Accurate prediction of the transition from laminar flow to turbulence remains an unresolved challenge despite its importance for understanding a variety of environmental, biological, and industrial phenomena. Well over a century of concerted effort has aimed toward a quantitative, mechanistic explanation of Osborne Reynolds' seminal observation of transition to turbulence in pipe flow, typically occurring when the ratio of inertial and viscous fluid dynamic forces -- the eponymous Reynolds number -- is approximately 2000. These studies have been confounded by subsequent observations that the Reynolds number at which transition occurs can be delayed to values as high as 100,000. This record-high laminar Reynolds number has not been exceeded in any similar flow configuration for more than 70 years, however, as it required experiments to be conducted using pipe lengths of up to 18 meters housed within a bomb shelter to eliminate ambient disturbances to the flow. Here, we demonstrate a benchtop jet flow that exhibits persistent laminar flow beyond a Reynolds number of 116,000, a value limited only by the maximum flow-generating capacity of the current facility. High-speed videography of the jet shape and flow velocimetry within the jet confirm the laminar nature of the flow, even in the presence of visible ambient flow disturbances arising from non-idealities in the facility design. The measured spatial evolution of the velocity profile within the jet, approaching a "top hat" shape with increasing downstream distance, appears to promote persistence of the laminar flow. These results suggest the existence of an empirically accessible flow regime in which turbulence might be circumvented at arbitrarily high Reynolds numbers.
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
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…
It has hitherto been widely considered that a mixing layer is unstable at all Reynolds numbers. However this is untenable from energy considerations, which demand that there must exist a non-zero Reynolds number below which disturbances cannot extract energy from the mean flow. It is shown here that a linear stability analysis of similarity solutions of the plane mixing layer, including the effects of flow non-parallelism, using the minimal composite theory and the properties of adjoints following Govindarajan & Narasimha (2005), resolves the issue by yielding non-zero critical Reynolds number…
A new Strouhal-Reynolds number relationship, $St=1/(A+B/Re)$, has been recently proposed based on observations of laminar vortex shedding from circular cylinders in a flowing soap film. Since the new $St$-$Re$ relation was derived from a general physical consideration, it raises the possibility that it may be applicable to vortex shedding from bodies other than circular ones. The work presented herein provides experimental evidence that this is the case. Our measurements also show that in the asymptotic limit ($Re\rightarrow\infty$), $St_{\infty}=1/A\simeq0.21$ is constant independent of rod s…
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.
The impact of wall roughness on fully developed laminar pipe flow is investigated numerically. The roughness is comprised of square bars of varying size and pitch. Results show that the inverse relation between the friction factor and the Reynolds number in smooth pipes still persists in rough pipes, regardless of the rib height and pitch. At a given Reynolds number, the friction factor varies quadratically with roughness height and linearly with roughness pitch. We propose a single correlation for the friction factor that successfully collapses the data.
Turbulent-laminar banded patterns in plane Poiseuille flow are studied via direct numerical simulations in a tilted and translating computational domain using a parallel version of the pseudospectral code Channelflow. 3D visualizations via the streamwise vorticity of an instantaneous and a time-averaged pattern are presented, as well as 2D visualizations of the average velocity field and the turbulent kinetic energy. Simulations for Reynolds numbers descending from 2300 to 700 show the gradual development from uniform turbulence to a pattern with wavelength 20 half-gaps near Re=1900, to a patt…
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…
In pipe, channel and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we here argue that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous …
Unsteady laminar vortex shedding over a circular cylinder is predicted using a deep learning technique, a generative adversarial network (GAN), with a particular emphasis on elucidating the potential of learning the solution of the Navier-Stokes equations. Numerical simulations at two different Reynolds numbers with different time-step sizes are conducted to produce training datasets of flow field variables. Unsteady flow fields in the future at a Reynolds number which is not in the training datasets are predicted using a GAN. Predicted flow fields are found to qualitatively and quantitatively…
A turbulent-laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasi-laminar region is not the linear Couette profile, but results from a non-trivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the var…
The aim of this Letter is to characterize the flow regimes of suspensions of finite-size rigid particles in a viscous fluid at finite inertia. We explore the system behavior as function of the particle volume fraction and the Reynolds number (the ratio of flow and particle inertia to viscous forces). Unlike single phase flows where a clear distinction exists between the laminar and the turbulent states, three different regimes can be identified in the presence of a particulate phase, with smooth transitions between them. At low volume fractions, the flow becomes turbulent when increasing the R…
Results of numerical simulations obtained by a staggered finite difference scheme together with an efficient immersed boundary method are presented to understand the effects of the shape of three-dimensional obstacles on the transition of a boundary layer from a laminar to a turbulent regime. Fully resolved Direct Numerical Simulations (DNS), highlight that the closer to the obstacle the symmetry is disrupted the smaller is the transitional Reynolds number. It has been also found that the transition can not be related to the critical roughness Reynolds number used in the past. The simulations …
The turbulent flow over monochromatic waves of moderate steepness is studied by means of wall resolved LES, and cover a range of wave ages and Reynolds numbers. We compute the Fourier modes of the flow and analyse the momentum balance for the mean and fundamental mode. At low wave ages, the form drag displays a large sensitivity to changes in Reynolds number, and the interaction between turbulent and wave-induced stresses increases with Reynolds number. At higher wave ages, a quasi-laminar regime is entered, where the wave-induced stress is primarily balanced by viscous stresses. To exploit th…
We present a novel moving immersed boundary method (IBM) and employ it in direct numerical simulations (DNS) of the closed-vessel swirling von Karman flow in laminar and turbulent regimes. The IBM extends direct-forcing approaches by leveraging a time integration scheme, that embeds the immersed boundary forcing step within a semi-implicit iterative Crank-Nicolson scheme. The overall method is robust, stable, and yields excellent results in canonical cases with static and moving boundaries. The moving IBM allows us to reproduce the geometry and parameters of the swirling von Karman flow experi…
In this article, we construct a novel 1D-model of microfluidic laminar flows in tapered circular and rectangular channels assuming the flow in channels fully developed. In the model, we take into account the inertance and dynamic pressure terms. The model can be used for a wide range of flows: from the pure capillary flow regime, where the capillary forces are the main driver of the liquid in the channel, to the external pressure flow regime where the external pressure applied to the liquid at the entrance to the channel is much larger than the capillary pressure in the channel, so that the ca…
The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study such fluctuations in order to measure the time-scale of the transition efficiently. The method is composed of two parts: (i) the measurement of typical fluctuations (the bulk part of an accumulative probability function) and (ii) the measurement of rare fluctuations (the tail part of the probability function) by employing dynamics where a feedback control o…
We study the inertial migration of finite-size neutrally buoyant spherical particles in dilute and semi-dilute suspensions in laminar square duct flow. We perform several direct numerical simulations using an immersed boundary method to investigate the effects of the bulk Reynolds number $Re_b$, particle Reynolds number $Re_p$ and duct to particle size ratio $h/a$ at different solid volume fractions $ϕ$, from very dilute conditions to $20\%$. We show that the bulk Reynolds number $Re_b$ is the key parameter in inertial migration of particles in dilute suspensions. At low solid volume fraction …
Forward-swept wings offer unique advantages in the aerodynamic performance of air vehicles. However, the low-Reynolds-number characteristics of such wings have not been explored in the past. In this work, we numerically study laminar separated flows over forward-swept wings with semi aspect ratios $sAR=0.5$ to 2 at a chord-based Reynolds number of 400. Forward-swept wings generate wakes that are significantly different from those of backward-swept wings. For low-aspect-ratio forward wings, the wakes remain steady due to the strong downwash effects induced by the tip vortices. For larger aspect…
A numerical study of the problem of laminar infinite flow of viscous incompressible fluid around a rotating circular cylinder at Reynolds number $ 50 \le {\rm Re} \le 500 $ and dimensionless rotation rate $ 0 \le α\le 7 $ has been carried out. The parametric map of flow regimes has been constructed, where two zones of steady and two zones of periodic solutions are signed out. The dependencies of the drag and lift coefficients on the rotation rate for $ {\rm Re} = 200 $ are studied in detail. Convergence of the numerical solution to the known asymptotic solution at large $ α$ is confirmed.
The convective heat transfer and flow behavior of graphene-water nanofluids are studied experimentally by focusing on transitional flow. Graphene-water nanofluids with different particle mass fractions (0.025, 0.1 and 0.2%) are produced following two-step method and using PVP as a surfactant. Thermo-physical characterization is performed by measuring viscosity and thermal conductivity of the nanofluids. Convection characteristics are experimentally studied from laminar to turbulent flow regimes. It is seen that pressure drop increases dramatically in the transition region, and laminar to turbu…
Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code ChannelFlow in a narrow computational domain tilted by $24^{\circ}$ with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances…
We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increas…
We show that Directed Percolation (DP) simulations in a pipe geometry in 3+1 dimensions fully capture the observed complex phenomenology of the transition to turbulence. At low Reynolds numbers (Re), turbulent puffs form and spontaneously relaminarize. At high Re, turbulent slugs expand uniformly into the laminar regions. In a spatiotemporally intermittent state between these two regimes of Re, puffs split and turbulent regions exhibit laminar patches. DP also captures the main quantitative features of the transition, with a superexponentially diverging characteristic lifetime below the transi…
The transitional boundary layer flow over a flat plate is investigated. The boundary layer flow is known to develop unstable Tollmien-Schlichting waves above a critical value of the Reynolds number. However, it is also known that this transition can be observed for sub-critical Reynolds numbers. In that case, the basin of attraction of the laminar state coexists with the sustained turbulence. In this article, the trajectory on the separatrix between these two states is simulated. The state on the separatrix is independent from the initial condition and is dynamically connected to both the lami…
The drag of turbulent flows can be drastically decreased by addition of small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view we will show in the following that for an appropriate choice of parameters polymers can reduce the drag beyond the suggested asymptotic limit, eliminating tur…
Regular patterns of turbulent and laminar fluid motion arise in plane Couette flow near the lowest Reynolds number for which turbulence can be sustained. We study these patterns using an extension of the minimal flow unit approach to simulations of channel flows pioneered by Jimenez and Moin. In our case, computational domains are of minimal size in only two directions. The third direction is taken to be large. Furthermore, the long direction can be tilted at any prescribed angle to the streamwise direction. We report on different patterned states observed as a function of Reynolds number, imp…
It is well known that the Boussinesq turbulent viscosity hypothesis can yield inaccurate predictions when complex f low features are involved, e.g. laminar-turbulent transition. The focus of the study is to explore the capability of a physics-based uncertainty quantification (UQ) approach to quantify the model-form uncertainty in Reynolds-averaged Naiver-Stokes (RANS) simulations of laminar-turbulent transitional flows over an Selig-Donovan (SD) 7003 airfoil. This methodology perturbs the modeled Reynolds stress tensor in the momentum equations; perturbations are injected into the amplitude, e…
We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations using a direct-forcing immersed boundary method to account for the dispersed phase. A volume of fluid approach is employed to solve the temperature field inside and outside of the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the …
It is well known that Boussinesq turbulent-viscosity hypothesis can introduce uncertainty in predictions for complex flow features such as separation, reattachment, and laminar-turbulent transition. This study adopts a recent physics-based uncertainty quantification (UQ) approach to address such model form uncertainty in Reynolds-averaged Naiver- Stokes (RANS) simulations. Thus far, almost all UQ studies have focused on quantifying the model form uncertainty in turbulent flow scenarios. The focus of the study is to advance our understanding of the performance of the UQ approach on two differen…
On the basis of the viscous Saint-Venant equations, hydraulic jumps in laminar open channel flow are obtained as continuous shock structures. Thanks to the inclusion of viscosity, the jumps are not abrupt, rendering the classic patchwork via the Rankine-Hugoniot shock relations unnecessary. The jumps arise as stable stationary solutions of the governing equations and lend themselves excellently to a Dynamical Systems analysis, manifesting themselves as near-parabolic trajectories in phase space. Based on this, we derive an analytic expression for the jump length as a function of the Froude and…
Large eddy simulations are performed to study tonal noise generation by a NACA0012 airfoil at an angle of attack ${α= 3}$ deg. and freestream Mach number of ${M_{\infty} = 0.3}$. Different Reynolds numbers are analyzed spanning ${0.5 \times 10^5 \le Re \le 4 \times 10^5}$. Results show that the flow patterns responsible for noise generation appear from different laminar separation bubbles, including one observed over the airfoil suction side and another near the trailing edge, on the pressure side. For lower Reynolds numbers, intermittent vortex dynamics on the suction side results in either c…
We study Kolmogorov flow on a three dimensional, periodic domain with aspect ratios fixed to unity. Using an energy method, we give a concise proof of the linear stability of the laminar flow profile. Since turbulent motion is observed for high enough Reynolds numbers, we expect the domain of attraction of the laminar flow to be bounded by the stable manifolds of simple invariant solutions. We show one such edge state to be an equilibrium with a spatial structure reminiscent of that found in plane Couette flow, with stream wise rolls on the largest spatial scales. When tracking the edge state,…
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…
The flow phenomena around a rotating elliptic cylinder in a channel is studied numerically. The value of the confinement parameter βis varied as \frac{1}{k}, where k = 2, 4, 6, and 8 respectively, to demonstrate the vortex-shedding patterns around the cylinder in the downstream wake. The non-dimensional rotation rate αtakes up 0.5, 1, and 2 as its value. Additionally, the Reynolds number (\textit{Re}) based on the cylinder diameter is taken to be 50, 100, and 150 respectively. A parametric study is performed to explain the changes in drag coefficient \textit{(C_{D})}, lift coefficient \textit{…
Annular Couette flow is the flow between two coaxial cylinders driven by the axial translation of the inner cylinder. It is investigated using direct numerical simulation in long domains, with an emphasis on the laminar-turbulent coexistence regime found for marginally low values of the Reynolds number. Three distinct flow regimes are demonstrated as the radius ratio $η$ is decreased from 0.8 to 0.5 and finally to 0.1. The high-$η$ regime features helically-shaped turbulent patches coexisting with laminar flow, as in planar shear flows. The moderate-$η$ regime does not feature any marked lamin…
The identification of stream in the straight pipe as a flexible rod has allowed to present the criterion expression for determination of transition of the laminar flow regime to the turbulent as a loss of stability of the rectilinear static structure of translational motion of stream in pipe and its transition to the flexural-vortical dynamic structure of translational motion, just as a flexible rod buckling. The introduced criterion allows to take into account an influencing of the inlet geometry, the pipe length, the flow velocity, and also of any physical factors on stability of the rectili…
Hysteresis has been observed in a study of the transition between laminar flow and vortex shedding in a quasi-two dimensional system. The system is a vertical, rapidly flowing soap film which is penetrated by a rod oriented perpendicular to the film plane. Our experiments show that the transition from laminar flow to a periodic Kármán vortex street can be hysteretic, i.e. vortices can survive at velocities lower than the velocity needed to generate them.
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.
An outline of the state space of planar Couette flow at high Reynolds numbers ($Re < 10^5$) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of {\it Hairpin Vortex State} (HVS) asymptotically approaches the primary (laminar) state with increasing $Re$. It is also predicted that the lower branch of HVS at high $Re$ belongs to the stability boundary that initiates transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criter…
We explore the laminar to turbulence transition of round jets at low Reynolds number (Re < 1000) using a novel experimental setup and linear stability theory (LST). The setup has a large domain and a low disturbance environment which increases the critical Re to approximately 500, permitting the appearance of a hitherto unknown puff-like instability (PFI). The instability is identified in the self-similar region of the jet through clean flow visualizations (FV) and further corroborated by particle image velocimetry (PIV) measurements. For 400< Re <700, the flow exhibits PFI embedded in a puff-…
We perform direct numerical simulations of laminar separated flows over finite-aspect-ratio swept wings at a chord-base Reynolds number of $Re = 400$ to reveal a variety of wake structures generated for a range of aspect ratios ($sAR=0.5-4$), angles of attack ($α=16^{\circ}-30^{\circ}$), and sweep angles ($Λ=0^{\circ}-45^{\circ}$). Flows behind swept wings exhibit increased complexity in their dynamical features compared to unswept-wing wakes. For unswept wings, the wake dynamics are predominantly influenced by the tip effects. Steady wakes are mainly limited to low-aspect-ratio wings. Unstead…
Large Eddy Simulations of a flow at a moderate Reynolds number over and around a three-dimensional hill have been performed. The main aim of the simulations was to study the effects of various inflow conditions (boundary layer thickness and laminar versus turbulent boundary layers) on the flow behind the hill. The main features of the flow behind the hill are similar in all simulations, however various differences are observed. The topology of the streamlines (friction lines) on the surface adjacent to the lower wall was found to be independent of the inflow conditions prescribed and comprised…
A study of fully developed plane turbulent channel flow subject to spanwise system rotation through direct numerical simulations is presented. In order to study both the influence of the Reynolds number and spanwise rotation on channel flow, the Reynolds number $Re = U_b h/ν$ is varied from a low 3000 to a moderate $31\,600$ and the rotation number $Ro = 2 Ωh/U_b$ is varied from 0 to 2.7, where $U_b$ is the mean bulk velocity, $h$ the channel half gap and $Ω$ the system rotation rate. The mean streamwise velocity profile displays also at higher $Re$ the characteristic linear part with a slope …
Turbulence in the flow of fluid through a pipe can be suppressed by buoyancy forces. As the suppression of turbulence leads to severe heat transfer deterioration, this is an important and undesirable phenomenon in both heating and cooling applications. Vertical flow is often considered, as the axial buoyancy force can help drive the flow. With heating measured by the buoyancy parameter $C$, our DNS show that shear-driven turbulence may either be completely laminarised or transitions to a relatively quiescent convection-driven state. Buoyancy forces cause a flattening of the base flow profile, …
