Low-speed Structures Research Articles

Turbulent/non-turbulent interface of the turbulent boundary-layer over a spanwise-heterogeneous converging/diverging riblets rough wall

Turbulent boundary layer (TBL) flows over various spanwise-heterogeneous rough walls exhibit spanwise variations in turbulence statistics, implying modifications of the turbulent/non-turbulent interface (T/NTI). In this work, based on the datasets of TBL flows over a spanwise-alternating converging/diverging riblets wall, we investigate behavior of T/NTI, properties of ‘bubble’ and ‘drop’ that are associated with T/NTI, as well as connections between T/NTI and large-scale structures within the boundary layer. The flow datasets were obtained through stereoscopic particle image velocimetry measurements on the cross-stream plane of the TBL flow at a Reynolds number Reθ = 1.3 × 104. The T/NTI and associated ‘bubble’ and ‘drop’ are identified using a kinetic energy criterion, while the large-scale structures by a streak detection algorithm. It is observed that the T/NTI height and the occurrence of ‘bubble’ and ‘drop’ display a spanwise-heterogeneous feature, with lower T/NTI height and higher occurrence probability of ‘bubble’ over the diverging section of riblets than over the converging section of riblets. Results of conditional average show that the ‘bubble’ is associated with positive streamwise fluctuations, common-down flow and a pair of counter-rotating streamwise vortices, while the ‘drop’ with negative streamwise fluctuation, common-up flow and a pair of counter-rotating streamwise vortices. Probability density functions of the ‘bubble’ size and fractal dimensions of the T/NTI are found similar for both the riblets and smooth wall flows. Furthermore, it is observed that the large-scale low-speed structures occurring preferentially over the converging section of riblets play a role in elevating T/NTI while the large-scale high-speed ones over the diverging section of riblets lowering down T/NTI.

Backflow structures in turbulent pipe flows at low to moderate Reynolds numbers

The statistical characteristics and the evolution of the backflow structures are investigated in wall-bounded flows at Reynolds numbers up to $Re_{\tau }=1000$ . The backflow is caused by the joining of large-scale high- and low-speed structures in the vicinity of the wall and is formed at the tail tip of the low-speed structure. The distribution density of the backflow structures and the percentage area of the backflow region on the wall both increase with the Reynolds number. The backflow structures have an average lifespan of 8 wall units which is found to be slightly longer in the pipe than the channel, and they are convected downstream at the average velocities of the buffer region of approximately 10 wall units, similar to Cardesa et al. (J. Fluid Mech., vol. 880, 2019, R3). The backflow structures occasionally split and merge, and can form detached from the wall. Evidence shows that the split, merged and wall-detached backflow structures are caused by the near-wall structures. The split backflow structures are on average, larger and more spanwise-elongated which are split due to the spanwise shearing of the near-wall streaks. A backflow structure is formed detached from the wall when the trailing end of its carrier low-speed structure ‘sits’ on the near-wall high-speed streaks. The wall-detached backflow structures tend to become wall-attached by approaching the wall when undergoing a similar life cycle to the normal backflow of growth and decay with spanwise elongation because the backflow region at the tail of the low-speed structure is continuously pressed down to the wall by the high-speed structure driven by persistent vortical structures in the buffer region.

Compressibility effects on statistics and coherent structures of compressible turbulent mixing layers

The effects of compressibility on the statistics and coherent structures of a temporally developing mixing layer are studied using numerical simulations at convective Mach numbers ranging from $M_c=0.2$ to $1.8$ and at Taylor Reynolds numbers up to 290. As the convective Mach number increases, the streamwise dissipation becomes more effective to suppress the turbulent kinetic energy. At $M_c=1.8$ , the streamwise dissipation increases much faster than the other two components in the transition region, even larger than pressure–strain redistribution, correlating with the streamwise elongated vortical structures at a higher level of compressibility. We confirm the existence of the large-scale high- and low-speed structures in the mixing layers, which accompany the spanwise Kelvin–Helmholtz rollers at low convective Mach number and dominate the mixing layer at higher convective Mach number. Conditional statistics demonstrate that the large-scale low-speed structures are lifted upwards by a pair of counter-rotating quasi-streamwise rollers flanking the structures. The small-scale vortical structures have an apparent preference for clustering into the top of the low-speed regions, which is directly associated with high-shearing motions on top of the low-speed structures. The high-speed structures statistically exhibit central symmetry with the low-speed structures. The statistics and dynamics of large-scale high- and low-speed structures in the compressible mixing layers resemble those in the outer region of the turbulent boundary layers, which reveals the universality of the large-scale structures in free shear and wall-bounded turbulence. A conceptual model is introduced for the large-scale high- and low-speed structures in turbulent mixing layers.

Experimental measurement of coherent structures in turbulent boundary layers using moving time-resolved particle image velocimetry

A moving time-resolved particle image velocimetry (MTRPIV) system was designed to measure the turbulent boundary layer (TBL). The combination of time-resolved particle image velocimetry and a translational moving system enables the MTRPIV to track the coherent structures with a long period and high temporal resolution. Based on the MTRPIV, the time-evolving of coherent structures within the TBL was measured and analyzed. The observation of the large-scale sweep collision with ejection shows that the strong collision causes the large-scale high- and low-speed coherent structures to break down. The time-evolving process of the hairpin packets shows that the low-speed fluid mass under the hairpin vortices is important for the generation of a whole hairpin packet. The small-scale low-speed structures increase their spatial scales by merging so that the independent hairpin vortices can be organized by merged larger-scale structures. The shear layer exceeding the length of 0.7–0.8 δ (δ is thickness of TBL) or 350–400 υUτ (υ and Uτ denote the kinematic viscosity and friction velocity, respectively) is unstable, and it will roll-up to generate a hairpin vortex. In the hairpin packet growth process, the inclination angle of the hairpin packet decreases from ∼13° to 8° in a time duration of 120 υUτ2, and the underlying low-speed fluid is elongated and then split. The analysis of the uniform momentum zones (UMZs) shows that the topmost UMZ has a relatively stable wall-normal position and convection speed. The lower UMZ is quasi-periodically generated and tends to move upward to merge with the upper UMZs. The hairpin packets impact the lower UMZs by inducing large-scale low-speed fluid mass to modulate the probability density function distribution of instantaneous streamwise velocity. The evolution of UMZs with velocity less than 0.5U∞ (U∞ denotes the free-stream velocity) is the result of the interaction of large- and small-scale streamwise fluctuation velocity.

On the structure of streamwise wall-shear stress fluctuations in turbulent channel flows

In this study, we use a two-dimensional clustering methodology to identify the high-and low-speed structures of the streamwise wall-shear fluctuations in turbulent channel flows at different Reynolds numbers. The statistical properties of the high- and low-speed structures, such as geometrical characteristics, fluctuating intensities and conditional velocity fluctuations, are shown to be remarkably asymmetrical. The low-speed structures are closely related with the celebrated attached eddies. Our work may aid to the future development of the attached-eddy model.

Local transport of passive scalar released from a point source in a turbulent boundary layer

Simultaneous measurements of streamwise velocity ($\tilde{U}$) and concentration ($\tilde{C}$) for a horizontal plume released at eight different vertical locations within a turbulent boundary layer are discussed in this paper. These are supplemented by limited simultaneous three-component velocity and concentration measurements. Results of the integral time scale ($\unicode[STIX]{x1D70F}_{c}$) of concentration fluctuations across the width of the plume are presented here for the first time. It is found that$\unicode[STIX]{x1D70F}_{c}$has two distinct peaks: one closer to the plume centreline and the other at a vertical distance of plume half-width above the centreline. The time-averaged streamwise concentration flux is found to be positive and negative, respectively, below and above the plume centreline. This behaviour is a resultant of wall-normal velocity fluctuations ($w$) and Reynolds shear stress ($\overline{uw}$). Confirmation of these observations is found in the results of joint probability density functions of$u$(streamwise velocity fluctuations) and$\tilde{C}$as well as that of$w$and$\tilde{C}$. Results of cross-correlation coefficient show that high- and low-momentum regions have a distinctive role in the transport of passive scalar. Above the plume centreline, low-speed structures have a lead over the meandering plume, while high-momentum regions are seen to lag behind the plume below its centreline. Further examination of the phase relationship between time-varying$u$and$c$(concentration fluctuations) via cross-spectrum analysis is consistent with this observation. Based on these observations, a phenomenological model is presented for the relative arrangement of a passive scalar plume with respect to large-scale velocity structures in the flow.

Structural differences between small and large momentum-defect turbulent boundary layers

We analyse how coherent structures in turbulent boundary layers (TBL) change in response to a strong adverse pressure gradient by using two direct numerical simulation databases. One zone of a zero-pressure-gradient TBL and three zones of a strongly decelerated TBL, corresponding to three ranges of mean velocity defect, with the shape factor varying from 1.54 to 3.75, are considered. We investigate the properties of three-dimensional sweeps, ejections and streamwise-velocity structures. The identified sweeps and ejections contribute everywhere more than 30% to the Reynolds shear stress in both flows. The effect of increasing mean velocity defect in the adverse-pressure-gradient TBL is significant. Streamwise-velocity structures and all wall-attached sweeps and ejections, that is near-wall ones and taller ones that reach the wall region (important in the logarithmic layer of the zero-pressure-gradient TBL), lose their streamwise elongation and become less organised. Wall-attached sweeps and ejections become progressively less numerous and spanwise elongated structures become more frequent. Their strength diminishes in comparison to wall-detached ones and they lose their role as the main contributors to the Reynolds shear stress. In terms of spatial organisation, a pair of side-by-side sweep and ejection is still the dominant configuration, but the probability of such an event has decreased. This fact, together with other results of spatial organisation of structures, does not point toward the presence of a Kelvin-Helmholtz-type instability or a varicose instability of low-speed structures in the outer region, two instabilities that have been suggested in the literature to explain the turbulence regeneration process in large velocity defect turbulent boundary layers.

Influence of a large-eddy breakup device on the frictional drag in a turbulent boundary layer

A direct numerical simulation of a spatially developing turbulent boundary layer with a large-eddy breakup (LEBU) device was performed to investigate the influence of the LEBU device on the near-wall turbulence and frictional drag. The LEBU device, which is thin and rectangular in shape, was located at 80% of the boundary layer thickness (δ). The LEBU device reduced the skin-friction coefficient (Cf) up to 17%. The breakdown of the outer structures passing through the LEBU device reduced the energy of the long wavelength motions (λz+>200) along the wall-normal direction. The reduction of Cf mainly arose from the contribution of the Reynolds shear stress by the difference in the spatial coherence of the outer high- and low-speed structures. We investigated the relationship between the large-scale motions and the velocity–vorticity correlations (vωz and −wωy), which directly contribute to Cf. The contributions of vωz and −wωy accounted for 80% of the total Cf reduction. The amount of the Cf reduction induced by vortex stretching arose from the contributions of the intense positive uL (uL+≈2) and the relatively weak negative uL (uL+≈−0.7). Owing to the negative contribution of the advective vorticity transport, the total Cf reduction was obtained under the negative uL even though drag reduction was achieved by the suppression of vortex stretching under the intense positive uL.

Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers

The effect of large-scale motions (LSMs) on the turbulent/non-turbulent (T/NT) interface is examined in a turbulent boundary layer. Using flow fields from direct numerical simulation, the shape of the interface and near-interface statistics are evaluated conditional on the position of the LSM. The T/NT interface is identified using the vorticity magnitude and a streak detection algorithm is adopted to identify and track the LSMs. Two-point correlation and spectral analysis of variations in the interface height show that the spatial undulation of the interface is longer in streamwise wavelength than the boundary-layer thickness, and grows with the Reynolds number in a similar manner to the LSMs. The average variation in the interface height was evaluated conditional on the position of the LSMs. The result provides statistical evidence that the interface is locally modulated by the LSMs in both the streamwise and spanwise directions. The modulation is different when the coherent structure is high- versus low-speed motion: high-speed structures lead to a wedge-shaped deformation of the T/NT interface, which causes an anti-correlation between the angles of the interface and the internal shear layer. On the other hand, low-speed structures are correlated with crests in the interface. Finally, the sudden changes in turbulence statistics across the interface are in line with the changes in the population of low-speed structures, which consist of slower mean streamwise velocity and stronger turbulence than the high-speed counterparts.

Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer

An array of surface hot-film shear-stress sensors together with a traversing hot-wire probe is used to identify the conditional structure associated with a large-scale skin-friction event in a high-Reynolds-number turbulent boundary layer. It is found that the large-scale skin-friction events convect at a velocity that is much faster than the local mean in the near-wall region (the convection velocity for large-scale skin-friction fluctuations is found to be close to the local mean at the midpoint of the logarithmic region). Instantaneous shear-stress data indicate the presence of large-scale structures at the wall that are comparable in scale and arrangement to the superstructure events that have been previously observed to populate the logarithmic regions of turbulent boundary layers. Conditional averages of streamwise velocity computed based on a low skin-friction footprint at the wall offer a wider three-dimensional view of the average superstructure event. These events consist of highly elongated forward-leaning low-speed structures, flanked on either side by high-speed events of similar general form. An analysis of small-scale energy associated with these large-scale events reveals that the small-scale velocity fluctuations are attenuated near the wall and upstream of a low skin-friction event, while downstream and above the low skin-friction event, the fluctuations are significantly amplified. In general, it is observed that the attenuation and amplification of the small-scale energy seems to approximately align with large-scale regions of streamwise acceleration and deceleration, respectively. Further conditional averaging based on streamwise skin-friction gradients confirms this observation. A conditioning scheme to detect the presence of meandering large-scale structures is also proposed. The large-scale meandering events are shown to be a possible source of the strong streamwise velocity gradients, and as such play a significant role in modulating the small-scale motions.

Visualization of Shear Stress With Micro Imaging Chip and Discrete Wavelet Transform

The two-dimensional low-speed structure of a turbulent boundary layer has been clearly visualized by a combination of a shear stress sensor using micro electro mechanical systems and the discrete wavelet transform. The application of two-dimensional discrete wavelet transforms to the visualization of wall shear stress data obtained using the micro shear stress imaging chip is described. The experiment was carried out under various Reynolds number conditions. It is shown that it is possible to visualize the low-speed streak structure as contours of two-dimensional wavelet level corresponding to spanwise wave number as a function of Reynolds number.

Detection of coherent structures in a turbulent boundary layer using a scanning LDV system

A scanning laser-Doppler velocimetric (LDV) system was used for detecting coherent structures in a turbulent boundary layer. This scanning LDV system gives instantaneous velocity profiles that enable uus to develop a new coherent structure detection technique based on the spatial structure of an event. This spatial detection was found to be relatively independent of threshold. A conditional sampling analysis based on the spatial size and location of low-speed structures indicated movement of the low-speed structure away from the wall corresponding to the movement of a high-speed structure toward the wall.