We present a data-driven feedforward control to attenuate large transient lift experienced by an airfoil disturbed by an extreme level of discrete vortex gust. The current analysis uses a nonlinear machine-learning technique to compress the high-dimensional flow dynamics onto a low-dimensional manifold. While the interaction dynamics between the airfoil and extreme vortex gust are parametrized by its size, gust ratio and position, the wake responses are well captured on this simple manifold. The effect of extreme vortex disturbance about the undisturbed baseline flows can be extracted in a physically interpretable manner. Furthermore, we call on phase-amplitude reduction to model and control the complex nonlinear extreme aerodynamic flows. The present phase-amplitude reduction model reveals the sensitivity of the dynamical system in terms of the phase shift and amplitude change induced by external forcing with respect to the baseline periodic orbit. By performing the phase-amplitude analysis for a latent dynamical model identified by sparse regression, the sensitivity functions of low-dimensionalized aerodynamic flows for both phase and amplitude are derived. With the phase and amplitude sensitivity functions, optimal forcing can be determined to quickly suppress the effect of extreme vortex gusts towards the undisturbed states in a low-order space. The present optimal flow modification built upon the machine-learned low-dimensional subspace quickly alleviates the impact of transient vortex gusts for a variety of extreme aerodynamic scenarios, providing a potential foundation for flight of small-scale air vehicles in adverse atmospheric conditions.
{"title":"Data-driven transient lift attenuation for extreme vortex gust–airfoil interactions","authors":"Kai Fukami, Hiroya Nakao, Kunihiko Taira","doi":"10.1017/jfm.2024.592","DOIUrl":"https://doi.org/10.1017/jfm.2024.592","url":null,"abstract":"We present a data-driven feedforward control to attenuate large transient lift experienced by an airfoil disturbed by an extreme level of discrete vortex gust. The current analysis uses a nonlinear machine-learning technique to compress the high-dimensional flow dynamics onto a low-dimensional manifold. While the interaction dynamics between the airfoil and extreme vortex gust are parametrized by its size, gust ratio and position, the wake responses are well captured on this simple manifold. The effect of extreme vortex disturbance about the undisturbed baseline flows can be extracted in a physically interpretable manner. Furthermore, we call on phase-amplitude reduction to model and control the complex nonlinear extreme aerodynamic flows. The present phase-amplitude reduction model reveals the sensitivity of the dynamical system in terms of the phase shift and amplitude change induced by external forcing with respect to the baseline periodic orbit. By performing the phase-amplitude analysis for a latent dynamical model identified by sparse regression, the sensitivity functions of low-dimensionalized aerodynamic flows for both phase and amplitude are derived. With the phase and amplitude sensitivity functions, optimal forcing can be determined to quickly suppress the effect of extreme vortex gusts towards the undisturbed states in a low-order space. The present optimal flow modification built upon the machine-learned low-dimensional subspace quickly alleviates the impact of transient vortex gusts for a variety of extreme aerodynamic scenarios, providing a potential foundation for flight of small-scale air vehicles in adverse atmospheric conditions.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"21 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
At high incidence, low-aspect-ratio wings present a unique set of aerodynamic characteristics, including flow separation, vortex shedding and unsteady force production. Furthermore, low-aspect-ratio wings exhibit a highly impactful tip vortex, which introduces strong spanwise gradients into an already complex flow. In this work, we explore the interaction between leading-edge flow separation and a strong, persistent tip vortex over a Reynolds number range of $600 leq Re leq 10{,}000$. In performing this study, we aim to bridge the insight gained from existing low-Reynolds-number studies of separated flow on finite wings ($Re approx 10^2$) and turbulent flows at higher Reynolds numbers ($Re approx 10^4$). Our study suggests two primary effects of the Reynolds number. First, we observe a break from periodicity, along with a dramatic increase in the intensity and concentration of small-scale eddies, as we shift from $Re = 600$ to $Re = 2500$. Second, we observe that many of our flow diagnostics, including the time-averaged aerodynamic force, exhibit reduced sensitivity to Reynolds number beyond $Re = 2500$, an observation attributed to the stabilising impact of the wing tip vortex. This latter point illustrates the manner by which the tip vortex drives flow over low-aspect-ratio wings, and provides insight into how our existing understanding of this flow field may be adjusted for higher-Reynolds-number applications.
{"title":"The effect of Reynolds number on the separated flow over a low-aspect-ratio wing","authors":"Luke Smith, Kunihiko Taira","doi":"10.1017/jfm.2024.748","DOIUrl":"https://doi.org/10.1017/jfm.2024.748","url":null,"abstract":"At high incidence, low-aspect-ratio wings present a unique set of aerodynamic characteristics, including flow separation, vortex shedding and unsteady force production. Furthermore, low-aspect-ratio wings exhibit a highly impactful tip vortex, which introduces strong spanwise gradients into an already complex flow. In this work, we explore the interaction between leading-edge flow separation and a strong, persistent tip vortex over a Reynolds number range of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007481_inline2.png\"/> <jats:tex-math>$600 leq Re leq 10{,}000$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In performing this study, we aim to bridge the insight gained from existing low-Reynolds-number studies of separated flow on finite wings (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007481_inline3.png\"/> <jats:tex-math>$Re approx 10^2$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) and turbulent flows at higher Reynolds numbers (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007481_inline4.png\"/> <jats:tex-math>$Re approx 10^4$</jats:tex-math> </jats:alternatives> </jats:inline-formula>). Our study suggests two primary effects of the Reynolds number. First, we observe a break from periodicity, along with a dramatic increase in the intensity and concentration of small-scale eddies, as we shift from <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007481_inline5.png\"/> <jats:tex-math>$Re = 600$</jats:tex-math> </jats:alternatives> </jats:inline-formula> to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007481_inline6.png\"/> <jats:tex-math>$Re = 2500$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Second, we observe that many of our flow diagnostics, including the time-averaged aerodynamic force, exhibit reduced sensitivity to Reynolds number beyond <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007481_inline7.png\"/> <jats:tex-math>$Re = 2500$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, an observation attributed to the stabilising impact of the wing tip vortex. This latter point illustrates the manner by which the tip vortex drives flow over low-aspect-ratio wings, and provides insight into how our existing understanding of this flow field may be adjusted for higher-Reynolds-number applications.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"5 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Roughness of the surface underlying the atmospheric boundary layer causes departures of the near-surface scalar and momentum transport in comparison with aerodynamically smooth surfaces. Here, we investigate the effect of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005421_inline1.png"/> <jats:tex-math>$56times 56$</jats:tex-math> </jats:alternatives> </jats:inline-formula> homogeneously distributed roughness elements on bulk properties of a turbulent Ekman flow. Direct numerical simulation in combination with an immersed boundary method is performed for fully resolved, three-dimensional roughness elements. The packing density is approximately <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005421_inline2.png"/> <jats:tex-math>$10,%$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and the roughness elements have a mean height in wall units of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005421_inline3.png"/> <jats:tex-math>$10 lesssim H^+ lesssim 40$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. According to their roughness Reynolds numbers, the cases are transitionally rough, although the roughest case is on the verge of being fully rough. We derive the friction of velocity and of the passive scalar through vertical integration of the respective balances. Thereby, we quantify the enhancement of turbulent activity with increasing roughness height and find a scaling for the friction Reynolds number that is verified up to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005421_inline4.png"/> <jats:tex-math>$Re_tau approx 2700$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The higher level of turbulent activity results in a deeper logarithmic layer for the rough cases and an increase of the near-surface wind veer in spite of higher <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005421_inline5.png"/> <jats:tex-math>$Re_tau$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We estimate the von Kármán constant for the horizontal velocity <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005421_inline6.png"/> <jats:tex-math>$kappa _{m}=0.42$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (offset <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005421_inline7.png"/> <jats:tex-math>$A=5.44$</jats:tex-
{"title":"Simulation and scaling analysis of periodic surfaces with small-scale roughness in turbulent Ekman flow","authors":"Jonathan Kostelecky, Cedrick Ansorge","doi":"10.1017/jfm.2024.542","DOIUrl":"https://doi.org/10.1017/jfm.2024.542","url":null,"abstract":"Roughness of the surface underlying the atmospheric boundary layer causes departures of the near-surface scalar and momentum transport in comparison with aerodynamically smooth surfaces. Here, we investigate the effect of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005421_inline1.png\"/> <jats:tex-math>$56times 56$</jats:tex-math> </jats:alternatives> </jats:inline-formula> homogeneously distributed roughness elements on bulk properties of a turbulent Ekman flow. Direct numerical simulation in combination with an immersed boundary method is performed for fully resolved, three-dimensional roughness elements. The packing density is approximately <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005421_inline2.png\"/> <jats:tex-math>$10,%$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and the roughness elements have a mean height in wall units of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005421_inline3.png\"/> <jats:tex-math>$10 lesssim H^+ lesssim 40$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. According to their roughness Reynolds numbers, the cases are transitionally rough, although the roughest case is on the verge of being fully rough. We derive the friction of velocity and of the passive scalar through vertical integration of the respective balances. Thereby, we quantify the enhancement of turbulent activity with increasing roughness height and find a scaling for the friction Reynolds number that is verified up to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005421_inline4.png\"/> <jats:tex-math>$Re_tau approx 2700$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The higher level of turbulent activity results in a deeper logarithmic layer for the rough cases and an increase of the near-surface wind veer in spite of higher <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005421_inline5.png\"/> <jats:tex-math>$Re_tau$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We estimate the von Kármán constant for the horizontal velocity <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005421_inline6.png\"/> <jats:tex-math>$kappa _{m}=0.42$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (offset <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005421_inline7.png\"/> <jats:tex-math>$A=5.44$</jats:tex-","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"11 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yaguang Xie, Qiang Du, Lei Xie, Zhicheng Wang, Siyi Li
Numerous studies have indicated that turbulence typically initiates along the boundary layer of the stationary disk within a rotor–stator cavity. To describe the transition process to turbulence on the stationary side of a closed rotor–stator cavity, a comprehensive approach combining global linear stability analysis with direct numerical simulation was adopted in the present study. The proposed model aligns with that of Yim et al. (J. Fluid Mech., vol. 848, 2018, pp. 631–647), who investigated the stability characteristics of the rotating-disk boundary layer in a rotor–stator cavity. In order to achieve a stable inflow for the stationary-disk boundary layer, we rotate the shroud together with the rotating disk. Through careful global stability analysis, the predominant spiral mode exhibiting the highest instability in the boundary layer of the stationary disk was discerned, corroborating observations from simulations. Initially, the spiral mode undergoes linear amplification, reaches a state of linear saturation and enters the nonlinear regime. Following nonlinear saturation in the flow field, a circular wave mode arises due to the influence of mean flow distortion. As the Reynolds number attained a sufficiently high level, the interplay between the downstream-propagating circular mode and spiral mode amplified disturbances in the boundary layer of the stationary disk, ultimately leading to the development of localised turbulence at the mid-radius of the rotor–stator cavity. Notably, the present study is the first to elucidate the coexistence of laminar–transitional–turbulent flow states in the stationary-disk boundary layer through direct numerical simulations.
{"title":"Onset of turbulence in rotor–stator cavity flows","authors":"Yaguang Xie, Qiang Du, Lei Xie, Zhicheng Wang, Siyi Li","doi":"10.1017/jfm.2024.536","DOIUrl":"https://doi.org/10.1017/jfm.2024.536","url":null,"abstract":"Numerous studies have indicated that turbulence typically initiates along the boundary layer of the stationary disk within a rotor–stator cavity. To describe the transition process to turbulence on the stationary side of a closed rotor–stator cavity, a comprehensive approach combining global linear stability analysis with direct numerical simulation was adopted in the present study. The proposed model aligns with that of Yim <jats:italic>et al.</jats:italic> (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 848, 2018, pp. 631–647), who investigated the stability characteristics of the rotating-disk boundary layer in a rotor–stator cavity. In order to achieve a stable inflow for the stationary-disk boundary layer, we rotate the shroud together with the rotating disk. Through careful global stability analysis, the predominant spiral mode exhibiting the highest instability in the boundary layer of the stationary disk was discerned, corroborating observations from simulations. Initially, the spiral mode undergoes linear amplification, reaches a state of linear saturation and enters the nonlinear regime. Following nonlinear saturation in the flow field, a circular wave mode arises due to the influence of mean flow distortion. As the Reynolds number attained a sufficiently high level, the interplay between the downstream-propagating circular mode and spiral mode amplified disturbances in the boundary layer of the stationary disk, ultimately leading to the development of localised turbulence at the mid-radius of the rotor–stator cavity. Notably, the present study is the first to elucidate the coexistence of laminar–transitional–turbulent flow states in the stationary-disk boundary layer through direct numerical simulations.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"78 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
John E. Sader, Wei Hou, Edward M. Hinton, D.I. Pullin, Tim Colonius
A two-dimensional body that moves suddenly in a viscous fluid can instantly generate vortices at its sharp edges. Recent work using inviscid flow theory, based on the Birkhoff–Rott equation and the Kutta condition, predicts that the ‘starting vortices’ generated by the sharp and straight edges of a body – i.e. the vortices formed immediately after motion begins – can be one of three distinct self-similar types. We explore the existence of these starting vortices for a flat plate and two symmetric Joukowski aerofoils immersed in a viscous fluid, using high-fidelity direct numerical simulations (DNS) of the Navier–Stokes equations. A lattice Green's function method is employed and simulations are performed for chord Reynolds numbers ranging from 5040 to 45 255. Vortices generated at the leading and trailing edges of the flat plate show agreement with the derived inviscid theory, for which a detailed assessment is reported. Agreement is also observed for the two symmetric Joukowski aerofoils, demonstrating the utility of the inviscid theory for arbitrary bodies. While this inviscid theory predicts an abrupt transition between the starting-vortex types, DNS shows a smooth transition. This behaviour occurs for all Reynolds numbers and is related to finite-time effects – there is a maximal time for which the (self-similar) starting vortices exist. We confirm the inviscid prediction that the leading-edge starting vortex of a flat plate can be suppressed dynamically. This has implications for the performance of low-speed aircraft such as model aeroplanes, micro air vehicles and unmanned air vehicles.
{"title":"The starting vortices generated by bodies with sharp and straight edges in a viscous fluid","authors":"John E. Sader, Wei Hou, Edward M. Hinton, D.I. Pullin, Tim Colonius","doi":"10.1017/jfm.2024.515","DOIUrl":"https://doi.org/10.1017/jfm.2024.515","url":null,"abstract":"A two-dimensional body that moves suddenly in a viscous fluid can instantly generate vortices at its sharp edges. Recent work using inviscid flow theory, based on the Birkhoff–Rott equation and the Kutta condition, predicts that the ‘starting vortices’ generated by the sharp and straight edges of a body – i.e. the vortices formed immediately after motion begins – can be one of three distinct self-similar types. We explore the existence of these starting vortices for a flat plate and two symmetric Joukowski aerofoils immersed in a viscous fluid, using high-fidelity direct numerical simulations (DNS) of the Navier–Stokes equations. A lattice Green's function method is employed and simulations are performed for chord Reynolds numbers ranging from 5040 to 45 255. Vortices generated at the leading and trailing edges of the flat plate show agreement with the derived inviscid theory, for which a detailed assessment is reported. Agreement is also observed for the two symmetric Joukowski aerofoils, demonstrating the utility of the inviscid theory for arbitrary bodies. While this inviscid theory predicts an abrupt transition between the starting-vortex types, DNS shows a smooth transition. This behaviour occurs for all Reynolds numbers and is related to finite-time effects – there is a maximal time for which the (self-similar) starting vortices exist. We confirm the inviscid prediction that the leading-edge starting vortex of a flat plate can be suppressed dynamically. This has implications for the performance of low-speed aircraft such as model aeroplanes, micro air vehicles and unmanned air vehicles.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"316 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fei He, Hongwei An, Marco Ghisalberti, Scott Draper, Chengjiao Ren, Paul Branson, Liang Cheng
Previous work suggests that the arrangement of elements in an obstruction may influence the bulk flow velocity through the obstruction, but the physical mechanisms for this influence are not yet clear. This is the motivation for this study, where direct numerical simulation is used to investigate flow through an array of cylinders at a resolution sufficient to observe interactions between wakes of individual elements. The arrangement is altered by varying the gap ratio <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400510X_inline2ab.png"/> <jats:tex-math>$G/d$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (1.2 – 18, <jats:italic>G</jats:italic> is the distance between two adjacent cylinders, <jats:italic>d</jats:italic> is the cylinder diameter), array-to-element diameter ratio <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400510X_inline2gf.png"/> <jats:tex-math>$D/d$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (3.6 – 200, <jats:italic>D</jats:italic> is the array diameter), and incident flow angle (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400510X_inline2b.png"/> <jats:tex-math>$0^{circ} - 30^{circ}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>). Depending on the element arrangement, it is found that the average root-mean-square lift and drag coefficients can vary by an order of magnitude, whilst the average time-mean drag coefficient of individual cylinders (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400510X_inline2c.png"/> <jats:tex-math>$overline{C_{d}}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>), and the bulk velocity are found to vary by up to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400510X_inline2d.png"/> <jats:tex-math>$50,%$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and a factor of 2, respectively. These arrangement effects are a consequence of the variation in flow and drag characteristics of individual cylinders within the array. The arrangement effects become most critical in the intermediate range of flow blockage parameter <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400510X_inline2e.png"/> <jats:tex-math>$mathit{Gamma_{D}^{prime}} = 0.5-1.5$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S00221120
{"title":"Obstacle arrangement can control flows through porous obstructions","authors":"Fei He, Hongwei An, Marco Ghisalberti, Scott Draper, Chengjiao Ren, Paul Branson, Liang Cheng","doi":"10.1017/jfm.2024.510","DOIUrl":"https://doi.org/10.1017/jfm.2024.510","url":null,"abstract":"Previous work suggests that the arrangement of elements in an obstruction may influence the bulk flow velocity through the obstruction, but the physical mechanisms for this influence are not yet clear. This is the motivation for this study, where direct numerical simulation is used to investigate flow through an array of cylinders at a resolution sufficient to observe interactions between wakes of individual elements. The arrangement is altered by varying the gap ratio <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400510X_inline2ab.png\"/> <jats:tex-math>$G/d$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (1.2 – 18, <jats:italic>G</jats:italic> is the distance between two adjacent cylinders, <jats:italic>d</jats:italic> is the cylinder diameter), array-to-element diameter ratio <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400510X_inline2gf.png\"/> <jats:tex-math>$D/d$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (3.6 – 200, <jats:italic>D</jats:italic> is the array diameter), and incident flow angle (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400510X_inline2b.png\"/> <jats:tex-math>$0^{circ} - 30^{circ}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>). Depending on the element arrangement, it is found that the average root-mean-square lift and drag coefficients can vary by an order of magnitude, whilst the average time-mean drag coefficient of individual cylinders (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400510X_inline2c.png\"/> <jats:tex-math>$overline{C_{d}}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>), and the bulk velocity are found to vary by up to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400510X_inline2d.png\"/> <jats:tex-math>$50,%$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and a factor of 2, respectively. These arrangement effects are a consequence of the variation in flow and drag characteristics of individual cylinders within the array. The arrangement effects become most critical in the intermediate range of flow blockage parameter <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400510X_inline2e.png\"/> <jats:tex-math>$mathit{Gamma_{D}^{prime}} = 0.5-1.5$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S00221120","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"175 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tali Khain, Michel Fruchart, Colin Scheibner, Thomas A. Witten, Vincenzo Vitelli
Chiral fluids – such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids – flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional (3-D) anisotropic chiral fluid, we predict counterintuitive phenomena such as motion at an angle to the direction of applied forces and spinning under the force of gravity.
{"title":"Trading particle shape with fluid symmetry: on the mobility matrix in 3-D chiral fluids","authors":"Tali Khain, Michel Fruchart, Colin Scheibner, Thomas A. Witten, Vincenzo Vitelli","doi":"10.1017/jfm.2024.535","DOIUrl":"https://doi.org/10.1017/jfm.2024.535","url":null,"abstract":"Chiral fluids – such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids – flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional (3-D) anisotropic chiral fluid, we predict counterintuitive phenomena such as motion at an angle to the direction of applied forces and spinning under the force of gravity.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"5 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Turbulence can have a strong effect on the fall speed of snowflakes and ice crystals. In this experimental study, the behaviour of thin disks falling in homogeneous turbulence is investigated, in a range of parameters relevant to plate crystals. Disks ranging in diameter from 0.3 to 3 mm, and in Reynolds number $Re = 10unicode{x2013}435$, are dispersed in two air turbulence levels, with velocity fluctuations comparable to the terminal velocity. For each case, thousands of trajectories are captured and reconstructed by high-speed laser imaging, allowing for statistical analysis of the translational and rotational dynamics. Air turbulence reduces the disk terminal velocities by up to 35 %, with the largest diameters influenced most significantly, which is primarily attributed to drag nonlinearity. This is evidenced by large lateral excursions of the trajectories, which correlate with cross-flow-induced drag enhancement as reported previously for falling spheres and rising bubbles. As the turbulence intensity is increased, flat-falling behaviour is progressively eliminated and tumbling becomes prevalent. The rotation rates of the tumbling disks, however, remain similar to those displayed in still air. This is due to their large moment of inertia compared to the surrounding fluid, in stark contrast with studies conducted in water. In fact, the observed reduction of settling velocity is opposite to previous findings on disks falling in turbulent water. This emphasizes the importance of the solid-to-fluid density ratio in analogous experiments that aim to mimic the behaviour of frozen hydrometeors.
{"title":"Turbulence effect on disk settling dynamics","authors":"Amy Tinklenberg, Michele Guala, Filippo Coletti","doi":"10.1017/jfm.2024.534","DOIUrl":"https://doi.org/10.1017/jfm.2024.534","url":null,"abstract":"Turbulence can have a strong effect on the fall speed of snowflakes and ice crystals. In this experimental study, the behaviour of thin disks falling in homogeneous turbulence is investigated, in a range of parameters relevant to plate crystals. Disks ranging in diameter from 0.3 to 3 mm, and in Reynolds number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005342_inline1.png\"/> <jats:tex-math>$Re = 10unicode{x2013}435$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, are dispersed in two air turbulence levels, with velocity fluctuations comparable to the terminal velocity. For each case, thousands of trajectories are captured and reconstructed by high-speed laser imaging, allowing for statistical analysis of the translational and rotational dynamics. Air turbulence reduces the disk terminal velocities by up to 35 %, with the largest diameters influenced most significantly, which is primarily attributed to drag nonlinearity. This is evidenced by large lateral excursions of the trajectories, which correlate with cross-flow-induced drag enhancement as reported previously for falling spheres and rising bubbles. As the turbulence intensity is increased, flat-falling behaviour is progressively eliminated and tumbling becomes prevalent. The rotation rates of the tumbling disks, however, remain similar to those displayed in still air. This is due to their large moment of inertia compared to the surrounding fluid, in stark contrast with studies conducted in water. In fact, the observed reduction of settling velocity is opposite to previous findings on disks falling in turbulent water. This emphasizes the importance of the solid-to-fluid density ratio in analogous experiments that aim to mimic the behaviour of frozen hydrometeors.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"31 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D.V. Lyubimov, T.P. Lyubimova, S. Meradji, B. Roux
This work is devoted to a theoretical and numerical study of the dynamics of a two-phase system vapour bubble in equilibrium with its liquid phase under translational vibrations in the absence of gravity. The bubble is initially located in the container centre. The liquid and vapour phases are considered as viscous and incompressible. Analysis focuses on the vibrational conditions used in experiments with the two-phase system SF$_6$ in the MIR space station and with the two-phase system para-Hydrogen (p-H$_2$) under magnetic compensation of Earth's gravity. These conditions correspond to small-amplitude high-frequency vibrations. Under vibrations, additionally to the forced oscillations, an average displacement of the bubble to the wall is observed due to an average vibrational attraction force related to the Bernoulli effect. Vibrational conditions for SF$_6$ correspond to much smaller average vibrational force (weak vibrations) than for p-H$_2$ (strong vibrations). For weak vibrations, the role of the initial vibration phase is crucial. The difference in the behaviour at different initial phases is explained using a simple mechanical model. For strong vibrations, the average displacement to the wall stops when the bubble reaches a quasi-equilibrium position where the resulting average force is zero. At large vibration velocity amplitudes this position is near the wall where the bubble performs only forced oscillations. At moderate vibration velocity amplitudes the bubble average displacement stops at a finite distance from the wall, then large-scale damped oscillations around this position accompanied by forced oscillations are observed. Bubble shape oscillations and the parametric resonance of forced oscillations are also studied.
这项研究致力于在无重力条件下，对处于与液相平衡状态的两相系统汽泡在平移振动下的动力学进行理论和数值研究。气泡最初位于容器中心。液相和汽相被认为是粘性和不可压缩的。分析的重点是在 MIR 空间站中两相体系 SF $_6$ 的实验中使用的振动条件，以及在地球引力的磁补偿下两相体系对位氢（p-H $_2$ ）的实验中使用的振动条件。这些条件对应于小振幅高频振动。在振动条件下，除了受迫振荡之外，由于与伯努利效应有关的平均振动吸引力，还观察到气泡向壁面的平均位移。SF_6$ 的振动条件对应的平均振动力（弱振动）要比 p-H_2$ 的小得多（强振动）。对于弱振动，初始振动阶段的作用至关重要。我们可以用一个简单的机械模型来解释不同初始阶段的行为差异。对于强振动，当气泡达到所产生的平均力为零的准平衡位置时，气泡壁的平均位移就会停止。在振动速度振幅较大时，该位置靠近气泡仅进行受迫振荡的壁面。在中等振动速度振幅下，气泡的平均位移停止在离壁的有限距离处，然后在该位置附近观察到大规模的阻尼振荡，并伴有受迫振荡。此外，还研究了气泡形状振荡和受迫振荡的参数共振。
{"title":"Vibration-induced wall–bubble interactions under zero-gravity conditions","authors":"D.V. Lyubimov, T.P. Lyubimova, S. Meradji, B. Roux","doi":"10.1017/jfm.2024.541","DOIUrl":"https://doi.org/10.1017/jfm.2024.541","url":null,"abstract":"This work is devoted to a theoretical and numerical study of the dynamics of a two-phase system vapour bubble in equilibrium with its liquid phase under translational vibrations in the absence of gravity. The bubble is initially located in the container centre. The liquid and vapour phases are considered as viscous and incompressible. Analysis focuses on the vibrational conditions used in experiments with the two-phase system SF<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400541X_inline1.png\"/> <jats:tex-math>$_6$</jats:tex-math> </jats:alternatives> </jats:inline-formula> in the MIR space station and with the two-phase system para-Hydrogen (p-H<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400541X_inline2.png\"/> <jats:tex-math>$_2$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) under magnetic compensation of Earth's gravity. These conditions correspond to small-amplitude high-frequency vibrations. Under vibrations, additionally to the forced oscillations, an average displacement of the bubble to the wall is observed due to an average vibrational attraction force related to the Bernoulli effect. Vibrational conditions for SF<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400541X_inline3.png\"/> <jats:tex-math>$_6$</jats:tex-math> </jats:alternatives> </jats:inline-formula> correspond to much smaller average vibrational force (weak vibrations) than for p-H<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400541X_inline4.png\"/> <jats:tex-math>$_2$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (strong vibrations). For weak vibrations, the role of the initial vibration phase is crucial. The difference in the behaviour at different initial phases is explained using a simple mechanical model. For strong vibrations, the average displacement to the wall stops when the bubble reaches a quasi-equilibrium position where the resulting average force is zero. At large vibration velocity amplitudes this position is near the wall where the bubble performs only forced oscillations. At moderate vibration velocity amplitudes the bubble average displacement stops at a finite distance from the wall, then large-scale damped oscillations around this position accompanied by forced oscillations are observed. Bubble shape oscillations and the parametric resonance of forced oscillations are also studied.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"242 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cheng Li, Yan Yang, William H. Matthaeus, Bin Jiang, Minping Wan, Shiyi Chen
We systematically study the dissipative anomaly in compressible magnetohydrodynamic (MHD) turbulence using direct numerical simulations, and show that the total dissipation remains finite as viscosity diminishes. The dimensionless dissipation rate $mathcal {C}_{varepsilon }$ fits well with the model $mathcal {C}_{varepsilon } = mathcal {C}_{varepsilon,infty } + mathcal {D}/R_L^-$ for all levels of flow compressibility considered here, where $R_L^-$ is the generalized large-scale Reynolds number. The asymptotic value $mathcal {C}_{varepsilon,infty }$ describes the total energy transfer flux, and decreases with increase of the flow compressibility, indicating non-universality of the dimensionless dissipation rate in compressible MHD turbulence. After introducing an empirically modified dissipation rate, the data from compressible cases collapse to a form similar to the incompressible MHD case depending only on the modified Reynolds number.
{"title":"Non-universality and dissipative anomaly in compressible magnetohydrodynamic turbulence","authors":"Cheng Li, Yan Yang, William H. Matthaeus, Bin Jiang, Minping Wan, Shiyi Chen","doi":"10.1017/jfm.2024.545","DOIUrl":"https://doi.org/10.1017/jfm.2024.545","url":null,"abstract":"We systematically study the dissipative anomaly in compressible magnetohydrodynamic (MHD) turbulence using direct numerical simulations, and show that the total dissipation remains finite as viscosity diminishes. The dimensionless dissipation rate <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005457_inline1.png\"/> <jats:tex-math>$mathcal {C}_{varepsilon }$</jats:tex-math> </jats:alternatives> </jats:inline-formula> fits well with the model <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005457_inline2.png\"/> <jats:tex-math>$mathcal {C}_{varepsilon } = mathcal {C}_{varepsilon,infty } + mathcal {D}/R_L^-$</jats:tex-math> </jats:alternatives> </jats:inline-formula> for all levels of flow compressibility considered here, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005457_inline3.png\"/> <jats:tex-math>$R_L^-$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the generalized large-scale Reynolds number. The asymptotic value <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005457_inline4.png\"/> <jats:tex-math>$mathcal {C}_{varepsilon,infty }$</jats:tex-math> </jats:alternatives> </jats:inline-formula> describes the total energy transfer flux, and decreases with increase of the flow compressibility, indicating non-universality of the dimensionless dissipation rate in compressible MHD turbulence. After introducing an empirically modified dissipation rate, the data from compressible cases collapse to a form similar to the incompressible MHD case depending only on the modified Reynolds number.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"57 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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