Flow Relaminarization Research Articles

LES of Stably Stratified Flow with Varying Thermophysical Properties

Large eddy simulations of stably stratified, turbulent channel flow subjected to a large temperature gradient have been performed by considering a broad spectrum of stratification. Due to a large thermal gradient across the channel, temperature-dependent fluid properties like viscosity (µ), density (ρ), and thermal conductivity (κ) are considered as variables. With increased stratification, a cluster of laminar patches appears in the near-wall region, and turbulent momentum and buoyancy fluxes are suppressed drastically in the core of the channel due to the formation of internal gravity waves. Variable viscosity results in flow relaminarization on the hot side of the channel (where viscosity is higher). Density tends to stablize the flow by blocking the upward movement of thermal plumes, while thermal conductivity pays the toll for viscosity at high Reynolds number. A mechanistic model for wall heat transfer is developed for buoyancy-effected flows. We have observed qualitatively and quantitatively the pronounced modifications in turbulent structure and flow statistics.

Numerical simulation of turbulent flow through Schiller’s wavy pipe

AbstractThe development of incompressible turbulent flow through a pipe of wavy cross-section was studied numerically by direct integration of the Navier–Stokes equations. Simulations were performed at Reynolds numbers of $4.5\times 10^{3}$ and $10^{4}$ based on the hydraulic diameter and the bulk velocity. Results for the pressure resistance coefficient ${\it\lambda}$ were found to be in excellent agreement with experimental data of Schiller (Z. Angew. Math. Mech., vol. 3, 1922, pp. 2–13). Of particular interest is the decrease in ${\it\lambda}$ below the level predicted from the Blasius correlation, which fits almost all experimental results for pipes and ducts of complex cross-sectional geometries. Simulation databases were used to evaluate turbulence anisotropy and provide insights into structural changes of turbulence leading to flow relaminarization. Anisotropy-invariant mapping of turbulence confirmed that suppression of turbulence is due to statistical axisymmetry in the turbulent stresses.

Numerical Investigation of Aerothermal Characteristics of the Blade Tip and Near-Tip Regions of a Transonic Turbine Blade

In modern gas turbine engines, the blade tips and near-tip regions are exposed to high thermal loads caused by the tip leakage flow. The rotor blades are therefore carefully designed to achieve optimum work extraction at engine design conditions without failure. However, very often gas turbine engines operate outside these design conditions which might result in sudden rotor blade failure. Therefore, it is critical that the effect of such off-design turbine blade operation be understood to minimize the risk of failure and optimize rotor blade tip performance. In this study, the effect of varying the exit Mach number on the tip and near-tip heat transfer characteristics was numerically studied by solving the steady Reynolds averaged Navier Stokes (RANS) equation. The study was carried out on a highly loaded flat tip rotor blade with 1% tip gap and at exit Mach numbers of Mexit = 0.85 (Reexit = 9.75 × 105) and Mexit = 1.0 (Reexit = 1.15 × 106) with high freestream turbulence (Tu = 12%). The exit Reynolds number was based on the rotor axial chord. The numerical results provided detailed insight into the flow structure and heat transfer distribution on the tip and near-tip surfaces. On the tip surface, the heat transfer was found to generally increase with exit Mach number due to high turbulence generation in the tip gap and flow reattachment. While increase in exit Mach number generally raises he heat transfer over the whole blade surface, the increase is significantly higher on the near-tip surfaces affected by leakage vortex. Increase in exit Mach number was found to also induce strong flow relaminarization on the pressure side near-tip. On the other hand, the size of the suction surface near-tip region affected by leakage vortex was insensitive to changes in exit Mach number but significant increase in local heat transfer was noted in this region.

Numerical simulation of flow turbulization and relaminarization by active external actions

The Menter γ - Reθ laminar-turbulent transition model is generalized in order to use it with turbulence models other than SST. The agreement with the results of the initial model and the experiment for computations in conjunction with the Spalart-Allmaras turbulence model is demonstrated. The influence of a local energy supply in the boundary layer region on the region of the laminar-turbulent transition at the supersonic flow is studied numerically. It is shown that the transition can be delayed by the energy supply.

Direct numerical simulations of laminar separation bubbles: investigation of absolute instability and active flow control of transition to turbulence

AbstractLaminar separation bubbles generated on a flat plate by an adverse pressure gradient are investigated using direct numerical simulations (DNSs). Two-dimensional periodic forcing is applied at a blowing/suction slot upstream of separation. Control of separation through forcing with various frequencies and amplitudes is examined. For the investigation of absolute instability mechanisms, baseflows provided by two-dimensional Navier–Stokes calculations are analysed by introducing pulse disturbances and computing the three-dimensional flow response using DNS. The primary instability of the time-averaged flow is investigated with a local linear stability analysis. Employing a steady flow solution as baseflow, the nonlinear and non-parallel effects on the self-sustained disturbance development are illustrated, and a feedback mechanism facilitated by the upstream flow deformation is identified. Secondary instability is investigated locally using spatially periodic baseflows. The flow response to pulsed forcing indicates the existence of an absolute secondary instability mechanism, and the results indicate that this mechanism is dependent on the periodic forcing. Results from three-dimensional DNS provide insight into the global instability mechanisms of separation bubbles and complement the local analysis. A forcing strategy was devised that suppresses the temporal growth of three-dimensional disturbances, and as a consequence, breakdown to turbulence does not occur. Even for a separation bubble that has transitioned to turbulence, the flow relaminarizes when applying two-dimensional periodic forcing with proper frequencies and amplitudes.

The effect of neutrally buoyant finite-size particles on channel flows in the laminar-turbulent transition regime

The presence of finite-size particles in a channel flow close to the laminar-turbulent transition is simulated with the Force Coupling Method which allows two-way coupling with the flow dynamics. Spherical particles with channel height-to-particle diameter ratio of 16 are initially randomly seeded in a fluctuating flow above the critical Reynolds number corresponding to single phase flow relaminarization. When steady-state is reached, the particle volume fraction is homogeneously distributed in the channel cross-section (ϕ ≅ 5%) except in the near-wall region where it is larger due to inertia-driven migration. Turbulence statistics (intensity of velocity fluctuations, small-scale vortical structures, wall shear stress) calculated in the fully coupled two-phase flow simulations are compared to single-phase flow data in the transition regime. It is observed that particles increase the transverse r.m.s. flow velocity fluctuations and they break down the flow coherent structures into smaller, more numerous and sustained eddies, preventing the flow to relaminarize at the single-phase critical Reynolds number. When the Reynolds number is further decreased and the suspension flow becomes laminar, the wall friction coefficient recovers the evolution of the laminar single-phase law provided that the suspension viscosity is used in the Reynolds number definition. The residual velocity fluctuations in the suspension correspond to a regime of particulate shear-induced agitation.

Nusselt number and friction factor in thermally stratified turbulent channel flow under Non-Oberbeck–Boussinesq conditions

In stably stratified turbulence, computations under Oberbeck–Boussinesq (OB) hypothesis of temperature-independent fluid properties may lead to inaccurate representation of the flow field and to wrong estimates of momentum/heat transfer coefficients. This is clearly assessed here comparing direct numerical simulations of stratified turbulence under OB conditions to simulations under NOB (Non-Oberbeck–Boussinesq) conditions of temperature-dependent fluid viscosity and thermal expansion coefficient. Compared to the OB case, NOB conditions may induce local flow relaminarization with significant variations (up to 30%) of heat and momentum transfer coefficients. Together with DNS results, we propose a phenomenological model (based on turbulent bursts) for heat transfer prediction in stratified turbulence under OB and NOB conditions. Implications of NOB assumptions on mixing efficiency (i.e. flux Richardson number Rif) and turbulent Prandtl number (Prt) are also discussed. These results are of specific importance in RANS modelling, where the condition Prt=1 is usually assumed (Reynolds analogy). Although this assumption is valid in some situations (i.e. boundary layer, pipe flow) there is uncertainty about its validity for stably-stratified turbulence. We demonstrate that this assumption is inaccurate when NOB effects become significant.

Assessment of Reynolds stresses tensor reconstruction methods for synthetic turbulent inflow conditions. Application to hybrid RANS/LES methods

Hybrid or zonal RANS/LES approaches are recognized as the most promising way to accurately simulate complex unsteady flows under current computational limitations. One still open issue concerns the transition from a RANS to a LES or WMLES resolution in the stream-wise direction, when near wall turbulence is involved. Turbulence content has then to be prescribed at the transition to prevent from turbulence decay leading to possible flow relaminarization. The present paper aims to propose an efficient way to generate this switch, within the flow, based on a synthetic turbulence inflow condition, named Synthetic Eddy Method (SEM). As the knowledge of the whole Reynolds stresses is often missing, the scope of this paper is focused on generating the quantities required at the SEM inlet from a RANS calculation, namely the first and second order statistics of the aerodynamic field. Three different methods based on two different approaches are presented and their capability to accurately generate the needed aerodynamic values is investigated. Then, the ability of the combination SEM+Reconstruction method to manufacture well-behaved turbulence is demonstrated through spatially developing flat plate turbulent boundary layers. In the mean time, important intrinsic features of the Synthetic Eddy method are pointed out. The necessity of introducing, within the SEM, accurate data, with regards to the outer part of the boundary layer, is illustrated. Finally, user’s guidelines are given depending on the Reynolds number based on the momentum thickness, since one method is suitable for low Reynolds number while the second is dedicated to high ones with a transition located around Reθ=3000.

Taylor-Couette flow control using the outer cylinder cross-section variation strategy

A numerical study of a controlled flow evolving in a Taylor-Couette system is presented in this paper. The study is devoted to investigate the effect of the outer cylinder cross-section variation on the flow behavior. It is aimed to make assessment of the flow response in terms of the criticality of the early transitional flow regimes and the accompanying flow topology alterations. The numerical simulations are carried out on the Fluent software package for a three-dimensional incompressible flow. The basic system is characterized by a height H = 200 mm, a ratio of the inner to the outer cylinders radii η = 0.9, an aspect ratio corresponding to the cylinders height reported to the gap length Г = 40 and a ratio of the gap to the radius of the inner cylinder δ = 0.1. The numerical deformation of the outer cylinder is executed using the dynamic mesh program according to a predefined function implemented in a homemade program as an UDF (user defined function). It is established that the first instability mode of transition is retarded from Ta c1 = 41.33, corresponding to the first Taylor number critical value, to Ta c1 = 70 when the deforming amplitude is equal to 15% the external cylinder diameter value. This flow relaminarization process is accompanied by substantial modifications in the flow behavior and configuration.

Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties

AbstractDirect numerical simulation (DNS) is used to study the behaviour of stably-stratified turbulent channel flow with temperature-dependent fluid properties: specifically, viscosity ($\ensuremath{\mu} $) and thermal expansion coefficient ($\ensuremath{\beta} $). The governing equations are solved using a pseudo-spectral method for the case of turbulent water flow in a channel. A systematic campaign of simulations is performed in the shear Richardson number parameter space (${\mathit{Ri}}_{\tau } = \mathit{Gr}/ {\mathit{Re}}_{\tau } $, where $\mathit{Gr}$ is the Grashof number and ${\mathit{Re}}_{\tau } $ the shear Reynolds number), imposing constant-temperature boundary conditions. Variations of ${\mathit{Ri}}_{\tau } $ are obtained by changing ${\mathit{Re}}_{\tau } $ and keeping $\mathit{Gr}$ constant. Independently of the value of ${\mathit{Ri}}_{\tau } $, all cases exhibit an initial transition from turbulent to laminar flow. A return transition to turbulence is observed only if ${\mathit{Ri}}_{\tau } $ is below a threshold value (which depends also on the flow Reynolds number). After the transient evolution of the flow, a statistically-stationary condition occurs, in which active turbulence and internal gravity waves (IGW) coexist. In this condition, the transport efficiency of momentum and heat is reduced considerably compared to the condition of non-stratified turbulence. The crucial role of temperature-dependent viscosity and thermal expansion coefficient is directly demonstrated. The most striking feature produced by the temperature dependence of viscosity is flow relaminarization in the cold side of the channel (where viscosity is higher). The opposite behaviour, with flow relaminarization occurring in the hot side of the channel, is observed when a temperature-dependent thermal expansion coefficient is considered. We observe qualitative and quantitative modifications of structure and wall-normal position of internal waves compared to previous results obtained for uniform or quasi-uniform fluid properties. From the trend we observe in the investigated low-Reynolds-number range, we can hypothesize that, whereas the effects of temperature-dependent viscosity may be masked at higher Reynolds number, the effects of temperature-dependent thermal expansion coefficient will persist.

Relaminarization of Axisymmetric Turbulent Flow With Combined Axial Jet and Side Injection in a Pipe

The effect of side mass injection on turbulent flow with axial entry to a circular duct in the form of centrally confined jet has been investigated. A standard κ-ε model modified for streamline curvature has been used for detailed analysis following a comparison with a κ-ω model for some test cases. Results show that flow stabilization and relaminarization could occur due to the side injection. The predicted recirculation zone, friction factor, total turbulent energy, turbulent shear stress, Taylor scale Reynolds number, and turbulent energy flux show gradual reduction with increase in the side injection velocity.

Turbidity current with a roof: Direct numerical simulation of self‐stratified turbulent channel flow driven by suspended sediment

In this work we present direct numerical simulations (DNS) of sediment‐laden channel flows. In contrast to previous studies, where the flow has been driven by a constant, uniform pressure gradient, our flows are driven by the excess density imposed by suspended sediment. This configuration provides a simplified model of a turbidity current and is thus called the turbidity current with a roof configuration. Our calculations elucidate with DNS for the first time several fascinating features of sediment‐laden flows, which may be summarized as follows. First, the presence of sediment breaks the symmetry of the flow because of a tendency to self‐stratify. More specifically, this self‐stratification is manifested in terms of a Reynolds‐averaged suspended sediment concentration that declines in the upward normal direction and a Reynolds‐averaged velocity profile with a maximum that is below the channel centerline. Second, this self‐stratification damps the turbulence, particularly near the bottom wall. Two regimes are observed, one in which the flow remains turbulent but the level of turbulence is reduced and another in which the flow relaminarizes in a region near the bottom wall, i.e., bed. Third, the analysis allows the determination of a criterion for the break between these two regimes in terms of an appropriately defined dimensionless settling velocity. The results provide guidance for the improvement of Reynolds‐averaged closures for turbulent flow in regard to stratification effects. Although the analysis reported here is not performed at the scale of large oceanic turbidity currents, which have sufficiently large Reynolds numbers to be inaccessible via DNS at this time, the implication of flow relaminarization is of considerable importance. Even a swift oceanic turbidity current which at some point crosses the threshold into the regime of relaminarization may lose the capacity to reentrain sediment that settles on the bed and thus may quickly die as it loses its driving force.

Intermittent turbulence in a pulsating pipe flow

Numerical simulations of the pulsating flow in a pipe of circular cross-section characterized by small imperfections are carried out to determine the conditions leading to the appearance of turbulence. The results show that in the oscillatory case (no steady velocity component of the basic flow), the critical value of the Reynolds number Rδ depends on the Womersley parameter α and, in particular, Rδ increases as α decreases. The critical value of Rδ of the plane wall case is recovered when α is larger than about 10. For moderate values of the Reynolds numbers but larger than the critical one, turbulence appears around flow reversal and breaks the symmetry of the flow, originating a steady velocity component. Moreover, turbulence is not present throughout the whole cycle and there are phases during which the flow relaminarizes. The presence of a steady pressure gradient tends to destabilize the flow and this destabilizing effect becomes larger as the steady velocity component is increased. When turbulence is present, its dynamics is similar to that of the steady case and a log-law layer can be identified both in the oscillatory and the pulsating case.

Dye-bubble interactions in an open channel flow

An innovative technique has been developed to visualize the effect that a localized surface reaction has in an open channel flow field. The working fluid is hexanoic acid mixed with mineral oil, and it flows over an aluminum plate embedded with sodium metal. Hexanoic acid and sodium metal react to form hydrogen gas and hexanoic salt. The hydrogen gas forms bubbles that rise to the surface and are convected downstream by the fluid. The rising bubbles induce the formation of counter-rotating vortices that straddle the reaction site. Bubble entrainment stretches and bends the dye filaments, and buoyancy transports the bubbles away from the reaction. The products of the reaction introduce velocity fluctuations into an otherwise laminar flow, inducing what has been described by some researchers as pseudoturbulence. Downstream of the reaction, far away from the disturbances caused by the buoyant bubbles, the velocity fluctuations dampen out and the flow relaminarizes.

DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms

Direct numerical simulations (DNS) and optimal control theory are used in a predictive control setting to determine controls that effectively reduce the turbulent kinetic energy and drag of a turbulent flow in a plane channel at Reτ = 100 and Reτ = 180. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. The algorithm used for the control optimization is based solely on the control objective and the nonlinear partial differential equation governing the flow, with no ad hoc assumptions other than the finite prediction horizon, T, over which the control is optimized.Flow relaminarization, accompanied by a drag reduction of over 50%, is obtained in some of the control cases with the predictive control approach in direct numerical simulations of subcritical turbulent channel flows. Such performance far exceeds what has been obtained to date in similar flows (using this type of actuation) via adaptive strategies such as neural networks, intuition-based strategies such as opposition control, and the so-called ‘suboptimal’ strategies, which involve optimizations over a vanishingly small prediction horizon T+ → 0. To achieve flow relaminarization in the predictive control approach, it is shown that it is necessary to optimize the controls over a sufficiently long prediction horizon T+ [gsim ] 25. Implications of this result are discussed.The predictive control algorithm requires full flow field information and is computationally expensive, involving iterative direct numerical simulations. It is, therefore, impossible to implement this algorithm directly in a practical setting. However, these calculations allow us to quantify the best possible system performance given a certain class of flow actuation and to qualify how optimized controls correlate with the near-wall coherent structures believed to dominate the process of turbulence production in wall-bounded flows. Further, various approaches have been proposed to distil practical feedback schemes from the predictive control approach without the suboptimal approximation, which is shown in the present work to restrict severely the effectiveness of the resulting control algorithm. The present work thus represents a further step towards the determination of optimally effective yet implementable control strategies for the mitigation or enhancement of the consequential effects of turbulence.

On the mechanism of turbulence suppression by spanwise surface oscillations

The attenuation of turbulent pulsations in near-wall flows by means of spanwise periodic surface oscillation is examined. A direct numerical simulation of the flow in a circular pipe with imposed rotational oscillations has shown that for Re=4000 and the optimal oscillation frequency, the degree of turbulence attenuation increases with increase in the oscillation amplitude until the flow relaminarizes. The estimated optimal frequency ω+=0.06. The results of applying the theory of the development of near-wall coherent structures agree qualitatively with those of numerical simulation. It is concluded that the intensity of the pulsations is reduced because the spanwise movements weaken the longitudinal vortices which cause turbulent bursts in near-wall flows.

Heat transfer and pressure drop in ice-water slurries

Heat transfer and pressure drop were experimentally investigated for ice-water slurries flowing turbulently in a 24.0 mm internal diameter, 4.596 m long, horizontal, stainless steel tube. The slurry velocity of the experiments was varied from 2.8 to 5.0 m/s which encompassed the range of applicability to ice-water slurry-based district cooling systems. The previously reported phenomenon of flow relaminarization in ice-water slurries was observed in the current experiments. A reduction in frictional pressure drop associated with the flow relaminarization was measured as the ice fraction increased. An ice fraction of 4% marked a division in the rate of reduction, and a pressure-drop correlation equation was developed for ice fractions above 4%. Heat transfer coefficients were determined over the velocity range of the experiments. Consistent with the flow relaminarization, the heat transfer coefficient decreased with increasing ice fraction. A correlation equation was also developed for heat transfer coefficients at ice fractions above 4%.

A stable algorithm for Reynolds stress turbulence modelling with applications to rectilinear and circular tidal flows

This paper employs one-point, linear eddy viscosity and differential second-moment (DSM) turbulence closures to predict the turbulent characteristics of both rectilinear and circular tidal flows. The numerical scheme is based on a finite volume approach applied to a non-staggered grid such that all flow variables are stored at one and the same set of nodes. Numerical stability is maintained through the implementation of apparent viscosities and source term linearization, which are essential if eddy viscosity terms are absent. A stable algorithm is devised for the Reynolds stresses which includes a non-linear velocity smoothing in order to stabilise the numerical scheme during flow reversal and relaminarization. Favourable agreement with the experimental rectilinear tidal data of Schröder (Tech. Rep. GK55 87/E/16, GKSS-Forshungszentrum Geesthacht, 1983) and McClean (Turbulence and Sediment Transport Measurements in a North Sea Tidal Inlet (the Jade), Springer, New York, 1987, p. 436) is reported. Numerical calculations of circular tidal flows are also presented which were motivated by the preliminary investigations of Davies and Jones (Int. j. numer. meth. fluids,12, 17 (1991)) and Davies (Continental Shelf. Res., 11, 1313 (1991)), who employed the one-equation, k–l, eddy viscosity turbulence model to simulate rectilinear and circular tidal flows. © 1998 John Wiley & Sons, Ltd.

A stable algorithm for Reynolds stress turbulence modelling with applications to rectilinear and circular tidal flows

This paper employs one-point, linear eddy viscosity and differential second-moment (DSM) turbulence closures to predict the turbulent characteristics of both rectilinear and circular tidal flows. The numerical scheme is based on a finite volume approach applied to a non-staggered grid such that all flow variables are stored at one and the same set of nodes. Numerical stability is maintained through the implementation of apparent viscosities and source term linearization, which are essential if eddy viscosity terms are absent. A stable algorithm is devised for the Reynolds stresses which includes a non-linear velocity smoothing in order to stabilise the numerical scheme during flow reversal and relaminarization. Favourable agreement with the experimental rectilinear tidal data of Schroder (Tech. Rep. GK55 87/E/16, GKSS-Forshungszentrum Geesthacht, 1983) and McClean (Turbulence and Sediment Transport Measurements in a North Sea Tidal Inlet (the Jade), Springer, New York, 1987, p. 436) is reported. Numerical calculations of circular tidal flows are also presented which were motivated by the preliminary investigations of Davies and Jones (Int, j. numer meth. fluids, 12, 17 (1991)) and Davies (Continental Shelf Res., 11, 1313 (1991)), who employed the one-equation, k-l, eddy viscosity turbulence model to simulate rectilinear and circular tidal flows.

On the universality of the velocity profiles of a turbulent flow in an axially rotating pipe

If a fluid enters an axially rotating pipe, it receives a tangential component of velocity from the moving wall, and the flow pattern change according to the rotational speed. A flow relaminarization is set up by an increase in the rotational speed of the pipe. It will be shown that the tangential- and the axial velocity distribution adopt a quite universal shape in the case of fully developed flow for a fixed value of a new defined rotation parameter. By taking into account the universal character of the velocity profiles, a formula is derived for describing the velocity distribution in an axially rotating pipe. The resulting velocity profiles are compared with measurements of Reich [10] and generally good agreement is found.