Universal threshold of the transition to localized turbulence in shear flows

Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows. By scaling analysis of a disturbed-flow model, this paper proposes a local Reynolds number Re_M to characterize the threshold of transition triggered by finite-amplitude disturbances. The Re_M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion. The lower critical Re_M observed in experiments of plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow are all close to 323, indicating the uniformity of mechanism governing the transition to localized turbulence.     

Intermittency as a transition to turbulence in pipes: A long tradition from Reynolds to the 21st century

Intermittencies are commonly observed in fluid mechanics, and particularly, in pipe flows. Initially observed by Reynolds (1883), it took one century for reaching a rather full understanding of this phenomenon whose irregular dynamics (apparently stochastic) puzzled hydrodynamicists for decades. In this brief (non-exhaustive) review, mostly focused on the experimental characterization of this transition between laminar and turbulent regimes, we present some key contributions for evidencing the two concomittant and antagonist processes that are involved in this complex transition and were suggested by Reynolds. It is also shown that a clear explicative model was provided, based on the nonlinear dynamical systems theory, the experimental observations in fluid mechanics only providing an applied example, due to its obvious generic nature.     

A mesoscopic modelling approach for direct numerical simulations of transition to turbulence in hypersonic flow with transpiration cooling

A rescaling methodology is developed for high-fidelity, cost-efficient direct numerical simulations (DNS) of flow through porous media, modelled at mesoscopic scale, in a hypersonic freestream. The simulations consider a Mach 5 hypersonic flow over a flat plate with coolant injection from a porous layer with 42 % porosity. The porous layer is designed using a configuration studied in the literature, consisting of a staggered arrangement of cylinder/sphere elements. A characteristic Reynolds number ${\mathit{Re}}_c$ of the flow in a pore cell unit is first used to impose aerodynamic similarity between different porous layers with the same porosity, $∊$, but different pore size. A relation between the pressure drop and the Reynolds number is derived to allow a controlled rescaling of the pore size from the realistic micrometre scales to higher and more affordable scales. Results of simulations carried out for higher cylinder diameters, namely 24 μm, 48 μm and 96 μm, demonstrate that an equivalent Darcy-Forchheimer behaviour to the reference experimental microstructure is obtained at the different pore sizes. The approach of a porous layer with staggered spheres is applied to a 3D domain case of porous injection in the Darcy limit over a flat plate, to study the transition mechanism and the associated cooling performance, in comparison with a reference case of slot injection. Results of the direct numerical simulations show that porous injection in an unstable boundary layer leads to a more rapid transition process, compared to slot injection. On the other hand, the mixing of coolant within the boundary layer is enhanced in the porous injection case, both in the immediate outer region of the porous layer and in the turbulent region. This has the beneficial effect of increasing the cooling performance by reducing the temperature near the wall, which provides a higher cooling effectiveness, compared to the slot injection case, even with an earlier transition to turbulence.     

Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe

The bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. The bubble characteristics were measured using a dual optical probe, while the liquid-phase turbulence was measured using hot-film anemometry. Measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. At low void fraction flow, the radial void fraction distribution showed a wall peak which changed to a core peak profile as the void fraction was increased. The liquid average velocity and the turbulence intensities were less uniform in the core region of the pipe as the void fraction profile changed from a wall to a core peak. In general, there is an increase in the turbulence intensities when the bubbles are introduced into the flow. However, a turbulence suppression was observed close to the wall at high liquid superficial velocities for low void fractions up to about 1.6%. The net radial interfacial force on the bubbles was estimated from the momentum equations using the measured profiles. The radial migration of the bubbles in the core region of the pipe, which determines the shape of the void profile, was related to the balance between the turbulent dispersion and the lift forces. The ratio between these forces was characterized by a dimensionless group that includes the area averaged Eötvös number, slip ratio, and the ratio between the apparent added kinetic energy to the actual kinetic energy of the liquid. A non-dimensional map based on this dimensionless group and the force ratio is proposed to distinguish the conditions under which a wall or core peak void profile occurs in bubbly flows.     

Tertiary and quarternary states of fluid flow and the transition to turbulence

The sequence of bifurcations from simple to complex forms of fluid motion can be studied numerically in the case of systems with high degrees of external symmetries. The relevance of tertiary and quarternary states for the problem of turbulence is discussed and as an example asymmetric traveling wave convection in a fluid layer heated from below is described.     

Application of the SAS turbulence model to predict the unsteady flow field behaviour in a forward centrifugal fan

In the current study, the unsteady flow in a centrifugal fan is carried out using Computational Fluid Dynamics calculation based on the Scale Adaptive Simulation (SAS) approach to model the turbulence phenomenon. The SAS concept is based on the introduction of the von Karman length scale into the turbulence scale equation. The information provided by the von Karman length scale allows SAS models to dynamically adjust to resolved structures in an Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulation, which results in a Large Eddy Simulation-like behaviour in unsteady regions of the flow field. At the same time, the model provides standard RANS capabilities in stable flow regions. The introduction of the von Karman length scale is based on the reformulation of Rottas's equation for the integral length scale. To validate the numerical results, the overall performances of the fan and the wall pressure fluctuations computed upon the volute casing surface are compared with the unsteady measured data.     

A variant of the low-Reynolds-number two-equation turbulence model applied to variable property mixed convection flows

Previous work has demonstrated that the low-Reynolds-number model of Launder and Sharma (1974) offers significant advantages over other two-equation turbulence models in the computation of highly non-universal buoyancy-influenced (or “mixed convection”) pipe flows. It is known, however, that the Launder and Sharma model does not possess high quantitative accuracy in regard to simpler forced convection flows. A variant of the low-Reynolds-number scheme is developed here by reference to data for constant property forced convection flows. The re-optimized model and the Launder and Sharma formulation are then examined against experimental measurements for mixed convection flows, including cases in which variable property effects are significant.     

Kinematics and dynamics of small-scale vorticity and strain-rate structures in the transition from isotropic to shear turbulence

We applied a technique that defines and extracts “structures” from a DNS dataset of a turbulence variable in a way that allows concurrent quantitative and visual analysis. Local topological and statistical measures of enstrophy and strain-rate structures were compared with global statistics to determine the role of mean shear in the dynamical interactions between fluctuating vorticity and strain-rate during transition from isotropic to shear-dominated turbulence. We find that mean shear adjusts the alignment of fluctuating vorticity, fluctuating strain-rate in principal axes, and mean strain-rate in a way that (1) enhances both global and local alignments between vorticity and the second eigenvector of fluctuating strain-rate, (2) two-dimensionalizes fluctuating strain-rate, and (3) aligns the compressional components of fluctuating and mean strain-rate. Shear causes amalgamation of enstrophy and strain-rate structures, and suppresses the existence of strain-rate structures in low-vorticity regions between enstrophy structures. A primary effect of shear is to enhance “passive” strain-rate fluctuations, strain-rate kinematically induced by local vorticity concentrations with negligible enstrophy production, relative to “active,” or vorticity-generating strain-rate fluctuations. Enstrophy structures separate into “active” and “passive” based on the level of the second eigenvalue of fluctuating strain-rate. We embedded the structure-extraction algorithm into an interactive visualization-based analysis system from which the time evolution of a shear-induced hairpin enstrophy structure was visually and quantitatively analyzed. The structure originated in the initial isotropic state as a vortex sheet, evolved into a vortex tube during a transitional period, and developed into a well-defined horseshoe vortex in the shear-dominated asymptotic state.     

Transition from vortex to wall driven turbulence production in the Taylor–Couette system with a rotating inner cylinder

Axisymmetrically stable turbulent Taylor vortices between two concentric cylinders are studied with respect to the transition from vortex to wall driven turbulent production. The outer cylinder is stationary and the inner cylinder rotates. A low Reynolds number turbulence model using the k‐ω formulation, facilitates an analysis of the velocity gradients in the Taylor–Couette flow. For a fixed inner radius, three radius ratios 0.734, 0.941 and 0.985 are employed to identify the Reynolds number range at which this transition occurs. At relatively low Reynolds numbers, turbulent production is shown to be dominated by the outflowing boundary of the Taylor vortex. As the Reynolds number increases, shear driven turbulence (due to the rotating cylinder) becomes the dominating factor. For relatively small gaps turbulent flow is shown to occur at Taylor numbers lower than previously reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Evolution of shock waves and the primary vortex loop discharged from a square cross-sectional tube

In this paper, a numerical and experimental investigation of the evolution of a transmitting shock wave and its associated primary vortex loop, which are discharged from the open end of a square cross-sectional tube, is described. The experiments were conducted in the square tube connected to a diaphragmless shock tube and the flowfield was visualized from the axial direction with diffusive holographic interferometry. The numerical simulations were carried out by solving the three-dimensional Euler equations with a dispersion-controlled scheme. The numerical results were displayed in the form of interferograms to compare them with experimental interferograms. Good agreement between the numerical and experimental results was obtained. More detailed numerical calculations were carried out, from which the three-dimensional transition of the shock wave configuration from an initial planar to a spherical shape and the development of the primary vortex loop from a square shaped to a three-dimensional structure were clearly observed and interpreted. Received 29 January 1998 / Accepted 22 May 1998     

Effect of a helical wire on mixed convection heat transfer to carbon dioxide in a vertical circular tube at supercritical pressures

Reactor core of a SCWR (supercritical water-cooled reactor) employs a tight lattice in order to efficiently remove heat from nuclear fuels. In the narrow sub-channels of a tight lattice reactor core, a helical wire instead of a complicated conventional spacer has been used as a turbulence generator and a space-keeper between the fuel rods.A series of experiments were performed in order to investigate an effect of a helical wire on heat transfer to upwardly flowing CO₂ in a electrically-heated circular tube with an inner diameter of 6.32 mm, where a helical wire with an outer diameter of 1.3 mm was tightly inserted inside the tube. The tube inner diameter corresponds to the equivalent hydraulic diameter of a sub-channel of a KAERI’s fuel assembly concept. The mass fluxes ranged from 400 to 1200 kg/m² s; the heat fluxes ranged from 30 to 90 kW/m²; and the pressures were 7.75 and 8.12 MPa. The corresponding Reynolds numbers at the test section inlet ranged from 1.8 × 10⁴ to 7.5 × 10⁴. The heat transfer rate reached almost twice the value obtained from the experiment with a plain tube of the same size near the pseudocritical temperature and the effect of a wire was attenuated as the temperature moved away from the pseudocritical temperature. The wall temperature distribution along the span between the contact points was a concave downward parabola. Near the pseudocritical temperature, the wall temperature showed relatively higher values, indicating a stagnant fluid around the wire. On the other hand, the wall temperature at the contact point showed a relatively lower value, indicating a fin function of a wire.     

Direct numerical simulation of transition to turbulence in an oscillatory channel flowSimulation numérique de la transition vers la turbulence d'un ecoulement oscillant dans une conduite bi-dimensionnelle

In this Note, we present results of the numerical simulation of transition to turbulence for a purely oscillatory channel flow. These simulations were performed for various values of the Reynolds number, the so-called Stokes parameter being equal to 4. The methodology used for the flow simulation relies on a combination of finite element space approximations with time-discretization by operator splitting; it has shown to be very effective, even when it is applied to relatively complex domains with strong expansions at the inlet and outlet of the channel. The numerical results obtained agree qualitatively well with previous experiments by other investigators. To cite this article: L.H. Juárez, E. Ramos, C. R. Mecanique 331 (2003).     

High-fidelity numerical simulation of the flow field around a NACA-0012 aerofoil from the laminar separation bubble to a full stall

In the present work, large eddy simulations of the flow field around a NACA-0012 aerofoil near stall conditions are performed at a Reynolds number of 5 × 10⁴, Mach number of 0.4, and at various angles of attack. The results show the following: at relatively low angles of attack, the bubble is present and intact; at moderate angles of attack, the laminar separation bubble bursts and generates a global low-frequency flow oscillation; and at relatively high angles of attack, the laminar separation bubble becomes an open bubble that leads the aerofoil into a full stall. Time histories of the aerodynamic coefficients showed that the low-frequency oscillation phenomenon and its associated physics are indeed captured in the simulations. The aerodynamic coefficients compared to previous and recent experimental data with acceptable accuracy. Spectral analysis identified a dominant low-frequency mode featuring the periodic separation and reattachment of the flow field. At angles of attack α ≤ 9.3°, the low-frequency mode featured bubble shedding rather than bubble bursting and reformation. The underlying mechanism behind the quasi-periodic self-sustained low-frequency flow oscillation is discussed in detail.