Turbulent Shear Flows Research Articles

Acoustic velocimetry imaging

We review a technique that we developed that combines shadowgraph or schlieren imaging with image processing tools to study the sound produced by turbulent shear flows. These flows are challenging acoustically because they are characterized by a distributed cloud of correlated sources that produce sound through multiple mechanisms. In the far field, 100 s of characteristic lengths from the source region, the pressure waves are purely acoustic, the apparent the source location shrinks to a point, and the common assumption is that the propagation behavior is spherical. In the near field, pressure signals from both acoustic and hydrodynamic (or evanescent) signatures are difficult to separate, especially when the convective Mach number of the sound-producing events is supersonic. Single-point measurements such as condenser-type microphones are blind to the direction of the approaching/departing pressure waves unless they are combined in arrays. Non-intrusive optical-based methods offer some benefit in this scenario and can be tailored in new and different ways. Examples include acoustic laser Doppler velocimetry and quantitative schlieren methods. Our technique combines modern digital camera technology (with high-resolution, high-speed capabilities) with tomographical image processing techniques images to yield a “picture” of the sound field that can provide quantitative assessment of the source distribution and source velocities. This optical technique is a strong complement for single-point or array microphone measurements.

Application of the exact regularized point particle method (ERPP) to bubble laden turbulent shear flows in the two-way coupling regime

Direct numerical simulations of a bubbly laden homogeneous shear flow have been carried out using the exact regularized point particle method as the inter-phase momentum coupling approach. The aim of this study consists in addressing the modulation of shear turbulence and the bubble clustering geometry in the presence of different inter-phase momentum coupling conditions. Suspensions with different combinations of the void fraction and Kolmogorov-based Stokes number, in the dilute regime, have been addressed. Bubbles suppress the turbulent kinetic energy and turbulent dissipation as well. Turbulent modulation occurs via the direct change of the Reynolds shear stress. In fact, the bubble energy source is proved to be negligible in the scale-by-scale turbulent energy budget. The bubble clustering, in agreement with the literature, occurs in the form of thin elongated structures. The clusters are aligned with the principal strain direction of the mean flow, as usual in shear flows. The bubble clustering and turbulent modification are strictly related: both increase with the Stokes number and are independent of the void fraction. The data show that the turbulent modification is disadvantaged when the bubble distribution is homogeneous (i.e., small Stokes number). Finally, the small-scale bubble clustering is slightly reduced by two-way coupling effects even though the clustering anisotropy still persists at small scales as it occurs for inertial particles.

Intermittency and Critical Scaling in Annular Couette Flow.

The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity and entrains fluid, by means of direct numerical simulation. Although for a radius ratio close to unity the system is similar to plane Couette flow, a qualitatively novel regime is identified for small radius ratio, featuring no oblique bands. An analysis of finite-size effects is carried out based on an artificial increase of the perimeter. Statistics of the turbulent fraction and of the laminar gap distributions are shown both with and without such confinement effects. For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects.

Formulating turbulence closures using sparse regression with embedded form invariance

A data-driven framework for formulation of closures of the Reynolds-Average Navier--Stokes (RANS) equations is presented. In recent years, the scientific community has turned to machine learning techniques to distill a wealth of highly resolved data into improved RANS closures. While the body of work in this area has primarily leveraged Neural Networks (NNs), we alternately leverage a sparse regression framework. This methodology has two important properties: (1) The resultant model is in a closed, algebraic form, allowing for direct physical inferences to be drawn and naive integration into existing computational fluid dynamics solvers, and (2) Galilean invariance can be guaranteed by thoughtful tailoring of the feature space. Our approach is demonstrated for two classes of flows: homogeneous free shear turbulence and turbulent flow over a wavy wall. This work demonstrates equivalent performance to that of modern NNs but with the added benefits of interpretability, increased ease-of-use and dissemination, and robustness to sparse training datasets.

Transitions between turbulent states in a two-dimensional shear flow

The bifurcations of large-scale jets in a turbulent shear flow driven by a Kolmogorov forcing are studied. These bifurcations, seen also in the mean velocity profile of the forced-dissipative system, are then reproduced using a system at equilibrium, namely, the truncated Euler equations. Statistical properties of the large-scale mode exhibit $1/f$ noise and are in qualitative agreement in both systems.

On the statistical evolution of viscous vortex-gas free shear layers

The temporal vortex-gas free shear layer is a Hamiltonian system of N-point vortices in a singly-periodic domain relevant to the (large-scale) development of plane (3D Navier–Stokes) turbulent shear layers. It has been shown (Suryanarayanan et al., 2014) that there are three distinct temporal regimes in its evolution, including an intermediate self-similar regime (RII) with a universal constant spreading rate, and a final state of relative equilibrium. Here, we study the evolution of vortex-gas free shear layers affected by viscosity as simulated by the addition of a random walk component to the motion of the vortices (Chorin, 1973). We show that while the momentum thickness of the layer, θ, scales as t1∕2 in the first and final regimes for the viscous system, it grows as t1 in the intermediate Regime II (observed here for momentum thickness Reynolds numbers Reθ from 50 to over 5000 across different simulations), with the same universal growth rate dθ∕dtΔU=0.0166±0.0002 as in the inviscid case. This suggests that the non-equilibrium universality of Regime II is robust to small perturbations of the Hamiltonian, and that this result could have general consequences for systems with long-range interactions. We further find that, even under conditions where the viscous shear stress is not negligible, the Reynolds shear stress adjusts itself in such a way that their sum is a constant in Regime II and equal to the value of the latter in the inviscid case. The implications of this observation on the dynamics of turbulent shear flows are elaborated.

A New Explicit Algebraic Wall Model for LES of Turbulent Flows Under Adverse Pressure Gradient

A new explicit algebraic wall law for the Large Eddy Simulation of flows with adverse pressure gradient is proposed. This new wall law, referred as adverse pressure gradient power law (APGPL), is developed starting from the power-law of Werner and Wengle (Turbulent Shear Flows, vol 8, Springer, New York, pp 155–168, 1993) in order to mimic an implicit non-equilibrium log-law based on Afzal’s law (Afzal, IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers, Kluwer Academic Publishers, Bochum, pp 95–118, 1996). No iterative method is needed for the evaluation of the wall shear stress from the APGPL contrary to the majority of models available in the literature. The APGPL model relies on the definition of three modes: the equilibrium power-law is used in regions of no or favourable pressure gradient, the APGPL is used in regions of adverse pressure gradient, and no wall model is used in separated flow regions. This model is assessed via Large Eddy Simulations of flows involving adverse pressure gradient and boundary layer separation using the Lattice Boltzmann Method on uniform nested grids. The flow around a clean and iced NACA23012 airfoil at Reynolds number $$Re = 1.88 \times 10^6$$ and the flow over the LAGOON landing gear at $$Re = 1.59 \times 10^6$$ are considered. Results are found in good agreement with those obtained by the non-equilibrium log-law and experimental and numerical data available in the literature.

Deep Learning Emulation of Subgrid‐Scale Processes in Turbulent Shear Flows

AbstractDeep neural networks (DNNs) are developed from a data set obtained from the dynamic Smagorinsky model to emulate the subgrid‐scale (SGS) viscosity (νsgs) and diffusivity (κsgs) for turbulent stratified shear flows encountered in the oceans and the atmosphere. These DNNs predict νsgs and κsgs from velocities, strain rates, and density gradients such that the evolution of the kinetic energy budget and density variance budget terms is similar to the corresponding values obtained from the original dynamic Smagorinsky model. These DNNs also compute νsgs and κsgs ∼2–4 times quicker than the dynamic Smagorinsky model resulting in a ∼2–2.5 times acceleration of the entire simulation. This study demonstrates the feasibility of deep learning in emulating the subgrid‐scale (SGS) phenomenon in geophysical flows accurately in a cost‐effective manner. In a broader perspective, deep learning‐based surrogate models can present a promising alternative to the traditional parameterizations of the subgrid‐scale processes in climate models.

Air Entrainment and Surface Fluctuations in a Turbulent Ship Hull Boundary Layer

Air entrainment due to turbulence in a free-surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations (DNS). In the experiments, the moving wall is created by a laboratory-scale device composed of a surface-piercing stainless steel belt that travels in a loop around two vertical rollers; one length of the belt between the rollers simulates the moving wall. The belt accelerates suddenly from rest until reaching constant speed and creates a temporally evolving boundary layer analogous to the spatially evolving boundary layer that would exist along a surface-piercing towed flat plate. We report cinematic laser-induced fluorescence measurements of water surface profile histories, cinematic observations and measurements of air entrainment events, and air bubble size distributions and motions. To complement the experiments, DNS of the temporally evolving turbulent boundary layer were conducted, considering both the air and water phases. Because of cost considerations, only a portion of the belt was simulated at a lower Reynolds number, keeping the Froude number, however, at the same levels as in the experiments. The results of the experiments and DNS are found to be in qualitative agreement and are used synergistically to explore the physics of the air entrainment process; quantitative agreement is not to be expected given the differences in setup and Reynolds numbers. In the experiments and DNS, the free-surface motion is found to consist of a region near the belt with fast-moving uncorrelated large-amplitude ripples and an outer region of small-amplitude propagating waves. Entrainment events similar to plunging breaking waves are found in the experiments, and these and other entrainment mechanisms are examined in detail in the DNS. The spatial distributions of bubble numbers and velocities are reported along with their diameter distributions.

Eulerian and Lagrangian analysis of coherent structures in separated shear flow by time-resolved particle image velocimetry

We investigate the turbulent shear flow that separates from a two-dimensional backward-facing step. We aim to analyze the unsteady separated and reattaching shear flow in both the Eulerian and Lagrangian frameworks in order to provide complementary insight into the self-sustaining coherent structures and Lagrangian transport of the entrainment process. The Reynolds number is Reh = 1.0 × 103, based on the incoming free-stream velocity and step height. The separated and reattaching shear flow as well as the recirculation region beneath is measured by time-resolved planar particle image velocimetry. As a result, time sequences of velocity vector fields in a horizontal–vertical plane in the center of the step model are obtained. In the Eulerian approach, a set of temporally orthogonal dynamic modes are extracted, and each one represents a single-frequency vortex pattern that neutrally evolves in time. The self-sustaining coherent structures are represented by reduced-order reconstruction of the identified high-amplitude dynamic modes, showing the basic unsteady flapping motion of the shear layer and the vortex rolling-up, pairing, and shedding processes superimposed on it. On the other hand, trajectories of passive fluid tracers depict the Lagrangian fluid transport by the entrainment process in the separated shear flow and identify the time-dependent vortex rolling-up process as well as complex vortex interactions. The contours of the finite-time Lyapunov exponent reveal the unsteady Lagrangian coherent structures that significantly shape the vortex patterns and contribute substantial parts to the fluid entrainment in the shear flow.

Turbulence statistics in a negatively buoyant multiphase plume

We investigate the turbulence statistics in a {multiphase plume made of heavy particles (particle Reynolds number at terminal velocity is 450)}. Using refractive-index-matched stereoscopic particle image velocimetry, we measure the locations of particles {whose buoyancy drives the formation of a multiphase plume,} {together with the local velocity of the induced flow in the ambient salt-water}. {Measurements in the plume centerplane exhibit self-similarity in mean flow characteristics consistent with classic integral plume theories.} The turbulence characteristics resemble those measured in a bubble plume, {including strong anisotropy in the normal Reynolds stresses. However, we observe structural differences between the two multiphase plumes. First, the skewness of the probability density function (PDF) of the axial velocity fluctuations is not that which would be predicted by simply reversing the direction of a bubble plume. Second, in contrast to a bubble plume, the particle plume has a non-negligible fluid-shear production term in the turbulent kinetic energy (TKE) budget. Third, the radial decay of all measured terms in the TKE budget is slower than those in a bubble plume.} Despite these dissimilarities, a bigger picture emerges that applies to both flows. The TKE production by particles (or bubbles) roughly balances the viscous dissipation, except near the plume centerline. The one-dimensional power-spectra of the velocity fluctuations show a -3 power-law that puts both the particle and bubble plume in a category different from single-phase shear-flow turbulence.

Turbulent shear flow over large Martian ripples

Turbulent shear flow over large Martian ripples

Turbulent shear flow over large Martian ripples

Turbulent shear flow over large Martian ripples

Drag Reduction in Turbulent Flows by Polymer and Fiber Additives

This article provides a review of the recent progress in understanding and predicting additives-induced drag reduction (DR) in turbulent wall-bounded shear flows. We focus on the reduction in friction losses by the dilute addition of high-molecular weight polymers and/or fibers to flowing liquids. Although it has long been reasoned that the dynamical interactions between polymers/fibers and turbulence are responsible for DR, it was not until recently that progress was made in elucidating these interactions in detail. Advancements come largely from numerical simulations of viscoelastic turbulence and detailed measurements in turbulent flows of polymer/fiber solutions. Their impact on current understanding of the mechanics and prediction of DR is discussed, and perspectives for further advancement of knowledge are provided.

Length scales in turbulent free shear flows

ABSTRACTWe address the important point of the proportionality between the longitudinal integral lengthscale (L) and the characteristic mean flow width (δ) using experimental data of an axisymmetric wake and a turbulent planar jet. This is a fundamental hypothesis when deriving the self-similar scaling laws in free shear flow. We show that L/δ is indeed constant, at least in a range of streamwise distances between 15 and 50 times the characteristic inlet dimension. We revisit turbulence closure models such as the Prandtl mixing length and the eddy viscosity in the light of the non-equilibrium dissipation scaling. We show that the mixing length model does not comply with the scalings stemming from the non-equilibrium version of the theory even if it does comply with the theory’s equilibrium version. Similarly, the eddy viscosity model holds in the case of the non-equilibrium version of the theory provided that the eddy viscosity is constant everywhere. We conclude by comparing the results of the different models with each other and with experimental data and with an improved model (following Townsend) that corrects for the eddy viscosity by considering the intermittency of the flow.

A scheme to correct the influence of calibration misalignment for cross-wire probes in turbulent shear flows

Velocity fluctuations, measured via multi-wire probes, are very sensitive to misalignment between the calibration coordinate system and that of the wind tunnel. The present study proposes a scheme to correct the erroneous velocity fluctuations processed from a misaligned calibration while investigating a wall-bounded turbulent shear flow. The scheme is based on the premise that the viscous-scaled spectral energy distribution in the small-scales is invariant with Reynolds number and solely depends on the viscous-scaled spatial resolution of the sensor. Energy spectra processed from the misaligned calibration, in this small-scale range, are compared with the ‘expected’ spectra obtained via synthetic experiments on a direct numerical simulation data set. The erroneous lateral velocity spectra is found to be either relatively amplified or attenuated, by almost the same factor, at all wall-normal distances across the shear flow. A unique gain, defined to be the correction ratio, is thus obtained by forcing the erroneous spectra onto the reference spectra in this scale range. This ratio is further used to rectify the time series of the lateral velocity fluctuations, acquired across the shear flow, via Fourier analysis. The scheme is shown to be effective for experiments conducted across a decade of Reynolds number and using probes of varying spatial resolution.

Nonlinear evolution of perturbations in high Mach number wall-bounded flow: Pressure–dilatation effects

We characterize the nonlinear evolution of perturbations in a high Mach number Poiseuille flow and contrast the behavior against an equivalent incompressible flow. The focus is on the influence of pressure–dilatation on (i) internal energy evolution, (ii) kinetic–internal energy exchange, and (iii) kinetic energy spectrum evolution. We perform direct numerical simulations of plane Poiseuille flow at different Mach numbers subject to a variety of initial perturbations. In all high-speed cases considered, pressure dilatation leads to energy equipartition between wall-normal velocity fluctuations (dilatational kinetic energy) and pressure fluctuations (a measure of internal energy). However, the effect of pressure–dilatation on the kinetic energy spectral growth can be varied. In cases wherein pressure–dilatation is larger than the turbulent kinetic energy production, spectral growth is considerably slow relative to an equivalent low Mach number case. When pressure–dilatation is smaller than production, the spectral growth is only marginally affected. As a consequence, in a high-speed Poiseuille flow, the spectral growth rate varies with the wall-normal distance depending on the local pressure effects. These findings provide valuable insight into the nonlinear aspects of breakdown toward turbulence in high speed wall-bounded shear flows.

Effect of mesoscopic structure on hydro-mechanical properties of fractures

Geothermal extraction usually requires reservoir fracturing to realize economic exploitation and fluid flow in hot-dry rock fractures has become a research hotspot. In the present study, gas flow through shear and tensile granite fractures was investigated to comparatively study effect of fracture mesoscopic structure evolution on fracture hydro-mechanical characteristics under confining stress ranging from 1 to 40 MPa and inlet pressure ranging from 0.005 to 3.6 MPa. Four major findings are reported herein. First, the conductivity of shear fractures is much higher than that of tensile fractures and the ratio of the former to the latter can be up to around 265 under the stress of 40 MPa. The second finding was that the Z2 values of tensile fractures are higher than shear fractures, indicating that the fracture surface of tensile fractures is rougher and has more mesoscopic asperities. When the two surfaces get to contact, tip contact and stress concentration happen, resulting in higher deformation in tensile fractures. The cluster coefficient characterizes fracture contact cluster property. Higher cluster coefficient indicates lower fracture deformation and lower viscous loss. Shear fractures have higher cluster coefficient than that of tensile fractures so shear fractures are weakly deformable. However, high flow velocity and Reynolds number easily occur in shear fractures, so transitional and turbulent flow dominates in shear fractures while laminar and transitional flow in tensile fractures. Third, a mechanical model relates the average imbedded depth to loading stress and lacunarity, a hydraulic aperture model based on void space and lacunarity and a friction factor model based on Reynolds number and lacunarity were built, respectively, based on the experimental data. Then a nonlinear flow model was proposed. The fourth finding was that parametric analysis on the cluster coefficient shows that the higher the cluster coefficient, the lower of fracture deformation is and the higher of hydraulic aperture is. When the cluster coefficient is high, less viscous loss occurs; however, the fluid velocity may be high, so the friction factor will be high since more inertial loss happens.

Upper edge of chaos and the energetics of transition in pipe flow

In the past two decades, our understanding of the transition to turbulence in shear flows with linearly stable laminar solutions has greatly improved. Regarding the susceptibility of the laminar flow, two concepts have been particularly useful: the edge states and the minimal seeds. In this nonlinear picture of the transition, the basin boundary of turbulence is set by the edge state's stable manifold and this manifold comes closest in energy to the laminar equilibrium at the minimal seed. We begin this paper by presenting numerical experiments in which three-dimensional perturbations are too energetic to trigger turbulence in pipe flow but they do lead to turbulence when their amplitude is reduced. We show that this seemingly counter-intuitive observation is in fact consistent with the fully nonlinear description of the transition mediated by the edge state. In order to understand the physical mechanisms behind this process, we measure the turbulent kinetic energy production and dissipation rates as a function of the radial coordinate. Our main observation is that the transition to turbulence relies on the energy amplification away from the wall, as opposed to the turbulence itself, whose energy is predominantly produced near the wall. This observation is further supported by the similar analyses on the minimal seeds and the edge states. Furthermore, we show that the time-evolution of production-over-dissipation curves provide a clear distinction between the different initial amplification stages of the transition to turbulence from the minimal seed.

Self-similar invariant solution in the near-wall region of a turbulent boundary layer at asymptotically high Reynolds numbers

At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in \emph{inner units}, the statistical properties of the flow become independent of the Reynolds number. We demonstrate the existence of a wall-attached non-chaotic exact invariant solution of the fully nonlinear 3D Navier-Stokes equations for a parallel boundary layer that captures the characteristic self-similar scaling of near-wall turbulent structures. The branch of travelling wave solutions can be followed up to $Re=1,000,000$. Combined theoretical and numerical evidence suggests that the solution is asymptotically self-similar and exactly scales in inner units for Reynolds numbers tending to infinity. Demonstrating the existence of invariant solutions that capture the self-similar scaling properties of turbulence in the near-wall region is a step towards extending the dynamical systems approach to turbulence from the transitional regime to fully developed boundary layers.