Near-wall Coherent Structures Research Articles

Analysis of Near-wall Coherent Structure of Spiral Flow in Circular Pipe Based on Large Eddy Simulation

Based on the large eddy simulation method, this study performed the three-dimensional transient numerical analysis of the near-wall flow field of the spiral flow in a circular pipe and applied the sub-grid model of the kinetic energy transport. The low-speed bands, streamwise vortices and hairpin vortices of the spiral flow in the near-wall region of the circular pipe are determined using the Q criterion. The ejection and sweeping of coherent structures are identified using the velocity vector of the near-wall region; moreover, the two methods of creating the hairpin vortices are established by the image time series. The results demonstrate that the development directions of the near-wall bands, streamwise vortices and hairpin vortices of the spiral flow in the circular pipe develop along the path of the spiral line. The average spanwise period of the low-speed bands in the near-wall region is approximately 120 wall units, the length is more than 900 wall units and the height is not more than 40 wall units. The separation distance of the streamwise vortices is about 119 wall units. It has a certain angle with the wall (approximately 22°). The average burst period of a hairpin vortices is less than 0.015 s.

Correlation between skin friction and enstrophy convection velocity in near-wall turbulence

The enstrophy convection velocity (denoted by uΩ) in the evolution equation of the boundary enstrophy is proportional to skin friction (denoted by τ) in an incompressible viscous flow, which can be determined globally as an optical flow problem from a time sequence of the boundary enstrophy fields. The correlation coefficient between |uΩ| and |τ| is evaluated in a turbulent channel flow at the friction Reynolds number Reτ=180, which is about 0.73 in the region of interest containing near-wall strong wall-normal velocity event associated with a sweep-ejection pair) and is approximately independent of the wall-normal coordinate in the viscous sublayer. This correlation coefficient is contributed mainly by strong near-wall coherent structures with high boundary enstrophy. The statistics of the difference between the normalized |uΩ| and |τ| are discussed. The statistical correlation between uΩ and τ elucidates the connection between near-wall flow structures and skin friction.

Fluctuation characteristics induced by energetic coherent structures in air-core vortex: The most complex vortex in the tidal power station intake system

The air-core vortex is the most complex vortex in the intake system of tidal power stations. Nearly all power plants prohibit the operation of units with air-core vortices, as these vortices not only contain air but also induce significant inflow fluctuations that can potentially lead to significant damage to the units. The current understanding of the fluctuation characteristics and mechanisms induced by energetic coherent structures in the air-core vortex flow is very limited. To address this, the coupled level-set and volume-of-fluid large-eddy simulations are conducted to investigate the energetic coherent structures that cause power output fluctuations. Two critical frequencies have been identified in the energy spectra of the velocity field: the air-core vortex meandering frequency and the shear vortex shedding frequency. The level and trend of the spectrum density at low frequencies are determined by the large-scale energy structure represented by the air-core vortex. The shear vortices are initially formed from a shear separation layer that eventually evolves into streamwise vortices downstream. When the air-core vortex enters the pipe, it breaks up and merges with the near-wall coherent structures. The enhanced velocity and pressure fluctuations, induced by air-core vortices and coherence structures, are analyzed using the turbulent kinetic energy transport equation, revealing that the production term dominates the development of turbulent kinetic energy. Moreover, the diffusion term is responsible for transferring energy through the evolution of turbulent structures. The energy loss induced by fluctuations is investigated using the entropy production method. We find that the direct dissipation of entropy production is mainly induced by air-core vortices, while the side-wall coherent structures in the pipe contribute to the turbulent dissipation.

Near-wall numerical coherent structures and turbulence generation in wall-modelled large-eddy simulation

Near-wall turbulence structures and generation in the wall-modelled large-eddy simulation (WMLES) are revealed. To elucidate the turbulence structures driving a near-wall turbulence generation in the WMLES, flat-plate turbulent boundary-layer flows calculated by the WMLES and direct numerical simulation (DNS) are closely investigated. A conditional-averaging technique is applied to the instantaneous flow fields and the near-wall statistical structures of the ejection and sweep pairs, which produce the turbulence, are revealed to exist even in the WMLES although the structures are non-physically elongated compared with those obtained by the DNS. Since the near-wall turbulence structures in the WMLES are revealed not to be disordered, but to be coherent structures with low- and high-speed fluids alternating in the spanwise direction, it is suggested that the near-wall turbulence generation in the WMLES is explained by the numerically elongated coherent structures. Furthermore, the Reynolds number effects of wall-bounded turbulent flows, i.e. the appearance of the outer peak in the energy spectrum of the streamwise velocity fluctuations at increasing Reynolds numbers, is found not to be reproduced by the WMLES, and the origin of the outer peak is discussed in association with the inner–outer-layer interactions. The near-wall turbulence structures in the WMLES could depend heavily on the computational grids and the numerical methods. Therefore, additional cases varying the grid resolutions and the numerical methods (numerical schemes and sub-grid-scale models) are also conducted to confirm the consistency of the present conclusions.

Study of compressible turbulent plane Couette flows via direct numerical simulation

Compressible turbulent plane Couette flows are studied via direct numerical simulation for wall Reynolds numbers up to $Re_w=10\ 000$ and wall Mach numbers up to $M_w=5$ . Various turbulence statistics are compared with their incompressible counterparts at comparable semilocal Reynolds numbers $Re^*_{\tau,c}$ . The skin friction coefficient $C_f$ , which decreases with $Re_w$ , only weakly depends on $M_w$ . On the other hand, the thermodynamic properties (mean temperature, density and others) strongly vary with $M_w$ . Under proper scaling transformations, the mean velocity profiles for the compressible and incompressible cases collapse well and show a logarithmic region with the Kárman constant $\kappa =0.41$ . Compared with wall units, the semilocal units yield a better collapse for the profiles of the Reynolds stresses. While the wall-normal and spanwise Reynolds stress components slightly decrease in the near-wall region, the inner peak of the streamwise component notably increases with increasing $M_w$ – indicating that flow becomes more anisotropic when compressible. In addition, the near-wall turbulence production decreases as $M_w$ increases – due to rapid wall-normal changes of viscosity caused by viscous heating. The streamwise and spanwise energy spectra show that the length scale of near-wall coherent structures does not vary with $M_w$ in semilocal units. Consistent with those in incompressible flows, the superstructures (the large-scale streamwise rollers) with a typical spanwise scale of $\lambda _z/h\approx 1.5{\rm \pi}$ become stronger with increasing $Re_w$ . For the highest $Re_w$ studied, they contribute about $40\,\%$ of the Reynolds shear stress at the channel centre. Interestingly, flow visualization and correlation analysis show that the streamwise coherence of these structures degrades with increasing $M_w$ . In addition, at comparable $Re^*_{\tau,c}$ , the amplitude modulation of these structures on the near-wall small scales is quite similar between incompressible and compressible cases – but much stronger than that in plane Poiseuille flows.

Scaling of pressure fluctuations in compressible turbulent plane channel flow

The purpose of the paper is to identify Mach-number effects on pressure fluctuations$p'$in compressible turbulent plane channel flow. We use data from a specifically constructed$(Re_{\tau ^\star },\bar {M}_{{CL}_x})$-matrix direct numerical simulation (DNS) database, with systematic variation of the centreline streamwise Mach number$0.32\leqslant \bar {M}_{{CL}_x}\leqslant 2.49$and of the HCB (Huanget al.,J. Fluid Mech., vol. 305, 1995, pp. 185–218) friction Reynolds number$66\leqslant Re_{\tau ^\star }\lessapprox 1000$. Strong$\bar {M}_{{CL}_x}$effects (enhanced by the increasingly cold-wall condition) appear for$\bar {M}_{{CL}_x}\gtrapprox 2$, for all$Re_{\tau ^\star }$, very close to the wall ($y^\star \lessapprox 15$). Compared with incompressible flow at the same$Re_{\tau ^\star }$, the wall root-mean-square$[p'_{rms}]^+_w$(in wall-units, i.e. scaled by the average wall shear stress$\bar {\tau }_w$) strongly increases with$\bar {M}_{{CL}_x}$. In contrast, the peak level across the channel,$[p'_{rms}]^+_{PEAK}$, slightly decreases with increasing$\bar {M}_{{CL}_x}$. In order to study the near-wall coherent structures we introduce a new wall-distance-independent non-local system of units, based for all$y$on wall friction and the extreme values of density and dynamic viscosity, namely, for cold walls$\{\bar {\tau }_w,\min _y\bar {\rho },\max _y\bar {\mu }\}$. The average spanwise distance between streaks, scaled by this length-unit, is nearly independent of$\bar {M}_{{CL}_x}$at constant$Re_{\tau ^\star }$. Using the in-plane (parallel to the wall) Laplacian$\nabla ^2_{xz}p'$we find that the$(+/-)\text {-}p'$wave-packet-like structures appearing inside the low-speed streaks ($y^\star \lessapprox 15$) with increasing$\bar {M}_{{CL}_x}\gtrapprox 2$are part of a more complex wave system with spanwise extent over several streaks, whose spatial density decreases rapidly with decreasing$\bar {M}_{{CL}_x}$or increasing$y^\star$. These$p'$wave packets appear to be collocated with strong$(+/-)$-$v'$events and could be responsible for compensating towards 0 the negative incompressible-flow correlation coefficient$c_{p'v'}$, with increasing$\bar {M}_{{CL}_x}$very near the wall.

Coherent near-wall structures and drag reduction by spanwise forcing

We examine interaction mechanisms between the drag-reducing streamwise-traveling waves of spanwise wall velocity applied at the wall of a turbulent channel flow, and near-wall turbulent coherent structures. In particular, we focus our analysis on the drag-reduction-induced modifications of the quasi-streamwise vortices that populate the near-wall region of turbulent flows through a conditional averaging procedure. We observe that, while the streamwise-traveling waves share most of the drag-reducing mechanisms with the spanwise wall oscillations, some important differences related to the finite phase speed of the wave and the different properties of the generalized Stokes layer exist.

Generalized boundary dilatation flux on a flexible wall

In this paper, by applying theoretical method to the governing equations of compressible viscous flow, we derive the theoretical formula of the boundary dilatation flux (BDF) on a flexible wall, which generalizes the most recent work of Mao et al. (Acta Mechanica Sinica 38 (2022) 321583) for a stationary wall. Different boundary sources of dilatation are explicitly identified, revealing not only the boundary generation mechanisms of vortex sound and entropy sound, but also some additional sources due to the surface vorticity, surface angular velocity, surface acceleration and surface curvature. In particular, the generation mechanism of dilatation at boundary due to the coupled divergence terms is highlighted, namely, the product of the surface velocity divergence (∇∂B·U) and the vorticity-induced skin friction divergence (∇∂B·τω). The former is attributed to the surface flexibility while the latter characterizes the footprints of near-wall coherent structures. Therefore, by properly designing the surface velocity distribution, the dilatation generation at the boundary could be controlled for practical purpose in near-wall compressible viscous flows.

Drag reduction using velocity control in Taylor–Couette flows

Direct numerical simulation of Taylor–Couette flow subject to opposition control is investigated at Reynolds number (Re) of 3000. The idea is to impose exact opposite velocities of the detection plane at the walls to counteract near-wall stream-wise vortices. In this study, various velocity control strategies, namely wall-normal, axial, combined and blowing only, have been investigated from the viewpoint of skin-friction drag reduction. Further, the effects of skipping spatial points in azimuthal and axial directions and in time have been investigated from a drag reduction point of view. Based on the emergence of a virtual wall that hinders the vertical transport of momentum (i.e. on reduction of Reynolds shear stress production as well as sweep ejection events), flow physics has been explained via statistical analysis of fluctuations, Reynolds shear stresses, and near-wall coherent structures. The spatial density of near-wall vortical structures shows a marked reduction, followed by quadrant contribution analysis of Reynolds shear stresses reveals a decrease in ejection and sweep events, leading to reduced production of Reynolds shear stresses and skin-friction drag.

On non-Kolmogorov turbulence in blood flow and its possible role in mechanobiological stimulation

The study of turbulence in physiologic blood flow is important due to its strong relevance to endothelial mechanobiology and vascular disease. Recently, Saqr et al. (Sci Rep 10, 15,492, 2020) discovered non-Kolmogorov turbulence in physiologic blood flow in vivo, traced its origins to the Navier–Stokes equation and demonstrated some of its properties using chaos and hydrodynamic-stability theories. The present work extends these findings and investigates some inherent characteristics of non-Kolmogorov turbulence in monoharmonic and multiharmonic pulsatile flow under ideal physiologic conditions. The purpose of this work is to propose a conjecture for the origins for picoNewton forces that are known to regulate endothelial cells’ functions. The new conjecture relates these forces to physiologic momentum-viscous interactions in the near-wall region of the flow. Here, we used high-resolution large eddy simulation (HRLES) to study pulsatile incompressible flow in a straight pipe of L/D=20. The simulations presented Newtonian and Carreau–Yasuda fluid flows, at R{e}_{m}approx 250, each represented by one, two and three boundary harmonics. Comparison was established based on maintaining constant time-averaged mass flow rate in all simulations. First, we report the effect of primary harmonics on the global power budget using primitive variables in phase space. Second, we describe the non-Kolmogorov turbulence in frequency domain. Third, we investigate the near-wall coherent structures in time and space domains. Finally, we propose a new conjecture for the role of turbulence in endothelial cells’ mechanobiology. The proposed conjecture correlates near-wall turbulence to a force field of picoNewton scale, suggesting possible relevance to endothelial cells mechanobiology.

Counter-rotating Taylor-Couette flows with radial temperature gradient

In the present work, counter-rotating turbulent Taylor-Couette flows with radial temperature gradient have been studied as an extension of previously studied simple-rotating turbulent Taylor-Couette flows. The rotation axis is orthogonal to the gravity vector. Direct Numerical Simulations (DNS) have been carried out for Reynolds number ranging from 1000 to 5000 and Richardson number varying from 0 to 0.4. The effect of variation of Reynolds number and Richardson number on the flow statistics, flow dynamics, and near-wall coherent structures are studied. For neutrally buoyant cases, near-wall coherent structures exist near the inner and the outer wall, with the core being almost vortex-free. With an increase in Richardson number, more dense and finer vortical structures spread out in the core in half the circumferential domain only. This behavior is due to the spatial stable or unstable stratification in the azimuthal direction, leading to the generation of turbulence in the lower half of the domain and mitigation of turbulence in the upper half of the domain. Further, the turbulent kinetic energy (TKE) budget analysis reveals an increase in turbulence on heating the outer cylinder wall due to an increase in the production term. Heating the outer cylinder wall leads to a slight decrease in skin friction for the inner cylinder.

Effect of secondary currents on the flow and turbulence in partially filled pipes

Large-eddy simulations of turbulent flow in partially filled pipes are conducted to investigate the effect of secondary currents on the friction factor, first- and second-order statistics and large-scale turbulent motion. The method is validated first and simulated profiles of the mean streamwise velocity, normal stresses and turbulent kinetic energy (TKE) are shown to be in good agreement with experimental data. The secondary flow is stronger in half- and three-quarters full pipes compared with quarter full or fully filled pipe flows, respectively. The origin of the secondary flow is examined by both the TKE budget and the steamwise vorticity equation, providing evidence that secondary currents originate from the corner between the free surface and the pipe walls, which is where turbulence production is larger than the sum of the remaining terms of the TKE budget. An extra source of streamwise vorticity production is found at the free surface near the centreline bisector, due to the two-component asymmetric turbulence there. The occurrence of dispersive stresses (due to secondary currents) reduces the contribution of the turbulent shear stress to the friction factor, which results in a reduction of the total friction factor of flows in half and three-quarters full pipes in comparison to a fully filled pipe flow. Furthermore, the presence of significant secondary currents inhibits very-large-scale motion (VLSM), which in turn reduces the strength and scales of near-wall streaks. Subsequently, near-wall coherent structures generated by streak instability and transient growth are significantly suppressed. The absence of VLSM and less coherent near-wall turbulence structures is supposedly responsible for the drag reduction in partially filled pipe flows relative to a fully filled pipe flow at an equivalent Reynolds number.

Three-dimensional characterization of Reynolds shear stress in near-wall coherent structures of polymer drag reduced turbulent boundary layers

Three-dimensional characterization of Reynolds shear stress in near-wall coherent structures of polymer drag reduced turbulent boundary layers

State estimation in turbulent channel flow from limited observations

Abstract

Taylor–Couette flows undergoing orthogonal rotation subject to thermal stratification

The present study involves direct numerical simulation of turbulent Taylor–Couette flow undergoing orthogonal rotation (gravity and rotation axis are perpendicular) subject to thermal stratification in the radial direction. The simulations were performed based on the finite-difference approach for a radius ratio (η) = 0.5 and an aspect ratio (Γ) = 2π, with Reynolds number (Re=UθDν) ranging from 1000 to 5000. For this wide gap, the role of spatially varying buoyancy forces (Ri ranging from 0 to 0.3) in flow physics has been explored using flow statistics, flow dynamics, near-wall coherent structures, and quadrant analysis. It is observed that near-wall streaks are concentrated at the outflow boundaries of Taylor vortex cells with uniform axial spacing, which decreases with the increasing Reynolds number. Heating of the outer cylinder results in more intense streaks and coherent structures in the half-circumferential domain due to unstable stratification aiding turbulence, while in the other half-domain, stable stratification mitigates turbulence. Quadrant contribution of ur′ and uθ′ reveals that on heating the outer cylinder, there is an increase in turbulence near both the walls due to the enhanced generation of Reynolds shear stresses (sweep and ejection events).

Direct numerical simulation of turbulent boundary layer premixed combustion under auto-ignitive conditions

In the present work, premixed combustion in a turbulent boundary layer under auto-ignitive conditions is investigated using direct numerical simulation (DNS). The turbulent inflow of the reactive DNS is obtained by temporal sampling of a corresponding inert DNS of a turbulent boundary layer at a location with Reτ= 360, where Reτ is the friction Reynolds number. The reactants of the DNS are determined by mixing the products of lean natural gas combustion and a H2/N2 fuel jet, resulting in a lean mixture of high temperature with a short ignition delay time. In the free stream the reaction front is stabilized at a streamwise location which can be predicted using the free stream velocity U∞ and the ignition delay time τig. Inside the boundary layer, combustion modifies the near-wall coherent turbulent structures considerably and turbulence results in reaction front wrinkling. The combustion modes in various regions were examined based on the results of displacement velocity, species budget and chemical explosive mode analysis (CEMA). It was indicated that flame propagation prevails in the near-wall region and auto-ignition becomes increasingly important as the wall-normal distance increases. The interactions of turbulence and combustion were studied through statistics of reaction front normal vector and strain rate tensor. It was found that the reaction front normal preferentially aligns with the most compressive strain rate in regions where the effects of heat release on the strain rate are minor and with the most extensive strain rate where its effects are significant. Negative correlations between the wall heat flux and flame quenching distance were observed. A new quenching mode, back-on quenching, was identified. It was found that the heat release rate at the wall is the highest when head-on quenching occurs and lowest when back-on quenching occurs.

Resolvent modelling of near-wall coherent structures in turbulent channel flow

Turbulent channel flow was analysed using direct numerical simulations at friction Reynolds numbers Reτ=180 and 550. The databases were studied using spectral proper orthogonal decomposition (SPOD) to identify dominant near-wall coherent structures, most of which turn out to be streaks and streamwise vortices. Resolvent analysis was used as a theoretical approach to model such structures, as it allows the identification of the optimal forcing and most amplified flow response; the latter may be related to the observed relevant structures obtained by SPOD, especially if the gain between forcing and response is much larger than what is found for suboptimal forcings or if the non-linear forcing is white noise. Results from SPOD and resolvent analysis were compared for several combinations of frequencies and wavenumbers. For both Reynolds numbers, the best agreement between SPOD and resolvent modes was observed for the cases where the lift-up mechanism from resolvent analysis is present, which are also the cases where the optimal resolvent gain is dominant. These results confirm the outcomes in our previous studies (Abreu et al., 2019; Abreu et al., 2020), where we used a DNS database of a pipe flow for the same Reynolds numbers.

Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows

Abstract

Data-Driven Pulsatile Blood Flow Physics with Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a purely data-driven and equation-free technique for reduced-order modeling of dynamical systems and fluid flow. DMD finds a best fit linear reduced-order model that represents any given spatiotemporal data. In DMD, each mode evolves with a fixed frequency and therefore DMD modes represent physically meaningful structures that are ranked based on their dynamics. The application of DMD to patient-specific cardiovascular flow data is challenging. First, the input flow rate is unsteady and pulsatile. Second, the flow topology can change significantly in different phases of the cardiac cycle. Finally, blood flow in patient-specific diseased arteries is complex and often chaotic. The objective of this study was to overcome these challenges using our proposed multistage dynamic mode decomposition with control (mDMDc) method and use this technique to study patient-specific blood flow physics. The inlet flow rate was considered as the controller input to the systems. Blood flow data were divided into different stages based on the inlet flow waveform and DMD with control was applied to each stage. The system was augmented to consider both velocity and wall shear stress (WSS) vector data, and therefore study the interaction between the coherent structures in velocity and near-wall coherent structures in WSS. First, it was shown that DMD modes can exactly represent the analytical Womersley solution for incompressible pulsatile flow in tubes. Next, our method was applied to image-based coronary artery stenosis and cerebral aneurysm models where complex blood flow patterns are anticipated. The flow patterns were studied using the mDMDc modes and the reconstruction errors were reported. Our augmented mDMDc framework could capture coherent structures in velocity and WSS with a fewer number of modes compared to the traditional DMD approach and demonstrated a close connection between the velocity and WSS modes.

Magnetic dissipation of near-wall turbulent coherent structures in magnetohydrodynamic pipe flows.

Relaminarization of wall-bounded turbulent flows by means of external static magnetic fields is a long-known phenomenon in the physics of electrically conducting fluids at low magnetic Reynolds numbers. Despite the large literature on the subject, it is not yet completely clear what combination of the Hartmann (M) and the Reynolds number has to be used to predict the laminar-turbulent transition in channel or pipe flows fed by upstream turbulent flows free of magnetic perturbations. Relying upon standard phenomenological approaches related to mixing length and structural concepts, we put forward that M/R_{τ}, where R_{τ} is the friction Reynolds number, is the appropriate controlling parameter for relaminarization, a proposal which finds good support from available experimental data.