Three-dimensional Instability Research Articles

Improved three-dimensional color-gradient lattice Boltzmann model for immiscible two-phase flows.

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible two-phase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulations are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic two-phase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.

Sidewall effects on heat transfer in narrow backward facing step in transitional regime

In this work, we study numerically with large eddy simulation, the effects induced by the three-dimensional geometry of the channel on the flow topology that exists when the three-dimensional intrinsic instabilities appear in a backward facing step flow with low aspect ratio for Reynolds in the transitional regime (Re = 1,000–1,600), and its impact on the heat flux in the lower wall. Under the transitional regime, the three-dimensional instabilities begin to appear, but they can be masked by the flows due to the presence of the side walls. The study is carried out with two boundary conditions in the sidewalls, slip, and no-slip, to discriminate between the three-dimensionality induced by the geometry and the intrinsic three-dimensional instabilities. The results obtained are compared between the two boundary conditions, establishing what type of flow prevails and its influence on time-averaged mean Nusselt number for all Reynolds.

Flow behavior and formability of hot-rolled Mg-8Gd-3Y alloy under double-pass isothermal compression

Multi-pass hot rolling can help overcome the poor formability of high-strength Mg-Gd-Y alloys at ambient and intermedium temperature. It is essential to explore deformation characteristics of the alloys under such discontinuous thermomechanical processing. In the current work, double-pass isothermal compression tests were carried out to study the flow behavior and formability of a hot-rolled Mg-8Gd-3Y alloy at the temperature range of 350–450 °C with a strain rate range of 0.001–0.1 s−1. Two kinds of hardening behavior characterized by higher second-pass peak stress than the first-pass unloading stress are discovered. One is caused by precipitation that occurs during holding at a temperature range of 350–400 °C under a strain rate of 0.1 s−1. The other is grain-growth-induced hardening and takes place at 450 °C with a strain rate range of 0.01–0.1 s−1. Based on the dynamic material model, three-dimensional power dissipation and instability maps were established, corroborating improved formability under double-pass isothermal compression. The results clarify that employing inter-pass holding during hot working can widen the suitable processing window and reduce deformation bands.

Evolution of Three-dimensional Relativistic Ion Weibel Instability: Competition with Kink Instability

Abstract In this paper, we report our recent findings on the relativistic Weibel instability and its nonlinear saturation by performing numerical simulations of collisionless plasmas. Analysis of the obtained numerical results revealed that the nonlinear phase of the Weibel instability can be described by characteristic phases based on the Weibel filaments’ current density in terms of particle and Alfvén limit currents. We also analyzed the relativistic kink instability based on the energy principle in the magnetohydrodynamic (MHD) regime, and found that the Weibel filaments do not suffer from the kink-type instability in the MHD regime up to 1000 . This finding allowed a magnetic field to be sustained by relativistic Weibel instability that was stable enough to be a seed for MHD dynamos.

Low-frequency oscillations in flow past an inclined prolate spheroid

We analyse the forces on a 45∘ inclined 6:1 prolate spheroid at Reynolds number ReD=8000. In contrast to flow at lower Reynolds numbers previously investigated, we now find a strong oscillatory behaviour in the global forces. The Strouhal number associated with the forces is 0.05 and the peak-to-peak value of the oscillations in the sideforce is more than 25% of the average. A Fourier transformation of the entire flow field reveals that the cause of the force fluctuations is spatial oscillations in one of the two primary vortices generated behind the spheroid. This phenomena is attributed to a three-dimensional vortex instability.

Three-dimensional wakes behind cylinders of square and circular cross-section: early and long-time dynamics

The flow in the near wake of a square cylinder at Reynolds numbers of 205 and 225, corresponding to three-dimensional wake instability modes $A$ and $B$, respectively, and that of the square’s circumscribed circular cylinder are examined by using three-dimensional Navier–Stokes numerical simulations. At small times, prior to the streamwise vortex shedding, a self-similar velocity is observed in the wake and no significant difference is observed in the dynamics of the flows past the square and the circular cylinders. The exponential growth of the three-dimensional instability reaches a saturation regime during this early time for the considered Reynolds numbers. Vortical structures in the wake at long times and shedding frequencies are very close for the square and the circular cylinders. The flow separation on the forward top and bottom corners of the square cylinder have the effect of increasing its effective width, making it comparable with the diameter of the circumscribed circular cylinder. Thus, Floquet multipliers and modes of the associated three-dimensional instabilities are shown to be very close for the two cylinders when using the circumscribed circular cylinder as the basis for a characteristic length scale. Most importantly, the wavenumber with the maximum growth rate, for modes $A$ and $B$, is approximately identical for the two cylinders.

Three-dimensional viscoelastic instabilities in microchannels

Whereas the flow of simple single-phase Newtonian fluids tends to become more complex as the characteristic length scale in the problem (and hence the Reynolds number) increases, for complex elastic fluids such as dilute polymer solutions the opposite holds true. Thus small-scale, so-called ‘microfluidic’ flows of complex fluids can exhibit rich dynamics in situations where the ‘equivalent’ flow of Newtonian fluids remains linear and predictable. In the recent study of Qin et al. (J. Fluid Mech., vol. 864, 2019, R2) of the flow of a dilute polymeric fluid past a $50~\unicode[STIX]{x03BC}\text{m}$ cylinder (in a $100\times 60~\unicode[STIX]{x03BC}\text{m}$ channel), a novel 3-D holographic particle velocimetry technique reveals the underlying complexity of the flow, including inherent three-dimensionality and symmetry breaking as well as strong upstream propagation effects via elastic waves.

The influence of hallux valgus and flatfoot deformity on metatarsus primus elevatus: A radiographic study

BackgroundMetatarsus primus elevatus (MPE), a dorsal elevation of the first metatarsal in relation to the lesser metatarsals on lateral-view radiographs, is an indicator of hallux rigidus. The angle between the articular surfaces of the base of the first metatarsal and the anterior part of the medial cuneiform (M1C1A) reflects the sagittal instability of the first tarsometatarsal (TMT) joint. MPE may also indicate instability of the first metatarsal. The purpose of this study was to identify the influence of hallux valgus (HV) and flatfoot (FF) deformities on measurements obtained from first metatarsal-related radiographic images. MethodsStanding radiographic images of 134 feet were investigated. In dorsoplantar-view radiographs, HV and intermetatarsal angles were evaluated. The position of the medial sesamoid was classified with a grading system (Hardy score). In lateral-view radiographs, MPE, M1C1A, and Meary's angle were measured. The subjects were divided into 4 groups: the normal group (G1), HV(−)FF(−); the HV group (G2), HV(+)FF(−); the FF group (G3), HV(−)FF(+); and the dual group (G4), HV(+)FF(+). The radiographic parameters were compared among the groups. ResultsMPE in the HV patients (G2 and G4) was less than that in the non-HV participants (G1 and G3). MPE in G4 was less than that in G3. The odds ratios of the Hardy score were higher in G2, G3 and G4 than in G1. The ratios were higher in the FF patients (G3 and G4) than in the non-FF participants (G1 and G2) and were higher in G4 than in G2. ConclusionsFF affects sesamoid dislocation, and the combination of HV and FF further increases sesamoid dislocation. Combined with M1C1A and the Hardy score, MPE may be a useful indicator of three-dimensional instability of the first TMT joint. First TMT joint-related operations may be considered for severe HV treatment in G4 patients.

Sensitivity analysis and passive control of the secondary instability in the wake of a cylinder

The stability properties of selected flow configurations, usually denoted as base flows, can be significantly altered by small modifications of the flow, which can be caused, for instance, by a non-intrusive passive control. This aspect is amply demonstrated in the literature by ad hoc sensitivity studies which, however, focus on configurations characterised by a steady base flow. Nevertheless, several flow configurations of interest are characterised by a time-periodic base flow. To this purpose, we propose here an original theoretical framework suitable to quantify the effects of base-flow variations in the stability properties of saturated time-periodic limit cycles. In particular, starting from a Floquet analysis of the linearised Navier–Stokes equations and using adjoint methods, it is possible to estimate the variation of a selected Floquet exponent caused by a generic structural perturbation of the base-flow equations. This link is expressed concisely using the adjoint operators coming from the analysis, and the final result, when applied to spatially localised disturbances, is used to build spatial sensitivity and control maps. These maps identify the regions of the flow where the placement of a infinitesimal small object produces the largest effect on the Floquet exponent and may also provide a quantification of this effect. Such analysis brings useful insights both for passive control strategies and for further characterising the investigated instability. As an example of application, the proposed analysis is applied here to the three-dimensional flow instabilities in the wake past a circular cylinder. This is a classical problem which has been widely studied in the literature. Nevertheless, by applying the proposed analysis we derive original results comprising a further characterisation of the instability and related control maps. We finally show that the control maps obtained here are in very good agreement with control experiments documented in the literature.

Three-dimensional small-scale instabilities of plane internal gravity waves

We study the evolution of three-dimensional (3-D), small-scale, small-amplitude perturbations on a plane internal gravity wave using the local stability approach. The plane internal wave is characterised by its non-dimensional amplitude, $A$, and the angle the group velocity vector makes with gravity, $\unicode[STIX]{x1D6F7}$. For a given $(A,\unicode[STIX]{x1D6F7})$, the local stability equations are solved on the periodic fluid particle trajectories to obtain growth rates for all two-dimensional (2-D) and 3-D perturbation wave vectors. For small $A$, the local stability approach recovers previous results of 2-D parametric subharmonic instability (PSI) while offering new insights into 3-D PSI. Higher-order triadic resonances, and associated deviations from them, are also observed at small $A$. Moreover, for small $A$, purely transverse instabilities resulting from parametric resonance are shown to occur at select values of $\unicode[STIX]{x1D6F7}$. The possibility of a non-resonant instability mechanism for transverse perturbations at finite $A$ allows us to derive a heuristic, modified gravitational instability criterion. We then study the extension of small $A$ to finite $A$ internal wave instabilities, where we recover and build upon existing knowledge of small-scale, small-amplitude internal wave instabilities. Four distinct regions of the $(A,\unicode[STIX]{x1D6F7})$-plane based on the dominant instability modes are identified: 2-D PSI, 3-D oblique, quasi-2-D shear-aligned, and 3-D transverse. Our study demonstrates the local stability approach as a physically insightful and computationally efficient tool, with potentially broad utility for studies that are based on other theoretical approaches and numerical simulations of small-scale instabilities of internal waves in various settings.

Improving performance of a semi-analytical model for nonlinear water waves

An efficient semi-analytical solution to the problem of nonlinear water waves propagating at a constant depth is derived using parallel computing techniques. The approach is based on the assumptions of an irrotational flow of an inviscid and incompressible fluid. Velocity potential and free-surface displacement functions are represented in a form based on Fourier series satisfying a formulated initial boundary-value problem by a proper selection of time-dependent coefficients. The eigenfunction expansions are resolved by means of a Fast Fourier Transform technique and a higher-order time-stepping procedure to provide an efficient spectral collocation method of computation of wave-induced free-surface flows. The application of the Fourier transform qualifies the semi-analytical algorithm for efficient parallelization. Hence, the numerical model performance is improved using the computing capabilities of a GPU. The derived semi-analytical approach is easy to implement and may be straightforwardly extended to cover the generation of waves in a flume or a basin. The ability of the model to reproduce nonlinear phenomena is demonstrated in simulations of two- and three-dimensional instabilities of a modulated Stokes wave. The model can be used to solve standard as well as complex wave problems in large computational domains considerably faster than its CPU-based counterpart.

Two-dimensionalization of a three-dimensional bluff body wake

The three-dimensional flow characteristics of a circular cylinder with synthetic jet control are numerically studied using large eddy simulation. The Reynolds number based on the diameter of the cylinder is Re = 500. The control effects and underlying mechanism are revealed to show how the synthetic jet changes the three-dimensional wake pattern. Analysis of the dynamic control process indicates that the blowing stroke helps the shear layer to assemble vorticity, and then, the suction stroke accelerates the detachment of the concentrated vorticity. The vortex shedding process will be gradually dominated by symmetric actuation of the synthetic jets. Thus, the asymmetric vortex shedding mode could be changed into a symmetric mode several periods after actuation at certain excitation frequencies, leading to significant suppression of lift fluctuations. A periodic pressure variation at the leeward surface of the circular cylinder caused by the changes of the separation point for the flow over a circular cylinder and recirculation region results in a large drag fluctuation. The excitation phase influences only the control process, but not the final state, while the excitation frequency plays an important role in the formation of different wake patterns. It is also found that the synthetic jet can completely suppress the formation of streamwise vortices due to the three-dimensional instability suppression and reduce the deformation of spanwise vortices, resulting in a conversion of the original three-dimensional flow into a two-dimensional one. Such two-dimensionalization can be achieved for both asymmetric and symmetric wake patterns, indicating that it is not influenced by the excitation phase and frequency as long as the actuation is two-dimensional.

Physical mechanism for origin of streamwise vortices in mode A of a square-section cylinder

In the present paper, physical mechanism responsible for origin of streamwise vortices in mode A appeared in the three-dimensional (3-D) wake transition of a square-section cylinder is investigated. Direct numerical simulations at a Reynolds number of 180 firstly show that such streamwise vorticity is not originated from lateral surfaces. Then through the analysis of local flow field in the immediate neighborhood of rear surface, based on the theory of vortex-induced vortex, a new physical mechanism is identified. At first, the vertical vorticity on rear surface is generated by the intrinsic three-dimensional instability with the same instability wavelength of mode A. Then the streamwise vorticity at a specific sign is induced by such vertical vorticity, convected and concentrated in the shear layers. Finally, streamwise vortices are formed and shed with alternatively shedding spanwise vortices in the near wake. Moreover, the effect of induced spanwise vorticity on original two-dimensional (2-D) spanwise vorticity is also presented in detail.

On secondary instability of a transitional separation bubble

It is well established in the natural transition of an attached boundary layer that the transition process starts with a two–dimensional primary instability (Tollmien–Schlichting wave, denoted as TS wave), followed by usually a three-dimensional secondary instability (fundamental mode or subharmonic mode) leading to the breakdown to turbulence. However, the transition process of a separation bubble (laminar flow or laminar boundary layer at separation and transition occurs downstream of the separation, leading to turbulence at reattachment) is less well understood, especially on the nature of secondary instability.The focus of this paper is on trying to advance our understanding of secondary instability of a transitional separation bubble on a flat plate with a blunt leading edge (separation is induced geometrically at the leading edge) under a very low free-stream turbulence level (< 0.1%). Large-Eddy Simulation (LES) is employed in the current study with a dynamic sub-grid-scale model. The numerical flow visualisation together with the spectral analysis has indicated that a three dimensional secondary instability, the elliptical instability, which occurs for fundamental frequency is the main mechanism at work whereas the subharmonic mode in the form of vortex-pairing is hardly active. There is no evidence for the existence of hyperbolic instability in the braid region either.

Three-Dimensional Instability of Opposite Polarity Nonthermal Dusty Plasma

Abstract Nonlinearity properties of obliquely wave propagation and instability in collisionless magnetized nonthermal dusty plasmas containing fluid of negative-positive grains are investigated. Zakharov-Kuznetsov equation is obtained and the three-dimensional wave instability is studied. The parameters such as polarity charge ratio, cyclotron frequency and fast nonthermal effectiveness of the instability properties and growth rate are theoretically studied. It is found that both positive and negative soliton profiles are formed depending on the fraction ratio of electron-ion nonthermality. Also, the growth rate was dependent nonlinearly on the direction cosines, the cyclotron frequency and the positive (negative) grain charge ratio, but independent of the fractional ratio of electron-ion nonthermality. Present discussion may be very significant regarding the observations of nonlinear phenomena in space.

Three-dimensional instabilities and negative eddy viscosity in thin-layer flows

The stability of flows in layers of finite thickness H is examined against small-scale three-dimensional (3D) perturbations and large-scale two-dimensional (2D) perturbations. The former provide an indication of a forward transfer of energy while the latter indicate an inverse transfer and the possibility of an inverse cascade. The analysis is performed using a Floquet-Bloch code that allows examination of the stability of modes with arbitrary large-scale separation. For thin layers, the 3D perturbations become unstable when the layer thickness H becomes larger than H>c1(νℓU/U)1/2=c1ℓURe−1/2, where U is the rms velocity of the flown, ℓU is the correlation length scale of the flow, ν is the viscosity, and Re=ℓUU/ν is the Reynolds number. At the same time, large-scale 2D perturbations also become unstable by an eddy viscosity mechanism when Re>c2, where c1,c2 are order 1 nondimensional numbers. These relations define different regions in parameter space where 2D and 3D instabilities can (co)exist and this allows us to construct a stability diagram. Implications of these results for fully turbulent flows that display a change of direction of cascade as H is varied are discussed.3 MoreReceived 1 June 2018DOI:https://doi.org/10.1103/PhysRevFluids.3.114601©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFlow instabilityTurbulenceFluid Dynamics

Three-dimensional interaction of a shock with a thin non-circular channel of low-density gas

Numerical simulation of three-dimensional interaction of a shock with thin circular or non-circular – elliptic or rectangular – low-density gas channel is presented. Euler’s equations for inviscid gas are solved using 5th-order finite-difference WENO scheme. Large-scaled shock wave precursor structure is described in detail. It is shown that in three-dimensional flow internal shear layer instabilities develop faster than in axisymmetric case. High-pressure jet cumulation effect is found to amplify moderately for elliptic and rectangular cases. An influence of channel cross-section shape on the precursor growth rate is studied. It is found that the duration of linear precursor growth phase is greatly increased for stretched channel cross-section shapes.

Flow-induced oscillations of three tandem rotating cylinders

The oscillation responses and the associated wake structures of three rotating tandem cylinders, mounted on elastic supports in both the streamwise (x-) and transverse (y-) directions, are numerically studied. Finite element computations are carried out at Reynolds number Re = 150, where the flow is two-dimensional (2-D), and at Re = 2000 (3-D flow), varying the reduced velocity (U*) in the range U* = 2–14. Each cylinder is placed at a distance of 5 diameters (5D) from its immediate neighbor. In the two-dimensional flow, the upstream and the second downstream cylinders are rotated at the rotation rate (α) of 1, while for the first downstream cylinder, α = 0, 0.5, and 1 are employed. In the 3-D computations, α = 1 is considered for the three bodies. It is observed that at Re = 150, all the cylinders exhibit three distinct lock-in modes, namely, modes I, II, and III. Depending on the rotation configuration, 2S, P + S, and 2P shedding patterns appear in the wake of upstream cylinder, while the downstream cylinders shed 2S, P, P + S, 2P, and T + P modes of primary vortices. In the 3-D flow (at Re = 2000), the upstream cylinder exhibits a bell-shaped profile in the variation of amplitude response as a function of U*. Oscillation responses of the two downstream bodies appear in three distinct regions. During high amplitude oscillations, the upstream cylinder sheds the 2P mode of primary vortices, while in the near wakes of the two downstream bodies, small and incoherent primary vortical structures form due to the presence of three-dimensional instability. Low and high amplitude responses are associated with weak and strong 3-D flow instabilities, respectively.

Local origin of mode-B secondary instability in the flow past a circular cylinder

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, $Re = U_{\infty}D/\nu$ with $U_\infty$, $D$ and $\nu$ 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 instability on orbits 1 & 2, which are symmetric counterparts of one another, is shown to undergo bifurcations at $Re\approx50$ and $Re\approx250$. Upon incorporating finite-wavenumber, finite-Reynolds number effects to compute corrected local instability growth rates, the inviscid instability on orbits 1 & 2 is shown to be suppressed for $Re\lesssim262$. Orbits 1 & 2 are thus shown to exhibit a synchronous instability for $Re\gtrsim262$, which is remarkably close to the critical Reynolds number for the mode-B secondary instability. Further evidence for the connection between the local instability on orbits 1 & 2, and the mode-B secondary instability, is provided via a comparison of the growth rate variation with span-wise wavenumber between the local and global stability approaches. In summary, our results strongly suggest that the three-dimensional short-wavelength instability on orbits 1 & 2 is a possible mechanism for the emergence of the mode B secondary instability.

Two- and Three-dimensional Nonlinear Instabilities of Whistler Waves

Abstract Recently, two-dimensional (2D) nonlinear instabilities of whistler waves from resonant wave–wave interaction have gained much attention in numerical simulations as well as observations in space plasmas. In this paper, both 2D and three-dimensional (3D) nonlinear instabilities of whistler waves are investigated using electron magnetohydrodynamics (EMHD). It is found that decay instabilities can excite waves with a broadband wavenumber spectrum, including highly oblique propagating whistler waves. Whistler waves with λ e k = 1 would excite counter-propagating whistler waves, and the wave with can produce both co- and counter-propagating whistler waves, where λ e is the electron inertial length and k is the wavenumber. Moreover, it is shown that 3D instabilities have similar nonlinear growth rate distributions as in 2D decay for the azimuthal wavelength much larger than λ e . These results suggest that nonlinear wave–wave interaction can play an important role in the scattering of whistler waves in the solar wind and the Earth’s magnetosphere, and are also helpful for understanding nonlinear wave–wave interaction in the formation and development of EMHD turbulence.