16 results
Influence of submergence ratio on flow and drag forces generated by a long rectangular array of rigid cylinders at the sidewall of an open channel
- Mete Koken, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 966 / 10 July 2023
- Published online by Cambridge University Press:
- 27 June 2023, A5
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This paper discusses how the submergence ratio, defined as the ratio between the flow depth, D, and the height, h, of the solid rigid cylinders forming the array affects flow and turbulence structure inside and around a rectangular array of cylinders placed adjacent to one of the channel sidewalls. As the array becomes submerged, a vertical shear layer develops in between the top face of the array and the free surface, which strongly increases flow three-dimensionality and modifies how the momentum exchange between the array and the surrounding open water regions occurs with respect to the case of an emerged array where only a horizontal shear layer forms as part of the incoming flow approaching the array is deflected laterally. Eddy-resolving simulations are conducted for several values of the solid volume fraction, ϕ, and of the submergence ratio, 1.0 ≤ D/h ≤ 4.0. Similar to the limiting case of an emerged array (D/h = 1.0), the width- and depth-averaged streamwise velocity inside the array reaches a constant value after an initial adjustment region in the submerged-array cases. For D/h ≥ 1.33, the mean normal velocities through the top and side faces of the array do not become equal to zero downstream of the initial adjustment region. The flow inside the array reaches an equilibrium regime where the local flux of fluid leaving the array through its side face is balanced by the local flux of fluid entering the array through its top face. This regime is observed until close to the end of the array. For D/h ≥ 2.0, the horizontal shear layer vortices do not generate successive regions of high and low streamwise velocity and bed friction velocity inside the array, as is observed in the emerged cases. With respect to the emerged case, the size of the shear layer vortices and the shear layer width increase for low submergence ratios before decreasing rapidly for D/h ≥ 1.33. Significant three-dimensional effects are present inside the array and the horizontal shear layer for cases with both emerged and submerged arrays. In the ϕ = 0.08 cases, strong upwelling and downwelling motions are observed inside the array for D/h ≥ 1.33, while the circulation of the streamwise-oriented cell of secondary flow forming close to the lateral face of the array peaks when the submergence ratio is close to 1.33. For constant ϕ, the total streamwise drag force normalized with the height and width of the array increases with increasing submergence ratio. As the array submergence increases, the cylinders near the front of the array contribute less to the total force acting on the cylinders forming the array. For constant D/h, the total streamwise drag force acting on the array increases with ϕ for the submerged and emerged cases.
Oscillatory flow around a vertical circular cylinder placed in an open channel: coherent structures, sediment entrainment potential and drag forces
- Wen-Yi Chang, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 964 / 10 June 2023
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- 30 May 2023, A22
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Flow and turbulent structures generated by the interaction of forced incoming oscillatory flow with a circular, vertical cylinder placed in an open channel with a horizontal bed are investigated using eddy-resolving simulations. Validation simulations performed with a Keulegan–Carpenter (KC) number of 20 and multiple-mode forcing corresponding to the laboratory experiment of Sumer et al. (J. Fluid Mech., vol. 332, 1997, pp. 41–70) show that detached eddy simulation (DES) predicts more accurately the amplification of the bed shear stress beneath the horseshoe vortex system (upstream side of the cylinder) and the maximum magnitude of the bed shear stress at the downstream (wake) side of the cylinder compared with unsteady Reynolds-averaged Navier–Stokes simulations. High-Reynolds-number DES simulations are then conducted with 1.5 ≤ KC ≤ 30.8 and one-mode sinusoidal forcing of the streamwise velocity in the approaching flow to investigate the changes in the wake vortex-flow regimes, the coherence of the horseshoe vortices and the generation of other near-bed coherent structures in the wake during the oscillatory cycle. The flow is periodic, no horseshoe vortices form and no vortices are shed in the wake for KC = 1.5. By contrast, for KC ≥ 8 horseshoe vortices are present over part of the oscillatory cycle and up to three wake vortices are shed over each half-cycle as KC is increased to 30.8. For an intermediate range of KC numbers, one (KC = 15.4) or two (KC = 8) of the vortices forming at the back of the cylinder during each half-cycle are washed around it when the flow reverses. The main horseshoe vortex and other horizontal near-bed vortices have a large capacity to amplify the bed shear stresses when the incoming velocity magnitude is significantly less than its peak value. Assuming the depth-averaged velocity in the incoming (undisturbed) oscillatory flow is the same in simulations conducted with different KC numbers, the peak values of the sediment entrainment potential measured by the mean (cycle-averaged) volumetric flux of sediment entrained from the bed over one oscillatory cycle occur for 8 ≤ KC ≤ 15.4. For all KC numbers, the in-line force variation over the oscillatory cycle is fairly well approximated by the Morison equation. For KC = 1.5, the in-line force is only due to inertia effects. For KC = 30.8, the maximum and minimum values of the phase-averaged in-line force are approximatively in phase with those of the incoming flow velocity. For KC ≥ 15, the phase-averaged in-line force coefficients vary between 0.8 and 1.1 during most of the oscillatory cycle (e.g. when the incoming flow velocity is not close to zero). This is different from cases with KC ≤ 8 where the in-line force coefficient is equal to zero twice during the oscillatory cycle as the in-line force becomes equal to zero for non-zero values of the incoming velocity. The largest cycle-to-cycle variations of the in-line force coefficient and in-line force are observed around KC = 8. For KC = 8 and 15.4, the cylinder is subject to relatively large phase-averaged spanwise drag forces that are comparable to the peak phase-averaged streamwise drag forces. As KC is increased to 30.8, the phase-averaged spanwise drag force becomes zero over the whole oscillatory cycle but the cylinder is still subject to large instantaneous spanwise forces over part of the oscillatory cycle.
Shallow mixing interfaces between parallel streams of unequal densities
- Zhengyang Cheng, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 945 / 25 August 2022
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- 12 July 2022, A2
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As opposed to the case of shallow mixing layers forming between parallel streams of unequal velocities and equal densities, the spatial development of the mixing interface (MI) between two parallel streams of unequal velocities and sufficiently large density contrast is controlled by the formation of a spatially developing, lock-exchange-like flow in transverse planes. Buoyancy effects are driven by the presence of a vertical density interface near the splitter plate. Eddy-resolving numerical simulations conducted in a wide and very long channel are used to investigate the mean flow structure and the effects of the lock-exchange-like flow and the associated coherent structures on mixing and the capacity of the flow to entrain sediment from the channel bed. When the two streams have unequal densities, quasi-two-dimensional Kelvin–Helmholtz (KH) vortices still form near the MI origin, but their coherence is lost over a much shorter distance compared with the case with no density contrast, and their cores are severely stretched in the transverse direction. A main cell of recirculating (cross-) flow forms in the mean flow, in between the fronts of the near-bed intrusion of heavier fluid and the free-surface intrusion of lighter fluid. The instantaneous flow fields contain streamwise-oriented vortical cells along the interface separating the regions containing heavier and lighter fluids. These vortical cells play an important role in enhancing mixing, similar to the KH billows forming in a classical lock-exchange flow. The regions of highest turbulence amplification are situated next to the boundaries of the main recirculating cell. Once the oscillating fronts of the intrusions get sufficiently close to the channel sidewalls, streamwise cells of secondary flow form near the channel boundaries. For cases with a strong density contrast, the free-surface mixing pattern is not a good indicator of mixing between the two streams. For the same flow velocities in the incoming channels, the two streams mix faster with increasing density difference between the two streams. This is because, as opposed to the KH vortices, coherent structures induced by the formation of the lock-exchange-like flow maintain their coherence and capacity to induce mixing at very large distances from the splitter plate. Meanwhile, the redistribution of the streamwise momentum leading to uniform, fully developed flow over the whole cross-section is delayed by buoyancy effects. Away from the splitter plate, the region with the highest sediment entrainment potential is situated next to the edge of the main recirculation cell on the high-speed side of the channel. For the same flow velocities in the incoming channels, the sediment entrainment capacity of the flow is much larger in the simulations conducted with density contrast between the incoming streams and peaks for the case when the faster stream contains the denser fluid.
Shallow mixing layers between non-parallel streams in a flat-bed wide channel
- Zhengyang Cheng, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 916 / 10 June 2021
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- 14 April 2021, A41
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When two converging flows of unequal velocities and different flow directions come into contact, large-scale coherent structures are generated. For shallow conditions and small angles between the incoming streams, the mixing layer (ML) forming downstream of the confluence apex contains quasi-two-dimensional, Kelvin–Helmholtz (KH) vortices. Due to flow shallowness (e.g. stabilizing effect of bed friction), these vortices gradually lose their coherence at large distances from the ML origin. For large angles between the incoming streams, the spatial development of the shallow ML is more complex as strongly coherent, streamwise-oriented-vortical (SOV) cells form in the vicinity of the shallow ML and helical cells of secondary flow are generated due to curvature effects. The present paper uses three-dimensional eddy-resolving numerical simulations to study the effects of varying the angles between the two incoming channels and the downstream channel, the velocity ratio (VR) of the incoming flows and the flow depth on flow, turbulence structure and sediment entrainment mechanisms inside the ML and its surroundings. The simulations are performed for highly idealized conditions in which the ML develops in a wide channel (no interactions with the channel banks), over a flat bed and the flow depth is constant. Simulation results show that the SOV cells play an important role in the redistribution of the streamwise momentum. Some of the SOV cells are subject to bimodal oscillations in the lateral direction which induce strong interactions between the SOV cells and the ML vortices and sharply increase mixing. As for the case of a shallow ML developing between parallel streams, vortex pairing ceases some distance from the ML origin, the KH vortices start losing their coherence and the ML assumes an undulatory shape. The paper describes the effects of VR, angle between the incoming streams (α = 0° and 60°), planform geometry (symmetric vs. asymmetric confluences with α = 60°) and flow shallowness on the transverse shift of the ML centreline, ML width, dynamics of the KH vortices and on the formation, position and circulation of the SOV cells. In most of the α = 60° cases, the largest bed shear stresses are induced beneath the SOV cells rather than beneath the high-speed stream and the SOV cells play a major role in enhancing mixing between the two streams.
Flow structure inside and around a rectangular array of rigid emerged cylinders located at the sidewall of an open channel
- Mete Koken, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 910 / 10 March 2021
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- 08 January 2021, A2
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Flow structure inside and around a rectangular array of emerged cylinders located adjacent to the sidewall of an open channel is investigated using eddy-resolving numerical simulations. This configuration is particularly relevant for understanding how patches of aquatic vegetation developing near a river's banks affect flow and transport. The array of width W = 1.6D and length L = 33D–35D (D is the flow depth) contains rigid cylinders. Simulations with incoming, fully developed turbulent flow (channel Reynolds number, ReD = 12 500) are conducted with different values of the solid volume fraction (0.02 < ϕ < 0.1), frontal area per unit volume of the array, a (0.41 < aW < 1.63), diameter of the solid cylinders (d = 0.1D and 0.2D) and cylinder shape (circular and square). The paper focuses on investigating flow and turbulence structure inside and downstream of the array and the role played by coherent structures (e.g. vortices forming in the horizontal shear layer at the lateral face of the array, vortices shed in the wake of the solid cylinders) in sediment entrainment and transport. Simulation results show that significant upwelling and downwelling motions are generated near the front and lateral faces of the array and inside the shear layer. Moreover, some distance from the front face of the array, the shear layer vortices generate successive regions of high and low streamwise velocity inside the patch. The frequency associated with these wave-like oscillations is approximately half of the frequency associated with the advection of vortices in the downstream part of the shear layer. These streamwise velocity oscillations induce spanwise patches of high and low bed friction velocity that extend over the regions occupied by the array and the horizontal shear layer. For sufficiently high array resistance, horseshoe vortices form around the upstream corner of the array and provide an additional mechanism for sediment entrainment. For aW > 0.5, mean-flow recirculation bubbles form behind the array. For constant aW, the total size of the region containing recirculation bubbles decreases with increasing d/D. Simulations results are used to quantify the effect of varying ϕ, aW, d/D and the cylinders’ shape on the streamwise decay of the mean streamwise velocity inside the array, turbulent kinetic energy distribution, mean streamwise drag forces acting on the cylinders and mean streamwise drag coefficients.
Near- and far-field structure of shallow mixing layers between parallel streams
- Zhengyang Cheng, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 904 / 10 December 2020
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- 07 October 2020, A21
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The dynamics of coherent structures forming in a turbulent shallow mixing layer (ML) between two parallel streams advancing in a constant-depth, open channel is investigated using three-dimensional, time-accurate simulations. The large channel length to flow depth ratio ($L_{x}/H = 400\text{--}800$) allows characterization of the spatial evolution of shallow MLs until the mean velocity difference between the two streams becomes less than 3% of the initial value at the end of the splitter plate. Away from the ML origin, the dynamics and coherence of the Kelvin–Helmholtz (KH) billows are affected by the destabilizing effect of the mean shear between the two streams and by the stabilizing effect of the bed friction. A linear decay of the entrainment coefficient α with the bed-friction factor, S, applies only over the region where merging of neighbouring KH billows is still observed (transition to quasi-equilibrium regime). At larger distances from the origin, where the billows are severely stretched in the streamwise direction before being destroyed, the rates of increase of the ML width, δ, and centreline shift, lcy, become very small and α is exponentially decaying with increasing S toward zero (quasi-equilibrium regime). During the initial stages of the quasi-equilibrium regime where the KH vortices are severely stretched, the ML assumes an undulatory shape in horizontal planes. New relationships are proposed to characterize the downstream variation of the non-dimensional ML width and centreline shift over the transition and quasi-equilibrium regimes. During the transition to equilibrium regime, the ML boundary on the fast-stream side remains close to vertical, while that on the slow-stream side becomes strongly tilted. The ML boundary on the slow-stream side becomes again close to vertical once the quasi-equilibrium regime is reached. During the transition to the equilibrium regime, the passage of the KH billows and the generation of streamwise cells of secondary flow generate regions of high instantaneous bed shear stress, such that the region where the erosive capacity of the flow peaks does not correspond to the fast stream. The paper also investigates the effects of flow shallowness and initial velocity ratio between the two streams on the turbulent kinetic energy inside the ML, the depth-averaged lateral momentum fluxes, the passage frequency and size of the KH billows and the wavelength and period of the undulatory motions of the ML during the early stages of the quasi-equilibrium regime.
On the flow and coherent structures generated by a circular array of rigid emerged cylinders placed in an open channel with flat and deformed bed
- Wen-Yi Chang, George Constantinescu, Whey Fone Tsai
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- Journal:
- Journal of Fluid Mechanics / Volume 831 / 25 November 2017
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- 13 October 2017, pp. 1-40
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The flow and the turbulence structure generated by a circular porous cylinder of diameter $D$ containing solid cylinders of diameter $d$ placed in an open channel of depth $h\approx 0.5D$ are investigated using eddy-resolving simulations which resolve the wakes past the individual solid cylinders in the array. The solid cylinders extend from the bed through the water surface. This geometrical set-up is directly relevant to understand the physics of flow past an emerged patch of aquatic vegetation developing in a river channel or over its floodplain. Simulations are conducted with different solid volume fractions (SVFs) of the porous cylinder ($0.034<\text{SVF}<0.23$), relative diameters of the solid cylinders ($d/D=0.03$ and 0.06) and with flat and equilibrium scour bathymetry corresponding to the start and respectively the end of the erosion and deposition process. Comparison with the limiting case of a solid cylinder ($\text{SVF}=1$) is also discussed. The bed shear stress distributions and the turbulent flow fields are used to explain the sediment erosion mechanisms inside and around the porous cylinder. Simulations of the flat-bed cases reveal that for sufficiently large SVF values ($\text{SVF}>0.2$), necklace vortices form around the upstream face of the cylinder, the downflow penetrates partially inside the porous cylinder and a region of strong flow acceleration forms on the sides of the porous cylinder. These flow features are used to explain the development of scour around high-SVF porous cylinders. The effects of the SVF and $d/D$ on generating ‘corridors’ of strong flow acceleration in between the solid cylinders and energetic eddies in the wake of these cylinders are discussed, as these flow features control the amplification of the bed shear stress inside the porous cylinder. Simulations results are also used to quantify the time-averaged drag forces on the cylinders in the array, to identify the regions where these forces are comparable to those induced on an isolated cylinder and the percentage of cylinders in the array subject to relatively large mean drag forces. A logarithmic decrease of the mean time-averaged streamwise drag coefficient of the solid cylinders, $\overline{C}_{d}$, with increasing non-dimensional frontal area per unit volume of the porous cylinder, $aD$, is observed. Behind the cylinder, the eddies shed in the separated shear layers (SSLs) of the porous cylinder, and, for sufficiently large SVFs, the von Kármán wake billows are the main coherent structures responsible for the amplification of the bed shear stress and sediment entrainment. This paper also analyses the vertical non-uniformity of the mean flow and turbulent kinetic energy, and discusses how the SVF and bathymetry affect the spatial extent of the wake region (e.g. length of the SSLs and steady wake, total wake length) and other relevant variables (e.g. strength of the bleeding flow, dominant wake frequencies, turbulence amplification in the near wake). For the relatively shallow flow conditions ($D/h\approx 2.0$) considered, the simulation results show that the antisymmetric (von Kármán) shedding of wake billows behind the porous cylinder is greatly weakened once equilibrium scour conditions are approached. Comparison with data from laboratory experiments and from 3-D and 2-D simulations conducted for long porous cylinders (no bed) is also discussed.
Free-surface gravity currents propagating in an open channel containing a porous layer at the free surface
- Ayse Yuksel-Ozan, George Constantinescu, Heidi Nepf
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- Journal:
- Journal of Fluid Mechanics / Volume 809 / 25 December 2016
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- 15 November 2016, pp. 601-627
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Large eddy simulation (LES) is used to study the evolution and structure of a lock-exchange, Boussinesq gravity current forming in a channel partially blocked by a porous layer. This configuration is used to understand how the characteristics of a surface layer containing floating vegetation affects the generation of thermally driven convective water exchange in a long shallow channel. The porous layer, which represents the roots of the floating vegetation, contains a staggered array of rigid square cylinders of edge length $D$ with solid volume fraction $\unicode[STIX]{x1D719}$. The cylinders extend over a depth $h_{1}<H$ below the free surface, where $H$ is the channel depth. The surface current of lighter fluid splits into two layers, one propagating slowly inside the porous layer and the other flowing beneath the porous layer. The main geometrical parameters of the porous layer, $\unicode[STIX]{x1D719}$ and $h_{1}/H$, have a large effect on the dynamics and structure of the surface current and the temporal variation of the front position. For cases with sufficiently large values of $h_{1}/H$ and $\unicode[STIX]{x1D719}$, the front within the porous layer approaches the triangular shape observed for low Reynolds number lock-exchange currents propagating in a channel containing cylinders over its whole volume ($h_{1}/H=1$), and the surface current transitions to a drag-dominated regime in which the front velocity is proportional to $t^{-1/4}$, where $t$ is the time since the current is initiated. For sufficiently high values of $\unicode[STIX]{x1D719}$, the velocity of the fluid inside the porous layer is close to zero at all locations except for those situated close to the lock gate and for some distance behind the front. Close to the front, lighter fluid from below penetrates into the porous layer due to unstable stratification at the bottom of the porous layer. Simulation results are also used to assess how $\unicode[STIX]{x1D719},h_{1}/H$ and the Reynolds number affect the rate at which the heavier fluid situated initially inside the porous layer is removed by the advancing surface current and the main mixing mechanisms. Based on the estimated time scales for flushing the porous (root) layer, we show that flushing can significantly enhance the overall rate of nutrient removal by the floating vegetation by maintaining a higher concentration of nutrients within the root layer.
Large eddy simulation of the velocity-intermittency structure for flow over a field of symmetric dunes
- Christopher J. Keylock, Kyoungsik S. Chang, George S. Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 805 / 25 October 2016
- Published online by Cambridge University Press:
- 23 September 2016, pp. 656-685
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Owing to their frequent occurrence in the natural environment, there has been significant interest in refining our understanding of flow over dunes and other bedforms. Recent work in this area has focused, in particular, on their shear-layer characteristics and the manner by which flow structures are generated. However, field-based studies, are reliant on single-, or multi-point measurements, rather than delimiting flow structures from the velocity gradient tensor, as is possible in numerical work. Here, we extract pointwise time series from a well-resolved large eddy simulation as a means to connect these two approaches. The at-a-point analysis technique is termed the velocity-intermittency quadrant method and relates the fluctuating, longitudinal velocity, $u_{1}^{\prime }(t)$, to its fluctuating pointwise Hölder regularity, $\unicode[STIX]{x1D6FC}_{1}^{\prime }(t)$. Despite the difference in boundary conditions, our results agree very well with previous experiments that show the importance, in the region above the dunes, of a quadrant 3 ($u_{1}^{\prime }<0$, $\unicode[STIX]{x1D6FC}_{1}^{\prime }<0$) flow configuration. Our higher density of sampling beneath the shear layer and close to the bedforms relative to experimental work reveals a negative correlation between $u_{1}^{\prime }(t)$ and $\unicode[STIX]{x1D6FC}_{1}^{\prime }(t)$ in this region. This consists of two distinct layers, with quadrant 4 ($u_{1}^{\prime }>0$, $\unicode[STIX]{x1D6FC}_{1}^{\prime }<0$) dominant near the wall and quadrant 2 ($u_{1}^{\prime }<0$, $\unicode[STIX]{x1D6FC}_{1}^{\prime }>0$) dominant close to the lower part of the separated shear layer. These results are consistent with a near-wall advection of vorticity into a region downstream of a temporarily foreshortened reattachment region, and the entrainment of slow moving and quiescent fluid into a faster, more turbulent shear layer. A comparison of instantaneous vorticity fields to the velocity-intermittency analysis shows how the pointwise results reflect larger-scale organisation of the flow. We illustrate this using results from two instantaneous datasets. In the former, extreme velocity-intermittency events corresponding to a foreshortened recirculation region (and high pressures on the stoss slope of the dune immediately downstream) arise, and the development of intense flow structures occurs as a consequence. In the other case, development of a ‘skimming flow’ with relatively little exchange between the inner and outer regions results in exceedances because of the coherence associated with this high velocity, high turbulence outer region. Thus, our results shed further light on the characteristics of dune flow in the near-wall region and, importantly for field-based research, show that useful information on flow structure can be obtained from single-point single velocity component measurements.
Numerical investigation of flow and turbulence structure through and around a circular array of rigid cylinders
- Kyoungsik Chang, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 776 / 10 August 2015
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- 06 July 2015, pp. 161-199
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This numerical study investigates flow and turbulence structure through and around a circular array of solid circular cylinders of diameter $d$. The region containing the array of rigid cylinders resembles a porous circular cylinder of diameter $D$. The porous cylinder Reynolds number defined with the steady incoming flow velocity is $\mathit{Re}_{D}=10\,000$. Fully three-dimensional (3D) large eddy simulations (LES) are conducted to study the effects of the volume fraction of solids of the porous cylinder ($0.023<\text{SVF}<0.2$) and $d/D$ on the temporal variation and mean values of the drag/lift forces acting on the solid cylinders and on the porous cylinder. The effects of the bleeding flow through the circular porous cylinder on the wake structure and the influence of the SVF and $d/D$ on the onset of flow three-dimensionality within or downstream of the porous cylinder and transition to turbulence are discussed. Results are compared with experimental data, predictions of theoretical models available in the literature and also with the canonical case of a solid cylinder ($\text{SVF}=1,d/D=1$). Three-dimensional LES predict that large-scale wake billows are shed in the wake of the porous cylinder for $\text{SVF}>0.05$, similar to the von Karman vortex street observed for solid cylinders. As the SVF decreases, the length of the separated shear layers (SSLs) of the porous cylinder and the distance from the back of the porous cylinder at which wake billows form increase. For sufficiently low volume fractions of solids (e.g. $\text{SVF}=0.05$, 0.023), no wake billows are shed and the interactions among the wakes of the solid cylinders are weak. Even for $\text{SVF}=0.023$, SSLs containing large-scale turbulent eddies form on the two sides of the porous cylinder, but their ends cannot interact to generate wake billows. In both regimes, the force acting on some of the solid cylinders within the array is highly unsteady. As opposed to results obtained based on 2D simulations, no intermediate regime in which the force acting on the solid cylinders is close to steady is present. Interestingly, an energetic low frequency corresponding to a Strouhal number defined with the diameter of the porous cylinder of approximately 0.2 is present within the porous cylinder and near-wake regions not only for cases where wake billows are generated but also for cases where no wake billows form. In the latter cases, this frequency is due to an instability acting on the SSLs which induces in-phase large-scale undulatory deformations of the two SSLs. A combined drag parameter for the porous cylinder ${\it\Gamma}_{D}=\overline{C}_{d}\,aD/(1-\text{SVF})$ is introduced, where $aD$ is the non-dimensional frontal area per unit volume of the porous cylinder. This parameter characterizes by how much the velocity of the bleeding flow at the back of the porous cylinder is reduced compared with the incoming flow velocity for a given total drag force acting on the porous cylinder. Results from simulations conducted with different values of the SVF, $d/D$ and mean time-averaged solid cylinder streamwise drag parameter, $\overline{C}_{d}$, show that ${\it\Gamma}_{D}$ increases monotonically with increasing $aD$. Several ways of defining the spatial extent of the wake region in a less ambiguous way are proposed.
Lock-exchange gravity currents propagating in a channel containing an array of obstacles
- Ayse Yuksel Ozan, George Constantinescu, Andrew J. Hogg
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- Journal:
- Journal of Fluid Mechanics / Volume 765 / 25 February 2015
- Published online by Cambridge University Press:
- 26 January 2015, pp. 544-575
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Large eddy simulation (LES) is used to investigate the evolution of Boussinesq gravity currents propagating through a channel of height $H$ containing a staggered array of identical cylinders of square cross-section and edge length $D$. The cylinders are positioned with their axes horizontal and perpendicular to the (streamwise) direction along which the lock-exchange flow develops. The effects of the volume fraction of solids, ${\it\phi}$, the Reynolds number and geometrical parameters describing the array of obstacles on the structure of the lock-exchange flow, total drag force acting on the gravity current, front velocity and global energy budget are analysed. Simulation results show that the currents rapidly transition to a state in which the extra resistance provided by the cylinders strongly retards the motion and dominates the dissipative processes. A shallow layer model is also formulated and similarity solutions for the motion are found in the regime where the driving buoyancy forces are balanced by the drag arising from the interaction with the cylinders. The numerical simulations and this shallow layer model show that low-Reynolds-number currents transition to a drag-dominated regime in which the resistance is linearly proportional to the flow speed and, consequently, the front velocity, $U_{f}$, is proportional to $t^{-1/2}$, where $t$ is the time measured starting at the gate release time. By contrast, high-Reynolds-number currents, for which the cylinder Reynolds number is sufficiently high that the drag coefficient for most of the cylinders can be considered constant, transition first to a quadratic drag-dominated regime in which the front speed determined from the simulations is given by $U_{f}\sim t^{-0.25}$, before undergoing a subsequent transition to the aforementioned linear drag regime in which $U_{f}\sim t^{-1/2}$. Meanwhile, away from the front, the depth-averaged gravity current velocity is proportional to $t^{-1/3}$, a result that is in agreement with the shallow water model. It is suggested that the difference between these two is due to mixing processes, which are shown to be significant in the numerical simulations, especially close to the front of the motion. Direct estimation of the drag coefficient $C_{D}$ from the numerical simulations shows that the combined drag parameter for the porous medium, ${\it\Gamma}_{D}=C_{D}{\it\phi}(H/D)/(1-{\it\phi})$, is the key dimensionless grouping of variables that determines the speed of propagation of the current within arrays with different $C_{D},{\it\phi}$ and $D/H$.
Internal bores: an improved model via a detailed analysis of the energy budget
- Zachary Borden, Eckart Meiburg, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 703 / 25 July 2012
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- 13 June 2012, pp. 279-314
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Internal bores, or internal hydraulic jumps, arise in many atmospheric and oceanographic phenomena. The classic single-layer hydraulic jump model accurately predicts the bore height and propagation velocity when the difference between the densities of the expanding and contracting layers is large (i.e. water and air), but fails in the Boussinesq limit. A two-layer model, which conserves mass separately in each layer and momentum globally is more accurate in the Boussinesq limit, but it requires for closure an assumption about the loss of energy across a bore. It is widely believed that bounds on the bore speed can be found by restricting the energy loss entirely to one of the two layers, but under some circumstances, both bounds overpredict the propagation speed. A front velocity slower than both bounds implies that, somehow, the expanding layer is gaining energy. We directly examine the flux of energy within internal bores using two- and three-dimensional direct numerical simulations and find that although there is a global loss of energy across a bore, a transfer of energy from the contracting to the expanding layer causes a net energy gain in the expanding layer. The energy transfer is largely the result of turbulent mixing at the interface. Within the parameter regime investigated, the effect of mixing is much larger than non-hydrostatic and viscous effects, both of which are neglected in the two-layer analytical models. Based on our results, we propose an improved two-layer model that provides an accurate propagation velocity as a function of the geometrical parameters, the Reynolds number, and the Schmidt number.
Tail structure and bed friction velocity distribution of gravity currents propagating over an array of obstacles
- Talia Tokyay, George Constantinescu, Eckart Meiburg
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- Journal:
- Journal of Fluid Mechanics / Volume 694 / 10 March 2012
- Published online by Cambridge University Press:
- 30 January 2012, pp. 252-291
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The bed friction velocity distribution and sediment entrainment potential of Boussinesq compositional gravity currents propagating over a series of obstacles and over a smooth surface, respectively, are analysed based on high-resolution, three-dimensional large-eddy simulations. The investigation focuses on the parameter regime for which currents with a high volume of release go through an extended slumping phase with approximately constant front velocity (Tokyay, Constantinescu & Meiburg, J. Fluid Mech., vol. 672, 2011, 570–605). Under these conditions, a quasi-steady regime is reached between consecutive obstacles that is similar to the steady regime observed for constant-density channel flows over bottom obstacles. At a given location, this quasi-steady regime is reached in the tail of the current after the passage of the front and the associated hydraulic jumps reflected from the first few downstream obstacles. A double-averaging procedure is employed to characterize the global changes in the structure of the tail region between currents with a high volume of release propagating over smooth surfaces and over obstacles. Reynolds-number-induced scale effects on the flow and turbulence structure within the tail region are discussed in some detail. The presence of this quasi-steady regime is significant, since the simulations with obstacles show that most of the sediment is entrained by the tail of the current, rather than by its front. A detailed analysis of the effects of the obstacle shape on the quasi-steady mean flow and turbulence structure is presented, which provides insight into why gravity currents over dunes can entrain more sediment than gravity currents over ribs of comparable size. Finally, the bed friction velocity distributions and the potential to entrain sediment are compared for a compositional current with a high volume of release during the slumping phase, and a current with a low volume of release for which transition to the buoyancy–inertia phase occurs a short time after the release of the lock gate.
Lock-exchange gravity currents with a high volume of release propagating over a periodic array of obstacles
- TALIA TOKYAY, GEORGE CONSTANTINESCU, ECKART MEIBURG
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- Journal:
- Journal of Fluid Mechanics / Volume 672 / 10 April 2011
- Published online by Cambridge University Press:
- 24 February 2011, pp. 570-605
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Large eddy simulations are employed to investigate the structure and evolution of a bottom-propagating compositional gravity current in a rectangular horizontal plane channel containing a series of identical large-scale obstacles (dunes and square ribs) at the channel bottom. Simulation results show that below a certain value of the additional drag force per unit streamwise length induced by the bottom obstacles (low drag cases), the gravity current propagating over an array of obstacles transitions to a regime where the average front velocity is close to constant. Past its initial stages, the total kinetic energy, Ek, increases in time proportional to t1/3, where t is the time since release. This behaviour is similar to the slumping phase observed for currents propagating over a flat bed, with the exception that in the latter case the temporal increase of Ek during the later stages of the slumping phase is much faster (Ek ~ t). Simulation results also show that above certain value of the drag force per unit streamwise length induced by the obstacles (high drag cases), the slumping phase can be very short. In this case, similar to currents propagating in a porous medium, the current transitions to a drag-dominated regime in which the front velocity decays proportionally to tβ, with β = −0.28, once the discharge of lock fluid at the position of the lock gate becomes close to constant in time.
Numerical simulations of lock-exchange compositional gravity current
- SENG KEAT OOI, GEORGE CONSTANTINESCU, LARRY WEBER
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- Journal:
- Journal of Fluid Mechanics / Volume 635 / 25 September 2009
- Published online by Cambridge University Press:
- 10 September 2009, pp. 361-388
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Compositional gravity current flows produced by the instantaneous release of a finite-volume, heavier lock fluid in a rectangular horizontal plane channel are investigated using large eddy simulation. The first part of the paper focuses on the evolution of Boussinesq lock-exchange gravity currents with a large initial volume of the release during the slumping phase in which the front of the gravity current propagates with constant speed. High-resolution simulations are conducted for Grashof numbers = 3150 (LGR simulation) and = 126000 (HGR simulation). The Grashof number is defined with the channel depth h and the buoyancy velocity ub = (g′ is the reduced gravity). In the HGR simulation the flow is turbulent in the regions behind the two fronts. Compared to the LGR simulation, the interfacial billows lose their coherence much more rapidly (over less than 2.5h behind the front), which results in a much faster decay of the large-scale content and turbulence intensity in the trailing regions of the flow. A slightly tilted, stably stratified interface layer develops away from the two fronts. The concentration profiles across this layer can be approximated by a hyperbolic tangent function. In the HGR simulation the energy budget shows that for t > 18h/ub the flow reaches a regime in which the total dissipation rate and the rates of change of the total potential and kinetic energies are constant in time. The second part of the paper focuses on the study of the transition of Boussinesq gravity currents with a small initial volume of the release to the buoyancy–inertia self-similar phase. When the existence of the back wall is communicated to the front, the front speed starts to decrease, and the current transitions to the buoyancy–inertia phase. Three high-resolution simulations are performed at Grashof numbers between = 3 × 104 and = 9 × 104. Additionally, a calculation at a much higher Grashof number ( = 106) is performed to understand the behaviour of a bottom-propagating current closer to the inviscid limit. The three-dimensional simulations correctly predict a front speed decrease proportional to t−α (the time t is measured from the release time) over the buoyancy–inertia phase, with the constant α approaching the theoretical value of 1/3 as the current approaches the inviscid limit. At Grashof numbers for which > 3 × 104, the intensity of the turbulence in the near-wall region behind the front is large enough to induce the formation of a region containing streaks of low and high streamwise velocities. The streaks are present well into the buoyancy–inertia phase before the speed of the front decays below values at which the streaks can be sustained. The formation of the velocity streaks induces a streaky distribution of the bed friction velocity in the region immediately behind the front. This distribution becomes finer as the Grashof number increases. For simulations in which the only difference was the value of the Grashof number ( = 4.7 × 104 versus = 106), analysis of the non-dimensional bed friction velocity distributions shows that the capacity of the gravity current to entrain sediment from the bed increases with the Grashof number. Past the later stages of the transition to the buoyancy–inertia phase, the temporal variations of the potential energy, the kinetic energy and the integral of the total dissipation rate are logarithmic.
Analysis of the flow and mass transfer processes for the incompressible flow past an open cavity with a laminar and a fully turbulent incoming boundary layer
- KYOUNGSIK CHANG, GEORGE CONSTANTINESCU, SEUNG-O PARK
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- Journal:
- Journal of Fluid Mechanics / Volume 561 / 25 August 2006
- Published online by Cambridge University Press:
- 09 August 2006, pp. 113-145
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The three-dimensional incompressible flow past a rectangular two-dimensional shallow cavity in a channel is investigated using large-eddy simulation (LES). The aspect ratio (length/depth) of the cavity is $L/D\,{=}\,2$ and the Reynolds number defined with the cavity depth and the mean velocity in the upstream channel is 3360. The sensitivity of the flow around the cavity to the characteristics of the upstream flow is studied by considering two extreme cases: a developing laminar boundary layer upstream of the cavity and when the upstream flow is fully turbulent. The two simulations are compared in terms of the mean statistics and temporal physics of the flow, including the dynamics of the coherent structures in the region surrounding the cavity. For the laminar inflow case it is found that the flow becomes unstable but remains laminar as it is convected over the cavity. Due to the three-dimensional flow instabilities and the interaction of the jet-like flow inside the recirculation region with the separated shear layer, the spanwise vortices that are shed regularly from the leading cavity edge are disturbed in the spanwise direction and, as they approach the trailing-edge corner, break into an array of hairpin-like vortices that is convected downstream the cavity close to the channel bottom. In the fully turbulent inflow case in which the momentum thickness of the incoming boundary layer is much larger compared to the laminar inflow case, the jittering of the shear layer on top of the cavity by the incoming near-wall coherent structures strongly influences the formation and convection of the eddies inside the separated shear layer. The mass exchange between the cavity and the main channel is investigated by considering the ejection of a passive scalar that is introduced instantaneously inside the cavity. As expected, it is found that the ejection is faster when the incoming flow is turbulent due to the interaction between the turbulent eddies convected from upstream of the cavity with the separated shear layer and also to the increased diffusion induced by the broader range of scales that populate the cavity. In the turbulent case it is shown that the eddies convected from upstream of the cavity can play an important role in accelerating the extraction of high-concentration fluid from inside the cavity. For both laminar and turbulent inflow cases it is shown that the scalar ejection can be described using simple dead-zone theory models in which a single-valued global mass exchange coefficient can be used to describe the scalar mass decay inside cavity over the whole ejection process.