Showing papers on "Open-channel flow published in 2013"

Direct Numerical Simulation of Turbulent Pipe Flow at Moderately High Reynolds Numbers

Abstract: Fully resolved direct numerical simulations (DNSs) have been performed with a high-order spectral element method to study the flow of an incompressible viscous fluid in a smooth circular pipe of radius R and axial length 25R in the turbulent flow regime at four different friction Reynolds numbers Reτ = 180, 360, 550 and \(1\text{,}000\). The new set of data is put into perspective with other simulation data sets, obtained in pipe, channel and boundary layer geometry. In particular, differences between different pipe DNS are highlighted. It turns out that the pressure is the variable which differs the most between pipes, channels and boundary layers, leading to significantly different mean and pressure fluctuations, potentially linked to a stronger wake region. In the buffer layer, the variation with Reynolds number of the inner peak of axial velocity fluctuation intensity is similar between channel and boundary layer flows, but lower for the pipe, while the inner peak of the pressure fluctuations show negligible differences between pipe and channel flows but is clearly lower than that for the boundary layer, which is the same behaviour as for the fluctuating wall shear stress. Finally, turbulent kinetic energy budgets are almost indistinguishable between the canonical flows close to the wall (up to y + ≈ 100), while substantial differences are observed in production and dissipation in the outer layer. A clear Reynolds number dependency is documented for the three flow configurations.

Fluid Drag Reduction with Shark-Skin Riblet Inspired Microstructured Surfaces

Abstract: Engineering marvels found throughout living nature continually provide inspiration to researchers solving technical challenges. For example, skin from fast-swimming sharks intrigue researchers since its low-drag riblet microstructure is applicable to many low drag and self-cleaning (antifouling) applications. An overview of shark skin related studies that have been conducted in both open channel (external) and closed channel (internal) flow experiments is presented. Significant work has been conducted with the open channel flow, and less with closed channel flow. The results provide design guidance when developing novel low drag and self-cleaning surfaces for applications in the medical, marine, and industrial fields. Experimental parameters include riblet geometry, continuous and segmented configurations, fluid velocity (laminar and turbulent flow), fluid viscosity (water, oil, and air), closed channel height dimensions, wettability, and scalability. The results are discussed and conceptual models are shown suggesting the effect of viscosity, coatings, and the interaction between vortices and riblet surfaces.

On the interaction between a turbulent open channel flow and an axial-flow turbine

Abstract: A laboratory experiment was performed to study the dynamically rich interaction of a turbulent open channel flow with a bed-mounted axial-flow hydrokinetic turbine. An acoustic Doppler velocimeter and a torque transducer were used to simultaneously measure at high temporal resolution the three velocity components of the flow at various locations upstream of the turbine and in the wake region and turbine power, respectively. Results show that for sufficiently low frequencies the instantaneous power generated by the turbine is modulated by the turbulent structure of the approach flow. The critical frequency above which the response of the turbine is decoupled from the turbulent flow structure is shown to vary linearly with the angular frequency of the rotor. The measurements elucidate the structure of the turbulent turbine wake, which is shown to persist for at least fifteen rotor diameters downstream of the rotor, and a new approach is proposed to quantify the wake recovery, based on the growth of the largest scale motions in the flow. Spectral analysis is employed to demonstrate the dominant effect of the tip vortices in the energy distribution in the near-wake region and uncover meandering motions.

Direct numerical simulation of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction

Abstract: We have performed direct numerical simulation of turbulent open channel flow over a smooth horizontal wall in the presence of finite-size, heavy particles. The spherical particles have a diameter of approximately 7 wall units, a density of 1.7 times the fluid density and a solid volume fraction of 5◊10 4 . The value of the Galileo number is set to 16.5, while the Shields parameter measures approximately 0.2. Under these conditions, the particles are predominantly located in the vicinity of the bottom wall, where they exhibit strong preferential concentration which we quantify by means of Voronoi analysis and by computing the particle-conditioned concentration field. As observed in previous studies with similar parameter values, the mean streamwise particle velocity is smaller than that of the fluid. We propose a new definition of the fluid velocity 'seen' by finite-size particles based on an average over a spherical surface segment, from which we deduce in the present case that the particles are instantaneously lagging the fluid only by a small amount. The particle-conditioned fluid velocity field shows that the particles preferentially reside in the low-speed streaks, leading to the observed apparent lag. Finally, a vortex eduction study reveals that spanwise particle motion is significantly correlated with the presence of vortices with the corresponding sense of rotation which are located in the immediate vicinity of the near-wall particles.

Reynolds-number scaling of turbulent channel flow

Abstract: Results of an experimental study of smooth-wall, fully developed, turbulent channel flow are presented. The Reynolds number (Rem) based on the channel height and the bulk mean velocity ranged from 10 000 to 300 000. The present results indicate that the skin-friction coefficient (Cf) closely follows a power law for Rem < 62 000. At higher Reynolds numbers, Cf is best described by a log law. Detailed two-component velocity measurements taken at friction Reynolds numbers of Reτ = 1000–6000 indicate that the mean flow and Reynolds shear stress display little or no Reynolds-number dependence. The streamwise Reynolds normal stress (u′2¯+), on the other hand, varies significantly with Reynolds number. The inner peak in u′2¯+ is observed to grow with Reynolds number. Growth in u′2¯+ farther from the wall is documented over the entire range of Reynolds number giving rise to a plateau in the streamwise Reynolds normal stress in the overlap region of the profile for Reτ = 6000. The wall-normal Reynolds normal stres...

Spatial fluctuations of fluid velocities in flow through a three-dimensional porous medium.

Abstract: We use confocal microscopy to directly visualize the spatial fluctuations in fluid flow through a three-dimensional porous medium. We find that the velocity magnitudes and the velocity components both along and transverse to the imposed flow direction are exponentially distributed, even with residual trapping of a second immiscible fluid. Moreover, we find pore-scale correlations in the flow that are determined by the geometry of the medium. Our results suggest that despite the considerable complexity of the pore space, fluid flow through it is not completely random.

Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures

Abstract: Estimation of the uncertainty in numerical predictions by Reynolds-averaged Navier-Stokes closures is a vital step in building confidence in such predictions. An approach to model-form uncertainty quantification that does not assume the eddy-viscosity hypothesis to be exact is proposed. The methodology for estimation of uncertainty is demonstrated for plane channel flow, for a duct with secondary flows, and for the shock/boundary-layer interaction over a transonic bump.

Large-Eddy Simulation in Hydraulics

Abstract: Preface 1 Introduction 1.1 The role and importance of turbulence in hydraulics 1.2 Characteristics of turbulence 1.3 Calculation approaches for turbulent flows 1.4 Scope and outline of the book 2 Basic methodology of LES 2.1 Navier-Stokes equations and Reynolds Averaging (RANS) 2.2 The idea of LES 2.3 Spatial filtering/averaging and resulting equations 2.4 Implicit filtering and Schumann's approach 2.5 Relation of LES to DNS and RANS 3 Subgrid-Scale (SGS) models 3.1 Role and desired qualities of an SGS-model 3.2 Smagorinsky model 3.3 Improved versions of eddy viscosity models 3.4 SGS models not based on the eddy viscosity concept 3.5 SGS models for the scalar transport equation 4 Numerical methods 4.1 Introduction 4.2 Discretization methods 4.3 Numerical accuracy in LES 4.4 Numerical errors 4.5 Solution methods for incompressible flow equations 4.6 LES grids 5 Implicit LES (ILES) 5.1 Introduction 5.2 Rationale for ILES and connection with LES using explicit SGS models 5.3 Adaptive Local Deconvolution Model (ALDM) 5.4 Monotonically Integrated LES (MILES) 6 Boundary and initial conditions 6.1 Periodic boundary conditions 6.2 Outflow boundary conditions 6.3 Inflow boundary conditions 6.4 Free surface boundary conditions 6.5 Smooth-wall boundary conditions 6.6 Rough-wall boundary conditions 6.7 Initial conditions 7 Hybrid RANS-LES methods 7.1 Introduction 7.2 Two-layer models 7.3 Embedded LES 7.4 Detached Eddy Simulation (DES) models 7.5 Scale-Adaptive Simulation (SAS) model 7.6 Final comments on hybrid RANS-LES models and future trends 8 Eduction of turbulence structures 8.1 Structure eduction from point signals: Two-point correlations and velocity spectra 8.2 Structure eduction from instantaneous quantities in 2D planes 8.3 Structure eduction from isosurfaces of instantaneous quantities in 3D space 9 Application examples of LES in hydraulics 9.1 Developed straight open channel flow 9.2 Flow over rough and permeable beds 9.3 Flow over bedforms 9.4 Flow through vegetation 9.5 Flow in compound channels 9.6 Flow in curved open channels 9.7 Shallow merging flows 9.8 Flow past in-stream hydraulic structures 9.9 Flow and mass exchange processes around a channel-bottom cavity 9.10 Gravity currents 9.11 Eco-hydraulics: Flow past an array of freshwater mussels 9.12 Flow in a water pump intake Appendix A - Introduction to tensor notation References Index

Flow adjustment at the leading edge of a submerged aquatic canopy

Abstract: [1] This paper describes the transition from open channel flow to flow over submerged vegetation using velocity measurements collected with acoustic Doppler velocimetry (ADV) and particle-image velocimetry (PIV). Submerged canopies were constructed from arrays of rigid circular cylinders of height h in water of depth H. Both the canopy density, described by the frontal area per volume (a), and degree of submergence (H/h) were varied. Flow adjustment occurs in three stages. First, velocity begins to decelerate upstream of the canopy, due to a high-pressure region generated at the canopy leading edge, and continues to decelerate within the canopy, due to canopy drag. Rapid flow deceleration within the canopy creates strong vertical flux out through the top of the canopy that extends over a length proportional to the canopy drag length scale, (CDa)−1, with CD being the canopy drag coefficient. Second, a mixing layer develops at the canopy interface, with the stress at the top of the canopy initially increasing, but eventually reaching a constant value. At this point, the flow within the canopy is fully developed. The length scale for mixing-layer development is related to canopy drag (CDa) and the depth ratio (H/h). In the third stage, the boundary layer above the mixing layer adjusts to the channel boundary conditions. A model is developed to predict the adjustment of vertically averaged velocity within the canopy. Measurements confirm that the flow adjustment is not dependent on canopy length.

How linear is wall-bounded turbulence?

Abstract: The relevance of Orr's inviscid mechanism to the transient amplification of disturbances in shear flows is explored in the context of bursting in the logarithmic layer of wall-bounded turbulence. The linearized problem for the wall normal velocity is first solved in the limit of small viscosity for a uniform shear and for a channel with turbulent-like profile, and compared with the quasiperiodic bursting of fully turbulent simulations in boxes designed to be minimal for the logarithmic layer. Many properties, such as time and length scales, energy fluxes between components, and inclination angles, agree well between the two systems. However, once advection by the mean flow is subtracted, the directly computed linear component of the turbulent acceleration is found to be a small part of the total. The temporal correlations of the different quantities in turbulent bursts imply that the classical model, in which the wall-normal velocities are generated by the breakdown of the streamwise-velocity streaks, is a better explanation than the purely autonomous growth of linearized bursts. It is argued that the best way to reconcile both lines of evidence is that the disturbances produced by the streak breakdown are amplified by an Orr-like transient process drawing energy directly from the mean shear, rather than from the velocity gradients of the nonlinear streak. This, for example, obviates the problem of why the cross-stream velocities do not decay once the streak has broken down.

Applicability of the local inertial approximation of the shallow water equations to flood modeling

Abstract: [1] Recent studies have demonstrated the improved computational performance of a computer algorithm based on a simplification of the shallow water equations—the so-called local inertial approximation—which has been observed to provide results comparable to the full set of equations in a range of flood flow problems. This study presents an extended view on the local inertial system, shedding light on those key elements necessary to understand its applicability to flows of practical interest. First, the properties of the simplified system with potential impact on the accuracy of the solutions are described and compared to the corresponding full-dynamic counterparts. In light of this discussion, the behavior of the solutions is then analyzed through a set of rigorously designed test cases in which analytical solutions to the shallow water system are available. Results show a general good agreement between the local inertial and full-dynamic models, especially in the lower range of subcritical flows (Fr < 0.5). In terms of steady nonuniform flow water profiles, the error introduced by the local inertial approximation leads to milder water depth gradients, which results in attenuated spatial changes in depth. In unsteady problems, the local inertial approximation leads to slower flood propagation speeds than those predicted by the full-dynamic equations. Even though our results suggest that the magnitude of these errors is small in a range of floodplain and lowland channels, it becomes increasingly relevant with increasing Fr and depth gradients.

DNS of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction

Abstract: We have performed direct numerical simulation of turbulent open channel flow over a smooth horizontal wall in the presence of finite-size, heavy particles. The spherical particles have a diameter of approximately 7 wall units, a density of 1.7 times the fluid density and a solid volume fraction of 0.0005. The value of the Galileo number is set to 16.5, while the Shields parameter measures approximately 0.2. Under these conditions, the particles are predominantly located in the vicinity of the bottom wall, where they exhibit strong preferential concentration which we quantify by means of Voronoi analysis and by computing the particle-conditioned concentration field. As observed in previous studies with similar parameter values, the mean streamwise particle velocity is smaller than that of the fluid. We propose a new definition of the fluid velocity "seen" by finite-size particles based on an average over a spherical surface segment, from which we deduce in the present case that the particles are instantaneously lagging the fluid only by a small amount. The particle-conditioned fluid velocity field shows that the particles preferentially reside in the low-speed streaks, leading to the observed apparent lag. Finally, a vortex eduction study reveals that spanwise particle motion is significantly correlated with the presence of vortices with the corresponding sense of rotation which are located in the immediate vicinity of the near-wall particles.

Mean and turbulent velocity fields near rigid and flexible plants and the implications for deposition

Abstract: [1] The transport of fine sediment and organic matter plays an important role in the nutrient dynamics of shallow aquatic systems, and the fate of these particles is closely linked to vegetation. We describe the mean and turbulent flow near circular patches of synthetic vegetation and examine how the spatial distribution of flow is connected to the spatial distribution of suspended sediment deposition. Patches of rigid, emergent, and flexible, submerged vegetation were considered, with two different stem densities. For the rigid emergent vegetation, flow adjustment was primarily two-dimensional, with flow deflected in the horizontal plane. Horizontal shear layers produced a von Karman vortex street. Flow through the patch shifted the vortex street downstream, resulting in a region directly downstream of the patch in which both the mean and turbulent velocities were diminished. Net deposition was enhanced within this region. In contrast, for the flexible, submerged vegetation, flow adjustment was three-dimensional, with shear layers formed in the vertical and horizontal planes. Because of strong vertical circulation, turbulent kinetic energy was elevated directly downstream of the patch. Consistent with this, deposition was not enhanced at any point in the wake. This comparison suggests that morphological feedbacks differ between submerged and emergent vegetation. Further, enhanced deposition occurred only in regions where both turbulent and mean velocities were reduced, relative to the open channel. Reduced deposition (indicating enhanced resuspension) occurred in regions of high turbulence kinetic energy, regardless of local mean velocity. These observations highlight the importance of turbulence in controlling deposition.

Petascale direct numerical simulation of turbulent channel flow on up to 786K cores

Abstract: We present results of performance optimization for direct numerical simulation (DNS) of wall bounded turbulent flow (channel flow). DNS is a technique in which the fluid flow equations are solved without subgrid modeling. Of particular interest are high Reynolds number (Re) turbulent flows over walls, because of their importance in technological applications. Simulating high Re turbulence is a challenging computational problem, due to the high spatial and temporal resolution requirements. An optimized code was developed using spectral methods, the method of choice for turbulent flows. Optimization was performed to address three major issues: efficiency of banded matrix linear algebra, cache reuse and memory access, and communication for the global data transposes. Results show that performance is highly dependent on characteristics of the communication network, rather than singlecore performance. In our tests, it exhibits approximately 80% strong scaling parallel efficiency at 786K cores relative to performance on 65K cores.

Investigation of the mobile granular layer in bedload transport by laminar shearing flows

Abstract: The mobile layer of a granular bed composed of spherical particles is experimentally investigated in a laminar rectangular channel flow. Both particle and fluid velocity profiles are obtained using particle image velocimetry for different index-matched combinations of particles and fluid and for a wide range of fluid flow rates above incipient motion. A full three-dimensional investigation of the flow field inside the mobile layer is also provided. These experimental observations are compared to the predictions of a two-phase continuum model having a frictional rheology to describe particle-particle interactions. Different rheological constitutive laws having increasing degrees of sophistication are tested and discussed.

Flow separation at the inner (convex) and outer (concave) banks of constant‐width and widening open‐channel bends

Abstract: There is a paucity of data and insight in the mechanisms of, and controls on flow separation and recirculation at natural sharply-curved river bends. Herein we report on successful laboratory experiments that elucidate flow structure in one constant-width bend and a second bend with an outer-bank widening. The experiments were performed with both a flat immobile gravel bed and mobile sand bed with dominant bedload sediment transport. In the constant-width bend with immobile bed, a zone of mainly horizontal flow separation (vertical rotational axis) formed at the inner bank that did not contain detectable flow recirculation, and an outer-bank cell of secondary flow with streamwise oriented rotational axis. Surprisingly, the bend with widening at the outer bank and immobile bed did not lead to a transverse expansion of the flow. Rather, flow in the outer-bank widening weakly recirculated around a vertical axis and hardly interacted with the inner part of the bend, which behaved as a constant-width bend. In the mobile bed experiment, downstream of the bend apex a pronounced depositional bar developed at the inside of the bend and pronounced scour occurred at the outside. Moreover the deformed bed promoted flow separation over the bar, including return currents. In the constant-width bend, the topographic steering impeded the generation of an outer-bank cell of secondary flow. In the bend with outer-bank widening, the topographic steering induced an outward expansion of the flow, whereby the major part of the discharge was conveyed in the central part of the widening section. Flow in the outer-bank widening was highly three dimensional and included return currents near the bottom. In conclusion, the experiments elucidated three distinct processes of flow separation common in sharp bends: flow separation at the inner bank, an outer-bank cell of secondary flow, and flow separation and recirculation in an outer-bank widening.

Microstructure-induced helical vortices allow single-stream and long-term inertial focusing

Abstract: Fluid inertia has been used to position microparticles in confined channels because it leads to precise and predictable particle migration across streamlines in a high-throughput manner. To focus particles, typically two inertial effects have been employed: inertial migration of particles in combination with geometry-induced secondary flows. Still, the strong scaling of inertial effects with fluid velocity or channel flow rate have made it challenging to design inertial focusing systems for single-stream focusing using large-scale microchannels. Use of large-scale microchannels (≥100 μm) reduces clogging over long durations and could be suitable for non-single-use flow cells in cytometry systems. Here, we show that microstructure-induced helical vortices yield single-stream focusing of microparticles with continuous and robust operation. Numerical and experimental results demonstrate how structures contribute to improve focusing in these larger channels, through controllable cross-stream particle migration, aided by locally-tuned secondary flows from sequential obstacles that act to bring particles closer to a single focusing equilibrium position. The large-scale inertial focuser developed here can be operated in a high-throughput manner with a maximum throughput of approximately 13000 particles per s.

Wall-parallel stereo particle-image velocimetry measurements in the roughness sublayer of turbulent flow overlying highly irregular roughness

Abstract: Stereo particle-image velocimetry measurements were conducted in a streamwise–spanwise (x − z) plane deep within the roughness sublayer (y = 0.047δ; δ is the boundary-layer thickness) of a zero-pressure-gradient turbulent boundary layer overlying highly irregular surface roughness replicated from a turbine blade damaged by foreign-material deposition. The ensemble-averaged streamwise velocity defect revealed the tendency of the roughness to promote channeling of the flow in the form of low-momentum pathways (LMPs) and high-momentum pathways. Enhanced turbulent and vortical activity was observed both between and along the spanwise boundaries of these streamwise-elongated pathways. In particular, streamwise pathways of wall-normal vortex cores of opposing rotational sense were observed along the spanwise boundaries of the identified LMP in the rough-wall flow. Conditional averaging revealed that these counter-rotating vortical motions are associated with streamwise flow against the mean-flow direction and could perhaps be the origination mechanism of the LMPs. Two-point correlation coefficients of velocity and swirling strength reflected large-scale streamwise coherence of these quantities along and outboard of the identified LMP in the rough-wall flow, supporting the notion that the motions responsible for the LMP have large-scale, streamwise coherence. Finally, the influence of different topographical scales of the roughness on the flow in the roughness sublayer was explored using low-order models of the original, full surface as originally proposed by R. Mejia-Alvarez and K. T. Christensen [Phys. Fluids 22(1), 015106 (2010)]. While a model containing only the largest topographical scales qualitatively reproduced the features of the full-surface flow, additional intermediate topographical scales were required to quantitatively reproduce the statistical and structural nature of the full-surface flow in the roughness sublayer.

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

Abstract: 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.

Velocity profiles in vegetated open-channel flows: combined effects of multiple mechanisms

Abstract: Vertical profile of longitudinal velocity in vegetated channels reflects complex mechanics of flow-vegetation interactions and determines the bulk flow velocity and flow rate. Most available models of velocity profiles in vegetated channels are based on a single physical concept that underpins theoretical considerations and data interpretation. However, measured velocity profiles suggest that the use of a single concept is not sufficient to cover all possible scenarios of flow-vegetation interactions. As a result, a number of models in which different concepts are applied to different flow regions have been recently developed. Within this framework, the overall velocity profile is represented with a set of linked segments. Although such segment-based models have improved velocity profile description, there is a need for more robust approaches and better analytical formulations. This paper proposes a new approach where a vertical velocity profile in vegetated channels is modelled as a linear superp...

Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

Abstract: Analytic results are derived for the apparent slip length, the change in drag and the optimum air layer thickness of laminar channel and pipe flow over an idealised superhydrophobic surface, i.e. a gas layer of constant thickness retained on a wall. For a simple Couette flow the gas layer always has a drag reducing effect, and the apparent slip length is positive, assuming that there is a favourable viscosity contrast between liquid and gas. In pressure-driven pipe and channel flow blockage limits the drag reduction caused by the lubricating effects of the gas layer; thus an optimum gas layer thickness can be derived. The values for the change in drag and the apparent slip length are strongly affected by the assumptions made for the flow in the gas phase. The standard assumptions of a constant shear rate in the gas layer or an equal pressure gradient in the gas layer and liquid layer give considerably higher values for the drag reduction and the apparent slip length than an alternative assumption of a vanishing mass flow rate in the gas layer. Similarly, a minimum viscosity contrast of four must be exceeded to achieve drag reduction under the zero mass flow rate assumption whereas the drag can be reduced for a viscosity contrast greater than unity under the conventional assumptions. Thus, traditional formulae from lubrication theory lead to an overestimation of the optimum slip length and drag reduction when applied to superhydrophobic surfaces, where the gas is trapped.

Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids

Abstract: We study the modal and non-modal linear instability of inertia-dominated channel flow of viscoelastic fluids modelled by the Oldroyd-B and FENE-P closures. The effects of polymer viscosity and relaxation time are considered for both fluids, with the additional parameter of the maximum possible extension for the FENE-P. We find that the parameter explaining the effect of the polymer on the instability is the ratio between the polymer relaxation time and the characteristic instability time scale (the frequency of a modal wave and the time over which the disturbance grows in the non-modal case). Destabilization of both modal and non-modal instability is observed when the polymer relaxation time is shorter than the instability time scale, whereas the flow is more stable in the opposite case. Analysis of the kinetic energy budget reveals that in both regimes the production of perturbation kinetic energy due to the work of the Reynolds stress against the mean shear is responsible for the observed effects where polymers act to alter the correlation between the streamwise and wall-normal velocity fluctuations. In the subcritical regime, the non-modal amplification of streamwise elongated structures is still the most dangerous disturbance-growth mechanism in the flow and this is slightly enhanced by the presence of polymers. However, viscoelastic effects are found to have a stabilizing effect on the amplification of oblique modes.

Wavy liquid films in interaction with a confined laminar gas flow

Abstract: A low-dimensional model capturing the fully coupled dynamics of a wavy liquid film in interaction with a strongly confined laminar gas flow is introduced. It is based on the weighted residual integral boundary layer approach of Ruyer-Quil & Manneville (Eur. Phys. J. B, vol. 15, 2000, pp. 357–369) and accounts for viscous diffusion up to second order in the film parameter. The model is applied to study two scenarios: a horizontal pressure-driven water film/air flow and a gravity-driven liquid film interacting with a co- or counter-current air flow. In the horizontal case, interfacial viscous drag is weak and interfacial waves are primarily driven by pressure variations induced by the velocity difference between the two layers. This produces an extremely thin interfacial shear layer which is pinched at the main and capillary wave humps, creating several elongated vortices in the wave-fixed reference frame. In the capillary wave region preceding a large wave hump, flow separation occurs in the liquid in the form of a vortex transcending the liquid–gas interface. For the gravity-driven film, a twin vortex (in the wave-fixed reference frame) linked to the occurrence of rolling waves has been identified. It consists of the known liquid-side vortex within the wave hump and a previously unknown counter-rotating gas-side vortex, which are connected by the same interfacial stagnation points. At large counter-current gas velocities, interfacial waves on the falling liquid film are amplified and cause flooding of the channel in a noise-driven scenario, while this can be delayed by forcing regular waves at the most amplified linear wave frequency. Our model is shown to exactly capture the long-wave linear stability threshold for the general case of two-phase channel flow. Further, for the two considered scenarios, it predicts growth rates and celerity of linear waves in convincing agreement with Orr–Sommerfeld calculations. Finally, model calculations of nonlinear interfacial waves are in good agreement with film thickness and velocity measurements as well as streamline patterns in both phases obtained from direct numerical simulations.