M. Cicolin, S. Chellini, B. Usherwood, B. Ganapathisubramani, Ian P. Castro
This work examines the influence of body porosity on the wake past nominally two-dimensional rectangular plates of fixed width $D$ in the moderate range of Reynolds numbers $Re = UD/nu$ (with $U$ the incoming velocity and $nu$ the kinematic viscosity) between 15 000 and 70 000. With porosity $beta$ defined as the ratio of open to total area of the plate, it is well established that as porosity increases, the wake shifts from the periodic von Kármán shedding behaviour to a regime where this vortex shedding is absent. This change impacts the fluid forces acting on the plate, especially the drag, which is significantly lower for a wake without vortex shedding. We analyse experimentally the transition between these two regimes using hot-wire anemometry, particle-image velocimetry and force measurements. Coherence and phase measurements are used to determine the existence of regular, periodic vortex shedding based on the velocity fluctuations in the two main shear layers on either side of the wake. Results show that, independent of $Re$ , the wake exhibits the classical Kármán vortex shedding pattern for $beta <0.2$ but this is absent for $beta >0.3$ . In the intermediate range, $0.2
{"title":"Vortex shedding behind porous flat plates normal to the flow","authors":"M. Cicolin, S. Chellini, B. Usherwood, B. Ganapathisubramani, Ian P. Castro","doi":"10.1017/jfm.2024.300","DOIUrl":"https://doi.org/10.1017/jfm.2024.300","url":null,"abstract":"This work examines the influence of body porosity on the wake past nominally two-dimensional rectangular plates of fixed width \u0000 \u0000 \u0000 $D$\u0000 \u0000 in the moderate range of Reynolds numbers \u0000 \u0000 \u0000 $Re = UD/nu$\u0000 \u0000 (with \u0000 \u0000 \u0000 $U$\u0000 \u0000 the incoming velocity and \u0000 \u0000 \u0000 $nu$\u0000 \u0000 the kinematic viscosity) between 15 000 and 70 000. With porosity \u0000 \u0000 \u0000 $beta$\u0000 \u0000 defined as the ratio of open to total area of the plate, it is well established that as porosity increases, the wake shifts from the periodic von Kármán shedding behaviour to a regime where this vortex shedding is absent. This change impacts the fluid forces acting on the plate, especially the drag, which is significantly lower for a wake without vortex shedding. We analyse experimentally the transition between these two regimes using hot-wire anemometry, particle-image velocimetry and force measurements. Coherence and phase measurements are used to determine the existence of regular, periodic vortex shedding based on the velocity fluctuations in the two main shear layers on either side of the wake. Results show that, independent of \u0000 \u0000 \u0000 $Re$\u0000 \u0000 , the wake exhibits the classical Kármán vortex shedding pattern for \u0000 \u0000 \u0000 $beta <0.2$\u0000 \u0000 but this is absent for \u0000 \u0000 \u0000 $beta >0.3$\u0000 \u0000 . In the intermediate range, \u0000 \u0000 \u0000 $0.2<beta <0.3$\u0000 \u0000 , there is a transitional regime that has not previously been identified; it is characterised by intermittent shedding. The flow alternates randomly between a vortex shedding and a non-shedding pattern and the total proportion of time during which vortex shedding is observed (the intermittency) decreases with increasing porosity.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"1 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140653902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We use Bayesian inference, accelerated by adjoint methods, to construct a quantitatively accurate model of the thermoacoustic behaviour of a conical flame in a duct. We first perform a series of automated experiments on a ducted flame rig. Next, we propose several candidate models of the rig's components and assimilate data into each model to find the most probable parameters for that model. We rank the candidate models based on their marginal likelihood (evidence) and select the most likely model for each component. We begin this process by rigorously characterizing the acoustics of the cold rig. When the flame is introduced, we propose several candidate models for the fluctuating heat release rate. We find that the most likely flame model considers velocity perturbations in both the burner feed tube and the outer duct, even though studies in the literature typically neglect either one of these. Using the most likely model, we infer the flame transfer functions for 24 flames and quantify their uncertainties. We do this with the flames in situ, using only pressure measurements. We find that the inferred flame transfer functions render the model quantitatively accurate, and, where comparable, broadly consistent with direct measurements from several studies in the literature.
{"title":"Adjoint-accelerated Bayesian inference applied to the thermoacoustic behaviour of a ducted conical flame","authors":"M. Yoko, M. Juniper","doi":"10.1017/jfm.2024.276","DOIUrl":"https://doi.org/10.1017/jfm.2024.276","url":null,"abstract":"We use Bayesian inference, accelerated by adjoint methods, to construct a quantitatively accurate model of the thermoacoustic behaviour of a conical flame in a duct. We first perform a series of automated experiments on a ducted flame rig. Next, we propose several candidate models of the rig's components and assimilate data into each model to find the most probable parameters for that model. We rank the candidate models based on their marginal likelihood (evidence) and select the most likely model for each component. We begin this process by rigorously characterizing the acoustics of the cold rig. When the flame is introduced, we propose several candidate models for the fluctuating heat release rate. We find that the most likely flame model considers velocity perturbations in both the burner feed tube and the outer duct, even though studies in the literature typically neglect either one of these. Using the most likely model, we infer the flame transfer functions for 24 flames and quantify their uncertainties. We do this with the flames in situ, using only pressure measurements. We find that the inferred flame transfer functions render the model quantitatively accurate, and, where comparable, broadly consistent with direct measurements from several studies in the literature.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"21 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140658601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The probability density function (PDF) for the free surface elevation in an irregular sea has an integral formulation when based on the cumulant generating function. To leading order, the result is Gaussian, whereas nonlinear extensions have long been limited to Gram–Charlier series approximations. As shown recently by Fuhrman et al. (J. Fluid Mech., vol. 970, 2023, A38), however, the second-order integral can be represented exactly in closed form. The present work extends this further, enabling determination of this PDF to even higher orders. Towards this end, a new ordinary differential equation (ODE) governing the PDF is first derived. Asymptotic solutions in the limit of large surface elevation are then found, utilizing the method of dominant balance. These provide new analytical forms for the positive tail of the PDF beyond second order. These likewise clarify how high-order cumulants (involving statistical moments such as the kurtosis) govern the tail, which is shown to get heavier with each successive order. The asymptotic solutions are finally utilized to generate boundary conditions, such that the governing ODE may be solved numerically, enabling novel determination of the PDF at third and higher order. Successful comparisons with challenging data sets confirm accuracy. The methodology thus enables the PDF of the surface elevation to be determined numerically, and the asymptotic tail analytically, to any desired order. Results are worked out explicitly up to fifth order. The theoretical probability of extreme surface elevations (typical of rogue waves) may thus be assessed quantitatively for highly nonlinear irregular seas, requiring only relevant statistical quantities as input.
{"title":"Heavy tails and probability density functions to any nonlinear order for the surface elevation in irregular seas","authors":"Mathias Klahn, Yanyan Zhai, D. Fuhrman","doi":"10.1017/jfm.2024.304","DOIUrl":"https://doi.org/10.1017/jfm.2024.304","url":null,"abstract":"The probability density function (PDF) for the free surface elevation in an irregular sea has an integral formulation when based on the cumulant generating function. To leading order, the result is Gaussian, whereas nonlinear extensions have long been limited to Gram–Charlier series approximations. As shown recently by Fuhrman et al. (J. Fluid Mech., vol. 970, 2023, A38), however, the second-order integral can be represented exactly in closed form. The present work extends this further, enabling determination of this PDF to even higher orders. Towards this end, a new ordinary differential equation (ODE) governing the PDF is first derived. Asymptotic solutions in the limit of large surface elevation are then found, utilizing the method of dominant balance. These provide new analytical forms for the positive tail of the PDF beyond second order. These likewise clarify how high-order cumulants (involving statistical moments such as the kurtosis) govern the tail, which is shown to get heavier with each successive order. The asymptotic solutions are finally utilized to generate boundary conditions, such that the governing ODE may be solved numerically, enabling novel determination of the PDF at third and higher order. Successful comparisons with challenging data sets confirm accuracy. The methodology thus enables the PDF of the surface elevation to be determined numerically, and the asymptotic tail analytically, to any desired order. Results are worked out explicitly up to fifth order. The theoretical probability of extreme surface elevations (typical of rogue waves) may thus be assessed quantitatively for highly nonlinear irregular seas, requiring only relevant statistical quantities as input.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"2 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140660796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Air-blast atomizers are extensively used for a variety of purposes. Due to its complexity, the atomization mechanism has not been elucidated. In this study, a mechanistic model is proposed to predict the droplet diameter distribution based on the atomization process of a planar liquid film with co-current gas flows, and its validity is examined by comparing the estimated and measured droplet diameters using high-speed image analysis and laser measurement. As a result, using high-speed imaging, we clarified that the bag film rupture is caused not by the turbulence of the gas flow but by the impact of floating droplets on the liquid film of the expanding bag when the film is thin enough. The average thickness of the liquid film at the bag breakup is of the order of micrometres and varies greatly, resulting in a dispersed distribution of droplet diameters. After the film ruptures, the bag film shrinks towards its transversal and vertical rims due to surface tension, forming large-diameter ligaments. During the contraction process of the bag film, tiny droplets of the order of micrometers are formed at the edge of the perforation. Finally, the remaining ligaments with large diameters fragment into large droplets with submillimetre diameters. The good agreement between the measured and predicted droplet diameter distributions validated the mechanistic model.
{"title":"Air-blast atomization of a liquid film","authors":"Ippei Oshima, Akira Sou","doi":"10.1017/jfm.2024.279","DOIUrl":"https://doi.org/10.1017/jfm.2024.279","url":null,"abstract":"Air-blast atomizers are extensively used for a variety of purposes. Due to its complexity, the atomization mechanism has not been elucidated. In this study, a mechanistic model is proposed to predict the droplet diameter distribution based on the atomization process of a planar liquid film with co-current gas flows, and its validity is examined by comparing the estimated and measured droplet diameters using high-speed image analysis and laser measurement. As a result, using high-speed imaging, we clarified that the bag film rupture is caused not by the turbulence of the gas flow but by the impact of floating droplets on the liquid film of the expanding bag when the film is thin enough. The average thickness of the liquid film at the bag breakup is of the order of micrometres and varies greatly, resulting in a dispersed distribution of droplet diameters. After the film ruptures, the bag film shrinks towards its transversal and vertical rims due to surface tension, forming large-diameter ligaments. During the contraction process of the bag film, tiny droplets of the order of micrometers are formed at the edge of the perforation. Finally, the remaining ligaments with large diameters fragment into large droplets with submillimetre diameters. The good agreement between the measured and predicted droplet diameter distributions validated the mechanistic model.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"74 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140665361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study experimentally investigates the wake structure of a porous square cylinder in terms of permeability over two decades of $Da$ (i.e. $2.4 times 10^{-5} < Da < 2.9 times 10^{-3}$ ). The porous cylinder, featuring a simple cubic lattice structure, was fabricated using an additive manufacturing technique. This unique method, combined with a periodic and scalable lattice structure, effectively isolates permeability from porosity, making it suitable for an in-depth parametric study. The key parameter, permeability, was directly estimated by measuring the pressure drop and superficial velocity for each porous case in an open-loop pipe flow system. The downstream flow fields were obtained using standard planar particle image velocimetry measurements in an open-loop wind tunnel. Based on the experimental data, structural modifications in the near wake were examined in relation to permeability, leading to the identification of four distinct flow regimes depending on $Da$ . Additionally, the downstream flow adjustment length ( $L_i$ ) was assessed by introducing a permeability-based source term into the momentum equation, facilitating the development of an analytical model for $L_i$ . The present experimental data support this analytical model, and our results further confirmed that $L_i$ plays a crucial role as a characteristic length scale in the near wake.
本研究通过实验研究了多孔方形圆柱体在二十倍于$Da$（即2.4 times 10^{-5} < Da < 2.9 times 10^{-3}$）的渗透率下的唤醒结构。多孔圆柱体具有简单的立方晶格结构，是利用增材制造技术制造的。这种独特的方法与周期性和可扩展的晶格结构相结合，有效地将渗透性与孔隙率隔离开来，使其适合于进行深入的参数研究。通过测量开环管道流动系统中每个多孔情况的压降和表层速度，可以直接估算出关键参数--渗透性。下游流场是在开环风洞中使用标准平面粒子图像测速仪测量得到的。根据实验数据，研究了近尾流的结构变化与渗透性的关系，从而根据 $Da$ 确定了四种不同的流态。此外，通过在动量方程中引入基于渗透率的源项，评估了下游流动调整长度（$L_i$），从而促进了 $L_i$ 分析模型的建立。目前的实验数据支持这一分析模型，我们的结果进一步证实了 $L_i$ 在近尾流中作为特征长度尺度起着至关重要的作用。
{"title":"The effect of permeability on the flow structure of porous square cylinders","authors":"Chansoo Seol, Taewoo Kim, Taehoon Kim","doi":"10.1017/jfm.2024.311","DOIUrl":"https://doi.org/10.1017/jfm.2024.311","url":null,"abstract":"This study experimentally investigates the wake structure of a porous square cylinder in terms of permeability over two decades of \u0000 \u0000 \u0000 $Da$\u0000 \u0000 (i.e. \u0000 \u0000 \u0000 $2.4 times 10^{-5} < Da < 2.9 times 10^{-3}$\u0000 \u0000 ). The porous cylinder, featuring a simple cubic lattice structure, was fabricated using an additive manufacturing technique. This unique method, combined with a periodic and scalable lattice structure, effectively isolates permeability from porosity, making it suitable for an in-depth parametric study. The key parameter, permeability, was directly estimated by measuring the pressure drop and superficial velocity for each porous case in an open-loop pipe flow system. The downstream flow fields were obtained using standard planar particle image velocimetry measurements in an open-loop wind tunnel. Based on the experimental data, structural modifications in the near wake were examined in relation to permeability, leading to the identification of four distinct flow regimes depending on \u0000 \u0000 \u0000 $Da$\u0000 \u0000 . Additionally, the downstream flow adjustment length (\u0000 \u0000 \u0000 $L_i$\u0000 \u0000 ) was assessed by introducing a permeability-based source term into the momentum equation, facilitating the development of an analytical model for \u0000 \u0000 \u0000 $L_i$\u0000 \u0000 . The present experimental data support this analytical model, and our results further confirmed that \u0000 \u0000 \u0000 $L_i$\u0000 \u0000 plays a crucial role as a characteristic length scale in the near wake.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"16 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140666252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Combustion instabilities in annular systems raise fundamental issues that are also of practical importance to aircraft engines and ground-based gas turbine combustors. Recent studies indicate that the injector plays a significant role in the stability of combustors by defining the flame dynamical response and setting the inlet impedance of the system. The present investigation examines the effects of combinations of injectors of two different types ( $U$ and $S$ ) on thermoacoustic instabilities in a laboratory-scale annular combustor and compares different circumferential staging strategies. The combustor operates in a stable fashion when all injection units belong to the $S$ -family, but exhibits large amplitude pressure oscillations when all these units are of the $U$ -type. When the system comprises a mix of $U$ - and $S$ -injectors, it is possible to determine the number of $S$ -injectors leading to stable operation. For a fixed proportion of $U$ - and $S$ -injectors, some arrangements give rise to stable operation while others do not. Results also show that introducing symmetry-breaking elements affects the system's modal dynamics. These experimental observations are interpreted in an acoustic energy balance framework used to derive an expression for the growth rate as a function of the describing functions of the flames formed by the different injectors and their respective azimuthal locations. Growth rates are determined for the different configurations and used to explain the various observations, estimate the system damping rate and predict the location of the nodal line when the standing mode prevails.
{"title":"Experiments on symmetry breaking of azimuthal combustion instabilities and their analysis combining acoustic energy balance and flame describing functions","authors":"V. Latour, D. Durox, A. Renaud, S. Candel","doi":"10.1017/jfm.2024.307","DOIUrl":"https://doi.org/10.1017/jfm.2024.307","url":null,"abstract":"Combustion instabilities in annular systems raise fundamental issues that are also of practical importance to aircraft engines and ground-based gas turbine combustors. Recent studies indicate that the injector plays a significant role in the stability of combustors by defining the flame dynamical response and setting the inlet impedance of the system. The present investigation examines the effects of combinations of injectors of two different types (\u0000 \u0000 \u0000 $U$\u0000 \u0000 and \u0000 \u0000 \u0000 $S$\u0000 \u0000 ) on thermoacoustic instabilities in a laboratory-scale annular combustor and compares different circumferential staging strategies. The combustor operates in a stable fashion when all injection units belong to the \u0000 \u0000 \u0000 $S$\u0000 \u0000 -family, but exhibits large amplitude pressure oscillations when all these units are of the \u0000 \u0000 \u0000 $U$\u0000 \u0000 -type. When the system comprises a mix of \u0000 \u0000 \u0000 $U$\u0000 \u0000 - and \u0000 \u0000 \u0000 $S$\u0000 \u0000 -injectors, it is possible to determine the number of \u0000 \u0000 \u0000 $S$\u0000 \u0000 -injectors leading to stable operation. For a fixed proportion of \u0000 \u0000 \u0000 $U$\u0000 \u0000 - and \u0000 \u0000 \u0000 $S$\u0000 \u0000 -injectors, some arrangements give rise to stable operation while others do not. Results also show that introducing symmetry-breaking elements affects the system's modal dynamics. These experimental observations are interpreted in an acoustic energy balance framework used to derive an expression for the growth rate as a function of the describing functions of the flames formed by the different injectors and their respective azimuthal locations. Growth rates are determined for the different configurations and used to explain the various observations, estimate the system damping rate and predict the location of the nodal line when the standing mode prevails.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"133 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140668991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S.J. Knechtel, T. Kaiser, A. Orchini, K. Oberleithner
First-order sensitivities and adjoint analysis are used widely to control the linear stability of unstable flows. Second-order sensitivities have recently helped to increase accuracy. In this paper, a method is presented to calculate arbitrary high-order sensitivities based on Taylor expansions of the incompressible base flow and its eigenproblem around a scalar parameter. For the incompressible Navier–Stokes equations, general expressions for the sensitivities are derived, into which parameter-specific information can be inserted. The computational costs are low since, for all orders, a linear equation system has to be solved, of which the left-hand-side matrix stays constant and thus its preconditioning can be exploited. Two flow scenarios are examined. First, the cylinder flow equations are expanded around the inverse of the Reynolds number, enabling the prediction of the two-dimensional cylinder base flow and its leading eigenvalue as a function of the Reynolds number. This approach computes accurately the base flow and eigenvalue even in the unstable regime, providing, when executed subsequently, a mean to calculate unstable base flows. This case gives a clear introduction into the method and allows us to discuss its constraints regarding convergence behaviour. Second, a small control cylinder is introduced into the domain of the cylinder flow for stabilization. Higher-order sensitivity maps are calculated by modelling the small cylinder with a steady forcing. These maps help to identify stabilizing areas of the flow field for Reynolds numbers within the laminar vortex shedding regime, with the required number of orders increasing as the Reynolds number rises. The results obtained through the proposed method align well with numerically calculated eigenvalues that incorporate the cylinder directly into the grid.
{"title":"Arbitrary-order sensitivities of the incompressible base flow and its eigenproblem","authors":"S.J. Knechtel, T. Kaiser, A. Orchini, K. Oberleithner","doi":"10.1017/jfm.2024.195","DOIUrl":"https://doi.org/10.1017/jfm.2024.195","url":null,"abstract":"First-order sensitivities and adjoint analysis are used widely to control the linear stability of unstable flows. Second-order sensitivities have recently helped to increase accuracy. In this paper, a method is presented to calculate arbitrary high-order sensitivities based on Taylor expansions of the incompressible base flow and its eigenproblem around a scalar parameter. For the incompressible Navier–Stokes equations, general expressions for the sensitivities are derived, into which parameter-specific information can be inserted. The computational costs are low since, for all orders, a linear equation system has to be solved, of which the left-hand-side matrix stays constant and thus its preconditioning can be exploited. Two flow scenarios are examined. First, the cylinder flow equations are expanded around the inverse of the Reynolds number, enabling the prediction of the two-dimensional cylinder base flow and its leading eigenvalue as a function of the Reynolds number. This approach computes accurately the base flow and eigenvalue even in the unstable regime, providing, when executed subsequently, a mean to calculate unstable base flows. This case gives a clear introduction into the method and allows us to discuss its constraints regarding convergence behaviour. Second, a small control cylinder is introduced into the domain of the cylinder flow for stabilization. Higher-order sensitivity maps are calculated by modelling the small cylinder with a steady forcing. These maps help to identify stabilizing areas of the flow field for Reynolds numbers within the laminar vortex shedding regime, with the required number of orders increasing as the Reynolds number rises. The results obtained through the proposed method align well with numerically calculated eigenvalues that incorporate the cylinder directly into the grid.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"114 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140669747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Moschopoulos, A. Spyridakis, Y. Dimakopoulos, J. Tsamopoulos
We study the motion and deformation of a single bubble rising inside a cylindrical container filled with a viscoelastic material. We solve numerically the mass and momentum balances along with the constitutive equation for the viscoelastic stresses, without assuming axial symmetry to allow the growth of three-dimensional disturbances. Hence, we may predict the emergence of the notorious knife-edge shape of the bubble, which is a result of a purely elastic instability triggered in the locality of the trailing edge. Our results compare well with existing experiments. We visualize, for the first time to the best of our knowledge, the flow kinematics and dynamics that arise downstream of the bubble. We propose two quantities, one kinematical and one geometrical, for the determination of the onset of the instability. We demonstrate that extension-rate thinning in the constitutive law is necessary for the emergence of the instability. Moreover, our results indicate that increasing (a) the deformability of the bubble and (b) the initial extension rate hardening of the viscoelastic material, prior to thinning, triggers the instability earlier. These novel findings help us formulate and propose a mechanism that controls the onset of the instability and explain why the knife-edge shape is not encountered as frequently.
{"title":"Unravelling the existence of asymmetric bubbles in viscoelastic fluids","authors":"P. Moschopoulos, A. Spyridakis, Y. Dimakopoulos, J. Tsamopoulos","doi":"10.1017/jfm.2024.316","DOIUrl":"https://doi.org/10.1017/jfm.2024.316","url":null,"abstract":"We study the motion and deformation of a single bubble rising inside a cylindrical container filled with a viscoelastic material. We solve numerically the mass and momentum balances along with the constitutive equation for the viscoelastic stresses, without assuming axial symmetry to allow the growth of three-dimensional disturbances. Hence, we may predict the emergence of the notorious knife-edge shape of the bubble, which is a result of a purely elastic instability triggered in the locality of the trailing edge. Our results compare well with existing experiments. We visualize, for the first time to the best of our knowledge, the flow kinematics and dynamics that arise downstream of the bubble. We propose two quantities, one kinematical and one geometrical, for the determination of the onset of the instability. We demonstrate that extension-rate thinning in the constitutive law is necessary for the emergence of the instability. Moreover, our results indicate that increasing (a) the deformability of the bubble and (b) the initial extension rate hardening of the viscoelastic material, prior to thinning, triggers the instability earlier. These novel findings help us formulate and propose a mechanism that controls the onset of the instability and explain why the knife-edge shape is not encountered as frequently.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"78 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140670549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We extend the resolvent framework to two-phase flows with low-inertia particles. The particle velocities are modelled using the equilibrium Eulerian model. We analyse the turbulent flow in a vertical pipe with Reynolds number of $5300$ (based on diameter and bulk velocity), for Stokes numbers $St^+=0-1$ , Froude numbers $Fr_z=-4,-0.4,0.4,4$ and $1/Fr_z = 0$ (gravity omitted). The governing equations are written in input–output form and a singular value decomposition is performed on the resolvent operator. As for single-phase flows, the operator is low rank around the critical layer, and the true response can be approximated using one singular vector. Even with a crude forcing model, the formulation can predict physical phenomena observed in Lagrangian simulations, such as particle clustering and gravitational effects. Increasing the Stokes number shifts the predicted concentration spectra to lower wavelengths; this shift also appears in the direct numerical simulation spectra and is due to particle clustering. When gravity is present, there are two critical layers, one for the concentration field, and one for the velocity field. For upward flow, the peak of concentration fluctuations shifts closer to the wall, in agreement with the literature. We explain this with the aid of the different locations of the two critical layers. Finally, the model correctly predicts the interaction of near-wall vortices with particle clusters. Overall, the resolvent operator provides a useful framework to explain and interpret many features observed in Lagrangian simulations. The application of the resolvent framework to higher $St^+$ flows in combination with Lagrangian simulations is also discussed.
{"title":"Resolvent analysis of turbulent flow laden with low-inertia particles","authors":"R. K. Schlander, S. Rigopoulos, George Papadakis","doi":"10.1017/jfm.2024.290","DOIUrl":"https://doi.org/10.1017/jfm.2024.290","url":null,"abstract":"We extend the resolvent framework to two-phase flows with low-inertia particles. The particle velocities are modelled using the equilibrium Eulerian model. We analyse the turbulent flow in a vertical pipe with Reynolds number of \u0000 \u0000 \u0000 $5300$\u0000 \u0000 (based on diameter and bulk velocity), for Stokes numbers \u0000 \u0000 \u0000 $St^+=0-1$\u0000 \u0000 , Froude numbers \u0000 \u0000 \u0000 $Fr_z=-4,-0.4,0.4,4$\u0000 \u0000 and \u0000 \u0000 \u0000 $1/Fr_z = 0$\u0000 \u0000 (gravity omitted). The governing equations are written in input–output form and a singular value decomposition is performed on the resolvent operator. As for single-phase flows, the operator is low rank around the critical layer, and the true response can be approximated using one singular vector. Even with a crude forcing model, the formulation can predict physical phenomena observed in Lagrangian simulations, such as particle clustering and gravitational effects. Increasing the Stokes number shifts the predicted concentration spectra to lower wavelengths; this shift also appears in the direct numerical simulation spectra and is due to particle clustering. When gravity is present, there are two critical layers, one for the concentration field, and one for the velocity field. For upward flow, the peak of concentration fluctuations shifts closer to the wall, in agreement with the literature. We explain this with the aid of the different locations of the two critical layers. Finally, the model correctly predicts the interaction of near-wall vortices with particle clusters. Overall, the resolvent operator provides a useful framework to explain and interpret many features observed in Lagrangian simulations. The application of the resolvent framework to higher \u0000 \u0000 \u0000 $St^+$\u0000 \u0000 flows in combination with Lagrangian simulations is also discussed.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"112 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140670170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper extends the work in Tee et al. (Intl J. Multiphase Flow, vol. 133, 2020, 103462) to investigate the effect of turbulent fluid motions on the translation and rotation of lifting and wall-interacting spheres in boundary layers. Each sphere was released from rest in smooth-wall boundary layers with $Re_tau =670$ and 1300 ( $d^+=56$ and 116, respectively) and allowed to propagate with the incoming fluid. Sphere and surrounding fluid motions were tracked simultaneously via three-dimensional particle tracking velocimetry and stereoscopic particle image velocimetry in streamwise–spanwise planes. Two-point correlations of sphere and fluid streamwise velocities yielded long positive regions associated with long fast- and slow-moving zones that approach and move over the spheres. The related spanwise correlations were shorter due to the shorter coherence length of spanwise fluid structures. In general, spheres lag the surrounding fluid. The less-dense lifting sphere had smaller particle Reynolds numbers varying from near zero up to 300. Its lift-offs coincided with oncoming fast-moving zones and fluid upwash. Wall friction initially retarded the acceleration of the denser sphere. Later, fluid torque associated with approaching high-velocity regions initiated forward rotation. The rotation, which was long-lived, induced sufficient Magnus lift to initiate repeated small lift-offs, reduce wall friction, and accelerate the sphere to higher sustained velocity. Particle Reynolds numbers remained above 200, and vortex shedding was omnipresent such that the spheres clearly altered the fluid motion. Spanwise fluid shear occasionally initiated wall-normal sphere rotation and relatively long-lasting Magnus side lift. Hence the finite sphere size contributed to multiple dynamical effects not present in point-particle models.
本文扩展了 Tee 等人（《Intl J. Multiphase Flow》，第 133 卷，2020 年，103462 期）的工作，研究了湍流运动对边界层中升降球和壁面相互作用球的平移和旋转的影响。在Re_tau =670$和1300（d^+分别为56$和116）的光滑壁边界层中，每个球体从静止状态被释放，并随进入的流体传播。通过三维粒子跟踪测速仪和立体粒子图像测速仪在流向跨度平面上同时跟踪球体和周围流体的运动。球体和流体流向速度的两点相关性产生了长的正区域，这些正区域与接近和越过球体的长的快速和慢速运动区相关。由于跨向流体结构的相干长度较短，因此相关的跨向相关性也较短。一般来说，球体滞后于周围的流体。密度较小的提升球的粒子雷诺数较小，从接近零到 300 不等。它的腾空与迎面而来的快速运动区和流体上冲相吻合。壁面摩擦起初减缓了密度较大的球体的加速度。后来，与接近高速区相关的流体扭矩引发了向前旋转。旋转持续了很长时间，产生了足够的马格努斯升力，使球体反复小幅升空，减少了壁面摩擦，并加速到更高的持续速度。粒子雷诺数保持在 200 以上，涡流脱落无处不在，因此球体明显改变了流体运动。横向流体剪切偶尔会引发壁面法向球体旋转和相对持久的马格努斯侧升力。因此，有限的球体尺寸产生了点粒子模型所没有的多种动力学效应。
{"title":"Effect of fluid motions on finite spheres released in turbulent boundary layers","authors":"Y. H. Tee, E. Longmire","doi":"10.1017/jfm.2024.291","DOIUrl":"https://doi.org/10.1017/jfm.2024.291","url":null,"abstract":"This paper extends the work in Tee et al. (Intl J. Multiphase Flow, vol. 133, 2020, 103462) to investigate the effect of turbulent fluid motions on the translation and rotation of lifting and wall-interacting spheres in boundary layers. Each sphere was released from rest in smooth-wall boundary layers with \u0000 \u0000 \u0000 $Re_tau =670$\u0000 \u0000 and 1300 (\u0000 \u0000 \u0000 $d^+=56$\u0000 \u0000 and 116, respectively) and allowed to propagate with the incoming fluid. Sphere and surrounding fluid motions were tracked simultaneously via three-dimensional particle tracking velocimetry and stereoscopic particle image velocimetry in streamwise–spanwise planes. Two-point correlations of sphere and fluid streamwise velocities yielded long positive regions associated with long fast- and slow-moving zones that approach and move over the spheres. The related spanwise correlations were shorter due to the shorter coherence length of spanwise fluid structures. In general, spheres lag the surrounding fluid. The less-dense lifting sphere had smaller particle Reynolds numbers varying from near zero up to 300. Its lift-offs coincided with oncoming fast-moving zones and fluid upwash. Wall friction initially retarded the acceleration of the denser sphere. Later, fluid torque associated with approaching high-velocity regions initiated forward rotation. The rotation, which was long-lived, induced sufficient Magnus lift to initiate repeated small lift-offs, reduce wall friction, and accelerate the sphere to higher sustained velocity. Particle Reynolds numbers remained above 200, and vortex shedding was omnipresent such that the spheres clearly altered the fluid motion. Spanwise fluid shear occasionally initiated wall-normal sphere rotation and relatively long-lasting Magnus side lift. Hence the finite sphere size contributed to multiple dynamical effects not present in point-particle models.","PeriodicalId":505053,"journal":{"name":"Journal of Fluid Mechanics","volume":"139 40","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140668421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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