Unsteady Vortical Flow Research Articles

Sound generation by a pair of co-rotating vortices using spectral acoustic analogy

The spectral acoustic analogy (AA) theory is used to study the acoustic generation by a pair of co-rotating vortices from the decomposition of wave packets. The use of a two-dimensional spectral AA formulation is based on the data obtained by conducting a direct simulation of unsteady compressible Navier-Stokes equations. By way of the spectral AA theory and convolution filtering operations, the role played by the wave packets of the vortices in the generation of the sound is thoroughly discussed. It is found that the far-field sound is generated by the linear superimposition of the interactions between the base flow and the remaining wave packets. Moreover, a notable wave packet of the co-rotating vortices, called the acoustic-related wave packet herein, is identified in the spectral domain, which not only contains all radiating components but also contributes to a discernible acoustic source. It potentially bridges the gap between the near-field wave packets and the far-field sound. The present methodology based on the spectral AA theory shows promise in providing insights into the mechanisms of sound generation in turbulent or unsteady vortical flows.

Investigation of Subgrid-Scale Models in Large Eddy Simulation on the Unsteady Flow Around a Hydrofoil Using OpenFOAM

In this paper, we investigate the unsteady Reynolds-averaged Navier–Stokes simulations of the turbulent cavitating flow around a hydrofoil CLE. The primary objective of this study was to highlight the effect of subgrid-scale turbulence method in the prediction of unsteady vortical flow. In this work, the Smagorinsky and wall-adapting local eddy viscosity (WALE) models are selected to close the large eddy simulation equations. To investigate the limitations of these two models, the interactions between cavitation and vortices, the predicted streamlines, the velocities components, and the pressure oscillations have been discussed. The numerical results were compared with experimental results. These results showed that regardless of the selected turbulence model the development cycle of cavitation pocket is characterized by three levels: (first stage) the growth of attached pocket, (second stage) the separation of the attached pocket, and (last stage) the development and collapse of detached structures. The comparison between these two models shows that the WALE model takes into account both the rotation and strain rates, whereas the Smagorinsky model only takes into account the deformation rate of the turbulent structure. Besides, the WALE model is highly adaptive for wall-bounded flows. This advantage is explained by this ability to recover the near-wall scaling for the eddy viscosity. The WALE model has adopted a treatment without damping function or wall functions. Due to its algebraic nature, it offers a high-speed and efficient scheme compared to the Smagorinsky model. The study of the flow structures by iso-surface of the Q-criterion showed that the WALE model can predict the transition from laminar to the turbulent regime.

Analysis of Unsteady Vortical Flow Field in Rotating Cascade Using Instantaneous Pressure Field Measurement and Smart Visualization of CFD

ターボ機械における非定常流動現象の解明には，実験解析とCFD解析を併用することが不可欠である．この観点から，瞬時圧力分布計測法およびCFD結果の知的可視化手法について述べている．瞬時圧力分布計測法では，動翼列内の非定常流れ場の過渡的な現象を捉えるために，30個の高応答圧力センサおよび時空間補間を駆使して，翼間１ピッチにわたるケーシング壁面上の瞬時圧力分布の時系列データを得る．CFD結果の知的可視化では，CFD結果から流体力学的に意味のある情報を抽出するために，特異点理論に基づいた渦中心の同定および限界流線のトポロジー解析を行う．瞬時圧力分布計測法およびCFD結果の知的可視化手法を軸流圧縮機動翼列のスパイク形旋回失速初生プロセスの解明に適用した事例を紹介している．

Networked-oscillator-based modeling and control of unsteady wake flows.

A networked-oscillator-based analysis is performed to examine and control the transfer of kinetic energy for periodic bluff body flows. The dynamics of energy fluctuations in the flow field are described by a set of oscillators defined by conjugate pairs of spatial proper orthogonal decomposition (POD) modes. To extract the network of interactions among oscillators, impulse responses of the oscillators to amplitude and phase perturbations are tracked. Tracking small energy inputs and using linear regression, a networked-oscillator model is constructed that reveals energy exchange among the modes. The model captures the nonlinear interactions among the modal oscillators through a linear approximation. A large collection of system responses is aggregated to capture the general network structure of oscillator interactions. The present networked-oscillator model describes the modal perturbation dynamics more accurately than the empirical Galerkin reduced-order model. The linear network model for nonlinear dynamics is subsequently utilized to design a model-based feedback controller. The controller suppresses the modal amplitudes that result in wake unsteadiness leading to drag reduction. The strength of the proposed approach is demonstrated for a canonical example of two-dimensional unsteady flow over a circular cylinder. The present formulation enables the characterization of modal interactions to control fundamental energy transfers in unsteady bluff body flows.

Network community-based model reduction for vortical flows.

A network community-based reduced-order model is developed to capture key interactions among coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic techniques to identify important vortical communities that are comprised of vortical elements that share similar dynamical behavior. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of these vortical interactions, the proposed methodology is applied to formulate reduced-order models for the inter-community dynamics of vortical flows, and predict lift and drag forces on bodies in wake flows. We demonstrate the capabilities of these models by accurately capturing the macroscopic dynamics of a collection of discrete point vortices, and the complex unsteady aerodynamic forces on a circular cylinder and an airfoil with a Gurney flap. The present formulation is found to be robust against simulated experimental noise and turbulence due to its integrating nature of the system reduction.

Effects of upstream tetrahedron length on flow characteristics around juncture of circular cylinder and flat plate

The influences of the length of tetrahedron juncture flow controller (JFC) and Reynolds number on the flow in the vertical symmetrical plane of the upstream region and near wake of a circular cylinder-flat plate juncture were studied experimentally in a towing water tank. The flow was analyzed by the particle-tracking flow visualization method and particle image velocimetry. The Reynolds number ranged from 500 to 6000. The inverse of nondimensional boundary-layer displacement thickness was from 3.27 to 10.33. The tetrahedron length-to-circular cylinder diameter ratio ranged from 0 to 1.4. The natural flow presented single-vortex, dual-vortex, triple-vortex, and unsteady vortical flow modes in different ranges of Reynolds numbers. The effects of the tetrahedron JFC installed at the leading edge of the juncture on the flow patterns significantly depended on the tetrahedron length and a little on the Reynolds number. Larger tetrahedron length was required to change flow modes and eliminate horseshoe vortices at larger Reynolds number. Within the range of Reynolds numbers <6000, the tetrahedron length-to-cylinder diameter ratio must be larger than about 1, so all flows near the upstream region of the juncture directed forward without reversal or vortices. The tetrahedron JFC significantly reduced the wall shear stress in the near wake of the juncture when compared with that of the natural flow.

Fast multipole method applied to Lagrangian simulations of vortical flows

Lagrangian simulations of unsteady vortical flows are accelerated by the multi-level fast multipole method, FMM. The combination of the FMM algorithm with a discrete vortex method, DVM, is discussed for free domain and periodic problems with focus on implementation details to reduce numerical dissipation and avoid spurious solutions in unsteady inviscid flows. An assessment of the FMM-DVM accuracy is presented through a comparison with the direct calculation of the Biot–Savart law for the simulation of the temporal evolution of an aircraft wake in the Trefftz plane. The role of several parameters such as time step restriction, truncation of the FMM series expansion, number of particles in the wake discretization and machine precision is investigated and we show how to avoid spurious instabilities. The FMM-DVM is also applied to compute the evolution of a temporal shear layer with periodic boundary conditions. A novel approach is proposed to achieve accurate solutions in the periodic FMM. This approach avoids a spurious precession of the periodic shear layer and solutions are shown to converge to the direct Biot–Savart calculation using a cotangent function.

Dynamics of an unsteady stagnation vortical flow via dynamic mode decomposition analysis

The dynamics of a large-scale stagnation vortex pair in an axisymmetric stagnation flow subject to a laminar wake disturbance is measured by time-resolved two-dimensional particle image velocimetry, and then quantitatively characterized by both the Eulerian velocity/vorticity fields and the Lagrangian finite-time Lyapunov exponents fields. This vortex pair is found to be the result of the forced response of the stagnation flow to the upstream shearing disturbances, and presents a dynamical evolution of quasi-periodic shedding due to short-wave elliptical instability. Dynamic mode decomposition analysis of both the Eulerian measure and the Lagrangian measure is taken for a quantitative description of this process. The sparsity-promoting scheme (Jovanovic et al. Phys Fluids 26(2):024,103, 2014), which integrates the mode identification and truncation as a whole, is used to distinguish those modes with dynamical significance from irrelevant ones with transient behavior. The superiority of this scheme is evidenced by the facts that it avoids the eigenvalue contamination problem, and credits higher priority to the sub-dominant modes directly associated with the system dynamics. It is found that the energetic mode with a frequency of 0.177 Hz, or about 10% of the maximum shear rate of the upstream wake, determines the quasi-periodical vortex formation process. Its half-order harmonic represents the vortex shedding event along one fixed direction. High-order even-quarter harmonics jointly contribute to the circular pattern of the vortex tube. In addition, a set of low-frequency odd-quarter harmonics are highlighted as the elliptical instability and the following vortex deformation process. Based on this finding, a reduce-order representation with 8 Eulerian modes or 56 Lagrangian modes is proposed to characterize the dominant dynamics of this unsteady vortical stagnation flow. In addition, the Eulerian measure seems to be more efficient than the Lagrangian measure in terms of reduced-order representation.

Unsteady vortical flow simulation in a Francis turbine with special emphasis on vortex rope behavior and pressure fluctuation alleviation

Hydro turbines operating at partial flow conditions usually have vortex ropes in the draft tube that generate large pressure fluctuations. This unsteady flow phenomenon is harmful to the safe operation of hydropower stations. This paper presents numerical simulations of the internal flow in the draft tube of a Francis turbine with particular emphasis on understanding the unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the air and the vortices. The pressure fluctuations induced by the vortex rope are alleviated by air admission from the main shaft center, with the water-air two phase flow in the entire flow passage of a model turbine simulated based on the homogeneous flow assumption. The results show that aeration with suitable air flow rate can alleviate the pressure fluctuations in the draft tube, and the mechanism improving the flow stability in the draft tube is due to the change of vortex rope structure and distribution by aeration, i.e. a helical vortex rope at a small aeration volume while a cylindrical vortex rope with a large amount of aeration. The preferable vortex rope distribution can suppress the swirl at the smaller flow rates, and is helpful to alleviate the pressure fluctuation in the draft tube. The analysis based on the vorticity transport equation indicates that the vortex has strong stretching and dilation in the vortex rope evolution. The baroclinic torque term does not play a major role in the vortex evolution most of the time, but will much increase for some specific aeration volumes. The present study also depicts that vortex rope is mainly associated with a pair of spiral vortex stretching and dilation sources, and its swirling flow is alleviated little by the baroclinic torque term, whose effect region is only near the draft tube inlet.

The effects of perforated cylinders on the vortex shedding on the suppression of a circular cylinder

The aim of this study is the control of unsteady vortical flow occurred downstream of a circular cylinder located in shallow water flow using concentrically located outer perforated cylinder. The porosities, β have been changed between 0.1 and 0.8 in the present study. The increments of porosity β were taken as 0.05 in the range of 0.1 and 0.8 with a hole diameter of d=10 mm. The ratio of inner cylinder diameter to outer cylinder diameter, Di /Do was selected as 0.25, 0.3, 0.4, 0.5 and 0.6 the inner cylinder diameter is Di =50mm where the outer cylinder diameter is Dd =100mm. Experiments were performed at a constant depth of the water level as h=50mm (half of the outer cylinder diameter). Free stream velocity was taken as U∞ =100 mm/s corresponding to a Reynolds number of Re Do =10000 based on the outer cylinder diameter. It has been observed that the inner circular cylinder was highly affected by the existence of surrounding outer perforated cylinders. It is observed that the intensity of Reynolds shear stress correlating, > is completely attenuated in the region both downstream of concentric cylinder and between the concentric cylinders. It is determined from the experiments that porosity, β=0.55 is the most effective parameter for control of flow structure that is occurred from the inner cylinder.

Aerodynamic and Structural Studies of a Flapping Wing in Forward Flight

Flapping flight is commonly seen in nature at low Reynolds numbers. This work investigates the physical aspects of forward flight for flapping unmanned aerial systems. The kinematics discussed in this paper is based on an anticlockwise figure-8-shaped flapping cycle. The evolution of the complex, unsteady vortical flow system that develops during the flapping motion is presented. Mechanisms for generating the lift and thrust are discussed, with emphasis on the unsteadiness of the flow features during both the downstroke and upstroke phases. A one-way fluid–structure interaction has been investigated, and the relative importance of aerodynamic forces is compared with respect to the inertial forces. The inhomogeneity of the wing in terms of mass distribution is studied, and it is shown that a higher density at the wing root is beneficial in respect to the mechanical power required to achieve the forward flight. Limited benefit is observed when higher material density at the leading edge is adopted.

Vortical Flow Structure in the Wake of an Estate Car

AbstractA finite volume simulation of unsteady vortical wake flow behind a square-back estate car is presented. The three-dimensional time-averaged incompressible Navier-Stokes equations are solved together with the Reynolds stress transport equations for turbulence. By virtue of the simulated surface streamlines, the physics of fluid can be extracted using the topological theory. In addition, the simulated topological singular points and lines of separation are plotted on the car surface. The vortical flow motions that developed behind the mirrors, wheels and car body are explored by means of the simulated time evolving vortex corelines. The formation and interaction of the vortex systems in the wake are examined by tracing the instantaneous streamlines in the vicinity of the simulated vortex corelines. The vortex street behind the estate car is also illustrated by the simulated streaklines. Finally the Hopf bifurcation phenomenon is revealed by the time-varying aerodynamic forces on the car.

New high-resolution-preserving sliding mesh techniques for higher-order finite volume schemes

This paper presents a new sliding mesh technique for the computation of unsteady viscous flows in the presence of rotating bodies. The compressible Euler and incompressible Navier–Stokes equations are solved using a higher-order (>2) finite volume method on unstructured grids. A sliding mesh approach is employed at the interface between computational grids in relative motion. In order to prevent loss of accuracy, two distinct families of higher-order sliding mesh interfaces are developed. These approaches fit naturally in a high-order finite volume framework. To this end, Moving Least Squares (MLS) approximants are used for the transmission of the information from one grid to another. A particular attention is paid for the study of the accuracy and conservation properties of the numerical scheme for static and rotating grids. The capabilities of the present solver to compute complex unsteady vortical flow motions created by rotating geometries are illustrated on a cross-flow configuration.

Acoustic-excited vortex shedding and acoustic nonlinearity at a rectangular slit with bias flow

Abstract The acoustical response of a slit with a mean bias flow is numerically studied. By means of a potential flow model based on the discrete vortex method and a spanwise-averaged three-dimensional Green׳s function, both unsteady vortical flow and slit impedance are obtained in a unified theoretical framework. The numerical simulation focuses on the acoustic-excited vortex structures of the slit flow while neglecting the viscous damping effect. Three representative flow features are demonstrated, which are the destabilized jet flow, the rolling up of vortex sheets and formation of vortex pairs, and the reversal flow with alternating vortex shedding on both sides of the slit. These features are corresponding to low, moderate, and high sound amplitude, respectively. The acoustic behavior of the slit can be divided into linear, transition, and nonlinear regimes. During its evolution through the three regimes, the resistance exhibits a constant value, a slight decrease, and a significant increase with the increasing sound amplitude. Correspondingly, the reactance first remains constant and then shows a modest decrease as the sound amplitude increases. The nonlinear effect also causes the gradual decrease of the mean bias velocity in company with the marked increase of the amplitude of the fluctuating velocity in the slit. The mean bias velocity decreases to about 80 percent of its linear value at the transition point where reversal flow begins to occur, and further decreases to only 10 percent in the highly nonlinear region. The slit impedance is also presented as a function of frequency and for different aspect ratios. And the effects of frequency and slit geometry are discussed.

Pressure measurements on a high-head Francis turbine during load acceptance and rejection

Hydraulic turbines are frequently used to maintain electrical grid parameters. An angular movement of the guide vanes (GVs) during transients such as load acceptance and rejection within short time raised significant concerns for increased wear and instabilities. The present work focuses on the pressure variations in a high-head Francis turbine during the transients. Six transient conditions were investigated including time-domain rotor–stator interaction. The measurements in the vaneless space and runner indicated the presence of unsteady vortical flow during transients. The vortices travelled to the runner and affected the flow in the blade channels. The GVs angular movement increases the pressure difference between the pressure and suction sides of the blade. The largest pressure variation was observed during the partial load rejection at the trailing edge of the blade. Preliminary results indicated that an appropriate closure of the GVs may minimize large pressure fluctuations in the runner.

Numerical study of gas-cyclone airflow: an investigation of turbulence modelling approaches

A numerical study of unsteady single-phase vortical flow inside a cyclone is presented. Two different geometric configurations have been considered, with the goal of assessing several different turbulence modelling approaches for this class of problem. The models investigated include three Reynolds-averaged Navier–Stokes models: a commonly used two-equation eddy-viscosity model, a differential Reynolds stress model (DRSM) and an eddy-viscosity model sensitised to rotational and curvature (RC) effects which was recently developed and implemented into a commercial CFD (computational fluid dynamics) code by the authors. Results were also obtained using large eddy simulation (LES). The computational results are analysed and compared with available experimental data. The RC-sensitised eddy-viscosity model shows significant improvement over the standard eddy-viscosity model. The RC-sensitised model, DRSM and LES model predictions of the mean flowfield are in good agreement with the experimental data. The results suggest that curvature- and rotation-sensitive eddy-viscosity models may provide a practical alternative to more computationally intensive approaches.

Numerical Investigations for the Effect of Slender Body on Dynamic Rolling Characteristics of a 80°/60° Double Delta Wing

The effect of slender body on the rolling characteristics of a double delta wing is found by comparing the numerical simulation results of the double delta wing and wing-body configuration. The coupled computation system solving the Navier-Stokes equations and the rolling motion equation alternatively to obtain the unsteady vortical flow around the two configurations while rolling. The results conclusively showed the upwash effect of the slender body enhanced the energy of strake vortex and merged vortex.The aerodynamic lag of double delta wing is weak, contrarily, the time lag effect of the wing-body configuration is significant. The asymmetry vortices structure nearby the trailing edge are believed to be the main reason for the unsteady time lag effect.

Dispersion and Deposition of Micro Particles over Two Square Obstacles in a Channel via Hybrid Lattice Boltzmann Method and Discrete Phase model

Dispersion and deposition of aerosol particles over two square cylinders confined in a channel in laminar unsteady vortical flow were investigated numerically. Lattice Boltzmann method was used to calculate fluid characteristics and modify Euler method was employed as Lagrangian particle tracing procedure to obtain particle trajectories. Drag, Saffman lift, gravity, buoyancy and Brownian motion are forces that were included in particle equation of motion. Augmentation of total deposition efficiency at staggered arrangement started at lower stokes number in comparison with inline arrangement. Presence of second obstacle increased deposition efficiency for Stokes number greater than 1. Particles having Stokes number smaller than 0.1, followed streamlines and were not captured by squares. Deposition efficiency increased slightly between Stokes numbers 1 to 5 with respect to stokes numbers from 0.1 to 1. Deposition efficiency had bigger growth rate at HD=5 with respect to HD=3. Ultra fine particles with stokes number smaller than 0.1 acted like fluid particles at their positions and dispersed in the vortices, in the periodic asymmetric behind the obstacles. Particles tend to move on vortices boundary as Stokes numbers increased from 0.1 to 1. At HD=3, particles could not move in the region between two obstacles.

Unsteady aerodynamics modeling for flight dynamics application

In view of engineering application, it is practicable to decompose the aerodynamics into three components: the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms, while the third is described using a one-order differential equation and a radial-basis-function (RBF) network. For an aircraft configuration, the mathematical models of 6-component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynamics, respectively. The results show that: (1) unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; (2) unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and (3) unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected. It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability are analyzed by numerical simulation.

Unsteady Vortical Flow Field in a Wind Turbine

Unsteady Vortical Flow Field in a Wind Turbine