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.

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Reτ= 5 200 are investigated based on two different methods, i.e., the FukagataIwamoto-Kasagi(FIK) identity(FUKAGATA, K., IWAMOTO, K., and KASAGI, N.Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows.Physics of Fluids, 14(11), L73–L76(2002)) and the Renard-Deck(RD) identity(DECK,S., RENARD, N., LARAUFIE, R., and WEISS, P.′E. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ= 13 650.Journal of Fluid Mechanics, 743, 202–248(2014)). The direct numerical simulation(DNS) data provided by Lee and Moser(LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Reτ≈ 5 200. Journal of Fluid Mechanics,774, 395–415(2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers.The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.

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.

The Simulation of High Reynolds Number Cavity Flow Based on Fractional Volumetric Lattice Boltzmann Method

The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two-chmensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective for simulating high Reynolds number flows. Simulations were carried out on a uniform grids system. The stream lines and the velocity profiles obtained from the simulations agree well with the standard lattice Boltzmann method simulations. Comparisons of detailed flow patterns with other studies via location of vortex centers are also satisfactory.

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.

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.

Numerical Simulation on Flow Past Two Side-by-Side Inclined Circular Cylinders at Low Reynolds Number

A series of three-dimensional numerical simulations is carried out to investigate the effect of inclined angle on flow behavior behind two side-by-side inclined cylinders at low Reynolds number Re=100 and small spacing ratio T/D=1.5 (T is the center-to-center distance between two side-by-side cylinders, D is the diameter of cylinder). The instantaneous and time-averaged flow fields, force coefficients and Strouhal numbers are analyzed. Special attention is focused on the axial flow characteristics with variation of the inclined angle. The results show that the inclined angle has a significant effect on the gap flow behaviors behind two inclined cylinders. The vortex shedding behind two cylinders is suppressed with the increase of the inclined angle as well as the flip-flop gap flow. Moreover, the mean drag coefficient, root-mean-square lift coefficient and Strouhal numbers decrease monotonously with the increase of the inclined angle, which follows the independent principle at small inclined angles.

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.

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.

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.

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.

Development of a new correlation to calculate permeability for flows with high Knudsen number

Flows with high Knudsen number play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow with high Knudsen number using modified lattice Boltzmann method （LBM） through a porous medium in a channel. The effect of collision between molecules and solid walls, which is required to accurately simulate transition flow regime, is taken into account using a modified relaxation time. Slip velocity on the wall, which is another significant difficulty in simulating transition flow regime, is captured using the slip reflection boundary condition （SRBC）. The geometry of porous medium is considered as in-line and staggered. The results are in good agreement with previous works. A new correlation is obtained between permeability, Knudsen number and porosity for flows in transition flow regimes.

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.

THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

Laminar-to-Turbulence Transition Revealed Through a Reynolds Number Equivalence

Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence c (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where c = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+= 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of c against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, c - 25, and for plate flow, c - 151.5. These findings suggest that a certain combination of c and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.

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.

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.

The Relation between the Coefficient of Friction and Pressure Drop by Using the Different Reynolds Number in a Circular Tube

This study explains the relationship between friction coefficient and pressure change at a range of Reynolds (21,056 - 28,574) and (0 - 1.4) solid loading ratio of two-phase flow (gas-solid) inside a circular copper pipe by using laboratory apparatus and solving the equations mathematically. An experimentally relationship of friction coefficient and pressure change with Reynolds number and flow velocity obtained also the relationship between the Solid loading ratio with friction coefficient and pressure change has been done for a Limit range of Reynolds number. It was noticed that the increase in friction coefficient and pressure change for two-phase flow was occurred when solid loading ratio increased. Also the relationship between pressure change and Reynolds number was direct proportion while the relationship between friction coefficient and Reynolds Number was inversely related.

Effect of fluid elasticity on the numerical stability of high-resolution schemes for high shearing contraction flows using OpenFOAM

Viscoelastic fluids due to their non-linear nature play an important role in process and polymer industries. These non-linear characteristics of fluid, influence final outcome of the product. Such processes though look simple are numerically challenging to study, due to the loss of numerical stability. Over the years, various methodologies have been developed to overcome this numerical limitation. In spite of this, numerical solutions are considered distant from accuracy, as first-order upwind-differencing scheme （UDS） is often employed for improving the stability of algorithm. To elude this effect, some works been reported in the past, where high-resolution-schemes （HRS） were employed and Deborah number was varied. However, these works are limited to creeping flows and do not detail any information on the numerical stability of HRS. Hence, this article presents the numerical study of high shearing contraction flows, where stability of HRS are addressed in reference to fluid elasticity. Results suggest that all I-IRS show some order of undue oscillations in flow variable profiles, measured along vertical lines placed near contraction region in the upstream section of domain, at varied elasticity number E ~ 5. Furthermore, by E, a clear relationship between numerical stability of HRS and E was obtained, which states that the order of undue oscillations in flow variable profiles is directly proportional to E.