Vortex-Induced Vibrations of Two Cylinders in Tandem Arrangement at Low Reynolds Number

The objective of this study is to apply numerical methods to investigate the effects of the spacing on the vortex shedding of two elastically mounted cylinders in tandem arrangement. 2-D computational simulations are carried out at low Reynolds number of 100. The study utilized a commercial software ANSYS FLUENT to carry out the computational simulations. First, a number of test cases, including flows past one and two cylinders with predetermined motions, are simulated to evaluate the solver’s accuracy. The vortex shedding and hydrodynamic forces from the current findings and those from literature show good agreement, which supports the accuracy of the current solver. Multiple simulations were the performed for flow around two elastically mounted cylinders in tandem arrangement. The subsequent relative flow fields demonstrated that for a certain range of spacing, vortex shedding was completely eliminated while it remained completely unaffected or partially reduced for other ranges of spacing. This suggests that the spacing between the two cylinders can be utilized as a passive method of suppressing vortex shedding.

Computational aerodynamics of low Reynolds number plunging,pitching and flexible wings for MAV applications

Micro air vehicles （MAV＇s） have the potential to revolutionize our sensing and information gathering capabilities in environmental monitoring and homeland security areas. Due to the MAV＇s＇ small size, flight regime, and modes of operation, significant scientific advancement will be needed to create this revolutionary capability. Aerodynamics, structural dynamics, and flight dynamics of natural flyers intersects with some of the richest problems in MAV＇s, inclu- ding massively unsteady three-dimensional separation, transition in boundary layers and shear layers, vortical flows and bluff body flows, unsteady flight environment, aeroelasticity, and nonlinear and adaptive control are just a few examples. A challenge is that the scaling of both fluid dynamics and structural dynamics between smaller natural flyer and practical flying hardware/lab experiment （larger dimension） is fundamentally difficult. In this paper, we offer an overview of the challenges and issues, along with sample results illustrating some of the efforts made from a computational modeling angle.

A STUDY ON THE MECHANISM OF HIGH-LIFT GENERATION BY AN AIRFOIL IN UNSTEADY MOTION AT LOW REYNOLDS NUMBER

The aerodynamic force and flow structure of NACA 0012 airfoil performing an unsteady motion at low Reynolds number (Re = 100) are calculated by solving Navier-Stokes equations. The motion consists of three parts: the first translation, rotation and the second translation in the direction opposite to the first. The rotation and the second translation in this motion are expected to represent the rotation and translation of the wing-section of a hovering insect. The flow structure is used in combination with the theory of vorticity dynamics to explain the generation of unsteady aerodynamic force in the motion. During the rotation, due to the creation of strong vortices in short time, large aerodynamic force is produced and the force is almost normal to the airfoil chord. During the second translation, large lift coefficient can be maintained for certain time period and (C) over bar (L), the lift coefficient averaged over four chord lengths of travel, is larger than 2 (the corresponding steady-state lift coefficient is only 0.9). The large lift coefficient is due to two effects. The first is the delayed shedding of the stall vortex. The second is that the vortices created during the airfoil rotation and in the near wake left by previous translation form a short 'vortex street' in front of the airfoil and the 'vortex street' induces a 'wind'; against this 'wind' the airfoil translates, increasing its relative speed. The above results provide insights to the understanding of the mechanism of high-lift generation by a hovering insect.

Effect of Spanwise Flexibility on Propulsion Performance of a Flapping Hydrofoil at Low Reynolds Number

Spanwise flexibility is a key factor influencing propulsion performance of pectoral foils. Performances of bionic fish with oscillating pectoral foils can be enhanced by properly selecting the spanwise flexibility. The influence law of spanwise flexibility on thrust generation and propulsion efficiency of a rectangular hydro-foil is discussed. Series foils constructed by the two-component silicon rubber are developed. NACA0015 shape of chordwise cross-section is employed. The foils are strengthened by fin rays of different rigidity to realize variant spanwise rigidity and almost the same chordwise flexibility. Experiments on a towing platform developed are carried out at low Reynolds numbers of 10 000, 15 000, and 20 000 and Strouhal numbers from 0.1 to 1. The following experimental results are achieved: (1) The average forward thrust increases with the St number increased; (2) Certain degree of spanwise flexibility is beneficial to the forward thrust generation, but the thrust gap is not large for the fins of different spanwise rigidity; (3) The fin of the maximal spanwise flexibility owns the highest propulsion efficiency; (4) Effect of the Reynolds number on the propulsion efficiency is significant. The experimental results can be utilized as a reference in deciding the spanwise flexibility of bionic pectoral fins in designing of robotic fish prototype propelled by flapping-wing.

Wave-current interaction with a vertical square cylinder at different Reynolds numbers

Large eddy simulation is performed to study three-dimensional wave-current interaction with a square cylinder at different Reynolds numbers, ranging from 1,000 to 600,000. The Keulegan-Carpenter number is relevantly a constant of 0.6 for all cases. The Strouhal number, the mean and the RMS values of the effective drag coefficient in the streamwise and transverse directions are computed for various Reynolds numbers, and the velocity of a rep- resentative point in the turbulent zone is simulated to find the turbulent feature. It is found that the wave-current interaction should be considered as three-dimensional flow when the Reynolds number is high; under wave-current effect, there exists a critical Reynolds number, and when the Reynolds number is smaller than the critical one, current effect on wave can be nearly neglected; conversely, with the Reynolds number increasing, wave-currentstructure interaction is sensitive to the Reynolds number.

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

An Investigation into the Effects of the Reynolds Number on High-Speed Trains Using a Low Temperature Wind Tunnel Test Facility

A series of tests have been conducted using a Cryogenic Wind Tunnel to study the effect of Reynolds number(Re)on the aerodynamic force and surface pressure experienced by a high speed train.The test Reynolds number has been varied from 1 million to 10 million,which is the highest Reynolds number a wind tunnel has ever achieved for a train test.According to our results,the drag coefficient of the leading car decreases with higher Reynolds number for yaw angles up to 30º.The drag force coefficient drops about 0.06 when Re is raised from 1 million to 10 million.The side force is caused by the high pressure at the windward side and the low pressure generated by the vortex at the lee side.Both pressure distributions are not appreciably affected by Reynolds number changes at yaw angles up to 30°.The lift force coefficient increases with higher Re,though the change is small.At a yaw angle of zero the down force coefficient is reduced by a scale factor of about 0.03 when the Reynolds number is raised over the considered range.At higher yaw angles the lift force coefficient is reduced about 0.1.Similar to the side force coefficient,the rolling moment coefficient does not change much with Re.The magnitude of the pitching moment coefficient increases with higher Re.This indicates that the load on the front bogie is higher at higher Reynolds numbers.The yawing moment coefficient increases with Re.This effect is more evident at higher yaw angles.The yawing moment coefficient increases by about 6%when Re is raised from 1 million to 10 million.The influence of Re on the rolling moment coefficient around the leeward rail is relatively smaller.It increases by about 2%over the considered range of Re.

A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number

It is well known that the Reynolds number has a significant effect on the vortex-induced vibrations(VIV) of cylinders. In this paper, a novel in-line(IL) and cross-flow(CF) coupling VIV prediction model for circular cylinders has been proposed, in which the influence of the Reynolds number was comprehensively considered. The Strouhal number linked with the vortex shedding frequency was calculated through a function of the Reynolds number. The coefficient of the mean drag force was fitted as a new piecewise function of the Reynolds number, and its amplification resulted from the CF VIV was also taken into account. The oscillating drag and lift forces were modelled with classical van der Pol wake oscillators and their empirical parameters were determined based on the lock-in boundaries and the peak-amplitude formulas. A new peak-amplitude formula for the IL VIV was developed under the resonance condition with respect to the mass-damping ratio and the Reynolds number. When compared with the results from the experiments and some other prediction models, the present model could give good estimations on the vibration amplitudes and frequencies of the VIV both for elastically-mounted rigid and long flexible cylinders. The present model considering the influence of the Reynolds number could generally provide better results than that neglecting the effect of the Reynolds number.

Numerical study on hydrodynamic characteristics of spherical bubble contaminated by surfactants under higher Reynolds numbers

It is of significance to investigate deeply the hydrodynamic featu res of the bubble co ntaminated by impurities in view of the fact that the industrial liquid is difficult to keep absolutely pure.On the basis of the finite volume method,the bubble interface contaminated by the surfactant(1-pentanol)is achieved through solving the concentration transport equations in liquid and along the bubble interface,and solving the absorption and desorption equation at the bubble interface.And the three-dimensional momentum equation is solved at the same time.It is investigated in detail on the influence of interfacial contamination degrees(described with the cap angleθ)on hydrodynamic characteristics of the spherical bubble when the bubble Reynolds number(Re)is larger than 200.Theθis realized by changing the surfactant concentration(C_(0)) in liquid.The present results show that the hydrodynamic characteristics,such as interfacial concentration,interfacial shear stress,interfacial velocity and wake flow,are related to both Re and C_(0) for the contaminated bubble.When C_(0) is relatively low in liquid(i.e.,the contamination degree of the bubble interface is relatively slight),the hydrodynamic characteristics of the bubble can still keep the 2 D features even if Re>200.The decrease ofθor the increase of Re can promote the appearance of the unsteady wake flow.For the present investigation,when Re>200 andθ≤60°,the hydrodynamic characteristics of the bubble show the 3D phenomena,which indicates that axisymmetric model is no longer valid.

Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows

A scale-similarity model of a two-point two-time Lagrangian velocity correlation(LVC) was originally developed for the relative dispersion of tracer particles in isotropic turbulent flows(HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence. Physical Review E, 80, 066313(2009)). The model can be expressed as a two-point Eulerian space correlation and the dispersion velocity V. The dispersion velocity denotes the rate at which one moving particle departs from another fixed particle. This paper numerically validates the robustness of the scale-similarity model at high Taylor micro-scale Reynolds numbers up to 373, which are much higher than the original values(R_λ = 66, 102). The effect of the Reynolds number on the dispersion velocity in the scale-similarity model is carefully investigated. The results show that the scale-similarity model is more accurate at higher Reynolds numbers because the two-point Lagrangian velocity correlations with different initial spatial separations collapse into a universal form compared with a combination of the initial separation and the temporal separation via the dispersion velocity.Moreover, the dispersion velocity V normalized by the Kolmogorov velocity V_η ≡ η/τ_η in which η and τ_η are the Kolmogorov space and time scales, respectively, scales with the Reynolds number R_λ as V/V_η ∝ R_λ^(1.39) obtained from the numerical data.

A new bionic MAV's flapping motion based on fruit fly hovering at low Reynolds number

On the basis of the studies on the high unsteady aerodynamic mechanisms of the fruit fly hovering the aerodynamic advantages and disadvantages of the fruit fly flapping motion were analyzed. A new bionic flapping motion was proposed to weaken the disadvantages and maintain the advantages, it may be used in the designing and manufacturing of the micro air vehicles （MAV＇s）. The translation of the new bionic flapping motion is the same as that of fruit fly flapping motion. However, the rotation of the new bionic flapping motion is different. It is not a pitching-up rotation as the fruit fly flapping motion, but a pitching-down rota- tion at the beginning and the end of a stroke. The numerical method of 3rd-order Roe scheme developed by Rogers was used to study these questions. The correctness of the numerical method and the computational program was justified by comparing the present CFD results of the fruit fly flapping motion in three modes, i.e., the advanced mode, the symmetrical mode and the delayed mode, with Dickinson＇s experimental results. They agreed with each other very well. Subsequently, the aerodynamic characteristics of the new bionic flapping motion in three modes were also numerically simulated, and were compared with those of the fruit fly flap- ping. The conclusions could be drawn that the high unsteady lift mechanism of the fruit fly hovering is also effectively utilized by this new bionic flapping. Compared with the fruit fly flapping, the unsteady drag of the new flapping decreases very much and the ratio of lift to drag increases greatly. And the great discrepancies among the mean lifts of three flapping modes of the fruit fly hovering are effectively smoothed in the new flapping. On the other hand, this new bionic flapping motion should be realized more easily. Finally, it must be pointed out that the above conclusions were just drawn for the hovering flapping motion. And the aerodynamic characteristics of the new bionic flapping motion in forward flight are going to be studied in the next step.

Numerical study on the hydrodynamics of agglomerates at intermediate Reynolds numbers

The flow pattern and hydrodynamics of a heterogeneous permeable agglomerate in a uniform upward flow at intermediate Reynolds numbers(1–40)are analyzed from three-dimensional(3 D)computational fluid dynamics simulations.Different from the homogeneous or stepwise-varying permeability models used in previous papers,a continuously radially varying permeability model is used in the present study.The effects of two dimensionless parameters,the Reynolds number and the permeability ratio,on the flow field and the hydrodynamics were investigated in detail.The results reveal that unlike the solid sphere,a small recirculating wake initially forms inside the agglomerate.The critical Reynolds number for the formation of the recirculating wake is lower than that of the solid sphere and it decreases with the increase of permeability ratio.A correlation of drag coefficient as a function of the Reynolds number and permeability ratio is proposed.Comparisons of drag coefficients obtained by different permeability models show that at intermediate Reynolds numbers(1–40),the effect of radially varying permeability on the drag coefficient must be considered.

Critical transition Reynolds number for plane channel flow

The determination of the critical transition Reynolds number is of practical importance for some engineering problems. However, it is not available with the current theoretical method, and has to rely on experiments. For supersonic/hypersonic boundary layer flows, the experimental method for determination is not feasible either. Therefore, in this paper, a numerical method for the determination of the critical transition Reynolds number for an incompressible plane channel flow is proposed. It is basically aimed to test the feasibility of the method. The proposed method is extended to determine the critical Reynolds number of the supersonic/hypersonic boundary layer flow in the subsequent papers.

Control of mean and fluctuating forces on a circular cylinder at high Reynolds numbers

A narrow strip is used to control mean and fluctuating forces on a circular cylinder at Reynolds numbers from 2.0 ×10^4 to 1.0 ×^ 10^5. The axes of the strip and cylinder are parallel. The control parameters are strip width ratio and strip position characterized by angle of attack and distance from the cylinder. Wind tunnel tests show that the vortex shedding from both sides of the cylinder can be suppressed, and mean drag and fluctuating lift on the cylinder can be reduced if the strip is installed in an effective zone downstream of the cylinder. A phenomenon of mono-side vortex shedding is found. The strip-induced local changes of velocity profiles in the near wake of the cylinder are measured, and the relation between base suction and peak value in the power spectrum of fluctuating lift is studied. The control mechanism is then discussed from different points of view.

Spatio-temporal instability of two-layer liquid film at small Reynolds numbers

The onset of instability with respect to the spatio-temporally growing disturbance in a viscosity-stratified two-layer liquid film flow is analyzed. The known results obtained from the temporal theory of instability show that the flow is unstable in the limit of zero Reynolds numbers. The present theory predicts the neutral stability in the same limit. The discrepancy is explained. Based on the mechanical energy equation, a new mechanism of instability is found. The new mechanism is associated with the convective nature of the disturbance that is not Galilei invariant.

OSCILLATION PHENOMENA IN FAR FIELD REGION OF PLANE JETS AT LOW REYNOLDS NUMBERS

Oscillation phenomena in far field region of plane jets are studied by lattice Boltzmann method over a range of Reynolds numbers ( Re ) from 16to 65.Numerical results show that the instantaneous centerline velocities show periodic oscillation behavior in far field region when Re>38.In contrast , the periodic behavior is invisible in corresponding flow field when Re≤38.For the cases of Re≤38 , the exchange of momentum due to straining motion gradually dominates the downstream flow filed , which qualitatively suggests the possibility of jet instability.

Influences of initial velocity,diameter and Reynolds number on a circular turbulent air/air jet

This paper assesses the suitability of the inflow Reynolds number defined by Reo -- UoD/v （here Uo and D are respectively the initial jet velocity and diameter while v is kinematic viscosity） for a round air/air jet. Specifically an experimental investigation is performed for the influences of Uo, D and Reo on the mean-velocity decay and spread coefficients （Ku, Kr） in the far field of a circular air jet into air from a smoothly contracting nozzle. Present measurements agree well with those previously obtained under similar inflow conditions. The relations Ku ∝ Uo and Kr ∝ 1/Uo for Uo 〈 5 m/s appear to work, while each coefficient approaches asymptotically to a constant for Uo 〉 6 m/s, regardless of the magnitudes of Reo and D. It is revealed that Reo may not be an appropriate dimensionless parameter to characterize the entire flow of a free air/air jet. This paper is the first paper that has challenged the suitability of Reo for turbulent free jets.

ON THE EFFECT OF REYNOLDS NUMBER ON VON KRMN'S CONSTANT

Fully developed turbulence measurements in pipe flow were made in the Reynolds number ranging from 10 x 10~3 to 350 x 10~3 with a hot-wire anemometer and a Pitot tube.Comparisons were made with the experimental results of previous work.The mean velocity profile and the turbulent intensity in the experiments in- dicate that for the mean velocity profile,in the fully developed turbulent pipe flow, von Kármán's constant κ is a function of Reynolds number,i.e.κ increases slowly with the Reynolds number.The empirical relationships could not be considered to be accurate enough to describe the fully developed turbulence over the whole Reynolds number range in pipe flow.

On two distinct Reynolds number regimes of a turbulent square jet

The effects of Reynolds number on both large-scale and small-scale turbulence properties are investigated in a square jet issuing from a square pipe. The detailed velocity fields were measured at five different exit Reynolds numbers of 8 × 10^3 〈 Re 〈 5 × 10^4. It is found that both large-scale properties （e.g,, rates of mean velocity decay and spread） and small-scale properties （e.g., the dimensionless dissipation rate constant A = εL/（u^2）^3/2） are dependent on Re for Re ≤ 3 ×10^4 or Reλ ≤ 190, but virtually become Re-independent with increasing Re or Reλ. In addition, for Reλ 〉 190, the value ofA = εL/（u^2）^3/2 in the present square jet converges to 0.5, which is consistent with the observation in direct numerical simulations of box turbulence, but lower than that in circular jet, plate wake flows, and grid turbulence. The discrepancies in critical Reynolds number and A = εL/（u^2）^3/2 among different turbulent flows most likely result from the flow type and initial conditions.