ (ratio of centre-to-centre spacing to cylinder diameter), are considered, namely, 1.4, 1.8, 2.5, 4.0 and 7.5. Both in-phase and antiphase forcing are investigated. Oscillation amplitude is varied from ${\rm \pi} /8$ to ${\rm \pi}$ , and forcing frequency, $FR$ (ratio of the oscillation frequency to the vortex-shedding frequency of a stationary cylinder) is varied from 0 to 5. The experimental investigation is done using laser-induced fluorescence, hot film anemometry and particle-image velocimetry (PIV). The interaction between the two cylinders under forcing results in new wake modes and vortex structures and a comprehensive study from the wake visualisations is conducted. Quantitative results are presented in terms of streamwise and cross-stream mean velocity profiles, centreline velocity recovery, peak velocity deficit, wake width, fluctuation intensity, circulation, vorticity contours and drag coefficient. The magnitude of streamwise velocity deficit and cross-stream velocity variation is strongly affected by the presence of second cylinder. The recirculation region behind the cylinders is found to extend further downstream with increase in the forcing. Scaling analysis is carried out to express the peak velocity deficit variation with forcing. It is observed that the relative strength of the vortices shed from inner and outer shear layers depends on the phase of oscillation. An experimental set-up for direct force measurement is designed and the drag force acting on the oscillating cylinders assembly is directly measured and the effect of forcing on the variation of ${C}_{d}$ is studied. An estimate for drag coefficient is also made from the PIV data following a detailed control volume analysis. It is observed that the set of forcing parameters that correspond to maximum and minimum drag also yield extrema in the values of circulation and fluctuation intensity.

Outer-layer similarity and energy transfer in a rough-wall turbulent channel flow

Direct numerical simulations (DNSs) are performed to investigate the roughness effects on the statistical properties and the large-scale coherent structures in the turbulent channel flow over three-dimensional sinusoidal rough walls. The outer-layer similarities of mean streamwise velocity and Reynolds stresses are examined by systematically varying the roughness Reynolds number $k^{+}$ and the ratio of the roughness height to the half-channel height $k / \delta$ . The energy transfer mechanism of turbulent motions in the presence of roughness elements with different sizes is explored through spectral analysis of the transport equation of the two-point velocity correlation and the scale-energy path display of the generalized Kolmogorov equation. The results show that, with increasing $k^+$ , the downward shift of the mean streamwise velocity profile in the logarithmic region increases and the peak intensities of turbulent Reynolds stresses decrease. At an intermediate Reynolds number ( $Re_{\tau }= 1080$ ), the length scale and intensity of the large-scale coherent structures increase for a small roughness ( $k^{+}=10$ ), which leads to failure of the outer-layer similarity in rough-wall turbulence, and decrease for a large roughness ( $k^{+}=60$ ), as compared with the smooth-wall case. The existence of the small roughness ( $k^{+}=10$ ) enhances the mechanism of inverse energy cascade from the inner-layer small-scale structures to the outer-layer large-scale structures. Correspondingly, the self-sustaining processes of the outer-layer large-scale coherent structures, including turbulent production, interscale transport, pressure transport and spatial turbulent transport, are all enhanced, whereas the large roughness ( $k^{+}=60$ ) weakens the energy transfer between the inner and outer regions.

Direct numerical simulation of adverse pressure gradient turbulent boundary layer up to [formula omitted

A direct numerical simulation of a moderate adverse pressure gradient turbulent boundary layer flow on a flat plate was performed on a fairly long domain with a Reynolds number from Reθ≃2000 to Reθ≃8000. The mean streamwise velocity profile does not exhibit a clear log region even at the highest Reynolds number. The Reynolds stresses exhibit a well defined peak in the outer region which moves away from the wall before to stabilise at a wall distance y of 0.45 boundary layer thickness after evolving over 20 local boundary layer thicknesses. These outer peaks are the consequences of an excess of production over dissipation and they all scale with the shear stress velocity for wall distance 0.2δ<y<0.85δ. The different terms of the Reynolds stresses equations are analysed in the outer region and the analysis confirms that the leading terms are the same as for a zero pressure gradient turbulent boundary layer except that the production and dissipation are not negligible in the outer region. The most significant contribution of scales smaller than two Taylor scales is on the pressure strain term of the shear stress equation. The probability of the occurrence of small scale vortices conditioned by the presence of an ejection or a sweep shows that the shear stress contained in ejections is associated with the production and transport of near wall vortices away from the wall. The local mean shear generated by the sweeps increases the production of near wall vortices. Lastly, the large scale structures analysed by means of two point correlations of the streamwise fluctuating velocity are shown to be strongly modified by the adverse pressure gradient. The correlation reveals a decoupling between the near wall streaks and the large scale streamwise structures enhanced by the adverse pressure gradient.

Flow Control in a Rectangular Open Channel using Two Impermeable Spur Dikes: A Numerical Study

The present study examines how adjusting vegetation patches in a rectangular open channel with two impermeable spur dikes alters the displacement of the recirculation region. The Reynolds stress turbulence model is implemented via the 3D numerical code FLUENT (ANSYS). Mean stream-wise velocity profiles were drawn at selected positions and at mid of flow depth i.e., 3.5 cm, a horizontal plane is cut through the open channel for analyzing velocity contours and streamline flow. The findings indicate that the stream-wise velocity profiles showed fluctuations in the presence of different shapes and arrangement of cylindrical patch discussed and the maximum velocity within the field of spur dike is of the order of 0.018 m/s due to the prism shape. By changing the position of the cylindrical patch, the location of the recirculation region displaces within the field of impermeable spur dike.

On the application of statistical turbulence models to the simulation of airflow inside a car cabin

Computational fluid dynamics simulations of airflow inside a full-scale passenger car cabin are performed using the Reynolds averaged Navier–Stokes equations. The performance of a range of turbulence models is examined by reference to experimental results of the streamwise mean velocity and turbulence intensity profiles, obtained using the hot-wire anemometry technique at different locations inside the car cabin. The models include three linear eddy-viscosity-based variants, namely, the realizable k–ε, the renormalization group k–ε, and the shear-stress transport k–ω models. The baseline Reynolds stress model (BSL-RSM), a second-moment-closure variant, and an Explicit Algebraic Reynolds Stress Model (BSL-EARSM) are also investigated. Visualization of velocity vectors and streamlines in different longitudinal planes shows a similar airflow pattern. The flow topology is mainly characterized by jet flows developing from the dashboard air vents and extending to the back-seats compartment resulting in a large vortex structure. Additionally, a comparison between numerical and experimental results shows a relatively good agreement of the mean velocity profiles. However, all models exhibit some limitations in predicting the correct level of turbulence intensity. Moreover, the realizability of the modeled Reynolds stresses and the structure of turbulence are analyzed based on the anisotropy invariant mapping approach. All models reveal a few amounts of non-realizable solutions. The linear eddy-viscosity-based models return a prevailing isotropic turbulence state, while the BSL-RSM and the BSL-EARSM models display pronounced anisotropic turbulence states.

On the effect of streamwise and spanwise spacing to height ratios of three-dimensional sinusoidal roughness on turbulent boundary layers

A developing zero pressure gradient (ZPG) turbulent boundary layer (TBL) over different three-dimensional (3D) sinewave roughnesses is investigated experimentally using single hot-wire anemometry. Seven different sinewave profiles are fabricated with the same amplitude and with different wavelengths in the streamwise (sx) and spanwise (sz) directions. The effects of varying sx and sz on turbulence statistics and the drag coefficient (Cf) are assessed. The wall-unit normalized streamwise mean velocity profile is shifted downward compared with the smooth wall profile for all roughnesses. The streamwise spacing to height ratio sx/k has a more significant effect on the roughness function ΔU+ and Cf compared with the spanwise spacing to height ratio sz/k. However, sz/k has a large impact on the streamwise turbulence intensities in the log and outer layer. An excellent collapse is observed among the mean streamwise velocity profiles plotted in defect form in the outer region. However, a lack of similarity between TBLs over different rough surfaces is observed in the outer region for the turbulence intensities profiles. For isotropic 3D sinusoidal roughness (equal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing spacing to height ratios. For anisotropic 3D sinusoidal roughness (unequal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing sz/sx from half to two in this study.

PIV measurement of turbulent flow in curved ducts with variable curvature convex wall

The fully developed turbulent flow through 120° curved ducts with variable curvature convex wall is investigated using particle image velocimetry (PIV) over a range of Reynolds numbers from 2 × 104 to 1.4 × 105. The profile of the convex wall adopts the blade pattern of classic centrifugal pumps, namely, spiral line (SL) and involute line (IL). A new coordinate (so’R) with streamwise and curvature radial directions is introduced to adapt to the requirements of variable curvature. Based on coordinate transformation, the profiles of mean streamwise velocity (us) and centrifugal velocity (uR), positions of velocity extreme, vorticity, total shear stress and root mean square (rms) velocities (us’and uR’) under the new coordinate system (so’R) are analyzed to investigate the effects of variable curvature and Reynolds number. The results provide a useful reference to perform curvature correction of turbulence models and guide the design of fluid machinery with variable curvature flow channel.

Development of a Prediction Model of the Pedestrian Mean Velocity Based on LES of Random Building Arrays

Wind speed in urban areas is influenced by the interaction between wind flow and building geometry; at the pedestrian level, the interaction is more complex, particularly with high building density. This study investigated the wind velocity distribution and the mean velocity ratio at the pedestrian level using the large-eddy simulation (LES) database based on random building arrays of several plan area densities, λp. The heights of random buildings are between 0.36 h and 3.76 h where h = 0.025 m. Mean streamwise velocity profiles were obtained at the pedestrian level for all arrays and were found to decrease as λp increased. Wind flow patterns at the pedestrian level were highly influenced by adjacent buildings, especially in denser conditions, λp &gt; 0.17. The pedestrian-level mean velocity was obtained around each building, and the relationship between the local mean velocity ratio, Vp(t) and the local frontal area density, λf(t) was analyzed. Subsequently, a prediction model was formulated based on the building’s aspect ratio, αp; the correlation for high-rise buildings with 2.64 h ≤ αp ≤ 3.76 h was high at 0.8, while a lower correlation was obtained for lower buildings due to random positioning and surrounding geometric effects. Therefore, the impact of high-rise buildings on pedestrian wind velocity can be estimated more accurately using the formulated model.

Flow over embankment gabion weirs in free flow conditions

In this study, a series of laboratory tests were performed to investigate the effects of side ramp slope, crest length, and porous media properties on the flow regimes, water-surface profiles, discharge coefficients, and energy dissipation in embankment gabion weirs with upstream and downstream slopes. 24 physical models of solid and gabion weirs with three different upstream/downstream slopes (90°, 45° and 26.5°) were created. To investigate the complexity of flow over the porous-fluid interface and through the porous material, three-dimensional (3D) numerical simulations were developed. In numerical simulation, the standard k-ε turbulence model was utilized. A structured mesh domain was used to simulate the physical model. Water surface profiles above the porous weirs were used for comparison between the numerical simulations and measured data. These comparisons helped determine variables in the numerical simulations. Numerical simulation enables visualization of streamlines around and through the gabion weirs. In addition, mean stream wise velocity profiles above and within the porous structures were obtained. Numerical simulations showed that a reduction in the slope of the upstream face leads to an increased curvature of streamlines and the velocity distribution exhibits a non-uniform wavy shape due to the geometrical properties of the weirs. As the velocity profiles move downstream, the velocity distribution within the porous structures were more affected by the presence of the pores. The experimental results show that decreasing upstream slopes, from 90° to 26.5°, leads to decreased discharge coefficients. However, in all cases, gabion weirs lead to greater discharge coefficients than those of similar solid weirs. For milder side slopes, discharge ratios (flow passing through all faces of the gabion weirs over the inlet discharge) decreased nonlinearly. Moreover, with increasing the inlet discharge, relative energy dissipation was reduced up to 45% in gabion weirs.

Velocity measurements in developing narrow open-channel flows with high free-stream turbulence: Acoustic Doppler Velocimetry (ADV) vs Laser Doppler Anemometry (LDA)

A developing narrow open-channel flow has been investigated using Acoustic Doppler Velocimetry (ADV) and Laser Doppler Anemometry (LDA). The objectives were to first characterize the flow environment with the LDA system alone, then quantify the intrusion effect of the ADV sensor immersion, and finally compare ADV-LDA measurements. The main features of the flow have been described. The turbulence levels measured in the outer flow region are high and almost isotropic due to the specificities of the flow (3D, narrow, developing). This contributes to a flattening of the mean streamwise velocity profile in this region. The intrusion effect of the ADV sensor is found to be dependent on Froude number (Fr=U0/gH with U0 the discharge velocity, H the flow depth, and g the gravity acceleration). Vertical flow below the sensor is amplified while the streamwise component of the flow is enhanced for “low” Fr (≤0.6) and reduced for “high” Fr (≥1.1). On the other hand, turbulence quantities are not affected by the sensor presence. Compared to the LDA, the ADV is shown to underestimate the mean flow and turbulence intensities, while not affecting Reynolds shear stress measurements. The underestimation of the turbulence intensities can be attributed to the lower sampling rate and larger sampling volume of the ADV, but the underestimations of the mean velocities are more likely linked to a constant bias that the ADV seems to have or to some type of ADV-intrinsic noise. Some implications for practical application are discussed.

하이브리드 난류 모델을 이용한 전류고정덕트 후류의 고정도 수치 해석

A hybrid turbulence model has developed by combining a sub-grid scale model using dynamic k equation in LES with k-ω SST model of RANS equation. To ascertain potential applicability of the hybrid turbulence model, fully developed turbulent channel flows at ReSUBτ/SUB=180 have been simulated of which computational domain has a top wall with coarse cells and a bottom wall with fine cells. The streamwise mean velocity and turbulent intensity profiles showed a good agreement with DNS data when using the hybrid model rather than using a single model in k-ω SST or dynamic k equation models. Computational simulations of turbulent flows around KVLCC2 with a pre-swirl duct have been mainly performed using the hybrid turbulence model. Compared to the results obtained from RANS simulation with k-ω SST model as well as LES with dynamic k equation SGS model, turbulent wakes of the duct in the present simulation using the hybrid turbulence model were very similar to that of LES. Also, the resistances acting on hull, rudder and duct in hybrid turbulence model were similar to those in RANS simulation whereas the viscous forces acting on the hull in LES had a significant error due to coarse cells inappropriate to the sub-grid scale model.

A new equivalent sand grain roughness relation for two-dimensional rough wall turbulent boundary layers

The effects of different geometries of two-dimensional (2-D) roughness elements in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) on turbulence statistics and drag coefficient are assessed using single hot-wire anemometry. Three kinds of 2-D roughness are used: (i) circular rods with two different heights, $k= 1.6$ and 2.4 mm, and five different streamwise spacing of $s_{x}= 6k$ to $24k$ , (ii) three-dimensional (3-D) printed triangular ribs with heights of $k= 1.6$ mm and spacing of $s_{x}= 8k$ and (iii) computerized numerical control (CNC) machined sinewave surfaces with two different heights, $k= 1.6$ and 2.4 mm, and spacing of $s_{x}= 8k$ . These roughnesses cover a wide range of ratios of the boundary layer thickness to the roughness height ( $23 &lt; \delta /k &lt; 41$ ), where $\delta$ is the boundary layer thickness. All roughnesses cause a downward shift on the wall-unit normalised streamwise mean velocity profile when compared with the smooth wall profiles agreeing with the literature, with a maximum downward shift observed for $s_{x}= 8k$ . In the fully rough regime, the drag coefficient becomes independent of the Reynolds number. Changing the roughness height while maintaining the same spacing ratio $s_{x}/k$ exhibits little influence on the drag coefficient in the fully rough regime. On the other hand, the effective slope $(ES)$ and the height skewness $(k_{sk})$ appear to be major surface roughness parameters that affect the drag coefficient. These parameters are used in a new expression for $k_{s}$ , the equivalent sand grain roughness, developed for 2-D uniformly distributed roughness in the fully rough regime.

Outer turbulent boundary layer similarities for different 2D surface roughnesses at matched Reynolds number

The outer layer similarity in zero pressure gradient (ZPG) boundary layers developing over different geometries of 2D roughness elements is assessed, using single hotwire anemometry. Two types of 2D roughness are used: circular rods and sinewave surfaces with two different heights, k = 1.6, and 2.4 mm, and three different streamwise spacings, i.e. sx=8k,12k, and 16k. These roughnesses cover a range of ratios of the boundary layer thickness (δ) to the roughness height (k) from δ/k = 21 to 45. As expected, all roughnesses caused a downward shift on the wall-unit normalised streamwise mean velocity profiles compared with smooth wall profiles, with a maximum shift observed for rods with a spacing of sx=8k, while the minimum shift is noticed for a sinewave surface with a spacing of sx=16k. The defect velocity profiles collapse entirely for all smooth and rough wall flows when normalised by the friction velocity. It was found that the shape factor, H is a suitable scaling parameter for improving the collapse of the data when using the diagnostic plot. The inner peak of the turbulence intensity profiles for the sinewave roughness is reduced gradually with increasing Reynolds number while the turbulent boundary layer (TBL) develops from a transitionally to a fully rough regime. Meanwhile, this inner peak disappears completely for all rod roughnesses, as the TBL is always in a fully rough regime, and the profiles exhibit only an outer peak, located at a wall-normal location y/δ≈0.06. The results suggest that Townsends similarity hypothesis for 2D surface roughness is relatively well approximated in the outer region of the flow as reflected by the collapse of the distributions of velocity defect, turbulence intensity, skewness, and flatness when scaled with δ.

Wall-resolved and wall-modelled large-eddy simulation of plane Couette flow

We describe wall-resolved and wall-modelled large-eddy simulation (LES) of plane Couette (PC) flow. Subgrid-scale (SGS) motion is represented using the stretched-spiral vortex SGS model and the virtual wall model is employed for wall-modelled LES. Cases studied include direct numerical simulation (DNS) at friction Reynolds numbers $Re_\tau = 220$ , wall-resolved LES at $Re_\tau \sim 500\text {--}3600$ and wall-modelled LES at $Re_\tau \sim 3600\text {--}2.8\times 10^{5}$ . All LES performed show the presence of approximately spanwise periodic sets of streamwise rolls. Averaged (including spanwise) wall-normal profiles of the mean streamwise velocity show a consistent log region across all Reynolds numbers. Two distinct measures of turbulent intensity are explored, one of which recognizes the roll structure and one that does not. The spanwise variation of turbulence flow metrics is investigated. Mean streamwise velocity profiles show substantial spanwise variation but collapse well when normalized by local skin-friction velocities. Similar collapse is found for streamwise turbulent intensities. For all present LES, the mean skin-friction variation with the plate Reynolds number is found to match a simple analytical form (Pirozzoli et al., J. Fluid Mech., vol. 758, 2014, pp. 327–343) while the scaled centre-plane, mean-velocity gradient exhibits an inverse ProductLog dependence. Both the mean-flow roll energy and circulation, scaled with outer variables, decrease monotonically for $Re_\tau \gtrsim 500$ . At lower $Re_\tau$ , the mean streamwise zero-velocity line follows a wavy form in the spanwise direction, while at our larger $Re_\tau$ , a mushroom shape emerges which could potentially enhance local momentum transport in the spanwise direction and be responsible for the weakening of the spanwise rolls.

Experimental study on the development of wake vortices behind screen cylinders

This work examined the development of the large-scale vortex structures in the wake of two screen cylinders with porosities β = 48% and 61% in the intermediate region at a Reynolds number of 7000 using two X-type hot-wire probes. The screen cylinders were made of stainless steel screen meshes rolled into a cylindrical shape. The results were compared with those of a solid cylinder (β = 0%) under the same flow conditions. It was shown that the formation of the large-scale vortices in the screen cylinder wakes involves different mechanisms. For the screen cylinder with β = 48%, they were generated due to wake instability (Kármán vortex), which closely resembled that of a solid cylinder. In contrast, for the screen cylinder with β = 61%, the vortices were formed owing to the shear-layer (Kelvin–Helmholtz) convective instability. These findings were justified by the streamwise evolution of the vortex shedding frequency, a stability analysis in the near wake using the mean streamwise velocity profiles, and the coherent and incoherent wake structures obtained by the phase-averaged analysis at different downstream locations.