doi:10.1017/jfm.2023.900 Mortimer et al. A dynamic model of CO2 storage in layered anticlines
JFM Papers
Reynolds number effects on a velocity–vorticity correlation-based skin-friction drag decomposition in incompressible turbulent channel flows
- Yunchao Zhao, Yitong Fan, Weipeng Li
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- 11 January 2024, A20
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A form of skin-friction drag decomposition is given based on the velocity–vorticity correlations, $\langle v\omega _z\rangle$ and $\langle -w\omega _y\rangle$, which represent the advective vorticity transport and vortex stretching, respectively. This identity provides a perspective to understand the mechanism of skin-friction drag generation from vortical motions and it has better physical interpretability compared with some previous studies. The skin-friction coefficients in incompressible turbulent channel flows at friction Reynolds numbers from 186 to 2003 are divided with this velocity–vorticity correlation-based identity. We mainly focus on the Reynolds number effects on the contributing terms, their scale-dependence and quadrant characteristics. Results show that the contributing terms and their proportions exhibit similarities and the same peak locations across the wall layer. For the first time, we find that the positive and negative regions in the spanwise pre-multiplied spectra of the turbulent inertia ($\langle v'\omega _z'\rangle +\langle -w'\omega _y'\rangle$) can be separated with a universal linear relationship of $\lambda _z^+=3.75y^+$. The linear relationship is adopted as the criterion to investigate the scale dependence of the velocity–vorticity coupling structures. It reveals that the negative and positive structures dominate the generation of friction drag associated with the advective vorticity transport and vortex stretching, respectively. Moreover, quadrant analyses of the velocity–vorticity correlations are performed to further examine the friction drag generation related to different quadrant motions.
Pressure drag reduction via imposition of spanwise wall oscillations on a rough wall
- Rahul Deshpande, Aman G. Kidanemariam, Ivan Marusic
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- Published online by Cambridge University Press:
- 11 January 2024, A21
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The present study tests the efficacy of the well-known viscous drag reduction strategy of imposing spanwise wall oscillations to reduce pressure drag contributions in transitional and fully rough turbulent wall flow. This is achieved by conducting a series of direct numerical simulations of a turbulent flow over two-dimensional (spanwise-aligned) semi-cylindrical rods, placed periodically along the streamwise direction with varying streamwise spacing. Surface oscillations, imposed at fixed viscous-scaled actuation parameters optimum for smooth wall drag reduction, are found to yield substantial drag reduction ($\gtrsim$25 %) for all the rough wall cases, maintained at matched roughness Reynolds numbers. While the total drag reduction is due to a drop in both viscous and pressure drag in the case of transitionally rough flow (i.e. with large inter-rod spacing), it is associated solely with pressure drag reduction for the fully rough cases (i.e. with small inter-rod spacing), with the latter being reported for the first time. The study finds that pressure drag reduction in all cases is caused by the attenuation of the vortex shedding activity in the roughness wake, in response to wall oscillation frequencies that are of the same order as the vortex shedding frequencies. Contrary to speculations in the literature, this study confirms that the mechanism behind pressure drag reduction, achieved via imposition of spanwise oscillations, is independent of the viscous drag reduction. This mechanism is responsible for weakening of the Reynolds stresses and increase in base pressure in the roughness wake, explaining the pressure drag reduction observed by past studies, across varying roughness heights and geometries.
Modelling the effect of roughness density on turbulent forced convection
- W. Abu Rowin, K. Zhong, T. Saurav, T. Jelly, N. Hutchins, D. Chung
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- 11 January 2024, A22
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By examining a systematic set of direct numerical simulations, we develop a model which captures the effect of roughness density on global and local heat transfer in forced convection. The surfaces considered are zero-skewed three-dimensional sinusoidal rough walls with solidities, $\varLambda$ (defined as the frontal area divided by the total plan area), ranging from low $\varLambda = 0.09$, medium $\varLambda = 0.18$ to high $\varLambda = 0.36$. For each solidity, we vary the roughness height characterised by the roughness Reynolds number, $k^+$, from transitionally rough to fully rough conditions. The findings indicate that, as the fully rough regime is approached, there is a pronounced breakdown in the analogy between heat and momentum transfer, whereby the velocity roughness function $\Delta U^+$ continues to increase and the temperature roughness function $\Delta \varTheta ^+$ attains a peak with increasing $k^+$. This breakdown occurs at higher sand-grain roughness Reynolds numbers ($k_s^+$) with increasing solidity. Locally, we find that the heat transfer can be meaningfully partitioned into two categories: exposed, high-shear regions experiencing higher heat transfer obeying a local Reynolds analogy and sheltered, reversed-flow regions experiencing lower and spatially uniform heat transfer. The relative contribution of these distinct mechanisms to the global heat transfer depends on the fraction of the total surface area covered by these regions, which ultimately depends on $\varLambda$. These insights enable us to develop a model for the rough-wall heat-transfer coefficient, ${C_{h,k}(k^+, \varLambda, Pr)}$, where $Pr$ is the molecular Prandtl number, that assumes different heat-transfer laws in exposed and sheltered regions. We show that the exposed–sheltered surface-area fractions can be modelled through simple ray tracing that is solely dependent on the surface topography and a prescribed sheltering angle. Model predictions compare well when applied to heat-transfer data of traverse ribs from the literature.
Rayleigh–Bénard convection with an immersed floating body
- Peter Frick, Sergei Filimonov, Andrei Gavrilov, Elena Popova, Andrei Sukhanovskii, Andrei Vasiliev
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- 11 January 2024, A23
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The paper presents the results of an experimental and numerical study of turbulent thermal convection in a rectangular box containing an extended immersed free-floating plate. Varying the values of control parameters, such as Rayleigh number, aspect ratio and vertical position of the plate, provides a wide range of possible modes, from immobile and purely periodic to stochastic. We have shown that stable periodic motions occur when the plate floats close to one of the heat exchangers. An increase in the distance between the plate and the heat exchanger breaks the periodic motion and (at moderate Rayleigh numbers) leads to a pronounced asymmetry, when the plate stays close to one of the walls most of the time, makes rare excursions to the opposite wall and immediately returns. As the Rayleigh number increases, the plate motions from one edge of the box to the other reappear, but always have an irregular character. Regarding the dependence of the system behaviour on the geometry of the box, both lower and upper limits of periodic plate motions were found in the experiments. In the numerical simulations, the upper limit was not achieved – the plate moves quasi-periodically through the chain of vortices of different signs even at the largest aspect ratio being considered. The heat-insulating floating plate provides the spatial and temporal variation of the heat flux and reduces the integral heat flux, but the reduction in heat flux depends significantly on the vertical position of the plate.
Time-delayed characteristics of turbulence in pulsatile pipe flow
- Xu Liu, Hongbo Zhu, Yan Bao, Narakorn Srinil, Dai Zhou, Zhaolong Han
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- 11 January 2024, A24
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Direct numerical simulations are performed to study temporal variations of the wall shear stresses and flow dynamics in the turbulent pulsatile pipe flow. The mechanisms, responsible for the paradoxical phenomenon for which the amplitude of the oscillating wall shear stress in the turbulent flow is smaller than that in the laminar flow for the same pulsation conditions, are investigated. It is shown that the delayed response of turbulence in the buffer layer generates a large magnitude of the radial gradient of the Reynolds shear stress near the wall, which counteracts the effect of the oscillating pressure gradient on the change of the streamwise velocity and hence reduces the amplitude of the wall shear stress. Such a delayed response consists of two processes: the delayed development of near-wall streaks and the subsequent energy redistribution from the streamwise velocity fluctuation to the other two co-existing components. This is a dynamical manifestation of the viscoelasticity of turbulent eddies. As the frequency is reduced, the variation of the friction Reynolds number results in a phase-wise variation of the time scale and intensity of the turbulence response, causing the hysteresis of the wall shear stress. Such a phase asymmetry is amplified by the increase of the pulsation amplitude. An examination of the energy spectra reveals that the near-wall streaks are stretched in the streamwise direction during the acceleration phase, and then break up into small-scale structures in the deceleration phase, accompanied by the enhanced dissipation that transforms the turbulent kinetic energy into heat.
Binary collision dynamics of equal-sized nanodroplets
- Yi-Feng Wang, Yi-Bo Wang, Zhi-Hui Cai, Qiang Ma, Yan-Ru Yang, Shao-Fei Zheng, Duu-Jong Lee, Xiao-Dong Wang
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- 11 January 2024, A25
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Binary nanodroplet collisions have received increasing attention, whilst the identification of collision outcomes and the viscous dissipation mechanism have remained poorly understood. Using molecular dynamics simulations, this study investigates binary nanodroplet collisions over wide ranges of Weber number (We), Ohnesorge number (Oh) and off-centre distances. Coalescence, stretching separation and shattering are identified; however, bouncing, reflexive separation and rotational separation reported for millimetre-sized collisions are not observed, which is attributed to the enhanced viscous effect caused by the ‘natural’ high-viscosity characteristics of nanodroplets. Intriguingly, as an intermediate outcome, holes form in retracting films at relatively high We, arising from the vibration and thermal fluctuation of the films. Due to the combined effects of inertial, capillary and viscous forces, binary nanodroplet collisions fall into the cross-over regime, so estimating viscous dissipation becomes extremely important for distinguishing outcome boundaries. Based on the criterion that stretching separation is triggered only when the residual off-centre kinetic energy exceeds the surface energy required for separation, the boundary equation between coalescence and stretching separation is established. Here, viscous dissipation is calculated by the extracted flow feature from simulations, showing that the ratio of viscous dissipation to the initial kinetic energy depends only on Oh, not on We. Because of complex viscous dissipation mechanisms, the same boundary equation in the cross-over regime has also not been satisfactorily revealed for macroscale collisions. Therefore, the proposed equation is tested for wide data sources from both macroscale and nanoscale collisions, and satisfying agreement is achieved, demonstrating the universality of the equation.
Coordinated suction and blowing of a cylinder array for thrust generation
- Dohyun Kim, Minhyeong Lee, Ehsan Mahravan, Daegyoum Kim
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- 11 January 2024, A26
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Various systems of mechanical devices and natural organisms use the repeated expansion and contraction of deformable structures to draw in and blow out fluid. Instead of such deformable continuous structures, a system that consists of multiple discrete bodies can also generate a directional flow through the cooperative movement of the individual bodies. In this study, we numerically investigate the collective effects of a multi-body system composed of eight circular cylinders, each of which oscillates separately in the radial direction to generate thrust. The cylinder array performs cooperative motion regulated by three motion parameters: phase difference, oscillation amplitude and frequency at a low Reynolds number ($Re = 10$). The phase difference between the cylinders is critical in determining the extent of the directional flow and the time-averaged thrust. The optimal phase difference that yields the maximum time-averaged thrust is consistent, regardless of the oscillation amplitude and frequency. However, the thrust generation performance becomes significantly weaker at a higher Reynolds number ($Re = 100$). This highlights that the hydrodynamic blockage in gaps between cylinders, which is induced by strong viscous diffusion at the low Reynolds number, is essential for the cooperative force generation of multiple closely spaced bodies. A new dimensionless geometric parameter based on the motion of the array is proposed to characterize the degree of bias in the generated flow and it successfully predicts the trend in the time-averaged thrust at the low Reynolds number with strong hydrodynamic blockage.
Numerical investigation of mixed-phase turbulence induced by a plunging jet
- Rong Li, Zixuan Yang, Wei Zhang
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- 11 January 2024, A27
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In nature and engineering applications, water jet plunging acts as a key process causing interface breaking and generating mixed-phase turbulence. In this paper, high-resolution numerical simulations of the plunging of a water jet into a quiescent pool were performed to investigate the statistical properties of mixed-phase turbulence, with a special focus on the closure problem of the Reynolds-averaged equation. We conducted phase-resolved simulations, with the air–water interface captured using a coupled level-set and volume-of-fluid method. Various cases were performed to analyse the effects of the Froude number and Reynolds number. The simulation results showed that the turbulence statistics are insensitive to the Reynolds number under investigation, while the Froude number influences the flow properties significantly. To investigate the closure problem of the mean momentum equation, the turbulent kinetic energy (TKE) and turbulent mass flux (TMF) and their transport equations were analysed further. It was discovered that the balance relationship of the TKE budget terms remained similar to many single-phase turbulent flows. The TMF is an additional unclosed term in mixed-phase turbulence over the single-phase turbulence. Our simulation results showed that the production term in its transport equation was highly correlated to TKE. Based on this finding, a closure model for the production term of TMF was further proposed.
Reflection of a rightward-moving oblique shock of first family over a steady oblique shock wave
- Miaomiao Wang, ZhongZiheng Xu, Ziniu Wu
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- 12 January 2024, A28
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The reflection of a rightward-moving oblique shock (RMOS) belonging to the first family, over an initially steady oblique shock wave (SOSW) produced by a wedge, is studied in this paper. To cover all possibilities, the problem is divided into a pre-shock reflection problem, for which the incident shock is assumed to reflect over the pre-interaction part of the SOSW, and a post-shock reflection problem, for which the incident shock is assumed to reflect over the post-interaction part. Such division, together with the definition of the equivalent problem defined on the reference frame co-moving with the nominal intersection point of the two shock waves, allows us to connect the reflection patterns with the six types of shock interference of Edney, which include type I–VI shock interferences depending on how an upstream oblique shock intersects a bow shock (types I and II are regular and Mach reflections of two shocks from the opposite sides; type III and type IV have two triple points or two Mach reflection configuration; type V and type VI are irregular and regular reflections of two shocks from the same side). We are thus able to identify all possible shock reflection types and find their transition conditions. Pre-shock reflection may yield IV, V and VI (of Edney's six types) shock interferences and post-shock reflection may yield I, II and III shock interferences. Pre- and post-shock reflections possibly occur at two different parts of the SOSW, and the complete reflection configuration may have one or both of them. Both transition condition study and numerical simulation are used to show how pre-shock reflection and post-shock reflection exist alone or coexist, leading to various types of combined pre-shock and post-shock reflections.
Order–disorder transitions within deformable particle suspensions in planar Poiseuille flow
- Paul C. Millett
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- 12 January 2024, A29
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Three-dimensional simulations of the ordering of elastic capsule suspensions within planar Poiseuille flow channels are reported. The simulations utilize the immersed boundary method coupled with the lattice Boltzmann method to capture the complex flow-induced capsule deformations and hydrodynamic interactions within the suspensions. A parametric study is presented whereby the confinement ratio and the particle deformability are varied independently within a two-dimensional range relevant to this ordering phenomenon. The initial distribution of capsules is random, and the simulations evolve the system from a disordered state to an ordered one, while an order parameter that quantifies the fraction of capsules belonging to one-dimensional train assemblies is computed throughout time. A monotonic increase in ordering is observed with increasing deformability. However, an optimal confinement ratio is identified corresponding to a peak in the order parameter. This peak is attributed to the competition between increasing long-range capsule attractions and decreasing in-plane capsule density (with fixed volume fraction) as the confinement ratio increases. Simulations are also performed to understand how dispersity in capsule size and deformability impact the degree of ordering. It is shown that ordering is quite sensitive to dispersity in capsule size, and much less sensitive to dispersity in deformability. Overall, the results provide important insights for the design of microfluidic devices.
The drag on a rising sphere along the axis in a short rotating cylinder of fluid: revisiting the data and theory
- M. Ungarish
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- 12 January 2024, A30
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We revisit the problem of a solid sphere rising slowly in a rotating short container filled with a slightly viscous fluid, with emphasis on the drag force. The data of the classical experiments of Maxworthy (J. Fluid Mech., vol. 31, 1968, pp. 643–655) and recent experiments of Kozlov et al. (Fluids, vol. 8 (2), 2023, paper 49), and the available geostrophic and quasi-geostrophic theories, are subjected to a novel scrutiny by combined reprocessing and comparisons. The measured drag is, consistently, about 20 % lower than the geostrophic prediction (assuming that flow is dominated by the Ekman layers, while in the inviscid cores the Coriolis acceleration is supported by the pressure gradient). The major objective is the interpretation and improvement of the gap between data and predictions. We show that the data cover a small range of relevant parameters (in particular the Taylor number $T$ and the height ratio $H$ of cylinder to particle diameter) that precludes a thorough and reliable assessment of the theories. However, some useful insights and improvements can be derived. The hypothesis that the discrepancy between data and the geostrophic prediction is due to inertial effects (not sufficiently small Rossby number $Ro$ in the experiments) is dismissed. We show that the major reason for the discrepancy is the presence of relatively thick Stewartson layers about the cylinder (Taylor column) attached to the sphere. The $1/3$ layer displaces the boundary condition of the angular velocity ($\omega = 0$) outside the radius of the particle. This observation suggests a semi-empirical correction to the theoretical quasi-geostrophic predictions (which takes into account the Ekman layers and the $1/4$ Stewartson layers); the corrected drag is in fair agreement with the data. We demonstrate that the inertial terms are negligible for $Ro\,T^{1/2} <0.4$. We consider curve-fit approximations, and point out some persistent gaps of knowledge that require further experiments and simulations.
Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence
- Diego C.P. Blanco, Ardeshir Hanifi, Dan S. Henningson, André V.G. Cavalieri
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- 16 January 2024, A31
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Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free-stream turbulence are considered in the present work. Within an input–output model, where nonlinear terms of the incompressible Navier–Stokes equations are treated as an external forcing, we manage to separate inputs related to perturbations coming through the intake of the numerical domain, whose evolution represents a linear mechanism, and the volumetric nonlinear forcing due to triadic interactions. With these, we perform the full reconstruction of the statistics of the flow, as measured in the simulations, to quantify pairs of wavenumbers and frequencies more affected by either linear or nonlinear receptivity mechanisms. Inside the boundary layer, different wavenumbers at near-zero frequency reveal streaky structures. Those that are amplified predominantly via linear interactions with the incoming vorticity occur upstream and display transient growth, while those generated by the nonlinear forcing are the most energetic and appear in more downstream positions. The latter feature vortices growing proportionally to the laminar boundary layer thickness, along with a velocity profile that agrees with the optimal amplification obtained by linear transient growth theory. The numerical approach presented is general and could potentially be extended to any simulation for which receptivity to incoming perturbations needs to be assessed.
Vortices over bathymetry
- J.H. LaCasce, A. Palóczy, M. Trodahl
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- 15 January 2024, A32
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There are numerous examples of long-lived, surface-intensified anticyclones over submarine depressions and troughs in the ocean. These often co-exist with a large-scale cyclonic circulation. The latter is predicted by existing barotropic theory but the anticyclone is not. We extend one such theory, which minimizes enstrophy while conserving energy, to two fluid layers. This yields a bottom-intensified flow with cyclonic circulation over a depression. The solution is steady, an enstrophy minimum and stable. When the Lagrange multiplier, $\lambda$, is near zero, the total potential vorticity (PV) becomes homogenized, in both layers. For positive $\lambda$, the surface PV is anticyclonic and strongest at intermediate energies. In quasi-geostrophic numerical simulations with a random initial perturbation PV, the bottom-intensified cyclonic flow always emerges. Vortices evolve independently in the layers and vortex mergers are asymmetric over the depression; cyclones are preferentially strained out at depth while only anticyclones merge at the surface. Both asymmetries are linked to the topographic flow. The deep cyclones feed the bottom-intensified cyclonic circulation while the asymmetry at the surface is only apparent after that circulation has spun up. The result of the surface merger asymmetry is often a lone anticyclone above the depression. This occurs primarily at intermediate energies, when the surface PV predicted by the theory is strongest. Similar results obtain in a full complexity ocean model but with a more pronounced asymmetry in surface vortex mergers and, with bottom friction, significant bottom flow beneath the central anticyclone.
On the time scales of spectral evolution of nonlinear waves
- Ashleigh Simonis, Alexander Hrabski, Yulin Pan
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- Published online by Cambridge University Press:
- 15 January 2024, A33
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As presented in Annenkov & Shrira (Phys. Rev. Lett., vol. 102, 2009, 024502), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ‘fast’ dynamic time scale of $O(\varepsilon ^{-2})$, with $\varepsilon$ a measure of wave steepness. This observation poses a challenge to wave turbulence theory that predicts an evolution with a kinetic time scale of $O(\varepsilon ^{-4})$. We revisit this unresolved problem by studying the same situation in the context of a one-dimensional Majda–McLaughlin–Tabak equation with gravity wave dispersion relation. Our results show that the kinetic and dynamic time scales can both be realised, with the former and latter occurring for weaker and stronger forcing perturbations, respectively. The transition between the two regimes corresponds to a critical forcing perturbation, with which the spectral evolution time scale drops to the same order as the linear wave period (of some representative mode). Such fast spectral evolution is mainly induced by a far-from-stationary state after a sufficiently strong forcing perturbation is applied. We further develop a set-based interaction analysis to show that the inertial-range modal evolution in the studied cases is dominated by their (mostly non-local) interactions with the low-wavenumber ‘condensate’ induced by the forcing perturbation. The results obtained in this work should be considered to provide significant insight into the original gravity wave problem.
Effect of tip speed ratio on coherent dynamics in the near wake of a model wind turbine
- Neelakash Biswas, Oliver R.H. Buxton
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- Published online by Cambridge University Press:
- 15 January 2024, A34
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The near wake of a small-scale wind turbine is investigated using particle image velocimetry experiments at different tip speed ratios ($\lambda$). The wind turbine model had a nacelle and a tower mimicking real-scale wind turbines. The near wake is found to be dominated by multiple coherent structures, including the tip vortices, distinct vortex sheddings from the nacelle and tower, and wake meandering. The merging of the tip vortices is found to be strongly dependent on $\lambda$. A convective length scale ($L_c$) related to the pitch of the tip vortices is defined that is shown to be a better length scale than turbine diameter ($D$) to demarcate the near wake from the far wake. The tower induced strong vertical asymmetry in the flow by destabilising the tip vortices and promoting mixing in the lower (below the nacelle) plane. The nacelle's shedding is found to be important in ‘seeding’ wake meandering, which, although not potent, exists close to the nacelle, and it becomes important only after a certain distance downstream ($x>3L_c$). A link between the ‘effective porosity’ of the turbine and $\lambda$ is established, and the strength and frequency of wake meandering are found to be dependent on $\lambda$. In fact, a decreasing trend of wake meandering frequency with $\lambda$ is observed, similar to vortex shedding from a porous plate at varying porosity. Such similarity upholds the notion of wake meandering being a global instability of the turbine, which can be considered as a ‘porous’ bluff body of diameter $D$.
Airfoil response to periodic vertical and longitudinal gusts
- Tong Wang, Li-Hao Feng, Yu-Tian Cao, Jin-Jun Wang
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- 17 January 2024, A35
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Gust response has consistently been a concern in engineering. Critical theories have been proposed in the past to predict the unsteady lift response of an airfoil experiencing vertical gusts by Atassi, and longitudinal gusts by Greenberg. However, their applicability for an airfoil with non-zero angles of attack still needs clarification. Thus, force measurements are conducted to examine these theories’ validity and quasi-steady corrections are applied to compensate potential disparities between the idealised and real flow conditions. Velocity measurements are performed to scrutinise the effect of gusts on the flow around the airfoil, and subsequently to reveal the underlying mechanism governing the airfoil's response to gust-induced perturbations. In the study, two pitching vanes are arranged upstream to generate periodic vertical and longitudinal gusts, whereas a downstream airfoil with angles of attack of 0–12° is subjected to two gust types. It is found that Greenberg's theory demonstrates superior predictive capability in pre-stall regimes, with the potential for its effectiveness to be expanded to post-stall regimes through theoretical refinements. In contrast, Atassi's theory exhibits significant deviations from experimental outcomes across the measured angles of attack. Nevertheless, a modified version of the theory aligns better with experimental results at small angles of attack, whereas substantial discrepancies persist as the angle of attack increases. In the pre-stall regime, the aerodynamic response of the airfoil to vertical gusts displays a linear correlation with the flow angle near the leading edge. In the post-stall regime, the vertical gust induces dynamic stall of the airfoil. The flow angle has an essential effect on the lift coefficient but it alone is inadequate to dictate the trend of the lift coefficient. The vorticity statistics show that negative vortex circulation strongly correlates with the lift coefficient. Thus, further correction of the theory or a new vortex model can be expected to predict the lift variation.
Impact of the numerical domain on turbulent flow statistics: scalings and considerations for canopy flows
- Atharva S. Sathe, Marco G. Giometto
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- 17 January 2024, A36
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Large eddy simulations (LES) are widely used to study the effects of surface morphology on turbulence statistics, exchange processes and turbulence topology in urban canopies. However, as LES are only approximations of reality, special attention is needed for the computational model set-up to ensure an accurate representation of the physical processes of interest. This paper shows that the choice of the numerical domain can significantly affect the accuracy of turbulent flow statistics, potentially causing a mismatch between numerical studies and experimental data. The study examines the influence of cross-stream aspect ratio (YAR), streamwise aspect ratio (XAR) and scale separation (SS) on first- and second-order flow statistics and turbulence topology. It is found that domains with a low YAR underestimate the velocity variance, while those with a low XAR overestimate the variance value. The study proposes a new approach based on the Buckingham Pi theorem to evaluate the effect of SS, as the existing method has major limitations for canopy flows. The results suggest that domains with small SS underpredict the variance value. To minimise the artificial impact of the numerical domain on turbulent flow statistics, the study recommends guidelines for future research, including a YAR of 3 or more, an XAR of 6 or more and an SS of 12 or more. Error tables are presented to allow researchers to select smaller domains than recommended, depending on their research interests in specific parts of the flow.
Sedimenting-particle redistribution in a horizontal Couette
- M. Davoodi, A. Clarke
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- 17 January 2024, A37
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Flow between axially rotating concentric cylinders is well known to exhibit rich dynamics. Hence, Taylor instabilities have been studied, both experimentally and theoretically, for many years. Although usually studied in the abstract, such geometries arise in a range of practical situations including drilling, when a drilling fluid flow enters a well via a pipe that is the centre body and returns via the annulus between the pipe and the borehole wall. In drilling, the centre body rotates and the annular flow contains rock cuttings. Here, we report the development of an Eulerian-Eulerian solver, based on OpenFOAM, that solves for this cuttings transport problem in the presence of both gravity and Taylor vortices. To check the reliability of the solver, we conduct a set of experiments spanning a wide range of complex flow regimes. We show that the model successfully predicts, in all regimes, the observed complex redistribution of particulates. However, for suspension flows under viscously dominated conditions, high particle concentrations and in rectilinear flow, particle pressure and normal stress differences are sufficient to capture particle migration. Results show that in more complex flows exemplified by the Taylor–Couette flow studied here, more realistic predictions of non-Brownian particle migration require inclusion of forces arising through the relative velocity of the two phases including lift forces originating both from inertia and particle rotation.
Viscous tubular-body theory for plane interfaces
- L. Koens, B.J. Walker
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- 17 January 2024, A38
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Filaments are ubiquitous within the microscopic world, occurring in biological and industrial environments and displaying a varied dynamics. Their wide range of applications has spurred the development of a branch of asymptotics focused on the behaviour of filaments, called slender-body theory (SBT). Slender-body theories are computationally efficient and focus on the mechanics of an isolated fibre that is slender and not too curved. However, SBTs that work beyond these limits are needed to explore complex systems. Recently, we developed tubular-body theory (TBT), an approach like SBT that allows the hydrodynamic traction on any isolated fibre in a viscous fluid to be determined exactly. This paper extends TBT to model fibres near plane interfaces by performing a similar expansion on the single-layer boundary integrals (BIs) for bodies by a plane interface. This provides a well-behaved SBT inspired approach for fibres by interfaces with a similar versatility to the BIs but without the singular kernels. The derivation of the new theory, called tubular-body theory for interfaces (TBTi), also establishes a criterion for the convergence of the TBTi series representation. The TBTi equations are solved numerically using a approach similar to boundary element methods (BEMs), called TBTi-BEM, to investigate the properties of TBTi empirically. The TBTi-BEM is found to compare favourably with an existing BEM and the lubrication singularity on a sphere, suggesting TBTi is valid for all separations. Finally, we simulate the hydrodynamics of helices beneath a free interface and a plane wall to demonstrate the applicability of the technique.
A dynamic model of ${\rm CO}_2$ storage in layered anticlines
- Patrick K. Mortimer, Nicola Mingotti, Andrew W. Woods
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- 18 January 2024, A39
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We explore ${\rm CO}_2$ injection into a layered permeable rock consisting of high permeability reservoir layers, separated by low permeability mudstone, and taking the shape of an anticline within a laterally extensive aquifer. We first show how the storage capacity of the formation depends on the capillary entry pressure of the inter-layer mudstone, so that ${\rm CO}_2$ cannot flow from one layer into the next. We then consider a formation composed of two layers, overlain by a cap rock. For injection into the lowest layer, we show that the injection rate, capillary entry pressure and buoyancy driven flux through the mudstone determine whether the lower or upper layer fills to the spill point first. We also show that at the end of the injection phase, ${\rm CO}_2$ may continue to flow from the lower to the upper layer. This implies that injection should be stopped once the injected volume matches the static capacity of the formation in order to prevent spilling after injection. We present a series of analogue experiments of a two layered system that illustrate some of the principles described by the model, and assess the implications of the results for field scale systems.