Spanwise Vortices Research Articles

Particles in turbulent separated flow over a bump: Effect of the Stokes number and lift force

Particle-laden turbulent flow that separates due to a bump inside a channel is simulated to analyze the effects of the Stokes number and the lift force on the particle spatial distribution. The fluid friction Reynolds number is approximately 900 over the bump, the highest achieved for similar computational domains. The presence of the bump creates a complex background flow with a recirculating region and a strong shear layer. A range of particle Stokes numbers are considered, each simulated with and without the lift force in the particle dynamic equation. The effect of the lift force on the particle concentration is dominant in regions of high spanwise vorticity, particularly at the walls and in the shear layer. The concentration change is of the order of thousands when compared to cases where the lift force is omitted. At a low Stokes number, the particles segregate at both top and bottom walls and are present in the recirculating region. As the Stokes number increases, particles bypass the recirculating region and their redistribution is mostly affected by the strong shear layer. Particles segregate at the walls and particularly accumulate in secondary recirculating regions behind the bump. At higher Stokes numbers, the particles create reflection layers of high concentration due to their inertia as they are diverted by the bump. The fluid flow is less influential, and this enables the particles to enter the recirculating region by rebounding off walls and create a focused spot of high particle concentration.

Three-dimensional visualization of destruction events of turbulent momentum transfer in a plane jet

Destruction events of momentum transfer as represented by the Reynolds (shear) stress via the pressure–rate-of-strain interaction in a plane jet are investigated using direct numerical simulation data. To obtain three-dimensional pictures of the turbulent structures, pseudo-three-dimensional data are constructed on the basis of Taylor’s frozen hypothesis from time series of the relevant quantities. The coherent motion in the plane jet is extracted by means of conditional sampling analogous to variable-interval time averaging. We obtain a large-scale coherent structure consisting of horseshoelike vortices and a Kármán-vortex-like very large spanwise vortex street. Furthermore, we find that the active Reynolds stress destruction is localized around the large-scale coherent vortex structure. However, the coherent structure itself does not contribute to the Reynolds stress destruction, but the remaining incoherent motions do. For the significant pressure–rate-of-strain events in the incoherent motion, we display invariant maps of the velocity gradient tensor and the principal axes of strain to facilitate a discussion of the consistency of the numerical results with an illustration by Hinze [Turbulence, 2nd ed. (McGraw-Hill, 1975), pp. 325–328] and with our own experimental results [Takahashi et al., “Experimental investigation on destruction of Reynolds stress in a plane jet,” Exp. Fluids 60, 46 (2019)]. Consequently, the present results suggest that the illustration of the Reynolds stress destruction by Hinze is not completely applicable to a plane jet.

Numerical simulations of flows around a dual step cylinder with different diameter ratios at low Reynolds number

Abstract Flows around a dual step cylinder are numerically investigated at a Reynolds number of 200 for three diameter ratios (D/d) of 2, 1.43 and 1.19. Simulation results reveal three distinctive vortex shedding modes: (i) the N-S mode for D/ d = 2 , (ii) the transition mode for D/ d = 1 . 43 , and (iii) the L-S mode for D/ d = 1 . 19 . The vortex shedding frequency transition from the smaller-diameter cylinder to the larger-diameter one, the dominant shedding frequency downstream of the larger cylinder, and the vortex interactions exhibit significant differences in the three vortex shedding modes. As D/ d = 2 , the direct cross-boundary and half-loop connections take place downstream of the step where vortex dislocations are essentially fixed. When decreasing D/d, two new vortex interactions, the double-half-loop and three-half-loop connections, appear with a larger spanwise vortex dislocation occurrence range. In addition, flows in different D/d cases are governed by a distinctive vortex shedding law. A pair of streamwise vortices occur downstream the centroid of the larger cylinder. This reduces the cylinder step effect on the local vortex shedding, absorbing the shear layer of the spanwise N-cell vortices, and making the hydrodynamic force coefficients smaller. Interestingly, these fluid force coefficients further decrease as D/d increases.

Analysis of the Interconnections between Classic Vortex Models of Coherent Structures Based on DNS Data

Low- and high-speed streaks (ejection, Q2, and sweep, Q4, events in quadrant analysis) are significant features of coherent structures in turbulent flow. Streak formation is closely related to turbulent structures in several vortex models, such as attached eddy models, streamwise vortex analysis models, and hairpin vortex models, which are all standard models. Vortex models are complex, whereby the relationships among the different vortex models are unclear; thus, further studies are still needed to complete our understanding of vortices. In this study, 30 sets of direct numerical simulation (DNS) data were obtained to analyze the mechanics of the formation of coherent structures. Image processing techniques and statistical analysis were used to identify and quantify streak characteristics. We used a method of vortex recognition to extract spanwise vortices in the x–z plane. Analysis of the interactions among coherent structures showed that the three standard vortex models all gave reasonably close results. The attached eddy vortex model provides a good explanation of the linear dimensions of streaky structures with respect to the water depth and Q2 and Q4 events, whereby it can be augmented to form the quasi-streamwise vortex model. The legs of a hairpin vortex envelop low-speed streaky structures and so move in the streamwise direction; lower-velocity vortex legs also gradually accumulate into a streamwise vortex. Statistical analysis allowed us to combine our present results with some previous research results to propose a mechanism for the formation of streaky structures. This study provides a deeper understanding of the interrelationships among different vortex models.

Large-eddy simulation of the effect of distributed plasma forcing on the wake of a circular cylinder

We conducted large-eddy simulation (LES) to investigate the effect of segmented plasma forcing on the wake of a circular cylinder, at a subcritical Reynolds number of 4700. The action of the plasma actuators was simulated by a body-force model developed by Shyy et al. [1]. The main objective of this study was to investigate the changes in the three-dimensionality of the wake, and the nature of separation on the cylinder surface, with the increasing power of segmented forcing. By observing the three-dimensional (3D) structures, and the separating streamlines close to the cylinder surface, we aim to provide more insight on the experimental findings of Bhattacharya and Gregory [2], which contained only two-dimensional (2D) velocity field data. To that end, we used segmented actuators with a spatial wavelength of 5d (d= cylinder diameter), and two separate blowing ratios of 0.2 and 0.7. At the lower blowing ratio (BR=0.2), spanwise vortex shedding was not canceled, although waviness developed in the spanwise vortices. However, there was no considerable difference in the separation angles between two adjacent spanwise locations. Forcing with higher blowing ratio (BR=0.7) completely disrupted the vortex shedding infront of the plasma region. The separation line on the surface of the cylinder developed significant periodicity leading to a spanwise variation of formation length. We show that such spanwise variation created spatially locked streamwise vortices which disrupted regular vortex shedding.

Noise Reduction Mechanisms of an Airfoil with Trailing Edge Serrations at Low Mach Number

Trailing-edge serrations have proven to be valid applications of trailing edge noise mitigation for an airfoil, while the physical noise reduction mechanism has not been adequately studied. We performed simulations employing Large-eddy simulation and the Lighthill–Curle method to reveal the variation in the hydrodynamic field and sound source due to the trailing edge serrations. The grid resolution and computational results were validated against experimental data. The simulation results show that: the trailing edge serrations impede the growth of spanwise vortices and promote the development of streamwise vortices near the trailing edge and the wake; the velocity fluctuations in the vertical cross-section of the streamwise direction near the trailing edge are reduced for the serrated airfoil, thereby obviously reducing the strength of the pressure fluctuations near the trailing edge; and the trailing edge serrations decrease the distribution of the sound source near the trailing edge and reduce the local peak value of sound pressure level in a specific frequency range as well as the overall sound pressure level. Moreover, we observed that, in the flow around the NACA0012 airfoil, the location where the strong sound source distribution begins to appear is in good agreement with the location where the separated boundary layer reattaches. It is therefore effective to reduce trailing edge noise by applying serrations on the upstream of the reattachment point.

Numerical Investigation of Multi-SDBD Plasma Actuators for Controlling Fluctuating Wind Load on Building Roofs

The present research aims to explore, by large-eddy simulation (LES), the potentiality and mechanism of multiple surface dielectric barrier discharge (multi-SDBD) plasma actuators to manipulate mean and fluctuating wind loads on a low-rise building. Three actuator configurations are located on the roof to induce directional wall jets in different directions. The effects of these configurations on flow structure and wind loads are studied in absence and presence of approaching flow. Results show that all subgrid-scale models can obtain accurate roof pressure, and for the diffusion and convection terms, the bounded central differencing scheme can provide more accurate predictions for the roof pressure. The control impact of active actuators gradually weakens with the increase of the approaching flow velocity. The direction of the wall jet can determine the position of the limited roof region with the reduced mean pressure coefficient. The multi-SDBD actuators continue to absorb the upstream flow and blow this flow downstream, meaning the wall jet exerts strong pressure on the local roof area at the end of the jet, which results in a significant reduction of the mean pressure coefficient. Furthermore, the counter-rotating vortices caused by the wall jet restrain the size and strength of the vortex shedding, thereby achieving the purpose of reducing the fluctuating pressure coefficient. Further analysis of the instantaneous vorticity fields indicates that the intensity and size of streamwise shedding vortices can be restrained by small-scale spanwise vortices induced by the plasma actuators. Under the action of the wall jet blowing from the trailing edge to the leading edge, the fluctuating lift and drag coefficients can be reduced by over 15% and the fluctuating pressure coefficient can be reduced by about 20% from the no actuation situation.

DNS in evolution of vorticity and sign relationship in wake transition of a circular cylinder: (pure) mode A

In the present paper, the spatio-temporal evolution of vorticity in the first wake instability, i.e., (pure) mode A, is investigated in order to understand the wake vortex dynamics and sign relationships among vorticity components. Direct numerical simulation (DNS) for the flow past a circular cylinder is performed, typically at a Reynolds number of 200, in the three-dimensional (3-D) wake transition. According to characteristics of time histories of fluid forces, three different stages are identified as the computational transition, the initial stage and fully developed wake. In the second initial stage, the original two-dimensional spanwise vortices become obviously three-dimensional associated with the streamwise or vertical vorticity intensified up to about 0.1. As a matter of fact, these additional vorticities, caused by the intrinsic 3-D instability, are already generated firstly on cylinder surfaces early in the computational transition, indicating that the three-dimensionality appeared early near the cylinder. The evolution of additional components of vorticity with features the same as mode A shows that (pure) mode A can be already formed in the late computational transition. Through careful analysis of the vorticity field on the front surface, in the shear layers and near wake at typical times, two sign laws are obtained. They illustrate intrinsic relationships among three vorticity components, irrelevant to the wavelength or Fourier mode and Reynolds number in (pure) mode A. Most importantly, the origin of streamwise vortices is found and explained by a new physical mechanism based on the theory of vortex-induced vortex. As a result, the whole process of formation and shedding vortices with these vorticities is firstly and completely illustrated. Other characteristics are presented in detail.

Heat transfer and flow characteristics of forced convection in PDMS microchannel heat sink

Recently, microfluidic devices are being widely used in various heat transfer applications and, thermal management in microchannels is a challenging issue. As a solution, different types of microchannel heat sinks have been employed to enhance the heat transfer. The flow characteristics in the microchannel heat sink have influence on the heat transfer rate and thermal management performance. Therefore, the simultaneous measurement of temperature and velocity fields is highly required to understand the single-phase heat transfer phenomena in the PDMS microchannel heat sink. In this study, μPIV-μLIF technique which can provide the velocity and temperature field information of micro-scale thermofluid flow was newly developed to analyze the heat transfer of forced convection in PDMS microchannel heat sink. Especially, flow characteristics in the microchannel heat sink were systematically investigated. At a high Re flow (Re = 10) with heating, a high-speed crossflow occurs in the microchannel heat sink. Spanwise vorticity and Reynolds shear stress, which contribute to heat transfer in the microchannel, exhibit higher values at Re = 10 with heating compared to the non-heating case. Variations in velocity and local Nu number were also compared to explain heat transfer enhancement in the microchannel heat sink. Temporal variations in the temperature field were evaluated to demonstrate the effect of flow on heat transfer. The results presented herein would be helpful for understanding heat transfer in microscale thermofluid flows and for designing microscale heat transfer devices.

Numerical identification of separation bubble in an ultra-high-lift turbine cascade using URANS simulation and proper orthogonal decomposition

The flow-field inside a gas turbine engine, especially in the low-pressure turbine, is very complicated as it is normally accompanied by unsteady flow structures, strong and rapidly changing pressure gradients, intermittent transition of boundary layer, and flow separation and reattachment, especially during off-design performance. In this article, flow separation and reattachment on the suction side of an ultra-high-lift low-pressure turbine blade is studied and characterized using 3D Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. For turbulence modeling, transitional-SST method (γ-Reθ) is adopted. The simulations are performed at the exit Reynolds numbers of 200,000 and 60,000, and at a constant isentropic exit Mach number of 0.4. The shape and extent of the separation bubble are primarily dependent on large vortical structures due to the Kelvin-Helmholtz instability and spanwise vortex tube shedding. Therefore, a better prediction of these phenomena could result in a more realistic separation bubble identification and consequently more accurate profile loss assessment. In order to better capture the transitional flow characteristics, which are not often readily available from conventional computational fluid dynamics simulations, the method of Proper Orthogonal Decomposition (POD) is used in this study. Non-coherent structures in the main flow, such as separation bubble, are investigated and studied. The POD modes of pressure-field are analyzed to clarify the generation of spanwise vortex tubes after separation point. In the higher Reynolds number, low-energy small-scale structures in the separation zone and downstream of the trailing edge are observed from the POD analysis. In the lower Reynolds number, high-energy large-scale structures shed from the separated shear layer are identified, which are responsible for increasing turbulent kinetic energy as well as increasing profile losses. This study also shows that the combination of URANS and POD can successfully be used to identify the separation bubble.

Statistical analysis of vortical structures in turbulent boundary layer over directional grooved surface pattern with spanwise heterogeneity

We examine the turbulent boundary layers developing over convergent-divergent riblets (C-D riblets) with three different heights (h+ = 8, 14, and 20) at Reθ = 723 using particle image velocimetry. It is observed that although a logarithmic region presents in the velocity profiles over the converging and diverging line, Townsend’s outer-layer similarity hypothesis is invalid. Compared to the smooth-wall case, C-D riblets with a height of 2.4% of the smooth-wall boundary layer thickness can cause a significant increase in the turbulence production activities over the converging region, as evidenced by a more than 50% increase in the turbulent shear stress and in the population of prograde and retrograde spanwise vortices. In contrast, the impact of riblets on the diverging region is much smaller. The slope of vortex packets becomes steeper, and they are more streamwise stretched in the outer layer over the diverging region, whereas their shape and orientation is less affected over the converging region. Furthermore, the number of uniform momentum zones across the boundary layer increases over the converging region, causing a reduction in the thickness of uniform momentum zones in the outer part of the boundary layer. Overall, while an increased riblet height affects a large portion of the boundary layer away from the wall over the converging region, the impact on the diverging region is largely confined within the near-wall region. Such distinct differences in the response of the boundary layer over the diverging and converging region are attributed to the opposite local secondary flow motion induced by C-D riblets.

Effects of heat transfer on separated boundary layer behavior under adverse pressure gradients

Separated boundary layers in a converging-diverging channel under two different wall heat transfer conditions, including the adiabatic wall and the cooled isothermal wall, have been investigated by using a large eddy simulation (LES) code coupled with a wall heat transfer module. The wall temperature of the cooled isothermal wall is 0.8 times of the inflow temperature, which is a typical value in a low-pressure turbine. The pressure distribution of the converging-diverging channel bottom wall is similar to that of a typical low-pressure turbine blade suction surface. The flow conditions are set as the exit isentropic Reynolds number (Re = 60,154) and the exit isentropic Mach number (Ma = 0.402). The results show that the cooled isothermal wall condition can increase the static pressure rise coefficient significantly, accelerate the transition process of the separation boundary layer, and suppress the separation. Furthermore, the cooled isothermal wall condition can decrease the frequency of the large-scale spanwise vortex rolled-up, reducing the influence of the spanwise vortex on the separated shear layer and decreasing the scales of the downstream hairpin vortex. In addition, the instability of the separated shear layer can be regarded as the superposition result of both the Tollmien-Schlichting (T-S) instability mechanism and the Kelvin-Helmholtz (K-H) instability mechanism, while the K-H instability mechanism on the whole is slightly more dominant in the presence of separation and reattachment. This trend is more obvious under the cooled isothermal wall condition.

Low-frequency dynamics of the flow around a finite-length square cylinder

Fluctuating pressure on the side faces, lee-ward face and free end of a finite-length square cylinder is measured simultaneously, together with the velocity in its free-end shear flow, to reveal their inherent connection. The width (d) of the tested model is 40 mm, and the aspect ratio is 5. All experiments are conducted in a low-speed wind tunnel at an oncoming flow velocity (U∞) of 10 m/s. The corresponding Reynolds number based on U∞ and d is 27,000. It is found that, the fluctuating pressure on the side faces and free end has remarkable low-frequency instability with the frequency of about 1/10 of the well-known spanwise Karman vortex shedding. Besides, a high-frequency component, corresponding to Karman vortex shedding, is also found in the fluctuating pressure on cylinder side faces. The low-frequency instability is in phase over the entire cylinder span, while the high-frequency component tends to be out of phase, especially at the lower part of the cylinder. The free-end shear flow flaps at the low frequency and strongly correlates with the modes of spanwise vortex shedding. Particularly, when the free-end shear flow flaps to its lower position, alternate spanwise vortex shedding with high pressure fluctuation occurs; when it flaps to its upper position, the occurrence probability of co-shedding with low pressure fluctuation increases significantly especially near the cylinder free end.

Experimental study on dominant vortex structures in near-wall region of turbulent boundary layer based on tomographic particle image velocimetry

Vortex structures are very popular research objects in turbulent boundary layers (TBLs) because of their prime importance in turbulence modelling. This work performs a tomographic particle image velocimetry measurement on the near-wall region ($y<0.1\unicode[STIX]{x1D6FF}$) of TBLs at three Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=1238$, 2286 and 3081. The main attention is paid to the wall-normal evolution of the vortex geometries and topologies. The vortex is identified with swirl strength ($\unicode[STIX]{x1D706}_{ci}$), and its orientation is recognized by using the real eigenvector of the velocity gradient tensor. The vortex inclination angles in the streamwise–wall-normal plane and in the streamwise–spanwise plane as functions of wall-normal positions are investigated, which provide useful information to speculate on the three-dimensional shape of the vortex tubes in a TBL. The difference between the orientations of vorticity and swirl is discussed and their inherent relationship is revealed based on the governing equation of vorticity. Linear stochastic estimation (LSE) is further deployed to directly extract three-dimensional vortex models. The LSE velocity fields for ejection events happening at different wall-normal positions shed light on the evolution of the topologies for the vortices dominating ejection events. LSE based on a centred prograde spanwise vortex provides a typical packet model, which indicates that the population density of the packets in a TBL is large enough to leave footprints in conditionally averaged flow fields. This work should help to settle the severe debate on the existence of packet structures and also lays some foundation for the TBL model theory.

LES investigation of the influence of cavitation on flow patterns in a confined tip-leakage flow

In the present paper, Large Eddy Simulations combined with the Zwart-Gerber-Belamri cavitation model are conducted to study the flow characteristics in a tip-leakage flow. A reasonable agreement is obtained between the numerical and experimental data. With the numerical results, the influence of cavitation in a tip-leakage flow on the gross features of tip-leakage vortex (TLV) and tip-separation vortex (TSV), the behavior of tip-leakage jet, the time-averaged vorticity field and turbulent kinetic energy (TKE) distributions are discussed in detailed. Our results demonstrate that more complex induced vortexes are observed in the non-cavitation case when compared with the cavitation case. Moreover, the results indicate that cavitation promotes the fusion of TLV and TSV. The narrower passageway in the gap when cavitation occurs increases the strength of tip-leakage jet, which leaves significant influence on local vorticity and turbulent kinetic energy. Cavitation trends to suppress the production of spanwise and pitchwise vorticity and promotes the TKE production. Further analysis shows that the spanwise and pitchwise flow patterns are mainly responsible for the TKE production. The fluctuations of v and w velocity and the corresponding spanwise and pitchwise velocity gradient components need to be controlled if a decrease in the viscous losses is desired.

Interaction of coherent flow structures in adverse pressure gradient turbulent boundary layers

With the aim to characterize the near-wall flow structures and their interaction with large-scale motions in the log-law region, time-resolved planar and volumetric flow field measurements were performed in the near-wall and log-law region of an adverse pressure gradient turbulent boundary layer following a zero pressure gradient turbulent boundary layer at a friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}=5000$. Due to the high spatial and temporal resolution of the measurements, it was possible to resolve and identify uniform-momentum zones in the region $z/\unicode[STIX]{x1D6FF}<0.15$ or $z^{+}<350$ and to relate them with well known coherent flow motions near the wall. The space–time results confirm that the turbulent superstructures have a strong impact even on the very near-wall flow motion and also their alternating appearance in time and intensity could be quantified over long time sequences. Using the time record of the velocity field, rare localized separation events appearing in the viscous sublayer were also analysed. By means of volumetric particle tracking velocimetry their three-dimensional topology and dynamics could be resolved. Based on the results, a conceptual model was deduced that explains their rare occurrence, topology and dynamics by means of a complex interaction process between low-momentum turbulent superstructures, near-wall low-speed streaks and tilted longitudinal and spanwise vortices located in the near-wall region.

On the detection of internal interfacial layers in turbulent flows

A novel approach to identify internal interfacial layers, or IILs, in wall-bounded turbulent flows is proposed. Using a fuzzy cluster method (FCM) on the streamwise velocity component, a unique and unambiguous grouping of the uniform momentum zones (UMZs) is achieved, thus allowing the identification of the IILs. The approach overcomes some of the key limitations of the histogram-based IIL identification methods. The method is insensitive to the streamwise domain length, can be used on inhomogeneous grids, uses all the available flow field data, is trivially extended to three dimensions and does not need user-defined parameters (e.g. number of bins) other than the number of zones. The number of zones for a given snapshot can be automatically determined by an a priori algorithm based on a kernel density estimation algorithm, or KDE. This automated approach is applied to compute the average number of UMZs as a function of Reynolds number $Re_{\unicode[STIX]{x1D70F}}$ in turbulent channel flows in several numerical simulations. This systematic approach reveals a dependence of the Reynolds number on the average number of UMZs in the channel flow; this supports previously reported observations in the boundary layer. The fuzzy clustering approach is applied to the turbulent boundary layer (experimental, planar particle image velocimetry) and channel flow (numerical, direct numerical simulation) at varying Reynolds numbers. The interfacial layers are characterized by a strong concentration of spanwise vorticity, with the outer-most layer located at the upper edge of the log layer. The three-dimensional interface identification reveals a streak-like organization. The large-scale motion (LSM) at the outer region of the channel flow boundary layer modulates the outer IIL. The corrugations of the outer IIL are aligned with the LSM and the conditional correlation of the inner and outer IIL height shows that extreme near-wall events leave their mark on the outer IIL corrugations.

Effects of surface shapes on properties of turbulent/non-turbulent interface in turbulent boundary layers

The effects of directional riblets surfaces on the turbulent/non-turbulent (T/NT) interface in turbulent boundary layers are experimentally investigated using two-dimensional time-resolved particle image velocimetry (PIV). The velocity field of streamwise—wall-normal plane for the smooth surface, converging and diverging riblets surfaces are measured. The interface is detected using the criterion of local kinetic energy. The statistical properties of interface height and conditional averaged velocity for different surfaces are analyzed. It is shown that, the converging and diverging riblets surfaces have little effect on the fractal dimension of the T/NT interface, but they cause the intermittency profile deviate from error function and the probability distribution of interface height deviate from Gaussian function. To be specific, the distribution of interface height for the converging riblets surface shows a positive skewness while it shows a negative skewness for the diverging riblets surface. Moreover, the conditional averaged streamwise velocity and spanwise vorticity across the interface are analyzed, and it is found that their self-similarities are preserved for different surfaces when normalized with respective friction velocity. The correlation analysis reveals that near-wall streamwise velocity fluctuation and interface height show a negative correlation.

Flow structures of a lobed mixer and effects of streamwise vortices on mixing enhancement

Large-scale vortices downstream of a lobed mixer are investigated experimentally using a nanoparticle-based planar laser scattering experimental system. The results are contrasted with additional measurements of a flat plate and a convoluted plate. Three streamwise vortices form downstream of the lobed mixer due to the pressure difference between the peak and trough regions of the trailing edge. This is not the case for the convoluted plate, where the streamwise structures are suppressed and do not appear downstream. Comparison of vortex sizes indicates that streamwise vortices contribute almost 80% of mixing enhancement, which is substantially higher than what could be expected from the increase of the interfacial surface area, especially in the far field of the present compressible mixing layer. It is also quite different from the effects of streamwise vortices on the mixing enhancement in incompressible mixing layers. That no streamwise vortices appear downstream of the convoluted plate indicates that the pressure difference around the corners of the peak and trough regions in the lobed mixer plays an important role for the appearance of the streamwise vortices. Three-dimensional views of the streamwise vortices show that a significant amount of fluid is entrained from the lower stream to the upper stream, resulting in the development of the streamwise vortices for the lobed mixer. The interaction of the streamwise and spanwise vortices then leads to the formation of a large number of small-scale vortices. These two mechanisms enlarge the interfacial surface area of the two streams greatly and substantially improve the turbulent mixing prominently. In addition, the presence of vortex clusters and T-shape vortices in the mixing layer indicate that they are common topological structures in such flows.

Large-eddy simulation of an open-channel flow bounded by a semi-dense rigid filamentous canopy: Scaling and flow structure

We have carried out a large-eddy simulation of a turbulent open-channel flow over a marginally dense, fully submerged, rigid canopy. The canopy is made of a set of rigid, slender cylinders normally mounted on a solid wall. The flow in the canopy is resolved stem-by-stem by means of an immersed boundary method. It is found that the flow behavior can be categorized according to the velocity distribution into two separate spatial regions: the canopy itself and the outer region above it. Within the region occupied by the canopy elements, the velocity magnitude is found to be related to the local shear stress. Outside the canopy, a logarithmic velocity profile matching the canonical turbulent open-channel flow over rough walls is recovered albeit the strong manipulation exerted by the canopy on the buffer layer. In the innermost layer, the presence of the stems is responsible for redistributing the local momentum fluctuations from a streamwise to a spanwise leading component, inhibiting the survival of the wall streamwise velocity streaks. On the other hand, the outer region presents a structure very similar to the well-known logarithmic boundary layer with the presence of large and energetic streamwise velocity streaks generated by a system of quasistreamwise vortices. These vortices strongly contribute to the intracanopy fluctuations through vigorous sweep and ejection events that affect all the region occupied by the stems. Consistent with the results of previous investigations [H. Nepf, “Flow and transport in regions with aquatic vegetation,” Annu. Rev. Fluid Mech. 44, 123–142 (2012)], it is found that the inflection point in the mean velocity profile, produced by the drag discontinuity at the canopy tip, promotes the appearance of another system of spanwise oriented vorticity structures. However, different from previous results reported in the literature [J. Finnigan, “Turbulence in plant canopies,” Annu. Rev. Fluid Mech. 32, 519–571 (2000)], in our simulations, the presence of alternating head up–head down hairpin vortices generated by a mutual induction of the counter-rotating spanwise vortices is not observed. Instead, we advocate that the modulation of the spanwise coherent vorticity is due to the action of the external logarithmic layer structures (i.e., the outer streamwise vortices that penetrate the canopy) rather than by upwash and downwash motions induced by the mutual interaction of the spanwise rollers.