The laminar-turbulent transition in the circular pipe flow has been tested experimentally. The critical Reynolds numbers for the flows of different gases (He, Ne, Ar, Kr, Xe, N2, CO2, SF6) and liquids (H2O, D2O, C2H5OH) have been compared. The difference up to 40% was observed. The possible reasons of non-universality of critical Reynolds number are discussed. The conclusion is the statistical approach is needed to penetrate into the nature of observed phenomenon.
A hallmark of fluid turbulence theory is the universal power law scaling of the velocity difference statistics between two points in space in the inertial range between the large energy injection scale and the small energy dissipation scale. Even at the highest Reynolds numbers available, laboratory and natural flows such universal power laws have not been convincingly demonstrated. Here we show for the decaying active grid turbulence of the Max Planck Variable Density Turbulence Tunnel that the velocity difference statistics at high Reynolds numbers do not exhibit a power law, but have a univ…
In this visualisation, the transition from laminar to turbulent flow is characterised by the intermittent ejection of wall fluid into the outer stream. The normalised thickness of the viscous flow layer reaches an asymptotic value but the physical thickness drops exponentially after transition. The critical transition pipe Reynolds number can be obtained simply by equating it with the asymptotic value of the normalised thickness of viscous flow layer. Key words: Transition, critical stability Reynolds number, critical transition Reynolds number, non-Newtonian pipe flow
A Reynolds-like Criterion for the Onset of Universal Active Turbulence
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Department of Physics, Indian Institute of Technology (IIT), Hyderabad（印度理工学院海德拉巴分校物理系）；Department of Mechanical Engineering, Indian Institute of Technology Kanpur（印度理工学院坎普尔分校机械工程系）
It is experimentally shown that the non-classical high Reynolds number energy dissipation behaviour, $C_ε \equiv εL/u^3 = f(Re_M)/Re_L$, observed during the decay of fractal square grid-generated turbulence is also manifested in decaying turbulence originating from various regular grids. For sufficiently high values of the global Reynolds numbers $Re_M$, $f(Re_M)\sim Re_M$.
A theoretical mechanism of laminar-turbulent transition originated from the deceleration of fluid streams on the walls of the channel or pipe is proposed. For Poiseuille flow an analytical expression relating the critical Reynolds number with the degree of disturbance of the flow is derived.
We study compressible turbulent flow in a circular pipe, at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies.Regarding velocity statistics, we find that Huang's transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of den…
The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, ${\rm Re}_s$, that ac…
Reynolds similitude, a key concept in hydrodynamics, states that two phenomena of different length scales with a similar geometry are physically identical. Flow properties are universally determined in a unified way in terms of the Reynolds number ${\cal R}$ (dimensionless, ratio of inertial to viscous forces in incompressible fluids). For example, the drag coefficient $c_D$ of objects with similar shapes moving in fluids is expressed by a universal function of ${\cal R}$. Certain studies introduced similar dimensionless numbers, that is, the superfluid Reynolds number ${\cal R}_s$, to charact…
In this work the numerical stability of a streamline singular hyperbolic/saddle critical point (HSP) and its relationship with the divergence of pressure force/fluid flux are numerically investigated at low Reynolds numbers. Three canonical configurations at different Reynolds numbers are considered: (a) an isolated circular cylinder; (b) side-by-side circular cylinders and (c) a near-wall circular cylinder. The objective is to investigate the behavior of a HSP subjecting to imbalanced shear-layer interaction and different Reynolds numbers. It is found that a HSP evolves along the shear-layer …
We employ the horizontal visibility algorithm to map the velocity and acceleration time series in turbulent flows with different Reynolds numbers, onto complex networks. The universal nature of velocity fluctuations in high Reynolds turbulent Helium flow is found to be inherited in the corresponding network topology. The degree distributions of the acceleration series are shown to have stretched exponential forms with the Reynolds number dependent fitting parameter. Furthermore, for acceleration time series, we find a transitional behavior in terms of the Reynolds number in all network feature…
We study the temporal linear instability of channel flow subject to a tensorial slip boundary condition that models the slip effect induced by microgroove-type super-hydrophobic surfaces. The microgrooves are not necessarily aligned with the driving pressure gradient. Pralits et al. Phys. Rev. Fluids 2, 013901 (2017) investigated the same problem and reported that a proper tilt angle of the microgrooves about the driving pressure gradient can reduce the critical Reynolds number and that the flow with a single superhydrophobic wall is much more unstable/less stable than that with two superhydro…
Direct numerical simulation is performed to study compressible, viscous flow around a circular cylinder. The present study considers two-dimensional, shock-free continuum flow by varying the Reynolds number between 20 and 100 and the freestream Mach number between 0 and 0.5. The results indicate that compressibility effects elongate the near wake for cases above and below the critical Reynolds number for two-dimensional flow under shedding. The wake elongation becomes more pronounced as the Reynolds number approaches this critical value. Moreover, we determine the growth rate and frequency of …
The way the increment statistics of turbulent velocity fluctuations scale with the increment size is a centerpiece of turbulence theories. We report data on decaying turbulence in the Max Planck Variable Density Turbulence Tunnel (VDTT), which show an approach of the inertial range statistics toward a nontrivial shape at small scales. By correcting for the contributions of energy decay to the large-scale statistics with a model, we find the scaling exponent of the second-order velocity increment statistics to be independent of the Reynolds number and equal to $0.693\pm0.003$ for $2000\lesssim …
From a critical review of Onsager's pioneering paper which was published in 1949 we conclude that his analysis was at odds with other workers in the field because instead of taking the infinite Reynolds number limit he simply set the viscosity equal to zero which is not the same thing.
We study the Reynolds number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (2010), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier-Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. U…
The Earth's atmosphere is an aerosol, it contains suspended particles. When air flows over an obstacle such as an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the obstacle. Instead the particles in the air may deviate from the path of the air and so collide with the surface of the obstacle. It is known that particle inertia can drive this deposition, and that there is a critical value of this inertia, below which no point particles deposit. Particle inertia is measured by the Stokes number, St. We show that near the critical value of the…
Experiments in an extraordinary turbulent boundary layer called the sink flow, displaying a perfect streamwise invariance, show a wide extent of logarithmic scaling for moments of streamwise velocity up to order 12, even at moderate Reynolds numbers. This is in striking contrast to canonical constant-pressure turbulent boundary layers that show such comprehensive log scaling only at ultra-high Reynolds numbers. This demonstrates that ultra-high Reynolds number is not necessary for comprehensive log scaling to occur; while specific details of the sink flow are special, the relevance to general …
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 t…
We investigated the side-wall effects on turbulent bands in channel flow at transitional Reynolds numbers by direct numerical simulations using the open source spectral-element code Nektar++. The width-to-height aspect ratio of 50:1 is considered for this study. Our study shows that turbulent bands can survive the collision with the side wall above bulk Reynolds number of Re around 1000 but decay below Re around 975, i.e. the critical Reynolds number should be approximately between the two Reynolds numbers. We also discussed about the underlying mechanism for the decay of the band at low Reyno…
A turbulent flow is characterized by velocity fluctuations excited in an extremely broad interval of wave numbers $k> Λ_{f}$ where $Λ_{f}$ is a relatively small set of the wave-vectors where energy is pumped into fluid by external forces. Iterative averaging over small-scale velocity fluctuations from the interval $Λ_{f}< k\leq Λ_{0}$, where $η=2π/Λ_{0}$ is the dissipation scale, leads to an infinite number of "relevant" scale-dependent coupling constants ( Reynolds numbers ) $Re_{n}(k)=O(1)$. It is shown that in the i.r. limit $k\rightarrow Λ_{f}$, the Reynolds numbers $Re(k)\rightarrow Re_{t…
In this article we describe, a numerical simulation has been performed for a channel flow with sudden expansion. Different geometric expansion ratios are considered in the current study such as 1:2, 1:3, and 1:4. The bifurcation phenomenon has been investigated for the baseline case and the critical Reynolds number is controlled using a passive modification in the channel. The geometry of sudden expansion channel is modified by introducing a two-dimensional plate along the center line of the channel at the expansion plane. This is one of the passive control techniques, which has been explored …
Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally applicable RANS models with predictive capabilities are still lacking. Recently, data-driven methods have been proposed as a promising alternative to the traditional approaches of turbulence model development. In this work we propose a data-driven, physics-informed machine learning approach for predicting discrepancies in RANS modeled Reynolds stresses. The discrepa…
It is presently believed that flows of viscoelastic polymer solutions in geometries such as a straight pipe or channel are linearly stable. Here we present experimental evidence that such flows can be nonlinearly unstable and can exhibit a subcritical bifurcation. Velocimetry measurements are performed in a long, straight micro-channel; flow disturbances are introduced at the entrance of the channel system by placing a variable number of obstacles. Above a critical flow rate and a critical size of the perturbation, a sudden onset of large velocity fluctuations indicates presence of a nonlinear…
The vortex dynamics of laminar flow past a rectangular cavity is investigated using simulations and experiments. The flow is three-dimensional and characterized by a large, dominant vortex structure that fills most of the cavity at moderate Reynolds numbers with a weak, yet significant flow in the axial direction along the vortex core. Classical bubble-type vortex breakdown is observed within the cavity above a certain critical Reynolds number, which is a function of the channel width. The critical Reynolds number for the onset of breakdown is determined as a function of channel width, and the…
In the turbulence modeling community, significant efforts have been made to quantify the uncertainties in the Reynolds-Averaged Navier--Stokes (RANS) models and to improve their predictive capabilities. Of crucial importance in these efforts is the understanding of the discrepancies in the RANS modeled Reynolds stresses. However, to what extent these discrepancies can be predicted or whether they are completely random remains a fundamental open question. In this work we used a machine learning algorithm based on random forest regression to predict the discrepancies. The success of the regressi…
The present work numerically investigates vortex-induced vibrations (VIV) of a two-dimensional circular cylinder with an axisymmetric slit at Reynolds number 500. The study examines the effects of slit shape (i.e., converging, diverging, and parallel slits), the effect of slit-area ratios, slit-width, and its angle with the freestream velocity on aerodynamic forces, vibration response, and associated flow characteristics. The results demonstrate that the addition of the slit assists the VIV suppression by adding an extra amount of flow to the main flow. It results in the stabilized wake with t…
The present study investigates the passive flow control phenomena over a two-dimensional circular cylinder using numerical simulations in the laminar regime. The aim is to explore one of the passive control techniques, which involves the introduction of a slit to the geometry of the cylinder. The two parameters, slit width ratio S/D (slit width/diameter) and slit angle (measured with respect to the incoming flow direction), play an essential role in determining the trend of critical Reynolds number (Rec). Most of the analysis invokes flow visualization and saturation amplitude methods to obtai…
Asymptotically large Reynolds number hydrodynamic turbulence is characterized by multi-scaling of moments of velocity increments and spatial derivatives. With decreasing Reynolds number toward $R_λ=R^{tr}_λ\approx 9.0$, the anomalous scaling disappears in favor of the "normal" one and close-to-Gaussian probability densities [Yakhot \& Donzis, {\bf 119}, 044501 (2017)]. The nature of this transition and its universality are subjects of this work. Here we consider Benard convection ( Prandtl number $Pr=1$) between infinite horizontal plates. It is shown that in this system the "competition" betw…
The plane Poiseuille flow is one of the elementary flow configurations. Although its laminar-turbulent transition mechanism is investigated intensively in the last century, the significant difference in the critical Reynolds number between the experiments and theory lacks a clear explanation. In this paper, an attempt is made to reduce this gap by analysing the Reynolds-Orr equation solution. Recent literature results showed that the usage of enstrophy (the volume integral of the vorticity) instead of the kinetic energy as the norm of perturbations predicts higher Reynolds numbers in the two-d…
Low order Carleman simulation of steady state flows at mild Reynolds numbers
Fondazione Istituto Italiano di Tecnologia（意大利理工大学基金会）；Center for Life Nano-Neuroscience at la Sapienza（罗马一大生命纳米神经科学中心）；Istituto per le Applicazioni del Calcolo “Mauro Picone（毛罗·皮科内计算应用研究所）；Italian National Research Council（意大利国家研究委员会）
The transition to turbulence in plane Poiseuille flow (PPF) is connected with the presence of exact coherent structures. In contrast to other shear flows, PPF has a number of different coherent states that are relevant for the transition. We here discuss the different states, compare the critical Reynolds numbers and optimal wavelengths for their appearance, and explore the differences between flows operating at constant mass flux or at constant pressure drop. The Reynolds numbers quoted here are based on the mean flow velocity and refer to constant mass flux, the ones for constant pressure dr…
The radial relative velocity between particles suspended in turbulent flow plays a critical role in droplet collision and growth. We present a simple and accurate approach to RV measurement in isotropic turbulence - planar 4-frame particle tracking velocimetry - using routine PIV hardware. This study demonstrates the feasibility of accurately measuring RV using routine hardware and verifies, for the first time, the path-history and inertial filtering effects on particle-pair RV at large particle separations experimentally.
We derive an effective equation of motion for the orientational dynamics of a neutrally buoyant spheroid suspended in a simple shear flow, valid for arbitrary particle aspect ratios and to linear order in the shear Reynolds number. We show how inertial effects lift the degeneracy of the Jeffery orbits and determine the stabilities of the log-rolling and tumbling orbits at infinitesimal shear Reynolds numbers. For prolate spheroids we find stable tumbling in the shear plane, log-rolling is unstable. For oblate particles, by contrast, log-rolling is stable and tumbling is unstable provided that …
Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with only modest progress made in the last few decades beyond the so-called `log law', which describes only the intermediate region in wall-bounded turbulence, i.e., $30-50 y^+ \text{ to } 0.1-0.2 R^+$ (in wall units) in a pipe of radius $R$. Here we propose a fundamentally new approach based on fractional calculus to model the {\em entire} mean velocity profile from the wall to the centerline of the pipe. Specifically, we represent the Reynolds stresses with a non-local fractional derivative of {\em variab…
We examine the onset of turbulence in Waleffe flow -- the planar shear flow between stress-free boundaries driven by a sinusoidal body force. By truncating the wall-normal representation to four modes, we are able to simulate system sizes an order of magnitude larger than any previously simulated, and thereby to attack the question of universality for a planar shear flow. We demonstrate that the equilibrium turbulence fraction increases continuously from zero above a critical Reynolds number and that statistics of the turbulent structures exhibit the power-law scalings of the (2+1)-D directed …
