Unsteady Vortex Research Articles

Four-dimensional particle tracking velocimetry measurements of unsteady three-dimensional vortex onset and progression for 5415 straight ahead, static drift, and pure sway

Large-scale towed system four-dimensional particle tracking velocimetry (4DPTV) implementation and measurements are presented for towing tank tests for a naval combatant 5415 ship model for straight ahead, static drift β = 10°, and pure sway βmax = 10° conditions. The results, for the first time, provide instantaneous volumetric flow field data around the ship model including near the hull surface, and a complete description of the sonar dome 3D unsteady vortex separation onset and progression due to the 4DPTV larger measurement volume and higher data rates in comparison with previous results using tomographic particle image velocimetry (TPIV); thereby, providing the essential data required for the assessment of current hybrid Reynolds-averaged Navier–Stokes/large eddy simulation turbulence modeling capabilities and guidance for the necessary modeling improvements. The 4DPTV system is summarized and compared with the previous TPIV, including the camera calibration procedures, trigger systems, and synchronization with the sway motion. Analysis procedures, including data reduction procedures and the 3D vortex core detection and voxel labeling techniques, are described. The identification of the complex vortex separations and breakdown is aided using complementary detached eddy simulations. The vortex–vortex interaction process is visualized from instantaneous volumetric datasets. The pros and cons of the 4DPTV vs TPIV, the comparison between the second- and third-generation vortex visualization technique, and the statistical convergence error analysis of sonar dome port vortex for β = 10° are discussed. Plans for increased spatial resolution of the 4DPTV system and additional data reduction techniques for detailed turbulence analysis are also discussed.

Force decomposition on flapping flexible plate via impulse theory and dynamic mode decomposition

Dynamic mode decomposition (DMD) is a widely used method to extract dynamic information from sequential flow data, aiding our comprehension of fluid dynamics and transport processes. While DMD can unveil internal system laws and predict unsteady flow phenomena, the connection between DMD modes and the nonlinear hydrodynamic behavior of solid bodies remains unexplored. This study investigated the internal relationship between DMD modes and their impact on hydrodynamic forces. We employed a penalty-immersed boundary method to simulate the behavior of a flapping flexible plate in a uniform incoming flow, generating extensive datasets of vorticity fields. By applying DMD to these datasets, we identified key modes governing the flow dynamics, including the shear layer, symmetric vortex street, and antisymmetric vortex street. Furthermore, we utilized the impulse theory to analyze the force characteristics of the plate based on the corresponding DMD modes. The net force is determined by the combined contributions of the impulse force and the vortex force. Our findings reveal that the net horizontal force is primarily influenced by the first two modes. Specifically, mode 1, characterized by a dimensionless frequency of f*=0, contributes to thrust, whereas mode 2, with f*=1, contributes to drag. This physical investigation holds relevance for fluid–structure systems involving the interaction dynamics of flexible structures with unsteady wake vortex systems.

Assessment of yaw-control effects on wind turbine-wake interaction: A coupled unsteady vortex lattice method and curled wake model analysis

Downstream wind turbines in a wind farm are affected by the wake of the upstream turbine. Therefore, wake steering has been introduced to alleviate the wake effect by yawing the shaft of the upstream wind turbine. In this scenario, the upstream and downstream wind turbines encounter non-uniform inflow in wake steering. In this study, the unsteady vortex lattice method (UVLM) was coupled with the curled wake model to consider the unsteady aerodynamics resulting from the wake steering. The proposed method was validated with the National Renewable Energy Laboratory (NREL) Phase VI experiment and Large Eddy Simulation (LES) data simulated with two-turbine case. Three NREL 5 MW wind turbines were simulated in wake steering conditions, and the power performance of the individual turbines and their root flapwise bending moments were investigated. The flow field investigation indicated that the counter-rotating vortices significantly influence the effective angle of attack and aerodynamic loads. In addition, a secondary effect was observed on the effective angle of attack of the rotor and wake deflection. The simulation results demonstrated the applicability of the UVLM in wake steering and its potential for analyzing the wake effects experienced by multiple wind turbines in a wind farm.

Coherent structure modification by a shear acting at the surface of a turbulent open channel

Recent experiments in the river Seine have revealed the presence of persistent large rolls. This finding has motivated the present numerical study of a turbulent open channel flow. Our pseudo-spectral direct numerical simulations are aimed at understanding how the shear at the surface, for instance produced by an external wind, can change vortical structures in the bulk. Simulations are run at a Reynolds number in the range [5times 10^3div 10^4], in line with similar laboratory experiments. We investigate how flow structures located near the bottom wall, near the surface or inside the bulk are modified by a surface shear. Statistical signatures are extracted through Fourier analysis of the simulated fields, and typical wavelengths of vortices or streaks are computed. Moreover, instantaneous fields are used to show the existence of upwelling and downwelling motions. These motions can be hindered by the presence of a large enough surface shear. This condition turns out to be necessary for the existence of streaks at the surface as well. Our investigation clarifies the dynamics of vortices in an open channel flow at moderate Reynolds number, indicating that unsteady vortex structures are indeed present, but the existence of long coherent rolls cannot be accounted for by the sole presence of shear at the surface. Numerical studies with a much longer domain and possibly at higher Reynolds numbers are needed to provide a firm answer to the question.

Numerical study on unsteady cavitation flow and vortex dynamics characteristics around the Delft Twist 11 hydrofoil

The objective of this study is to explore the unsteady cavitation characteristics and the mechanism of cavitation-vortex interaction around a twist hydrofoil. The cavitation conditions were simulated using the Partially-Averaged Navier-Stokes (PANS) method in conjunction with a homogeneous flow cavitation model. The numerical method employed in this study successfully captures the intricate shedding process of cavitation on the hydrofoil surface. Furthermore, the cavity morphology obtained at various time instants exhibits a remarkable agreement with the experimental results. The simulation results of the unsteady characteristics of cavitation shedding on the hydrofoil surface revealed that the shedding process could be divided into primary and secondary shedding phases. The primary shedding happened as a result of the re-entrant jet flow generated by the adverse pressure gradient at the cavitation tail. Notably, the secondary shedding was predominantly caused by the combined effects of the re-entrant jet and the side re-entrant jet flow. During the primary shedding process, the cavitation experienced disturbances from the side re-entrant jets, causing it to roll and be drawn upwards into a U-shape cavity structure. Subsequently, as the secondary shedding happened, the side re-entrant jets contributed to the formation of a secondary U-shape cavity at the cavitation tail. The investigation on the cavitation-vortex interaction around the hydrofoil showed a strong consistency between the distribution of vortices and cavitation. The foot of the primary U-shape vortex was attached to the hydrofoil surface, while the shedding vortex tail on both sides exhibited secondary U-shape vortex structures. The primary U-shape vortex formation resulted from the combined effects of suction and rotation generated by the side re-entrant jets and re-entrant jets on both sides of the hydrofoil. The secondary U-shape vortex was induced by secondary shedding cavitation which produced by rotational effects at the stable cavitation tail.

Three-Dimensional Unsteady Axisymmetric Viscous Beltrami Vortex Solutions to the Navier–Stokes Equations

This paper is aimed at eliciting consistency conditions for the existence of unsteady incompressible axisymmetric swirling viscous Beltrami vortices and explicitly constructing solutions that obey the conditions as well as the Navier–Stokes equations. By Beltrami flow, it is meant that vorticity, i.e., the curl of velocity, is proportional to velocity at any local point in space and time. The consistency conditions are derived for the proportionality coefficient, the velocity field and external force. The coefficient, whose dimension is of [length−1], is either constant or nonconstant. In the former case, the well-known exact nondivergent three-dimensional unsteady vortex solutions are obtained by solving the evolution equations for the stream function directly. In the latter case, the consistency conditions are given by nonlinear equations of the stream function, one of which corresponds to the Bragg–Hawthorne equation for steady inviscid flow. Solutions of a novel type are found by numerically solving the nonlinear constraint equation at a fixed time. Time dependence is recovered by taking advantage of the linearity of the evolution equation of the stream function. The proportionality coefficient is found to depend on space and time. A phenomenon of partial restoration of the broken scaling invariance is observed at short distances.

Role of unsteady tip leakage flow in acoustic resonance inception of a multistage compressor

In previous studies, a theoretical model was developed after Acoustic Resonance (AR) was experimentally detected in a four-stage compressor, and AR inception was proposed to be triggered by an unknown sound source, which is a pressure perturbation of a specific frequency with a suitable circumferential propagation speed. The present paper, which is not dedicated to the simulation of acoustic field, aims to identify the specific sound source generated by the unsteady tip leakage flow using the unsteady Computational Fluid Mechanics (CFD) approach. After a comprehensive analysis of an Unsteady Reynolds Averaged Navier-Stokes (URANS) simulation, a pressure perturbation of non-integer multiple of rotor frequency is found at the blade tip. Since the essence of the tip leakage flow is a jet flow driven by the pressure difference between two sides of blade, a simplified tip leakage flow model is adopted using Large Eddy Simulation (LES) in order to simulate the jet flow through a tip clearance. It is found that the convection velocity of shedding vortices fits the expected propagation speed of the sound source, the frequency is also close to one of the dominating frequencies in the URANS simulation, and the resultant combination frequency coincides with the experimentally measured AR frequency. Since such a simplified model successfully captures the key physical mechanisms, it is concluded that this paper provides a piece of unambiguous evidence on the role of unsteady tip leakage vortex in triggering the AR inception of the multistage compressor.

A Numerical Unsteady Analysis of a Plunging Wing

Numerical simulation of unsteady motion of wing through undisturbed fluid is formulated using Unsteady Vortex Lattice Method. A free-wake algorithm is developed using a fourth order Adam-Bashforth technique. Rankine vortex model is used to avoid numerical singularities and wake decay algorithm is used to model the viscous dissipation of the shed wake. The resulting MN x MN equations are solved for unknown Γwing using LU decomposition, where M and N are number of divisions of the wing along chord and span respectively. The aerodynamic coefficient of lift, CL, induced drag, CDi , distribution of circulation, Γ and wake geometry are calculated for unsteady plunging motion. Effect of cross-flow is studied. The results are found to be in good agreement with available literature.

High-fidelity simulation of blade vortex interaction of helicopter rotor based upon TENO scheme

Numerical simulation methods for unsteady vortex field of helicopter rotor with high resolution and low dissipation TENO8-AA primitive variables reconstruction schemes are established based on moving-embedded grid and Navier-Stokes equations. Firstly, the Targeted Essentially Non-Oscillatory (TENO) scheme are developed by employing ENO-like candidate stencil selection strategy, and the candidate stencil is adopted with optimal weight in smooth region while it is discarded completely in discontinuous region, which reduces the dissipation and dispersion errors and approaches better spectral properties. Then, the aerodynamic characteristics of Helishape-7A model rotor in Blade Vortex Interaction (BVI) state and the flowfield of Lynx rotor in hover are simulated, which validates that the blade tip vortex trajectory with larger wake age and more details of vortex can be captured by TENO8-AA scheme with only a quarter of grid points and half time comparing to WENO-JS scheme. Moreover, the simulation accuracy of thrust coefficient is improved by up to 36%. Finally, the analyses for BVI and aeroacoustic characteristics of Operational Loads Survey (OLS) rotor are conducted, and the different forms of interaction mechanism are explored, such as oblique and parallel interactions. The results indicate that TENO scheme not only ensures the resolution of simulation in discontinuous region, but also minimizes the numerical dissipation in smooth region dominated by blade tip vortex. Therefore, the acoustic pressure peak prediction error of rotor in BVI state is significantly reduced to 5.6% and 0.8% at two microphone locations, respectively.

Strongly coupled fluid–structure interaction analysis of aquatic flapping wings based on flexible multibody dynamics and the modified unsteady vortex lattice method

Because of their superior efficiency and low detectability compared to conventional submarine-shaped vehicles, bionic underwater vehicles such as Mantabot are playing increasingly important roles in ocean exploration. However, current research on manta-inspired robots is limited to structural design and pure hydrodynamics analysis of pectoral fin performance, with other aspects such as hydroelasticity and optimal design of flapping wings rarely addressed. This work presents a novel method for analyzing aquatic flapping wings by coupling flexible multibody dynamics with a modified unsteady vortex lattice method. The flexible multibody system is solved by using the absolute nodal coordinate formulation, and the conventional unsteady vortex lattice method is modified to accommodate dynamic stall. Compactly supported radial basis functions are used to transfer the hydroelastic forces and structural displacements across the interface meshes while satisfying global energy conservation, and a predictor–corrector method is used to stabilize the iteration procedure. Three different experiments are used to validate the flexible multibody dynamics solver, the modified unsteady vortex lattice solver, and the proposed fluid–structure interaction framework, respectively. Finally, the hydroelastic framework is demonstrated for a fin-like wing, and how flexibility and movement affect the flapping wing dynamics is examined. Numerical examples show that reducing the structural stiffness of the aquatic flapping wing within a certain range improves the propulsive efficiency but also reduces the thrust coefficient, and how the stiffness distribution affects the thrust and propulsive efficiency remains consistent over a range of the Strouhal number.

Wake flow control of a square cylinder via distributed jets over the rear porous surface

An active control method was used to attenuate the unsteady vortex shedding in the wake of a square cylinder. Distributed jets were applied to the rear porous surface at a Reynolds number of 1.07 × 104. The strength of the jets was measured using the dimensionless jet momentum coefficient CQ. The dynamic mode decomposition, instantaneous vorticity evolution, and time-averaged characteristics, e.g., turbulent kinetic energy, streamlines, velocity profiles and Reynolds stress distributions of the wake flow field were used to analyze the control effects. The results suggest that with increasing CQ, two jet vortices gradually form near the rear cylinder wall and compete with the vortex shedding. Consequently, the vortex shedding pattern became nearly symmetrical, whereas the jet vortices remained asymmetrical. The vortex shedding process was pushed downstream. The fluctuations in the wake, particularly near cylindrical walls, were significantly suppressed. Thus, this scheme was successful, indicating potential for drag reduction and energy efficiency. Better control effects were associated with higher CQ in the present study.

Numerical research on drag-reduction characteristics of a body of revolution based on periodic forcing

Effective drag-reduction technology is important for enhancing navigation speed, extending endurance, and enabling efficient energy usage of underwater vehicles. In this study, we investigated the effectiveness of a body of revolution to influence the turbulent boundary-layer properties by performing numerical simulations and varying a periodic sinusoidal force in a series of annular slots. The selected control parameters included the normalized periodic force amplitude and periodic force frequency; the effects of these parameters on drag reduction have not been demonstrated in previous studies. The surface pressure and velocity analyses revealed that frictional drag accounted for 71.7% of the total drag reduction, and it was the dominant contributor to the drag-reduction effect. Unsteady vortices were generated in the boundary layer, and a retarded fluid region was created on the surface. A clockwise vortex was generated downstream of the annular slots during blowing, reducing the pressure drag on the surface of the revolution body. The clockwise vortex weakened when suction was applied. The results of this research might provide ideas for solving the drag-reduction problem in the design of revolving-body-type underwater vehicles.

Unsteady vortex shedding dynamics behind a circular cylinder in very shallow free-surface flows

The turbulent wake generated by a horizontal circular cylinder in free-surface flows of increasing shallowness with submergence-to-diameter ratios between 0.5 and 2.1 are investigated using large-eddy simulation. At Froude number (Fr) = 0.26, the free-surface deformation is small with little influence on the wake, whereas at Fr = 0.53 there is a drop in the free-surface downstream of the cylinder that impacts the coherence of the vortex shedding. Irrespective to the relative submergence, the close location of the cylinder to the bottom wall generates an asymmetric von-Kármán vortex street. Proper Orthogonal Decomposition (POD) is used to analyse the spatio-temporal coherence of the turbulent structures shed in the cylinder wake. The spatial patterns of the first two POD modes, those containing the most energy, depict the von-Kármán vortices. As Fr increases, the energy content of the first pair of POD modes decreases from 56% at Fr = 0.26 to 26.8% at Fr = 0.53, as large-scale vortices lose coherence more rapidly with shallower conditions. This energy redistribution leads to the smaller flow structures to contain a relatively higher energy when Fr is larger. The frequency of the dominating vortex shedding determined from the spectra of the POD temporal coefficients unveils that the first two coefficients feature a dominant peak at the von-Kármán vortex shedding frequency. At Fr< 0.45, the reconstructed flow field using the first 20 POD modes agrees well with the instantaneous velocities from LES, whereas free-surface effects on the wake dynamics at increasing Fr requires more POD modes to reconstruct the flow field with reduced error.

Experimental study of the turbulent flow in the wake of a horizontal axis tidal current turbine

A scaled-model of a horizontal axis tidal current turbine (HATCT) is tested in the CNR-INM Circulating Water Channel. The experiments are designed to establish in the first place the performances of the turbine at different working settings. The second goal is to investigate the hydrodynamics generated by the turbine in the near wake using the Particle Image Velocimetry (PIV) technique. For this purpose, velocity measurements are performed in a longitudinal plane and phase-locked to the rotor angle in order to resolve the wake structure at different working regimes. The analysis of the axial and radial velocity fields reveals the flow features of the slipstream, as well as its expansion and dependence on the turbine operating parameters. Analysis of the non-diagonal terms of the Reynolds stress tensor provides insight into the onset of tip vortex pairing and of vortex instabilities. Furthermore the separate contributions of transport, production and dissipation to the turbulent kinetic energy in the wake field are discussed in detail. The vortex unsteadiness is captured and correlated with the evolution of the kinetic energy transport and production terms. Understanding these phenomenologies is an important step to develop computational tools able to estimate the radiated noise or the potential impact of turbulence on performances of further rotors placed in the wake, as in an array of tidal turbines.

Deep learning predictions of unsteady aerodynamic loads on an airfoil model pitched over the entire operating range

For the design and certification of wind turbines, it is essential to provide fast and accurate unsteady aerodynamic load prediction models for the whole operational range of angle of attack, up to 180° for vertical-axis and 90° for horizontal-axis wind turbines. This work describes a computationally efficient unsteady forces prediction model based on a deep learning approach, namely the bidirectional long short-term memory (BiLSTM) algorithm, for an airfoil pitched over the full operational range of angles of attack up to 180°. No model has been developed to capture the unsteady forces at high angles of attack. Novel features based on operating conditions and the steady polars of the airfoil are used as inputs for the BiLSTM model. Direct measurements of steady and unsteady forces on a NACA 0021 airfoil model were conducted at reduced frequencies up to 0.075 and a Reynolds number of 120 000 in an open-jet wind tunnel for model learning and testing. The unsteady forces vary significantly from the steady values at high pitching amplitudes and post-stall angles, which, if not accounted for when simulating wind turbine performance, would result in inaccurate predictions. Furthermore, measurements revealed the effect of unsteady vorticity development and shedding on aerodynamic forces under forward and reverse flow conditions. The BiLSTM model is capable of capturing the underlying physics of unsteady aerodynamic forces under extreme operating conditions.

Evolution of unsteady vortex structures in the tip region of an axial compressor rotor

The evolution of unsteady vortex structures in the tip region of an axial compressor rotor is investigated based on delayed detached eddy simulation. The vortex structures are identified by the LTcri method, and the velocity fields are visualized by the particle tracing method. The results show that the evolution of the tip leakage vortex (TLV) can be divided into three phases: the generation phase, the development phase, and the dissipation phase. The unsteadiness of the flow field mainly appears in the dissipation phase as a consequence of the unsteady secondary tip leakage. There are three primary unsteady vortex structures caused by the tip leakage flow (TLF), and these vortex structures are related to each other as a feedback loop. The intermittent formation of the vortex ropes leads to the breakdown of the TLV and thus results in the roll-up of the backflow vortex (BFV) due to the radial velocity gradient. The secondary leakage of the BFV locally enhances the TLF jet and affects the formation of the vortex ropes in turn. This feedback loop causes the unsteady behavior of the TLF and has great impacts on the performance and stability of the compressors.

인공지능 기법과 차수 저감 모델을 이용한 익형 유동장 예측

Aerodynamics design optimization with high accuracy and reliability requires huge computational cost because of numerous repetition of CFD. The huge computational cost of CFD based aerodynamics design optimization is the biggest obstacle of practical application. In this research, artificial intelligence techniques and reduced order model are utilized to reduce the computational cost for predicting airfoil flow field. Various airfoil flow fields, including various flow conditions, airfoil shapes, and unsteady vortex shedding, are trained and tested with POD, GPR, CNN, and LSTM methods. As a result, the POD-GPR method showed good accuracy for the dataset with high linearity. On the other hand, the conditional U-net method showed good performance for the dataset with high nonlinearity. In addition, the unsteady flow field is trained and tested with POD-LSTM and conditional U-net method for extrapolation and interpolation of the flow field, respectively. In conclusion, the computational cost for predicting the airfoil flow field is reduced by order of magnitudes with acceptable errors for design optimization.

Parameter Optimization of Foldable Flapping-Wing Mechanism for Maximum Lift

AbstractA lot of flapping-wing mechanisms have been proposed to mimic the flight characteristics of biological flyers. However, it is difficult to find studies that consider the unsteady aerodynamics in the design of the flapping-wing mechanisms. This paper presents a systematic approach to optimize the design parameters of a foldable flapping-wing mechanism (FFWM) with a proper aerodynamics model. For the kinematic model, the eight design parameters are defined to determine the reference configuration of the FFWM. The geometrical constraints of each design parameter are derived, and the kinematic analysis is conducted using the plane vector analysis method. The aerodynamic simulation using an unsteady vortex lattice method is performed to compute the aerodynamic loads induced by the flapping motion. An optimization problem is formulated to search for the optimal design parameters that maximize the average lift force considering the required power corresponding to the aerodynamic torques. The parameter optimization problem is solved for three different length ratios of the outer wing to the inner wing using a genetic algorithm. The optimization results show that increasing the outer wing length can cause a significant loss in the required power. The optimal design parameters found by the proposed approach allow the FFWM to generate maximum lift force with appropriate consideration of the required power.

Experimental investigation on cylinder noise and its reductions by identifying aerodynamic sound sources in flow fields

Through anechoic wind tunnel tests, this study comprehensively investigates the noise and drag reductions on a circular cylinder with dimples. Dimples built on a surface pattern fabric cover the cylinder surface as one of the passive flow control methods. The force, noise, and flow field measurements are performed at diameter-based Reynolds numbers ranging from 3×104 to 1.3×105, covering the sub-critical, critical, and supercritical regimes. The force and noise measurement results show that dimple fabric simultaneously reduces noise and drag in the critical regime. The changes in flow structures were characterized by the Time-resolved Particle Image Velocimetry (TR-PIV) measurements. Based on the vortex sound theory, the flow analysis shows that the dominant sound sources are found to be concentrated near the cylinder surface, which is caused by the unsteady vortex motions near the separation locations during the process of vortex shedding. The cross-correlation between the synchronized TR-PIV and microphone measurements further supports the conclusions. Moreover, the cylinder noise reductions controlled by the dimples are directly associated with the reduced sound sources in the critical and supercritical regimes, corresponding to the reduced strength of the vortex shedding.

Research on the drag reduction characteristics and mechanism of a cylinder covered with porous media

As an effective drag reduction control method, porous media have attracted extensive attention in various engineering fields. In this paper, the large eddy simulation method is used to study the flow problem around a cylinder with and without porous media covering at subcritical Reynolds numbers. The drag reduction characteristics and the mechanism of a cylinder covered with porous media were studied. The results of the aerodynamic drag coefficient show that when the Reynolds number is 5.6 × 104 and when the porous media are arranged on the leeward side of the cylinder at an azimuth angle of 270°, the drag reduction rate is the largest, reaching 8.53%. The flow field results indicate that after porous media covering, the large-scale wake vortex shedding was effectively suppressed, the vortex shedding frequency was reduced, the vortexes in the wake area became thinner and longer, and the vorticity decreased. It is confirmed that porous media can stabilize the wake shear layer and suppress the unsteady vortex motion in the wake. Meanwhile, airflow can penetrate the porous media, leading to velocity slip at the interface between the porous media and the airflow, making the free shear layer more stable, and strengthen the wake vortex.