Periodic Flow Regimes Research Articles

Effect of Flow Interference between Cylinders Subjected to a Cross Flow over a Cluster of Three Equally Spaced Cylinders

In this paper, flow over a cluster of three equally spaced circular cylinders was studied by numerical simulation based on the turbulence model k-kl-ω for two incidence angles β = 0° and 60°, at different Reynolds numbers, and flow interference pattern characteristics between cylinders, characteristics of force parameters, and Strouhal number of each cylinder with different spacing ratios ranging from 1.5 to 4 at Re 8 × 104, 2 × 105 and 2 × 106 were obtained. Analyzing the flow field around three cylinders, the following results have been obtained: (1) at incidence angle β = 0° and 60°, the wake was nearly symmetrical if S/D ≥ 2.0; (2) at β = 60°, S/D = 1.5, and Re = 2 × 105, an asymmetric periodic flow pattern occurred in the wake region which produced a significant effect on the surface mechanical parameters and Strouhal number, and this was observed for the first time. The periodic flow regime of the wake region also occurred at S/D = 1.35 and 1.5, without the same phenomenon at S/D = 1.7 and 2.0; this phenomenon is described for the first time in this paper; (3) the phenomenon of periodic flow regime in the wake region was intrinsic and related to Reynolds number and space ratio. In addition, the characteristics of force parameters of three cylinders were mainly affected by the interference between cylinders, at 1.5 < S/D < 4, which indicated that the drag coefficient of three cylinders reduces with different Reynolds numbers and increases with enlargement of the spacing ratio for upstream cylinders at incidence angle 0°. At incidence angle 60° and S/D = 1.5~4, the Strouhal number decreases with the enlargement of spacing ratio for the upstream cylinders, but the Strouhal number increases for the downstream cylinder, which is another prominent flow interference influence. The results indicated the effect of flow interference between cylinders subjected to a cross flow over a cluster of three equally spaced cylinders, considering the flow pattern, surface mechanical parameters and Strouhal number, which should be considered in the establishment of standard design codes in fields such as offshore wind turbine engineering for flow interference around groups of cylinders.

Dynamics-augmented cluster-based network model

In this study we propose a novel data-driven reduced-order model for complex dynamics, including nonlinear, multi-attractor, multi-frequency and multiscale behaviours. The starting point is a fully automatable cluster-based network model (CNM) (Li et al., J. Fluid Mech., vol. 906, 2021, A21) that kinematically coarse grains the state with clusters and dynamically predicts the transitions in a network model. In the proposed dynamics-augmented CNM (dCNM) the prediction error is reduced with trajectory-based clustering using the same number of centroids. The dCNM is first exemplified for the Lorenz system and then demonstrated for the three-dimensional sphere wake featuring periodic, quasi-periodic and chaotic flow regimes. For both plants, the dCNM significantly outperforms the CNM in resolving the multi-frequency and multiscale dynamics. This increased prediction accuracy is obtained by stratification of the state space aligned with the direction of the trajectories. Thus, the dCNM has numerous potential applications to a large spectrum of shear flows, even for complex dynamics.

Identifying steady and pulsatile two-phase flow regimes with pressure drop signals and acoustic emissions

Identifying two-phase flow regimes is vital for understanding phase-change heat and mass transfer processes. Traditionally, flow regime identification has relied on subjective flow visualization studies, which are then converted to flow regime maps applicable to specific operating conditions. However, these conventional, largely subjective, maps fall short in predicting abrupt changes in flow patterns that often occur during regular operation of vapor compression and absorption heat pumps and other thermal systems. Conventional flow regime maps are also inadequate for addressing the transient, intermittent, or periodic flow regimes that occur in boiling and condensation enhanced using acoustic and other emerging techniques. Therefore, there is a pressing need for alternative flow regime identification techniques that can adapt and reliably track rapid and local changes in two-phase hydrodynamics. Promising candidates for dynamic flow pattern classification include high-resolution pressure drop signals and acoustic emission spectra, which can provide insights into the local hydrodynamics within a flow channel. To assess the feasibility of these measurement techniques, differential pressure and condenser microphone measurements are recorded alongside high-speed videos of a two-phase flow of saturated R134a. The total mass flux and vapor quality are varied to understand the effects of phase velocity and liquid inventory on wave propagation in the channel. Additionally, forced oscillations are introduced to a steady two-phase flow to analyze their impact on flow patterns and their corresponding pressure drop and acoustic signals. Statistical analyses, including Gaussian mixture modeling, are employed to reveal characteristic pressure drop probability associated with each flow pattern, which form the basis for developing a model capable of predicting flow regimes in both steady and oscillating flows. The resulting framework introduces a new flow regime identification technique that can adapt to dynamic operating conditions, benefiting a wide range of thermal systems and phase-change processes.

A numerical study of natural convection through a vertical heated channel with a confined circular cylinder

This study examines thermal flow structures and heat transfer through a vertical heated channel with an adiabatic circular cylinder symmetrically positioned between lateral walls. A two-dimensional numerical simulation is conducted covering a range of parameters including Rayleigh numbers Ra = 8.9 × 106–8.9 × 108, cylinder positions relative to the channel height h = 0–0.50, and blockage ratios (the ratio of cylinder diameter to channel width) β = 0.25–0.75. Three distinct flow regimes are observed at different Rayleigh numbers and blockage ratios, including steady symmetric, unsteady periodic, and unsteady asymmetric flow regimes. The steady symmetric and unsteady periodic flows are observed at all blockage ratios, while the unsteady asymmetric flow is only observed at the highest blockage ratio of β = 0.75 for Rayleigh numbers above 8.9 × 107. It is found that the presence of the cylinder significantly enhances mixing and turbulence in the channel, which in turn enhances heat transfer through the channel. A 64.3% enhancement of heat transfer is achieved at β = 0.50 and h = 0.05 for Ra = 8.9 × 108.

Flow regime identification and flow instability analysis of oscillatory flows over twin circular cylinders

Oscillatory flows past two identical circular cylinders are investigated by two-dimensional direct numerical simulations in the parameter space of gap ratio (0.5 ≤ G ≤ 4.0), angle of flow incidence (0° ≤ α ≤ 90°) and Keulegan–Carpenter number (4 ≤ KC ≤ 12) with a constant Reynolds number Re = 150, where G = L/D, KC = UmT/D and Re = UmD/υ with D being the dimeter of the identical cylinders, L the shortest surface-to-surface distance between the two cylinders, Um and T being the velocity amplitude and period of the sinusoidal oscillatory flow, respectively, and α is defined as the angle between the flow direction to the line connecting the centers of the two cylinders. Comparing with the tandem or side-by-side arrangements of twin circular cylinders in oscillatory flows, the staggered twin cylinders (0° < α < 90°) involve more diverse flow regimes, including the periodic, quasi-periodic and chaotic flow states, due to the inherent asymmetric flow interference around the cylinder pair. In addition to introducing four flow regimes for the tandem and side-by-side arrangements, this study newly identifies 11 flow regimes for the staggered twin cylinders. The newly reported flow regimes in this work are collaboratively identified through the flow visualizations, steady streaming, frequency spectra of fluid forces and Lissajous phase diagrams, as well as the temporal-spatial symmetry features of the wake flows. Connecting with the previous work by Zhao and Cheng [“Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers,” J. Fluid Mech. 751, 1–37 (2014)], this study presents overall regime maps in the KC-α plane for varied gap ratios. It is found that the flow regimes previously and presently identified for the tandem and side-by-side arrangements may also appear for the staggered twin cylinders. The present numerical results suggest the sensitive dependence of the flow regimes on the parameters of KC, α, and G. It is also found that a specific flow regime with narrow parameter bands may appear within another flow regime, forming the abnormal regime hole in the regime map. To understand the profound influence of the control parameters on the flow regime transition, and the relevant temporal-spatial symmetry breaking, the linear Floquet stability analysis is conducted in this work. It was confirmed that the variation of the KC number may result in the Ky symmetry breaking over several periodic flow regimes, while the change of the angle of flow incidence may account for the H2 symmetry covering various periodic and quasi-periodic flow regimes. The stability analysis also explains the temporal flow transition and the abnormal occurrence of the regime holes within either quasi-periodic or chaotic flow regimes.

Novel prediction of fluid forces on obstacle in a periodic flow regime using hybrid FEM-ANN simulations

Novel prediction of fluid forces on obstacle in a periodic flow regime using hybrid FEM-ANN simulations

Numerical prediction of transient electrohydrodynamic instabilities under an alternating current electric field and unipolar injection

In this paper, a direct numerical simulation (DNS) of dielectric fluid flow subjected to unipolar injection under an alternating current (AC) electric field is carried out. The effect of frequency f of pulsed direct current (PDC) and AC on the transient evolution of electroconvection and their subcritical bifurcations are investigated in details. Electroconvection under PDC or AC tends to exhibit oscillating flow due to the periodic boundary condition of charge density and potential compared to the direct current (DC) case. The results demonstrate that under the PDC field, the linear criterion Tc decreases with increasing frequency, while the nonlinear stability criterion Tf is hardly affected. Under the AC field, a critical frequency fc = 0.0316 is found, which separates electroconvection into two typical flow regimes—periodic flow regime (f < fc) and inhibited flow regime (f ≥ fc)—depending on whether free charges can reach the collector electrode before electric field inversion. AC-electrohydrodynamics (EHD) systems promote various flow patterns with relatively lower voltage regimes than DC-EHD systems. These mechanisms of electroconvection under the PDC/AC field offer unique possibilities for fluid flow control in biological EHD-driven flow and portable EHD applications.

Effects of flow unsteadiness and chemical kinetics on the reaction yield in a T-microreactor

Experimental flow visualizations and velocity measurements are used jointly with numerical simulations to investigate the mixing and monitor the reaction progress in the periodic flow regimes occurring in a T-shaped microreactor. We considered the effects of different kinetic constants, with very different characteristic chemical time scales resulting in a wide range of Damköhler numbers.A remarkable agreement between experiments and simulations is found both in terms of flow pattern and reaction progress. Two different flow regimes are present for increasing Reynolds number. The first is the periodic asymmetric regime, characterized by the shedding of vorticity-blobs along the mixing channel leading to a further increase of the mixing performance compared to the steady engulfment regime. The second regime is the periodic asymmetric one, which is mainly a poorly mixed segregated regime with periodic oscillation at the interface between the two reactants. The mixing degree significantly increases in the unsteady asymmetric regime, whereas it predictably drops down in the unsteady symmetric regime. In the periodic asymmetric regime the reaction yield follows the same function of the Damköhler number, describing the residence to chemical time-scale ratio, and of a non-dimensional kinetic constant, taking into account also fluid properties, previously proposed for the steady vortex and engulfment regimes. In the periodic symmetric regime, the reaction yield is found to depend only on the Damköhler number, with the same dependence previously highlighted for the steady segregated regime.

Numerical investigation on the flow around an inclined prolate spheroid

Numerical simulations are performed for the flow around an inclined 5:2 prolate spheroid in a uniform freestream. The Reynolds number (Re = 300, 500, 700, and 1000) and incidence angle (α = 0°–90°) are considered as significant parameters affecting the wake transitions, where α = 0° indicates flow parallel to the major axis of the prolate spheroid, and the Re is based on the inflow velocity U0 and the volume-equivalent sphere diameter De of the spheroid. In the range considered of Re and α, eight flow regimes are identified: (i) steady axisymmetric (SA) flow regime; (ii) steady planar symmetric flow regime; (iii) steady asymmetric (SAS) flow regime; (iv) periodic planar symmetric flow regime with non-zero mean lift or “Zig-zig-like” (Zz-like) mode; (v) periodic asymmetric flow regime with double-sided vortex shedding; (vi) multi-periodic asymmetric flow regime with double-sided vortex shedding and low frequency modulation (MPADL); (vii) multi-periodic asymmetric flow regime with single-sided vortex shedding and low frequency modulation (MPASL); and (viii) weakly chaotic state. Three of them are new and first reported, i.e., SAS, MPADL, and MPASL modes. The wake structure of the Zz-like mode is different from that of the zig-zig mode in the sphere/disk wake with a pair of streamwise vortices extending to the near wake. It is found that the elongated body can delay the onset of unsteadiness at small incidence angles. A flow regime map in the considered (Re, α) space is then provided. Finally, the physical mechanisms of the low-frequency phenomena observed at different wake modes are explored.

On the Control of the 2D Navier–Stokes Equations with Kolmogorov Forcing

This paper is devoted to the control problem of a nonlinear dynamical system obtained by a truncation of the two-dimensional (2D) Navier–Stokes (N-S) equations with periodic boundary conditions and with a sinusoidal external force along the x-direction. This special case of the 2D N-S equations is known as the 2D Kolmogorov flow. Firstly, the dynamics of the 2D Kolmogorov flow which is represented by a nonlinear dynamical system of seven ordinary differential equations (ODEs) of a laminar steady state flow regime and a periodic flow regime are analyzed; numerical simulations are given to illustrate the analysis. Secondly, an adaptive controller is designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime; the value of the Reynolds number is determined using an update law. Then, a static sliding mode controller and a dynamic sliding mode controller are designed for the system of seven ODEs representing the approximation of the dynamics of the 2D Kolmogorov flow to control its dynamics either to a steady-state regime or to a periodic regime. Numerical simulations are presented to show the effectiveness of the proposed three control schemes. The simulation results clearly show that the proposed controllers work well.

Beware of symmetry breaking and periodic flow regimes in axisymmetric CVD reactor setups

We compute the solution space in the laminar flow regime of a vertical, stagnation point, realistic chemical vapor deposition reactor. Compared to the solution space acquired in our previous work [N. Cheimarios, E.D. Koronaki, A.G. Boudouvis, Enabling a commercial computational fluid dynamics code to perform certain nonlinear analysis tasks, Comput. Chem. Eng. 35 (2011) 2632-2645] for a 2D axisymmetric case, 3D computations reveal a much richer solution space which if not investigated thoroughly crucial information for the process maybe lost. In particular, axisymmetric solutions can co-exist with non-axisymmetric and periodic solutions, due to buoyancy. It is found that non-axisymmetric flows can appear only in the region of mixed convection flows, which argues the use of only 2D axisymmetric models for this type of flows.

Nonstationary periodic wave regimes on a falling liquid film

The theoretical and numerical study of the periodic regimes of free flowing liquid film is carried out. As a result of the theoretical analysis, a simple three-harmonic model was obtained. The obtained model allowed demonstrating the basic mechanisms of the periodic flow regime. Calculations on the full model, the Nepomnyashchy equation and three harmonic models are performed. The results of the numerical solutions of the Nepomnyashchy equation and new model qualitatively consistent with the results of the solution of the full model are presented.

Direct numerical simulations of creeping to early turbulent flow in unbaffled and baffled stirred tanks

It has been known for a long time that the fluid flow and several global quantities, such as the power and pumping numbers, are about the same in baffled and unbaffled mechanically stirred vessels at low Reynolds numbers, but bifurcate at some intermediate Re and take drastically different values in fully turbulent flow. However, several details are not yet completely understood, notably concerning the relation of this bifurcation with the flow features and the transition to turbulence. In order to shed light on these issues, computational fluid dynamics was employed to predict the flow field in two vessels stirred by a six-bladed Rushton turbine at Reynolds numbers from 0.2 to 600 (covering the range from creeping flow to early turbulent flow). The two vessels differed only for the presence or absence of peripheral baffles. All simulations were conducted by a finite volume method in time-dependent mode, and a sliding-mesh technique was used in the baffled case to deal with the relative motion of baffles and impeller blades. A sensitivity analysis proved that a grid of about 5 million finite volumes was adequate to yield grid-independent results. The study proved that the bifurcation between quantities related to baffled and unbaffled tanks occurs when the inner (near-impeller) and outer (near-wall/baffles) flow fields interact significantly. It also elucidated the mechanisms of transition to turbulence in baffled and unbaffled tanks, notably showing in this latter case the existence (in the rotating reference frame of the impeller) of a periodic flow regime which involves a travelling wave instability.

Steady and unsteady regimes in a T-shaped micro-mixer: Synergic experimental and numerical investigation

Despite the very simple geometry, T-shaped micro-mixers are characterized by different flow regimes when operated for liquid mixing. In this work, experiments and direct numerical simulations are employed jointly to investigate such flow regimes. First, a novel methodology is proposed to provide a quantitative comparison with numerical predictions starting from simple flow visualization experiments that use non-collimated light. This method is applied and validated in the steady flow regimes. Moreover, flow visualizations provide for the first time an experimental support to the flow dynamics scenarios for the periodic unsteady flow regimes previously proposed in the literature on the basis of numerical simulations. In particular, at a Reynolds number, based on the bulk velocity and on the hydraulic diameter of the mixing channel, of approximately 225, the flow passes from a steady engulfment regime to an unsteady asymmetric regime, which is characterized by a periodic dynamics of the three-dimensional structures present in the mixer. In this regime, the flow in the mixing channel always remains asymmetric promoting, thus, the mixing between the two streams. By further increasing the Reynolds number, another change in flow dynamics is observed. In the new regime, called periodic symmetric regime, the flow always maintains a double mirror symmetry in the mixing channel and this leads to a dramatic decrease of mixing. The flow unsteadiness is mainly due to a periodic shift of the vortical structures in the top part of the mixer along the direction parallel to the incoming flow.

Structure of a free convective flow over a horizontal heated surface under conditions of conjugate heat transfer

The paper presents the results of an experimental and numerical study of the structure of a plume formed over a heated disk under conditions of conjugate heat transfer in a wide range of Grashof number. The data on the temperature field in the plume is compared with the visualization patterns. Numerical simulation was performed using the Ansys Fluent code, where the problem of the flow of a compressible gas in conditions of conjugate heat transfer in an unsteady formulation was solved under the assumption of laminar flow regime. As a result of a comparison of the results of physical and numerical experiments, there is a conclusion about a good qualitative concurrence of the flow structure. The heat transfer characteristics were studied experimentally and numerically: the local heat transfer coefficient, the heat flow from the heated disk, and the local and average Nusselt numbers. It is shown that the establishment of a periodic flow regime leads to a violation of the monotonicity of the distribution of the local heat transfer coefficient. In general, the data is in satisfactory agreement with the results of known works.

Unsteady mixing of binary liquid mixtures with composition-dependent viscosity

The laminar mixing of two miscible liquids in a T junction is investigated through Direct Numerical Simulations. In particular the liquids have the same density and the same viscosity, but the viscosity of the mixture strongly depends on composition and can be up to three times larger or smaller than that of the pure liquids; this is aimed at mimicking the behavior of many aqueous and organic mixtures of interest in the pharmaceuticals and fine chemistry industry. The mixing process is found to be largely affected by the dependence of viscosity on composition. When the viscosity of the mixture is larger than that of the pure components, a viscous layer forms at the confluence of the inlet flows, which tends to keep the two streams separated, resulting in a shift of the engulfment regime towards larger Reynolds numbers. On the contrary, when the viscosity of the mixture is lower than that of the pure components, an acceleration of the fluid at the center of the mixing channel takes place, leading to an enhancement of the degree of mixing. At larger Reynolds number, unsteady, time periodic flow regimes, able to strongly increase the degree of mixing, are established for all types of mixtures. Although fluid oscillations are all characterized by typical Strouhal numbers lying in the range 0.1–0.3, the onset of the unsteady regimes, together with the corresponding vortical structures, strongly depends on the fluid rheology.

Unsteadiness and transition to turbulence in woven spacer filled channels for Membrane Distillation

To characterize the performance of Membrane Distillation (MD) modules, channels filled with woven spacers were investigated by Computational Fluid Dynamics (including Direct Numerical Simulations and the use of the SST k-ω turbulence model) and by parallel experiments with Thermochromic Liquid Crystals. The cases considered here regard mutually orthogonal filaments with a spacer pitch to channel height ratio P/H=2, two spacer orientations θ with respect to the main flow (0° and 45°), and bulk Reynolds numbers Re from ∼200 to ∼2000, an interval of great interest in practical MD applications. For both values of θ, CFD predicted steady-state flow for Re up to ∼300, and chaotic flow for Re larger than ∼400. In the intermediate range Re≈300-400, periodic flow regimes were predicted for both orientations. These regimes were of particular interest and complexity, as they exhibited a slow global oscillation of the flow superimposed on high order harmonics corresponding to fast local oscillations. Experiments confirmed the appearance of unsteadiness for Re>∼300. Heat transfer and friction were little affected by unsteadiness and exhibited a smooth behaviour with Re. The agreement with the experimental results was good using DNS, and acceptable using RANS.

Periodically Fully Developed Heat and Fluid Flow Characteristics in a Furrowed Wavy Channel

abstractPeriodically fully developed two-dimensional (2D) flow in a furrowed wavy channel is investigated numerically at various Reynolds numbers (100–2123). For the laminar and transitional flow regime, the study is done for six geometrically different channels; corresponding to various nondimensional amplitude (0.05, 0.075, and 0.1) and wavelength (0.5 and 1). Critical Reynolds number—for the onset of periodic flow—decreases with increasing amplitude and wavelength. A flow regime map—demarcating steady and unsteady flow regime—is proposed. It is shown that the size of the vortex in streamlines and waviness in isotherms increase with increasing Reynolds number, amplitude and wavelength. The performance of wavy as compared to straight channel is studied with the help of ratio of Nusselt number, friction factor and area-goodness factor, and thermal-performance factor. With increasing Reynolds number, all these parameters remain almost constant in the steady regime and increase almost linearly in the unsteady regime. For the largest Reynolds number (close to 2000) studied here, the increase in the Nusselt number ratio—within the periodic flow regime—is 11.21% and 133% for the amplitude equal to 0.075 and 0.1, respectively, at a wavelength of 0.5; at a wavelength of 1.0, the increase is 101%, 134%, and 181% for the amplitude of 0.05, 0.075, and 0.1, respectively.

High-resolution high-order upwind compact scheme-based numerical computation of natural convection flows in a square cavity

In this paper, a higher-order accuracy method is proposed for the solution of time-dependent nature convection problems based on the stream function-vorticity form of Navier–Stokes equations, in which an optimized third-order upwind compact scheme (Opt-UCD3) with high resolution is proposed to approximate the nonlinear convective terms, the fourth-order symmetrical Padé compact scheme is utilized to discretize the viscous terms, the fourth-order compact scheme on the nine-point 2D stencil is used for approximating the stream-function Poisson-type equation and the third-order TVD Runge–Kutta method is employed for the time discretization. To assess numerical capability of the newly proposed algorithm, particularly its spatial behavior, a problem with analytical solution and another one with a steep gradient are numerically solved. Moreover, the nature convection flows in the square cavity with adiabatic horizontal walls and differentially heated vertical walls are also computed for the wide range of Rayleigh numbers (103<Ra<1010). The characteristic parameters such as Nusselt number, velocity, and streamline show excellent agreement with benchmark solutions and some accurate results available in the literature. Additionally, the detailed features of flow phenomena for the higher Rayleigh numbers (108<Ra<1010) are delineated. The results show that the natural convection flow looses stability firstly via a Hopf bifurcation at Rac1 to the periodic flow regime, and then undergoes second bifurcation at a critical Rayleigh number Rac2 to quasi-periodic flow regime, and eventually transits to turbulent through a further bifurcation. In the periodic regime, there exist at least two branches of solutions. All of the results are agree well with ones in the literature and show the capabilities of the present method to properly simulate the unsteady nature convection problems.

Evolution of secondary whirls in thermoconvective vortices: Strengthening, weakening, and disappearance in the route to chaos.

The appearance, evolution, and disappearance of periodic and quasiperiodic dynamics of fluid flows in a cylindrical annulus locally heated from below are analyzed using nonlinear simulations. The results reveal a route of the transition from a steady axisymmetric vertical vortex to a chaotic flow. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario is verified in this convective flow. In the transition to chaos we find the appearance of subvortices embedded in the primary axisymmetric vortex, flows where the subvortical structure strengthens and weakens, that almost disappears before reforming again, leading to a more disorganized flow to a final chaotic regime. Results are remarkable as they connect to observations describing formation, weakening, and virtual disappearance before revival of subvortices in some atmospheric swirls such as dust devils.