Turbulent Oscillatory Flow Research Articles

Direct numerical simulations of oscillatory boundary layers over rough walls

Numerical simulations of turbulent oscillatory flow over a bed made of fixed, identical spherical particles have been performed. Oscillations are imposed through a shear-driven forcing by means of an harmonic velocity boundary condition on the bed. A parametric study on the effect of the particle size and Reynolds number, spanning from the laminar to the fully-turbulent regimes, has been performed. Results show that the temporal evolution of the flow over the rough bed is modified compared to the classical Stokes’ solution for smooth-wall laminar boundary layers. In the turbulent cases, the phase shift in the velocity at various distances from the bed is reduced compared to the laminar case. The phase shift reduction seems predominantly dependent on the Reynolds number rather than the bed morphology, which suggests that a unique curve may exist for large enough values of the Reynolds number. Turbulence is observed during the deceleration phases of the cycle, with the presence of a logarithmic layer in the velocity profile, and “canonical” distribution of Reynolds shear stress and turbulent kinetic energy production. During the acceleration, the logarithmic region is suppressed and the Reynolds shear stress changes sign. Nevertheless, the turbulent kinetic energy production becomes only slightly negative, because the shear is also very small during these phases. A good correlation between Reynolds and shear stresses is also evidenced from the eddy viscosity profiles, which show the presence of plateau in the outer layers approximately constant across the phases of the cycle. Turbulence in the outer layers is related to structures which develop during previous cycles and propagate from the bed to the bulk of the channel. When the flow is fully developed, anisotropy maps show similar distributions to unidirectional wall-bounded flows, while departures from canonical distributions during the transient phases are mild, because the flow responds very rapidly to the time-varying forcing.

Selection of vortex ripple dimensions in sinusoidal oscillatory flows. Part 1. Ripple dimensions and fluid kinematics

Subaqueous vortex ripples in equilibrium are characterized by their unique geometry and dimensions. Motivated by the recent direct numerical simulation study of oscillatory turbulent flow over a wavy bottom by Önder & Yuan (J. Fluid Mech., vol. 858, 2019, pp. 264–314), the objective of this study is to further investigate the fluid dynamical controls that determine the distinctive equilibrium dimensions of vortex ripples. We use direct numerical simulations to investigate the differences in flow kinetics between sinusoidal oscillatory flow over equilibrium and out-of-equilibrium vortex ripples. In comparison with the equilibrium case, the spanwise coherent vortices, the averaged bottom shear stress on overlying flow and the shear stress distribution on the ripple surface are identified as the key fluid dynamical controls on equilibrium dimensions. Based on these controls, we propose mechanisms in the selection of vortex ripple dimensions. We observe that the flow adjusts in such a way that the interaction between overlying flow and vortex ripples tends to generate the strongest coherent vortices while the ripple surface (or overlying flow) experiences the smallest shear stress averaged over ripple wavelength during the selection process. Through a triple decomposition of the flow, the component of the ripple-induced fluctuation is found to dictate these fluid dynamical controls, which implies that this component plays an important role in the evolution of vortex ripples.

An experimental and numerical study of turbulent oscillatory flow over an irregular rough wall

The hydrodynamics of turbulent oscillatory flow over a gravel-based irregular rough wall is investigated using laser-Doppler anemometry measurements of velocities in a large oscillatory flow tunnel and direct numerical simulation (DNS) of the Navier–Stokes equations. The same periodic irregular roughness was used for both experiments and DNS. Four flow shapes are investigated: sinusoidal, skewed, asymmetric and combined skewed–asymmetric. The experiments were conducted for target Reynolds numbers (based on the Stokes length and standard deviation of free-stream velocity) of$R_{\delta,\sigma }=800$and$R_{\delta,\sigma }=1549$; DNS was conducted for flows with target$R_{\delta,\sigma }=800$. Boundary layer thickness, bottom phase lead and friction factor are in good agreement with previous studies. For the first time, evidence of Prandtl's secondary flows of the second kind in oscillatory flow is presented. Turbulence structure is visualised using isosurfaces of$\lambda _{2}$(Jeong & HussainJ. Fluid Mech., vol. 285, 1995, pp. 69–94), revealing densely packed structures that grow stronger and weaker in correspondence with the free-stream velocity. Reynolds and dispersive stresses peak just below the highest roughness crest, with dispersive stress vanishing a short distance above the roughness. Bursts of turbulence kinetic energy and wake kinetic energy are generated each flow half-cycle, with variable behaviour depending on flow shape. Non-Gaussian turbulence statistics are observed that originate near the wall, becoming increasingly non-Gaussian far from the wall. Probability density functions of turbulence statistics can be closely approximated by a fourth-order Gram–Charlier distribution at most phases and elevations, though when statistics deviate more strongly from Gaussian, streamwise and wall-normal (spanwise) statistics are better described by a Pearson type IV (VII) distribution.

Morphodynamics of vortex ripple creation under constant and changing oscillatory flow conditions

The morphodynamics of orbital vortex ripples due to oscillatory flow and induced sediment transport was studied numerically. The methodology was based on large-eddy simulations of the full coupling of turbulent oscillatory fluid flow, bed and suspended sediment transport, and bed evolution. The Immersed Boundary method was implemented for the imposition of fluid and sediment boundary conditions on the mobile bed surface. Results are presented for ripple creation starting from flat or rippled beds, as well as results of ripples adapting to changing flow (wave) direction. The computed equilibrium ripple dimensions are in agreement with existing empirical predictions; however, the computed ripple profile is not as steep in the vicinity of the ripple crest as the analytical one in Sleath (1984). The time needed for the bed geometry to reach equilibrium, in cases where the initial bed is almost flat or it is formed by ripples that shorten towards equilibrium, is longer than in cases where the initial bed is formed by ripples that widen towards equilibrium. Moreover, the ripple crests are reoriented when the flow changes direction by 45°; the new equilibrium ripple crestline is perpendicular to the flow direction. Finally, the numerical results are compared with corresponding results of flow above fixed ripples. The bed load flux does not present substantial differences between the fixed and mobile bed cases. On the contrary, a strong increase of the suspended load flux is observed for the mobile bed case in comparison to the fixed bed case. • LES Coupling between oscillatory flow, sediment transport, and bed morphodynamics. • Same flow forcing results into same bed equilibrium regardless of initial bed form. • Evolution of ripples longer than equilibrium ones is slower than for shorter ones. • Ripples are reoriented perpendicular to the flow direction. • Suspended load over mobile rippled bed is larger than over fixed ripples.

The effect of varying degrees of stenosis on transition to turbulence in oscillatory flows

Many complications in physiology are associated with a deviation in flow in arteries due to a stenosis. The presence of stenosis may transition the flow to weak turbulence. The degree of stenosis as well as its configuration whether symmetric or non-symmetric to the parent artery influences whether the flow would stay laminar or transition to turbulence. Plenty of research efforts focus on investigating the role of varying degrees of stenosis in the onset of turbulence under steady and pulsatile flow conditions. None of the studies, however, have focused on investigating this under oscillatory flow conditions as flow reversal is a major occurrence in a number of physiologic flows, and is of particular relevance in cerebrospinal fluid flow research. Following up on the previous work in which a 75% stenosis was studied, this contribution is a detailed investigation of the role of degrees of stenosis on transition in an oscillatory flow. A cylindrical pipe with 25%, 50% and 60% reductions in area in axisymmetric and eccentric configurations is studied for transition with 3 different pulsation frequencies of a purely oscillatory flow. Cycle averaged Reynolds numbers between 1800 and 2100 in steps of 100 are studied for each configuration resulting in 72 simulations each conducted on 76,800 CPU cores of a modern supercomputer. It is found that a higher degree of stenosis and eccentricity causes earlier transition to turbulence in oscillatory flow. The results further demonstrate that a higher frequency of oscillation results in larger hydrodynamic instability in the flow, which is more prominent in smaller degrees of stenosis.

RANSE Modeling of the Oscillatory Flow Over Two‐Dimensional Rigid Ripples

AbstractThe oscillatory turbulent flow over two‐dimensional ripples is numerically simulated. Both the profile of the ripples and the values of the parameters used in the present study are typical of vortex ripples at the bottom of sea waves. The flow is computed numerically by using a RANSE approach. The results show that, as the ratio between the fluid excursion and the ripple wavelength is increased, the vortex shed on one side of the ripple crest is no longer the mirror image of the vortex shed on the other side and the dynamics of the vortex structures becomes quite complex. Moreover, the formation of steady recirculating cells, which might distort the profile of ripples in an erodible bed, is observed. A horizontal steady streaming is also generated, whose positive/negative direction depends on the values of the parameters.

An Experimental Investigation of Acceleration‐Skewed Oscillatory Flow Over Vortex Ripples

AbstractA full‐scale experimental study of acceleration‐skewed oscillatory flow over vortex ripples, which is an approximation of wave‐driven flow over a rippled seabed, was conducted in an oscillatory water tunnel. Three acceleration‐skewed‐flow tests and a reference sinusoidal‐flow tests were involved in this study. In each test, two‐dimensional vortex ripples were generated from a coarse‐sand movable bed, and the flow field was measured with a particle image velocimetry. The dominant feature of phase‐averaged flow is the generation of onshore (offshore) coherent vortices during the onshore (offshore) half‐cycle. The acceleration skewness expedites the offshore‐onshore flow reversal and therefore speeds up the ejection of offshore vortex, while the opposite occurs for the onshore vortex. The ripple‐averaged flow is similar to the acceleration‐skewed turbulent oscillatory flow over a flat bed in terms of leading Fourier harmonics, boundary layer thickness, and cycle‐averaged flow, suggesting a possible analogy between the two. From the aspect of flow turbulence, acceleration skewness elongates the offshore accelerating quarter, so the turbulence embedded in the offshore vortex can be better developed. This, together with a quick ejection process, allows the offshore vortex to carry a significant amount of residual turbulence to the onshore‐side ripple flank, which may even enhance the production of turbulence within the onshore half‐cycle. Some results on pressure field and form drag are also presented in this paper.

Numerical investigation on turbulent oscillatory flow through a jet pump.

A jet pump with an asymmetrical channel can induce a time-averaged pressure drop in oscillatory flow, which can effectively suppress Gedeon streaming in looped thermoacoustic engines. In this work, the flow characteristics and time-averaged pressure drop caused by a jet pump in turbulent oscillatory flow are investigated through numerical simulation. Through the analysis of the dimensionless governing equations, the emphasis is put on the effects of Womersley number and maximum acoustic Reynolds number on the performance of the jet pump. Meanwhile, the steady flow resistance coefficients are also measured numerically. The results indicate that the oscillatory flow resistance coefficients are relatively insensitive to Womersley number when it is less than 46. Moreover, the oscillatory flow resistance coefficients agree well with the steady state flow results, which validate the quasi-static assumption in turbulent oscillatory flow. However, further increasing Womersley number will lead to a reduction in the time-averaged pressure drop. The simulation method and results, as well as the hydrodynamic mechanism beneath the results, are presented and discussed in detail.

Mobility Parameter and Sand Grain Size Effect on Sediment Transport Over Vortex Ripples in the Orbital Regime

AbstractThe objective of this numerical study is the assessment of the effect of the mobility parameter ψ and the ratio ao/Dg (ao is the orbital amplitude and Dg is the sand grain diameter) on sediment transport induced by oscillatory flow over orbital vortex ripples. A large eddy simulation model was employed for the coupled simulation of the three‐dimensional turbulent oscillatory flow and the corresponding bed and suspended sediment transport. The immersed boundary method was implemented for the imposition of fluid flow and suspended sediment transport boundary conditions on the bed surface. Results are presented for oscillatory flow over fixed ripples with dimensions based on three values of ψ and for three cases of ao/Dg that span the range of typical values for vortex ripples in the orbital regime. It was found that the net bed load (nondimensional), qb, was always in the onshore direction and its magnitude decreased with increasing ao/Dg, while the effect of ψ on qb was stronger for ψ < 50 than for ψ > 50. On the other hand, the net suspended load (nondimensional), qs, was always in the offshore direction, and its magnitude increased with increasing ψ and increasing ao/Dg. The relative contribution of bed load versus suspended load on the total sediment load was found to depend on both ψ and ao/Dg, and the distinction between bed and suspended load dominance was quantified with a single parameter based on the ratio of the free‐stream velocity to the sand grain settling velocity.

Analytical and Explicit Solutions to Implicit Wave Friction-Factor Equations Based on the Lambert W Function

ABSTRACT Li, S. and Liu, Y., 2018. Analytical and explicit solutions to implicit wave friction-factor equations based on the Lambert W function. Calculation of the friction factor of turbulent oscillatory fluid flow is a significant issue in accessing bed shear stress and sediment entrainment in coastal areas. A fast, robust calculation is necessary for intensive scientific simulations. However, some widely used friction-factor equations belong to the group of implicit and transcendental equations. Common procedures for obtaining accurate solutions are based on root-solving techniques such as the Newton–Raphson iterative method, with substantial computation cost and potential failure of solution convergence. The present note offers a simple and highly accurate procedure for explicitly calculating the friction factors. First, explicit analytical solutions of the friction-factor equations are derived using the Lambert W function, which is a newly recognized elementary transcendental function. Then, the anal...

Modeling the turbulent boundary layer at the bottom of sea wave

We investigate the turbulent oscillatory flow generated by propagating surface waves close to the sea bottom focusing our attention on moderate values of the Reynolds number Rδ of the bottom boundary layer. For such moderate values of Rδ, turbulent fluctuations appear only during parts of the oscillation cycle and the flow recovers a laminar-like behaviour in the remaining parts. Different roughness sizes are considered and both the smooth and the rough flow regimes are analysed. The aim of the present investigation is to test the performance of different two-equation turbulence models to compute the flow field over both smooth and rough walls and for moderate values of the Reynolds number. The considered models are the e−ω model by Saffman and Wilcox (1974), two k−ω models (Wilcox (1988) and a model derived from Wilcox (1992)), a low-Reynolds number k−ε model (Foti and Scandura, 2004) and the model by Menter et al. (2003). To evaluate the performance of the models, the numerical predictions of the bottom shear stress are compared both with experimental measurements and with results of direct numerical simulations (DNS). All the models are found to provide fair results for high values of Rδ and for a smooth wall. For moderate values of Rδ, when turbulence is observed only during parts of the oscillating cycle, only one of the low-Reynolds number k−ω models is able to describe the rapid growth of the wall shear stress due to turbulence appearance. On the other hand, if a rough wall is considered, the performance of the models greatly depends on the size of the roughness.

Numerical modeling investigation on turbulent oscillatory flow over a plane rough bed composed by randomly arrayed particles

A three-dimensional numerical model is established to simulate the turbulent oscillatory boundary layer over a fixed and rough bed composed by randomly arrayed solid spheres based on the lattice Boltzmann method and the large eddy simulation model. The equivalent roughness height, the location of the theoretical bed and the time variation of the friction velocity are investigated using the log-fit method. The time series of turbulent intensity and Reynolds stress are also investigated. The equivalent roughness height of cases with Reynolds numbers of 1×104–6×104 is approximately 2.81 d (grain size). The time variation of the friction velocity in an oscillatory cycle exhibits sinusoidal-like behavior. The friction factor depends on the relative roughness in the rough turbulent regime, and the pattern of solid particles arrayed as the rough bed in the numerical simulations has no obvious effect on the friction factor.

Turbulent oscillatory flow along unidirectional current over square ribs

The objective of this research is to examine the turbulent flow characteristics over a series of square rib elements under the combined action of surface wave and unidirectional current. The velocity data were analyzed to determine the distributions of the mean velocity, turbulent kinetic energy, Reynolds shear stress, and the contribution of burst-sweep cycles. These were used for the characterization of flow over square rib due to the superposition of surface waves of different frequencies and thereby compare the results with the current-only case. Mean velocity profiles over the rib roughness, illustrate the well-known downward shift from the flat surface data. Also, the thickness of turbulent boundary layer increases with the superposition of surface wave when compared to current-only flow. Particular attention is also given to understand the behaviour of higher-order moments to explicitly account for turbulent momentum transport characteristics over rib roughness under wave-current interactions.

Numerical Predictions of Early Stage Turbulence in Oscillatory Flow across Parallel-Plate Heat Exchangers of a Thermoacoustic System

This work focuses on the predictions of turbulent transition in oscillatory flow subjected to temperature gradients, which often occurs within heat exchangers of thermoacoustic devices. A two-dimensional computational fluid dynamics (CFD) model was developed in ANSYS FLUENT and validated using the earlier experimental data. Four drive ratios (defined as maximum pressure amplitude to mean pressure) were investigated: 0.30%, 0.45%, 0.65% and 0.83%. It has been found that the introduction of the turbulence model at a drive ratio as low as 0.45% improves the predictions of flow structure compared to experiments, which indicates that turbulent transition may occur at much smaller flow amplitudes than previously thought. In the current investigation, the critical Reynolds number based on the thickness of Stokes’ layer falls in the range between 70 and 100. The models tested included four variants of the RANS (Reynolds-Averaged Navier–Stokes) equations: k-ε, k-ω, shear-stress-transport (SST)-k-ω and transition-SST, the laminar model being used as a reference. Discussions are based on velocity profiles, vorticity plots, viscous dissipation and the resulting heat transfer and their comparison with experimental results. The SST-k-ω turbulence model and, in some cases, transition-SST provide the best fit of the velocity profile between numerical and experimental data (the value of the introduced metric measuring the deviation of the CFD velocity profiles from experiment is up to 43% lower than for the laminar model) and also give the best match in terms of calculated heat flux. The viscous dissipation also increases with an increase of the drive ratio. The results suggest that turbulence should be considered when designing thermoacoustic devices even in low-amplitude regimes in order to improve the performance predictions of thermoacoustic systems.

LARGE-EDDY SIMULATION OF OSCILLATORY FLOW AND MORPHODYNAMICS OVER RIPPLES

The objective of the present study was to study the morphodynamical development of ripples in a movable bed. The methodology is based on the coupling of fluid flow, sediment transport and morphodynamics. A well-resolved large-eddy simulation (LES) is employed for the simulation of the three-dimensional turbulent oscillatory flow and the corresponding bed and suspended sediment transport over a rippled bed. The evolution of the bed form is obtained by the numerical solution of the Exner equation based on the spanwise-mean flow and sediment transport conditions. The Immersed Boundary method is implemented for the imposition of fluid and sediment boundary conditions on the moving bed surface. Results are presented for ripple creation and propagation from a quasi-flat bed, as well as results of initially sinusoidal ripples adapting to water conditions, based on the mobility number, ψ. The numerical model demonstrates phenomena of ripple creation, propagation and migration, resulting in ripple lengths in agreement with those predicted by empirical equations. It was shown that under the same hydrodynamic forcing, the bed tends to reach the same equilibrium state, regardless of the initial bed form.

LDV에 의한 정사각 단면 180° 곡덕트에서 난류진동유동의 유동특성

In the present study the characteristics of turbulent oscillatory flows in a square-sectional curved duct were investigated experimentally. A series of experiments for air flow were conducted to measure axial velocity profiles, secondary flow velocity profiles and pressure distributions. The measurements were made by a Laser Doppler Velocimeter (LDV) system with a data acquisition and processing system which includes Rotating Machinery Resolve (RMR) and PHASE software. The results from the experiment are summarized as follows. (1) The maximum velocity moved toward the outer wall from the region of a bend angle of . The velocity distribution had a positive value extended over the total phase in the region of a bend angle of . (2) Secondary flows were generally proportional to the velocity of the main flow. The intensity of the secondary flow was about 25% as much as that in the axial direction. (3) Pressure distributions were effects of the oscillatory Dean number and respective region.

EULER-LAGRANGE SIMULATIONS OF SEDIMENT TRANSPORT IN OSCILLATORY BOUNDARY LAYERS WITH BEDFORMS

Accurate prediction of sediment transport in the presence of bedforms such as sand ripples requires an advanced understanding of how dynamic sediment beds interact with turbulent oscillatory flows. In this paper we propose a new approach for simulating these interactions, based on a fixed grid multiphase Euler-Lagrange simulation, that fully couples dynamic bed evolution to the motion of a sub-grid scale Lagrangian sediment phase. The sediment phase is evolved by computing hydrodynamic and inter-particle forces and torques acting on individual particles, and is coupled to the fluid phase through the volume-filtered Navier-Stokes equations. We validate the approach for sediment transport applications using hindered settling velocity tests, and show very good agreement with the experimental data of Baldock et al. (2004). We then apply the approach to simulate sediment transport and ripple bed morphology in oscillatory flow conditions corresponding to the experimental studies of Van der Werf et al. (2007). During the simulation, particles near ripple surface are isolated from immobile ones below allowing the computation to devote resources only to particles that may be become mobilized. Although preliminary in nature, the simulation results demonstrate that that the model can correctly capture the near bed velocities, suspended sediment concentrations, and pick-up of sediment by key vortical structures.

Longitudinal dispersion of turbulent oscillatory pipe flows

In the present study, we examine the longitudinal dispersion of oscillatory pipe flows in the turbulent range which is not well covered before. An analytical analysis was first performed using the homogenization approach (i.e. multiple scale perturbation analysis) to predict the magnitude of the longitudinal dispersion induced by a turbulent oscillatory flow forced by a sinusoidal pressure gradient inside a circular pipe. An axisymmetric co-axial eddy viscosity model was adopted to resolve the radial distribution of velocities and turbulent shear stresses. Based on the derived kinematic characteristics, the longitudinal dispersion coefficient for the turbulent oscillatory pipe flow was then quantified. The results demonstrated that a dimensionless parameter \(\alpha \), which is the ratio of the oscillatory velocity amplitude divided by the frequency and pipe radius, determines the flow structure as well as the magnitude of the induced longitudinal dispersion coefficient. Experiments were also conducted to quantify the longitudinal dispersion coefficient under different frequencies and oscillatory velocity magnitudes. The measurement approaches were based on the non-invasive laser imaging techniques of particle image velocimetry and planar laser induced fluorescence. The experimental conditions covered a relatively wide range of boundary Reynolds number \((\hbox {Re}_\delta )\) from 100 to 1,000, and included both laminar and turbulent flow regimes. The results showed that when the flow enters the conditional turbulence regime, i.e. \(\hbox {Re}_\delta \ge 500\), the longitudinal dispersion coefficient increases drastically. The analytical predictions based on the homogenization approach in the present study agree well with the measured longitudinal dispersion coefficients.

The flow over bedload sheets and sorted bedforms

Field surveys show the existence of morphological patterns (named bed load sheets in fluvial enviroments and sorted bedforms in coastal environments) which consist of alternate bands of coarse and fine sediments and are characterized by a negligible spatial variation of the bottom elevation. Previous analyses show that these bottom patterns are self-organizing features which are originated by the interaction of poorly sorted sediments, fractional sediment transport and turbulence dynamics. Presently, we describe the results of an investigation of turbulence dynamics over a flat bottom but characterized by alternate bands of small and large roughness. Turbulence characteristics are obtained by means of the two-equation turbulence model of Saffman (1970) which is shown to provide a reliable description of turbulence structure both in steady and oscillatory flows, as those generated in coastal environments by surface wave propagation. Moreover, the turbulence model can describe both smooth and rough walls and provide fair results also at moderate values of the Reynolds number. The results are validated by comparing the predictions of the model with the experimental data of Jensen et al. (1989) and Fredsøe et al. (1993) who measured the velocity field and the bottom shear stress under a turbulent oscillatory flow over a plane bed with a uniform roughness and sudden spatial change of the roughness size, respectively. The measurements of Fredsøe et al. (1993) were simulated also by Fuhrman et al. (2011) by means of the k–ω turbulence model of Wilcox (2006, 2008) and an indirect comparison of the model results with the results of Fuhrman et al. (2011) can be made. The investigation shows that the streamwise advection of turbulence plays a significant role such that turbulence is more intense over the rough bottom than over the smooth bottom, if a region close to the bottom is considered. However, moving far from the bottom, an opposite trend is found. Moreover, the results clearly show that the streamwise variations of the horizontal velocity component induce a significant vertical component of the velocity which should be taken into account if an accurate description of transport phenomena is to be obtained.

On the Non-linear Damping of Mechanical Oscillators in Flows of 4He

In the studies of both classical and quantum turbulence, significant attention is devoted to the investigation of the behavior of various submerged resonators. Upon entering the turbulent regime, the oscillators start to experience a significant drag force, which varies non-linearly with velocity. We present an empirical way of modeling such systems, and calculate the expected resonant response of such oscillators near the fundamental frequency as a function of the applied driving force. We apply the model to the crossover from linear to non-linear drag forces and compare with previous models as well as selected experimental data on the transition to turbulence in oscillatory flow of 4He.