The modified Townsend-Perry attached eddy model of Vassilicos et al (2015) combines the outer peak/plateau behaviour of rms streamwise turbulence velocity profiles and the Townsend-Perry log-decay of these profiles at higher distances from the wall. This model was validated by these authors for high Reynolds number tur- bulent pipe flow data and is shown here to describe equally well and with about the same parameter values turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well.
We study the laminar and turbulent channel flow over a viscous hyper-elastic wall and show that it is possible to sustain an unsteady chaotic turbulent-like flow at any Reynolds number by properly choosing the wall elastic modulus. We propose a physical explanation for this effect by evaluating the shear stress and the turbulent kinetic energy budget in the fluid and elastic layer. We vary the bulk Reynolds number from 2800 to 10 and identify two distinct mechanisms for turbulence production. At moderate and high Reynolds numbers, turbulent fluctuations activate the wall oscillations, which, i…
We show a method, for direct numerical simulations, to trigger and maintain turbulent bands directly at low Reynolds numbers in channel flow. The key is to impose a moving localised force which induces a local flow with sufficiently strong inflectional instability. With the method, we can trigger and maintain turbulent bands at Reynolds numbers down to $Re \simeq 500$. More importantly, we can generate any band patterns with desired relative position and orientation. The usual perturbation approach resorts to turbulent fields simulated at higher Reynolds numbers, random noise, or localised vor…
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…
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 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…
We present a unique method for solving for the Reynolds stress in turbulent canonical flows, which is based on momentum balance for a control volume moving at the local mean velocity. Comparisons with experimental and computational data in simple geometries show quite good agreement. An alternate picture for the turbulence momentum transport is offered, based on the closed-form expression for the Reynolds stress. The turbulence momentum balance is verified using DNS data. This approach has potential applications in aerodynamics, and also represents a possible method for determining the Reynold…
Using the previously developed model to describe laminar/turbulent states of a viscous fluid flow, which treats the flow as a collection of coherent structures of various size (Chekmarev, Chaos, 2013, 013144), the statistical temperature of the flow state is determined as a function of the Reynolds number. It is shown that at small Reynolds numbers, associated with laminar states, the temperature is positive, while at large Reynolds numbers, associated with turbulent states, it is negative. At intermediate Reynolds numbers, the temperature changes from positive to negative as the size of the c…
The effects of Reynolds number and Stokes number on particle-pair relative velocity (RV) were investigated systematically using a recently developed planar four-frame particle tracking technique in a novel homogeneous and isotropic turbulence chamber.
Numerical simulations of turbulent round jets, using explicit-filtered LES technique, are performed, for three different Reynolds numbers(Re = 3600, 88000, 400000), to understand the Reynolds number effect on subsonic jets with Mach number 0.9. Eigth-order compact schemes are used for spatial derivative estimation. Second order Runge-Kutta method is used for Time evolution of flow. One-parameter fourth-order compact filter is used for low-pass explicit filtering of transported variables. Decreased centreline axial velocity decay rate and reduced turbulence intensities are observed as jet Reyno…
In this report we briefly summarize the set-up and results for direct numerical simulations (DNS) of turbulent channel flows with riblets. The DNS are carried out with OpenFOAM which allows the use of an unstructured mesh. The present results were presented at the European Drag Reduction and Flow Control Meeting in 2015.
The Reynolds-averaged Navier-Stokes (RANS) equations are widely used in turbulence applications. They require accurately modeling the anisotropic Reynolds stress tensor, for which traditional Reynolds stress closure models only yield reliable results in some flow configurations. In the last few years, there has been a surge of work aiming at using data-driven approaches to tackle this problem. The majority of previous work has focused on the development of fully-connected networks for modeling the anisotropic Reynolds stress tensor. In this paper, we expand upon recent work for turbulent chann…
Using the Lagrangian transport of momentum, the Reynolds shear stress can be expressed in terms of basic turbulence parameters. In this view, the Reynolds stress gradient represents the lateral transport of streamwise momentum, balanced by the u2 transport, pressure and shear force terms in the momentum equation. We extend this formalism to other turbulence parameters such as diagonal components of the Reynolds stress, and also to more complex flows (boundary layer flows with adverse pressure gradients and pipe flows with swirl). Data from direct numerical simulations (DNS) are used to validat…
We present a unique method for solving for the Reynolds stress in turbulent canonical flows, based on the momentum balance for a control volume moving at the local mean velocity. A differential transform converts this momentum balance to a solvable form. Comparisons with experimental and computational data in simple geometries show quite good agreements. An alternate picture for the turbulence momentum transport is offered, as verified with data, where the turbulence momentum is transported by the mean velocity while being dissipated by viscosity. The net momentum transport is the Reynolds str…
The Reynolds number dependence of the dimensionless dissipation rate is derived directly from the Karman-Howarth equation in terms of the inverse of the integral scale Reynolds number and a coefficient which depends on the second- and third-order structure functions. Fitting this form to the results from a direct numerical simulation indicates that the coefficient is effectively constant.
Iterative coarse-graining procedure based on Wyld's perturbation expansion is applied to the problem of Navier-Stokes turbulence. It is shown that the low-order calculation gives the fixed-point Reynolds number $ Re_{fp}$ (coupling constant) almost identical to the Reynolds number of the recently discovered transition to anomalous scaling of the moments of {\bf "velocity derivatives"}. Using this result as a dynamic constraint, it is argued that in the vicinity of the fixed point (integral scale) the high-order non-linearities, generated by the procedure, are irrelevant. The infra-red divergen…
The turbulence statistics of the intermittent region in a supersonic turbulent boundary layer are studied by direct numerical simulation. Recently, Kwon et al. (2016) have shown that this intermittent behavior, consisting of the coexistence of turbulent and non-turbulent flows separated by an interface, could result in perils when the traditional Reynolds decomposition is used to analyze data. Here, we extend the study of turbulent/non-turbulent interfaces to the supersonic regime and report turbulence statistics conditioned to the interface. We show that the mathematical artefact of the tradi…
This study presents a deep learning-based framework to reconstruct high-resolution turbulent velocity fields from extremely low-resolution data at various Reynolds numbers using the concept of generative adversarial networks (GANs). A multiscale enhanced super-resolution generative adversarial network (MS-ESRGAN) is applied as a model to reconstruct the high-resolution velocity fields, and direct numerical simulation (DNS) data of turbulent channel flow with large longitudinal ribs at various Reynolds numbers are used to evaluate the performance of the model. The model is found to have the cap…
Using the Lagrangian transport of momentum, the Reynolds stress can be expressed in terms of basic turbulence parameters. The Reynolds stress gradient represents the lateral transport of stream-wise momentum, balanced by the u2 transport, pressure and shear force terms in the momentum equation. Data from direct numerical simulations (DNS) have been used to validate this approach, with a good degree of consistency and agreement. This expression for the Reynolds stress gradient adds a transport equation to the Reynolds-averaged Navier-Stokes (RANS) equation, so that the turbulence structure can …
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 …
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 …
Second and third order longitudinal structure functions and wavenumber spectra of isotropic turbulence are computed using the EDQNM model and compared to results of the multifractal formalism. At the highest Reynolds number available in windtunnel experiments, $R_λ=2500$, both the multifractal model and EDQNM give power-law corrections to the inertial range scaling of the velocity increment skewness. For EDQNM, this correction is a finite Reynolds number effect, whereas for the multifractal formalism it is an intermittency correction that persists at any high Reynolds number. Furthermore, the …
Turbulent motions in a fluid relax at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the relaxation rate is not generally known. This paper concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reached higher Reynolds numbers than ever before and covered a wide range of them ($10^4 < Re = UM/ν< 5\times10^6$), we measured the relaxation rate with the unprecedented precision of about 2\%. Here $U$ is the mean speed of the flow, $M$ the forcing scal…
The small scales of turbulence in a high-Reynolds-number jet ($Re_λ \approx 350$) are investigated with a \textmu PIV setup to overcome the optical limitations of conventional tomographic PIV setups. With the aim of validating the performances of tomographic long-distance \textmu PIV, analyses are carried out involving statistical aspects of the small scales of turbulence. The technique is assessed and the data are bench-marked to be applied to the analysis of any three dimensional small-scale phenomena in large-scale flow domains.
There exists continuous demand of improved turbulence models for the closure of Reynolds Averaged Navier-Stokes (RANS) simulations. Machine Learning (ML) offers effective tools for establishing advanced empirical Reynolds stress closures on the basis of high fidelity simulation data. This paper presents a turbulence model based on the Deep Neural Network(DNN) which takes into account the non-linear relationship between the Reynolds stress anisotropy tensor and the local mean velocity gradient as well as the near-wall effect. The construction and the tuning of the DNN-turbulence model are detai…
The elementary structures of turbulence, i.e., vortex tubes, are studied using velocity data obtained in laboratory experiments for boundary layers and duct flows at microscale Reynolds numbers 332-1934. While past experimental studies focused on intense vortex tubes, the present study focuses on all vortex tubes with various intensities. We obtain the mean velocity profile. The radius scales with the Kolmogorov length. The circulation velocity scales with the Kolmogorov velocity, in contrast to the case of intense vortex tubes alone where the circulation velocity scales with the rms velocity …
Direct numerical simulation is used to investigate the decay exponent of isotropic homogeneous turbulence over a range of Reynolds numbers sufficient to display both high and low Re number decay behavior. The initial turbulence is generated by the stirring action of the flow past many small randomly placed cubes. Stirring occurs at 1/30th of the simulation domain size so that the low-wavenumber and large scale behavior of the turbulent spectrum is generated by the fluid and is not imposed. It is shown that the decay exponent in the resulting turbulence closely matches the theoretical predictio…
Direct numerical simulations (DNS) of fully-developed turbulent channel flows for very low Reynolds numbers have been performed with a larger computational box sizes than those of existing DNS. The friction Reynolds number was decreased down to 60, where the friction Reynolds number is based on the friction velocity and the channel half width. When the Reynolds number was decreased to 60 with small computational box size, the flow became laminar. Using a large box, we found that a localized turbulence was observed to sustain in the form of periodic oblique band. This type of locally disordered…
In this paper, a turbulence model based on deep neural network is developed for turbulent flow around airfoil at high Reynolds numbers. According to the data got from the Spalart-Allmaras (SA) turbulence model, we build a neural network model that maps flow features to eddy viscosity. The model is then used to replace the SA turbulence model to mutually couple with the CFD solver. We build this suitable data-driven turbulence model mainly from the inputs, outputs features and loss function of the model. A feature selection method based on feature importance is also implemented. The results sho…
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…
In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E \textbf{92}, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us…
New scaling relations for the mean velocity and Reynolds shear stress in viscous sublayer were proposed based on the application of matched asymptotic expansion method to the mean momentum balance. It was shown that the new parameter $Λ_+$ is relevant for the wall turbulence in addition to the friction velocity. From the proposed new scaling of the viscous sublayer the power law for the mean velocity in the overlap region was derived. The complete or incomplete similarity of the parameter $Λ_+$ was shown to be the key factor, which determines whether the mean velocity obeys the power law or lo…
Using exact relations between velocity structure functions (Hill, Hill and Boratav, and Yakhot) and neglecting pressure contributions in a first approximation, we obtain a closed system and derive simple order-dependent rescaling relationships between longitudinal and transverse structure functions. By means of numerical data with turbulent Reynolds numbers ranging from $\Re_λ=320$ to $\Re_λ=730$, we establish a clear correspondence between their respective scaling range, while confirming that their scaling exponents do differ. This difference does not seem to depend on Reynolds number. Making…
Here we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity ($u$) in a high Reynolds number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26000. Taylor's frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise ($λ_x$) and spanwise ($λ_y$) length scales to the streamwise variance at a given wall height ($z$). At low Reynolds numbers, the shape of the 2-D spectra at a consta…
Direct numerical simulation of a turbulent channel flow with heat transfer was performed at very low Reynolds numbers. Two different thermal boundary conditions were studied, and temperature was considered as a passive scalar. The computations were carried out with huge computational boxes (up to 327.7 x 2 x 128 in the streamwise, wall-normal, and spanwise directions, respectively). The emphases of this paper are to investigate the large-scale structure (puff) in the intermittent-turbulent flow including the scalar fields and to provide the values of the transitional and critical Reynolds numb…
In this work, we carried out direct numerical simulations in large channel domains and studied the kinematics and dynamics of fully localised turbulent bands at Reynolds number Re = 750. Our results show that the downstream end of the band features fast streak generation and travels into the adjacent laminar flow, whereas streaks at the upstream end continually and relatively more slowly decay. This asymmetry is responsible for the transverse growth of the band. We particularly investigated the mechanism of streak generation at the downstream end, which engines the growth of the band. We ident…
We carry out Direct Numerical Simulation (DNS) of flows in closed rectangular ducts with several aspect ratios. The Navier-Stokes equations are discretized through a second-order finite difference scheme, with non-uniform grids in two directions. The duct cross-sectional area is maintained constant as well as the flow rate, which allows to investigate which is the appropriate length scale in the Reynolds number for a good scaling in the laminar and in the fully turbulent regimes. We find that the Reynolds number based on the half length of the short side leads to a critical Reynolds number whi…
A symbolic regression-based implicit algebraic stress turbulence model: incorporating the production of non-dimensional Reynolds stress deviatoric tensor
We present measurements of fluid particle accelerations in turbulent water flows between counter-rotating disks using three-dimensional Lagrangian particle tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation of fluid particle acceleration at Taylor microscale Reynolds numbers between 200 and 690. We also obtained indirect, non-intrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our experimental data provide strong support to the theoretical …
It is extremely uncommon to be able to predict the velocity profile of a turbulent flow. In two-dimensional flows, atmosphere dynamics, and plasma physics, large scale coherent jets are created through inverse energy transfers from small scales to the largest scales of the flow. We prove that in the limits of vanishing energy injection, vanishing friction, and small scale forcing, the velocity profile of a jet obeys an equation independent of the details of the forcing. We find another general relation for the maximal curvature of a jet and we give strong arguments to support the existence of …
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…
Turbulence in fluids is an ubiquitous phenomenon, characterized by spontaneous transition of a smooth, laminar flow to rapidly changing, chaotic dynamics. In 1883, Reynolds experimentally demonstrated that, in an initially laminar flow of water, turbulent motions emerge without any measurable external disturbance. To this day, turbulence remains a major unresolved phenomenon in fluid mechanics; in particular, there is a lack of a mathematical model where turbulent dynamics emerge naturally from a laminar flow. Recently, we proposed a new theory of turbulence in gases, according to which turbul…
An approximate method to compute mean velocity profiles in turbulent flows is developed. This approach is based on the equation connecting the Reynolds stress and mean velocity. By using the measured values of pressure drop and average (bulk) flow velocity, such characteristics of a turbulent flow as the mean velocity and Reynolds stress distributions were calculated and compared with the experimental measurements in different pipes and channels for various fluids and gases. These show good agreement for a wide range of Reynolds numbers.
In this work we address the open problem of high Reynolds number limit in hydrodynamic turbulence, which we modify by considering a vanishing random (instead of deterministic) viscosity. In this formulation, a small-scale noise propagates to large scales in an inverse cascade, which can be described using qualitative arguments of the Kolmogorov-Obukhov theory. We conjecture that the limit of the resulting probability distribution exists as $\mathrm{Re} \to \infty$, and the limiting flow at finite time remains stochastic even if forcing, initial and boundary conditions are deterministic. This c…
A conservative coupled finite difference-boundary element computational procedure for the simulation of turbulent magnetohydrodynamic flow in a straight rectangular duct at finite magnetic Reynolds number is presented. The flow is assumed to be periodic in the streamwise direction and is driven by a mean pressure gradient. The duct walls are considered to be electrically insulating. The co-evolution of the velocity and magnetic fields as described respectively by the Navier-Stokes and the magnetic induction equations, together with the coupling of the magnetic field between the conducting doma…
The Variable Density and Speed of Sound Vessel (VDSSV) produces subsonic turbulent flows that are both compressible and observable at all scales with existing instrumentation including hot wires and particle tracking. We realize this objective by looking at the flow of a heavy gas (sulfur hexafluoride $SF_6$), with a speed of sound almost three times lower than for air. By switching between air and $SF_6$, we isolate the influence of the turbulent Mach number (up to $M_t$ = 0.17) on turbulence statistics from the influences of changes in the Reynolds number (up to $R_λ$ = 1600), and boundary c…
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.
Turbulent flow separation induced by a protuberance on one of the walls of an otherwise planar channel is investigated using Direct Numerical Simulations. Different bulge geometries and Reynolds numbers - with the highest friction Reynolds number simulation reaching a peak of Reτ = 900 - are addressed to understand the effect of the wall curvature and of the Reynolds number on the dynamics of the recirculating bubble behind the bump. Most of the drag is due to the form contribution, whilst the friction contribution does not change appreciably with respect to an equivalent planar channel flow. …
The streamwise and transverse velocities are measured simultaneously in isotropic grid turbulence at relatively high Reynolds numbers, Re(lambda) = 110-330. Using a conditional averaging technique, we extract typical intermittency patterns, which are consistent with velocity profiles of a model for a vortex tube, i.e., Burgers vortex. The radii of the vortex tubes are several of the Kolmogorov length regardless of the Reynolds number. Using the distribution of an interval between successive enhancements of a small-scale velocity increment, we study the spatial distribution of vortex tubes. The…
Due to its very low viscosity, cryogenic helium has been used for years to generate high Reynolds turbulent flows. The measurement of velocity fluctuations in such high Reynolds flows is however a challenging issue, as it is necessary to develop small size (typically micron-length), robust sensors, to measure the whole spectrum of fluctuations of the velocity, which may extend to hundreds of kHz and possibly higher. SBT has developed for years different facilities, in particular taking benefit of the refrigeration capacities available at CEA Grenoble. In this article we present the current sta…
For low-Reynolds number shear-flows of neutrally-buoyant suspensions, the shear stress is often modeled using an effective viscosity that depends only on the solid fraction. As the Reynolds number ($Re$) is increased and inertia becomes important, the effective viscosity also depends on the Reynolds number itself. The current experiments measure the torque for flows of neutrally-buoyant particles in a coaxial-cylinder rheometer for solid fractions, $ϕ$, from 10\% to 50\% and Reynolds numbers based on particle diameter from 2 to 1,000. For experiments for Reynolds of O(10) and solid fractions l…
The most elementary structures of turbulence, i.e., vortex tubes, are studied using velocity data obtained in a laboratory experiment for boundary layers with microscale Reynolds numbers 295-1258. We conduct conditional averaging for enhancements of a small-scale velocity increment and obtain the typical velocity profile for vortex tubes. Their radii are of the order of the Kolmogorov length. Their circulation velocities are of the order of the root-mean-square velocity fluctuation. We also obtain the distribution of the interval between successive enhancements of the velocity increment as the…
