FLOW FIELD ANALYSES OF PLANE JET AT LOW REYNOLDS NUMBERS USING LATTICE BOLTZMANN METHOD

A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The results show that the mean centerline velocity decays as x-1/3 and the jet spreads as x2/3 in the self-similar region, which are consistent with the theoretical predictions and the experimental data. The time histories and PSD analyses of the instantaneous centerline velocities indicate the periodic behavior and the interaction between periodic components of velocities should not be neglected in the far field region, although it is invisible in the near field region.

NUMERICAL SIMULATION OF UNSTEADY FLOW AROUND A CIRCULAR CYLINDER AT HIGH REYNOLDS NUMBERS

A Lagrangian-Eulerian hybrid scheme to solve unsteady N-S equation in two-dimensional incompressible fluid at high Reynolds numbers is presented in this paper. A random walk is imposed to simulate the viscous diffusion, the vortex-in-cell method is used to obtain the convection velocity, and nascent vortices are created on a cylinder to satisfy the zero-slip condition. The impulsively started flow around a circular cylinder and the separation induced by a pair of incident vortices symmetrically approaching a circular cylinder have been successfully simulated by the hybrid scheme. The impulsively started flow from rest has been computed at Reynolds numbers 3000 and 9500. Comparisons are made with those results of finite-difference method, vortex method and flow visualization. Agreement is good. The particular attention has been paid to the evolutions of flow pattern. A topological analysis has been proposed in the region of the near wake. The bulge, isolated secondary vortex, a pair of secondary vortices, ' forewake phenomenon and other patterns are simulated numerically. The separation induced by a pair of incident vortices approaching a circular cylinder has been investigated by using the same scheme. The rebounding phenomenon of the incident vortex is observed and is attributed to the effect of the secondary vortex. In particular, we have found that a tertiary vortex can be formed near the surface; this phenomenon has been verified by flow visualization reported recently.

Determination of Strouhal Numbers at High Reynolds Numbers

Leeward of natural elevations, like mountains and hills, the air flow becomes turbulent and often times damaging and hazardous to aviation and downwind populations. There is currently a trend for massive construction projects, the result of which are megastructures that behave similarly to these natural elevations and create analogous turbulence conditions. Examples five mega projects were analyzed, and it was estimated that the Reynolds number variation in these buildings, is from 6.10g and 7.109, for winds between 10 m/s and 50 m/s. In this work, the authors present a first numerical approach to this phenomenon by calculating the Strouhal numbers induced by winds blowing against large-volume bodies, in the range of high Reynolds numbers. For this study, satellite images depicting von K^irm^n cloud streets leeward of isolated islands were used. The methodology employed was based on a satellite image where streets watch von K^rnfin vortex, from NOAA-ARL （National Oceanic and Atmospheric Administration-Air Resource Laboratory） prognosis was obtained for a grid point near the island, then determined the inversion layer and meteorological data （wind, temperature and pressure）, was measured from the satellite image the distances separating the vortices to calculate the period, the Reynolds number and Strouhal. The studied results of the cases are displayed graphically, where it is possible to observe a data dispersion as well as a rising trend of the Strouhal number as the Reynolds number increases.

Unsteady Numerical Simulation of Flow around 2-D Circular Cylinder for High Reynolds Numbers

In this paper, 2-D computational analyses were conducted for unsteady high Reynolds number flows around a smooth circular cylinder in the supercritical and upper-transition flow regimes, i.e. 8.21×104〈Re〈1.54×106. The calculations were performed by means of solving the 2-D Unsteady Reynolds-Averaged Navier-Stokes （URANS） equations with a k-ε turbulence model. The calculated results, produced flow structure drag and lift coefficients, as well as Strouhal numbers. The findings were in good agreement with previous published data, which also supplied us with a good understanding of the flow across cylinders of different high Reynolds numbers. Meanwhile, an effective measure was presented to control the lift force on a cylinder, which points the way to decrease the vortex induced vibration of marine structure in future.

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.

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.

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.

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 16 to 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 mo- tion gradually dominates the downstream flow filed, which qualitatively suggests the possibility of iet instability.

Study of poly-disperse aerosols deposition in turbulent flow with different Reynolds numbers

The turbulent deposition mechanism is one of the main mechanisms of aerosol deposition in nuclear power plant tubes.An experimental study of poly-disperse aerosol deposition in a horizontal tube is conducted,where the nominal Reynolds number(Re)is in a range of 3600–200,000.The aerosol deposition velocity first increases and then decreases with the increase of Res,and at high Re,particle rebound occurs during aerosol deposition in the tube.When the Re is low,the aerosol deposition velocity increases with the increase of aerosol diameter.When the Re is greater than 60,000,the deposition velocity first increases and then decreases with the increase of aerosol diameter due to particle surface rebound.A new aerosol deposition model has been developed by establishing the energy conservation equation of the rebounded particles in the viscous sublayer.The calculated results of the new model are in good agreement with these experimental results,and the error between the aerosol deposition velocity calculated by the model and experimental results is between−60%and 150%.

Wavelet solutions of Burgers' equation with high Reynolds numbers

A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.

Direct numerical simulation of turbulent flow over backward-facing at high Reynolds numbers

Direct numerical simulation(DNS) was performed for the first time to study the flow over a backward-facing step at a high Reynolds number on a coarse grid.The flow over backward-facing step is the typical turbulent flow controlled by large eddy,in which the effect of small eddy could be negligible as an approximation.The grid dimension could easily satisfy the resolution requirement to describe the characteristics of a large eddy flow.Therefore,direct numerical simulation of N-S equations to obtain the turbulent flow field on the coarse grid could be realized.Numerical simulation of a two-dimensional flow over a backward-facing step at a Reynolds number Re=44000 was conducted using Euler-Lagrange finite element scheme based on the efficient operator-splitting method(OSFEM).The flow field was descretized by triangle meshes with 16669 nodes.The overall computational time only took 150 min on a PC.Both the characteristics of time-averaged and instantaneous turbulent flow were simultaneously obtained.The analysis showed that the calculated results were in good agreement with the test data.Hence,the DNS approach could become the reality to solve the complex turbulent flow with high Reynolds numbers in practical engineering.

Study on effects of thickness on airfoil-stall at low Reynolds numbers by cusp-catastrophic model based on GA(W)-1 airfoil

The phenomena of an airfoil stall present the behaviors of catastrophe and hysteresis at low Reynolds numbers.Numerical simulation results of two-dimensional airfoil GA(W)-1 show that the width of the hysteresis loop of airfoil stall will gradually decrease and even disappear with the decrease of thickness ratio.These nonlinear characteristics are in accordance with the topological features of the cusp catastrophic model.According to the topological invariant principle,a novel topological mapping method is developed to establish the mapping relationship between cusp catastrophic model and stall characteristics of the airfoil,then the effect of thickness ratio on airfoil stall is successfully described quantitatively by cusp catastrophic model.Further,based on the established topological mapping relationship,combined with the mean flow field of the airfoil stall,potential function approach of cusp catastrophic model is first introduced to interpret the catastrophe and hysteresis of the airfoil stall,and it is found that as the thickness ratio decreases,the system’s maximal potential energy gradually disappears,and the short separation bubble at the leading edge of the airfoil changes to long separation bubble,so the airfoil stall changes from a bistable system to a monostable system.

A Comparison of Experimental and Numerical Studies Performed on a Low-Pressure Turbine Blade Cascade at High-Speed Conditions, Low Reynolds Numbers and Various Turbulence Intensities

This paper focuses on a comparison of experimental and numerical investigations performed on a low-pressure mid-loaded turbine blade at operating conditions comprised of a wide range of Math numbers （from 0.5 - 1.1）, Reynolds numbers （from 0.4e＋5 - 3.0e＋5）, flow incidence （-15 - 15 degrees） and three levels of free-stream tur- bulence intensities （2, 5 and 10%）. The experimental part of the work was performed in a high-speed linear cas- cade wind tunnel. The increased levels of turbulence were achieved by a passive grid placed at the cascade inlet. A two-dimensional flow field at the center of the blade was traversed pitch-wise upstream and downstream the cascade by means of a five-bole probe and a needle pressure probe, respectively. The blade loading was measured using the surface pressure taps evenly deployed at the blade mid-span along the suction and the pressure side. The inlet turbulence was investigated using the constant temperature anemometer technique with a dual sensor probe. Experimentally evaluated values of turbulent kinetic energy and its dissipation rate were then used as inputs for the numerical simulations. An in-house code based on a system of the Favre-averaged Navier-Stokes equation closed by a two-equation k-co turbulence model was adopted for the predictions. The code utilizes an algebraic model of bypass transition valid both for attached as for separated flows taking in account the effect of free-stream turbulence and pressure gradient. The resulting comparison was carried out in terms of the kinetic en- ergy loss coefficient, distributions of downstream wakes and blade velocity. Additionally a flow visualization was performed by means of the Schlieren technique in order to provide a further understanding of the studied phe- nomena. A few selected cases with a particular interest in the attached and separated flow transition are compared and discussed.

Characteristics of settling of dilute suspension of particles with different density at high Reynolds numbers

Dilute suspension of particles with same density and size develops clusters when settle at high Reynolds number(≥250).It is due to particles entrapment in the wakes produced by upstream particles.In this work,this phenomenon is studied for suspension having particles with different densities by numerical simulations.The particle-fluid interactions are modelled using immersed boundary method and inter-particle collisions are modelled using discrete element method.In simulations,settling Reynolds number is always kept above 250 and the suspension solid volume fraction is nearly 0.1 percent.Two particle density ratios(i.e.density of heavy particles to lighter particles)equal to 4:1 and 2:1 and particles with same density are studied.For each density ratio,the percentage volume fraction of each particle density is nearly varied from 0.8 to 0.2.Settling characteristics such as microstructures of settling particle,average settling velocity and velocity fluctuations of settling particles are studied.Simulations show that for different density particles settling characteristics of suspension is largely dominated by heavy particles.At the end of paper,the underlying physics is explained for the anomalies observed in simulation.

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.

Fluid flow and heat transfer characteristics of spiral coiled tube: Effects of Reynolds number and curvature ratio

Numerical analysis was performed to investigate flow and heat transfer characteristics in spiral coiled tube heat exchanger. Radius of curvature of the spiral coiled tube was gradually increased as total rotating angle reached 12n. As the varying radius of curvature became a dominant flow parameter, three-dimensional flow analysis was performed to this flow together with different Reynolds numbers while constant wall heat flux condition was set in thermal field. From the analysis, centrifugal force due to curvature effect is found to have significant role in behavior of pressure drop and heat transfer. The centrifugal force enhances pressure drop and heat transfer to have generally higher values in the spiral coiled tube than those in the straight tube. Even then, friction factor and Nusselt number are found to follow the proportionality with square root of the Dean number. Individual effect of flow parameters of Reynolds number and curvature ratio was investigated and effect of Reynolds number is found to be stronger than that of curvature effect.