We study the flow dynamics inside a high-speed rotating cylinder after introducing strong symmetry-breaking disturbance factors at cylinder wall motion. We propose and formulate a mathematically robust stochastic model for the rotational motion of cylinder wall alongside the stochastic representation of incompressible Navier-Stokes equations. We employ a comprehensive stochastic computational fluid dynamics framework combining spectral/$hp$ element method and probabilistic collocation method to obtain high-fidelity realizations of our mathematical model in order to quantify the propagation of parametric uncertainty for dynamics-representative quantities of interests. We observe that the modeled symmetry-breaking disturbances cause a flow instability arising from the wall. Utilizing global sensitivity analysis approaches, we identify the dominant source of uncertainty in our proposed model. We next perform a qualitative and quantitative statistical analysis on the fluctuating fields characterizing the fingerprints and measures of intense and rapidly evolving non-Gaussian behavior through space and time. We claim that such non-Gaussian statistics essentially emerge and evolve due to an intensified presence of coherent vortical motions initially triggered by the flow instability due to symmetry-breaking rotation of the cylinder. We show that this mechanism causes memory effects in the flow dynamics in a way that noticeable anomaly in the time-scaling of enstrophy record is observed in the long run apart from the onset of instability. Our findings suggest an effective strategy to exploit controlled flow instabilities in order to enhance the turbulent mixing in engineering applications.
Instabilities in flow through and around a circular array of cylinders
School of Aeronautics and Astronautics, Sun Yat-sen University（中山大学航空航天学院）；School of Mechanical Engineering, Nanjing University of Science and Technology（南京理工大学机械工程学院）；Department of Mechanical Engineering, National University of Singapore（新加坡国立大学机械工程系）
We perform a three-dimensional, short-wavelength stability analysis on the numerically simulated two-dimensional flow past a circular cylinder for Reynolds numbers in the range $50\le Re\le300$; here, $Re = U_{\infty}D/ν$ with $U_\infty$, $D$ and $ν$ being the free-stream velocity, the diameter of the cylinder and the kinematic viscosity of the fluid, respectively. For a given $Re$, inviscid local stability equations from the geometric optics approach are solved on three distinct closed fluid particle trajectories (denoted as orbits 1, 2 & 3) for purely transverse perturbations. The inviscid i…
This experimental study reports on the behavior of a filament attached to the rear of a three- dimensional cylinder. The axis of the cylinder is placed normal to a uniform incoming flow and the filament is free to move in the cylinder wake. The mean position of the filament is studied as a function of the filament length L. It is found that for long (L/D > 6.5, where D is the cylinder diameter) and short (L/D < 2) filaments the mean position of the filament tends to align with the incoming flow, whereas for intermediate filament lengths (2 < L/D < 6.5) the filament lies down on the cylinder an…
The `Rayleigh line' $μ=η^2$, where $μ=Ω_o/Ω_i$ and $η=r_i/r_o$ are respectively the rotation and radius ratios between inner (subscript `i') and outer (subscript `o') cylinders, is regarded as marking the limit of centrifugal instability (CI) in unstratified inviscid Taylor-Couette flow, for both axisymmetric and non-axisymmetric modes. Non-axisymmetric stratorotational instability (SRI) is known to set in for anticyclonic rotation ratios beyond that line, i.e. $η^2<μ<1$ for axially stably-stratified Taylor-Couette flow, but the competition between CI and SRI in the range $μ<η^2$ has not yet b…
It is shown that a channel flow of a dilute polymer solution between two widely spaced cylinders hindering the flow is an important paradigm of an unbounded flow in the case in which the channel wall is located sufficiently far from the cylinders. The quantitative characterization of instabilities in a creeping viscoelastic channel flow between two widely spaced cylinders reveals two elastically driven transitions, which are associated with the breaking of time-reversal and mirror symmetries: Hopf and forward bifurcations described by two order parameters $\mbox{v}_{rms}$ and $\barω$, respecti…
Characterizing the boundary layer transition to turbulence around realistic hypersonic vehicles is a challenging task due to the numerous parameters that affect the process. To address this challenge, the cone-cylinder-flare (CCF) geometry has been designed to provide a flow topology that captures various transition mechanisms observed on reentry objects, such as absolute and convective instabilities, which are dependent on the free stream conditions. In this study, a global linear stability analysis is performed on the CCF model at Mach=6.0 to investigate and map the dominant instabilities at…
Flows forced by a precessional motion can exhibit instabilities of crucial importance, whether they concern the fuel of a flying object or the liquid core of a telluric planet. So far, stability analyses of these flows have focused on the special case of a resonant forcing. Here, we address the instability of the flow inside a precessing cylinder in the general case. We first show that the base flow forced by the cylinder precession is a superposition of a vertical or horizontal shear flow and an infinite sum of forced modes. We then perform a linear stability analysis of this base flow by con…
Couette Taylor instabilities in the small-gap regime
School of Mathematics and Statistics, Beijing Institute of Technology（北京理工大学数学与统计学院）；Laboratoire J.A.Dieudonné, I.U.F., Université Côte d’Azur（J.A. Dieudonné实验室，法国高等教育研究院，蔚蓝海岸大学）；Department of Mathematics, The Ohio State University（俄亥俄州立大学数学系）
A kinematic approach for the identification of flow instabilities is proposed. By defining a flow instability in the Lagrangian frame as the increased folding of lines of fluid particles, subtle perturbations and unstable growth thereof are detected early based solely on the curvature change of material lines over finite time. The material line curvature is objective, parametrization independent, and can be applied to flows of general complexity without knowledge of the base flow. An analytic connection between the growth of Eulerian velocity modes perturbing a general shear flow and the induc…
Transverse and lateral confinement effects on the oscillations of a free cylinder in a viscous flow
不同类型的不稳定性的自由圆柱体（直径$D$，长度$L$）已被研究在一个粘性流（速度$U$）之间的平行垂直壁的水平宽度$W$在距离$H$：的影响的限制参数$D/H$和$L/W$进行了研究。随着$D/H$的增加，从稳定流过渡到横向于壁面的振荡，然后过渡到轴相对于水平面角度振荡的颤振运动。这两种类型的振荡可以在过渡域中叠加。横向振荡的频率$f$在以下范围内与横向约束$L/W$无关：0.055 \le L/W \le 0.94 $ for a given cylinder velocity $ V_{cx} $ and increases only weakly with $ $. These results are accounted for by assuming a 2D local flow over the cylinder with a characteristic velocity independent of $ $. These results are accounted for by assuming a 2D local flow over the cylinder with a characteristic velocity independent of $ L/W $ for a given $ V_{cx} $ value. The experimental v…
The stability of annular electromagnetic pumps (EMPs) is investigated through 3D direct numerical simulations. When induction effects dominate dissipative processes, linear induction EMPs become unstable and lead to non-axisymmetric states relatively different from what was predicted by previous theoretical models. We show that the 3D destabilization of the flow is deeply connected to the axisymmetric state, and always appears as a secondary bifurcation from a locally stalled flow, even if the applied magnetic field is axisymmetric. Finally, we model a configuration aiming to optimize the effi…
We perform direct numerical simulations to characterize the three-dimensional wake dynamics of long inclined circular cylinders with inhomogeneous end boundary conditions. Three Reynolds numbers, $\Rey=100$, 200 and 300 are considered to reveal the roles of the intrinsic secondary instabilities and the extrinsic end boundary effects in shaping the three-dimensional flows. At $\Rey=100$, the end boundary effects are felt over the entire cylinder span by inducing oblique vortex shedding, which is associated with stronger spanwise flow in the wake than a parallel shedding. The Strouhal number of …
We investigate the prediction of the turbulent flow around a canonical square cylinder at Re= 22000 solving the unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The limitations of URANS modelling are overcome through the application of a data assimilation technique involving a feedback control term, allowing to drive the URANS predictions towards reference data. Using regularly-spaced temporally-resolved reference data that are extracted from DNS, we assess the abilities of the data assimilation methodology in improving the unsteady URANS predictions. While improving the low-frequen…
We study magnetic Taylor-Couette flow in a system having nondimensional radii $r_i=1$ and $r_o=2$, and periodic in the axial direction with wavelengths $h\ge100$. The rotation ratio of the inner and outer cylinders is adjusted to be slightly in the Rayleigh-stable regime, where magnetic fields are required to destabilize the flow, in this case triggering the axisymmetric helical magnetorotational instability (HMRI). Two choices of imposed magnetic field are considered, both having the same azimuthal component $B_ϕ=r^{-1}$, but differing axial components. The first choice has $B_z=0.1$, and yie…
Fluid instabilities arise in a variety of contexts and are often unwanted results of engineering imperfections. In one particular model for a magnetized target fusion reactor, a pressure wave is propagated in a cylindrical annulus comprised of a dense fluid before impinging upon a plasma and imploding it. Part of the success of the apparatus is a function of how axially-symmetric the final pressure pulse is upon impacting the plasma. We study a simple model for the implosion of the system to study how imperfections in the pressure imparted on the outer circumference grow due to geometric focus…
Global wake instabilities of low aspect-ratio flate-plates
本文研究了垂直于来流放置的平板后发展的三维定常尾流的线性不稳定性。这里考虑的是以低长宽比$L$为特征的板。通过在$1 \le L \le 6$范围内改变该纵横比，识别出三种不稳定情形。对于非常低的纵横比$1 \le L \le 2$，流动首先是不稳定的，当雷诺数增加时，由一个稳定的全球模式，打破了顶部/底部平面反射对称。对称定常流通过一个叉状分叉分叉，朝向一个非对称定常尾流分叉，类似于球体和圆盘后面的轴对称尾流的情况。对于大展弦比$2.5 \le L \le 6$，第一不稳定模态也破坏了顶底对称性，但是是不稳定的。对于二维圆柱后的尾迹，出现了Hopf分叉。最后，一个中间制度$2 \le L \le 2.5$被发现的流动变得第一不稳定的非定常模式，打破了左/右平面反射对称。
Although the stability properties of the wake past impervious bluff bodies have been widely examined in the literature, similar analyses regarding the flow around and through porous ones are still lacking. In this work, the effect of the porosity and permeability on the wake patterns of porous rectangular cylinders is numerically investigated at low to moderate Reynolds numbers in the framework of direct numerical simulation combined with local and global stability analyses. A modified Darcy-Brinkman formulation is employed here so as to describe the flow behavior inside the porous media, wher…
Elastic instabilities and bifurcations in flows of wormlike micellar solutions past single and two vertically aligned microcylinders: Effect of blockage and gap ratios
This study aims to shed light on hypersonic attachment-line instabilities with large sweep Mach numbers. Highly swept flows over a cold cylinder that give rise to large sweep Mach numbers are studied. High fidelity base flows are obtained by solving full Navier-Stokes equations with a high-order shock-fitting method. Using local and global stability theories, an attachment-line mode is found to be dominant for the laminar-turbulent transition along the leading edge that agrees well with experimental observations Gaillard1999. The behavior of this mode explains the reason why the transition occ…
The wake flow around a circular cylinder at $Re\approx100$ performing rotatory oscillations has been thoroughly discussed in the literature, mostly focusing on the modifications to the natural Bénard-von Kármán vortex street that result from the forced shedding modes locked to the rotatory oscillation frequency. The usual experimental and theoretical frameworks at these Reynolds numbers are quasi-two-dimensional, since the secondary instabilities bringing a three-dimensional structure to the cylinder wake flow occur only at higher Reynolds numbers. In the present paper we show that a three-dim…
A new framework for the analysis of unstable oscillator flows is explored. In linear settings, temporally growing perturbations in a non-parallel flow represent unstable eigenmodes of the linear flow operator. In nonlinear settings, self-sustained periodic oscillations of finite amplitude are commonly described as nonlinear global modes. In both cases the flow dynamics may be qualified as being endogenous, as opposed to the exogenous behaviour of amplifier flows driven by external forcing. This paper introduces the endogeneity concept, a specific definition of the sensitivity of the global fre…
The emergence and understanding of new design paradigms that exploit flow induced mechanical instabilities for propulsion or energy harvesting demands robust and accurate flow structure interaction numerical models. In this context, we develop a novel two dimensional algorithm that combines a Vortex Particle-Mesh (VPM) method and a Multi-Body System (MBS) solver for the simulation of passive and actuated structures in fluids. The hydrodynamic forces and torques are recovered through an innovative approach which crucially complements and extends the projection and penalization approach of Coque…
University of Cambridge（剑桥大学）；German Aerospace Center (DLR)（德国航空航天中心（DLR））
The 100 MW cryogenic liquid oxygen/hydrogen multi-injector combustor BKD operated by the DLR Institute of Space Propulsion is a research platform that allows the study of thermoacoustic instabilities under realistic conditions, representative of small upper stage rocket engines. We use data from BKD experimental campaigns in which the static chamber pressure and fuel-oxidizer ratio are varied such that the first tangential mode of the combustor is excited under some conditions. We train an autoregressive Bayesian neural network model to forecast the amplitude of the dynamic pressure time serie…
Keio University（庆应义塾大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Argonne National Laboratory（阿贡国家实验室）；KTH Royal Institute of Technology（瑞典皇家理工学院）
We use Gaussian stochastic weight averaging (SWAG) to assess the model-form uncertainty associated with neural-network-based function approximation relevant to fluid flows. SWAG approximates a posterior Gaussian distribution of each weight, given training data, and a constant learning rate. Having access to this distribution, it is able to create multiple models with various combinations of sampled weights, which can be used to obtain ensemble predictions. The average of such an ensemble can be regarded as the `mean estimation', whereas its standard deviation can be used to construct `confiden…
In many shear- and pressure-driven wall-bounded turbulent flows secondary motions spontaneously develop and their interaction with the main flow alters the overall large-scale features and transfer properties. Taylor-Couette flow, the fluid motion developing in the gap between two concentric cylinders rotating at different angular velocity, is not an exception, and toroidal Taylor rolls have been observed from the early development of the flow up to the fully turbulent regime. In this manuscript we show that under the generic name of ``Taylor rolls'' there is a wide variety of structures that …
Non-axisymmetric modes of magnetorotational and possible hydrodynamical instabilities in the upcoming DRESDYN-MRI experiments -- linear and nonlinear dynamics
