Showing papers on "Reynolds number published in 2003"
TL;DR: In this article, the authors present a new approach for generating artificial velocity data which reproduces first and second order one point statistics as well as a locally given autocorrelation function.
1,058 citations
TL;DR: In this article, the effects of Reynolds number in the nominal case of an infinitely long and non-confined cylinder in a smooth oncoming flow are discussed, from about Re = 47 to 2 x 10(5), i.e., from the onset of vortex shedding up to the end of the subcritical regime.
939 citations
TL;DR: In this paper, the lattice Boltzmann equation (LBE) is applied to high Reynolds number incompressible flows, some critical issues need to be addressed, noticeably flexible spatial resolution, boundary treatments for curved solid wall, dispersion and mode of relaxation, and turbulence model.
861 citations
TL;DR: In this article, a symmetry-preserving discretization of the Navier-Stokes equations is shown to be stable on any grid, and conserves the total mass, momentum and kinetic energy.
582 citations
TL;DR: A general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations is presented, to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy.
Abstract: We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.
490 citations
TL;DR: In this paper, an experimental investigation has been performed on the laminar convective heat transfer and pressure drop of water in 13 different trapezoidal silicon microchannels, and dimensionless correlations for the Nusselt number and the apparent friction constant are obtained for the flow of water.
446 citations
TL;DR: In this article, the stability analysis of flow past a spinning circular cylinder placed in a uniform stream is investigated via two-dimensional computations, and a stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation.
Abstract: Flow past a spinning circular cylinder placed in a uniform stream is investigated via two-dimensional computations. A stabilized finite element method is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The Reynolds number based on the cylinder diameter and free-stream speed of the flow is 200. The non-dimensional rotation rate, α (ratio of the surface speed and freestream speed), is varied between 0 and 5. The time integration of the flow equations is carried out for very large dimensionless time. Vortex shedding is observed for α < 1.91. For higher rotation rates the flow achieves a steady state except for 4.34 < α < 4:70 where the flow is unstable again. In the second region of instability, only one-sided vortex shedding takes place. To ascertain the instability of flow as a function of α a stabilized finite element formulation is proposed to carry out a global, non-parallel stability analysis of the two-dimensional steady-state flow for small disturbances. The formulation and its implementation are validated by predicting the Hopf bifurcation for flow past a non-rotating cylinder. The results from the stability analysis for the rotating cylinder are in very good agreement with those from direct numerical simulations. For large rotation rates, very large lift coefficients can be obtained via the Magnus effect. However, the power requirement for rotating the cylinder increases rapidly with rotation rate.
431 citations
TL;DR: A family of three-dimensional traveling waves for flow through a pipe of circular cross section that provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.
Abstract: A family of three-dimensional traveling waves for flow through a pipe of circular cross section is identified. The traveling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.
426 citations
TL;DR: In this article, the Fair and Geyer equation was used to calculate the settling velocity of a small diameter cylindrical vessel in the presence of the wall effect, and two new correlations of the same forms were developed using the corrected data.
Abstract: Sphere drag data from throughout the twentieth century are available in tabular form. However, much of the data arose from experiments in small diameter cylindrical vessels, where the results might have been influenced by the wall effect. Wall effect corrections developed by others were applied to 178 of the 480 data points collected. This corrected data set is believed to be free of the influence of wall effects. Existing drag and settling velocity correlations were compared to this data set. In addition, new correlations of the same forms were developed using the corrected data. Two new correlations of sphere terminal velocity are proposed, one applicable for all Reynolds numbers less than 2310 5 , and the other designed to predict settling velocities with exceptional accuracy for terminal Reynolds numbers less than 4,000, a region that contains almost all applications of interest in environmental engineering. The trial and error solution for settling velocity using the Fair and Geyer equation for drag should be retired in favor of the direct calculation available from these new correlations.
413 citations
TL;DR: In this article, the authors investigated the noise radiated by a subsonic circular jet with a Mach number of 0.9 and a Reynolds number of 65000 computed by a compressible Large Eddy Simulation (LES) and demonstrated the feasibility of using LES to predict accurately both the flow field and sound radiation on a domain including the acoustic field.
Abstract: This study investigates the noise radiated by a subsonic circular jet with a Mach number of 0.9 and a Reynolds number of 65000 computed by a compressible Large Eddy Simulation (LES). First, it demonstrates the feasibility of using LES to predict accurately both the flow field and the sound radiation on a domain including the acoustic field. Mean flow parameters, turbulence intensities, velocity spectra and integral length scales are in very good agreement with experimental data. The noise generated by the jet, provided directly by the simulation, is also consistent with measurements in terms of sound pressure spectra, levels and directivity. The apparent location of the sound sources is at the end of the potential core in accordance with some experimental observations at similar Reynolds numbers and Mach numbers. Second, the noise generation mechanisms are discussed in an attempt to connect the flow field with the acoustic field. This study shows that for the simulated moderate Reynolds number jet, the predominant sound radiation in the downstream direction is associated with the breakdown of the shear layers in the central jet zone.
365 citations
TL;DR: In this paper, the authors demonstrate the merits of flow rate time dependency through periodic forcing, and demonstrate that the best results occur when both inlets are pulsed out of phase, leading to good mixing within 2 mm downstream of the confluence, i.e. about 1 s of contact.
Abstract: Many microfluidic applications require the mixing of reagents, but efficient mixing in these laminar (i.e., low Reynolds number) systems is typically difficult. Instead of using complex geometries and/or relatively long channels, we demonstrate the merits of flow rate time dependency through periodic forcing. We illustrate the technique by studying mixing in a simple “T” channel intersection by means of computational fluid dynamics (CFD) as well as physically mixing two aqueous reagents. The “T” geometry selected consists of two inlet channel segments merging at 90 degrees to each other, the outlet segment being an extension of one of the inlet segments. All channel segments are 200 µm wide by 120 µm deep, a practical scale for mass-produced disposable devices. The flow rate and average velocity after the confluence of the two reagents are 48 nl s−1 and 2 mm s−1 respectively, which, for aqueous solutions at room temperature, corresponds to a Reynolds number of 0.3. We use a mass diffusion constant of 10−10 m2 s−1, typical of many BioMEMS applications, and vary the flow rates of the reagents such that the average flow rate remains unchanged but the instantaneous flow rate is sinusoidal (with a DC bias) with respect to time. We analyze the effect of pulsing the flow rate in one inlet only as well as in the two inlets, and demonstrate that the best results occur when both inlets are pulsed out of phase. In this case, the interface is shown to stretch, retain one fold, and sweep through the confluence zone, leading to good mixing within 2 mm downstream of the confluence, i.e. about 1 s of contact. From a practical viewpoint, the case where the inlets are 180 degrees out of phase is of particular interest as the outflow is constant.
TL;DR: In this article, a method for large eddy simulation (LES) is presented in which the subgrid-scale modeling is achieved by filtering procedures alone, and the procedure derives from a deconvolution model, and provides a mathematically consistent approximation of unresolved terms arising from any type of nonlinearity.
Abstract: A method for large eddy simulation (LES) is presented in which the sub-grid-scale modeling is achieved by filtering procedures alone The procedure derives from a deconvolution model, and provides a mathematically consistent approximation of unresolved terms arising from any type of nonlinearity The formal steps of primary filtering to obtain LES equations, approximate deconvolution to construct the subgrid model term and regularization are combined into an equivalent filter This filter should be an almost perfect low pass filter below a cut-off wavenumber and then fall off smoothly The procedure has been applied to a pressure-velocity-entropy formulation of the Navier–Stokes equations for compressible flow to perform LES of two fully developed, turbulent, supersonic channel flows and has been assessed by comparison against direct numerical simulation (DNS) data Mach numbers are 15 and 30, and Reynolds numbers are 3000 and 6000, respectively Effects of filter cut-off location, choice of differentiation scheme (a fifth-order compact upwind formula and a symmetric sixth-order compact formula were used), and grid refinement are examined The effects are consistent with, and are readily understood by reference to, filtering characteristics of the differentiation and the LES filter All simulations demonstrate a uniform convergence towards their respective DNS solutions
TL;DR: In this paper, a high-order compact method for large eddy simulation (LES) of compressible turbulent flows is presented, which is applicable to the conservative form of the governing equations, thereby allowing total energy conservation.
TL;DR: In this paper, three-dimensional steady states and traveling wave solutions of the Navier-Stokes equations are computed in plane Couette and Poiseuille flows with both free slip and no-slip boundary conditions.
Abstract: Three-dimensional steady states and traveling wave solutions of the Navier–Stokes equations are computed in plane Couette and Poiseuille flows with both free-slip and no-slip boundary conditions. They are calculated using Newton’s method by continuation of solutions that bifurcate from a two-dimensional streaky flow then by smooth transformation (homotopy) from Couette to Poiseuille flow and from free-slip to no-slip boundary conditions. The structural and statistical connections between these solutions and turbulent flows are illustrated. Parametric studies are performed and the parameters leading to the lowest onset Reynolds numbers are determined. In all cases, the lowest onset Reynolds number corresponds to spanwise periods of about 100 wall units. In particular, the rigid-free plane Poiseuille flow traveling wave arises at Reτ=44.2 for Lx+=273.7 and Lz+=105.5, in excellent agreement with observations of the streak spacing. A simple one-dimensional map is proposed to illustrate the possible nature of ...
TL;DR: In this article, the viability and accuracy of large-eddy simulation with wall modeling for high Reynolds number complex turbulent flows is investigated by considering the flow around a circular cylinder in the supercritical regime.
TL;DR: In this paper, experimental observations of liquid microchannel flows are reviewed and results of computer experiments concerning channel entrance, wall slip, non-Newtonian fluid, surface roughness, viscous dissipation and turbulence effects on the friction factor are discussed.
Abstract: Experimental observations of liquid microchannel flows are reviewed and results of computer experiments concerning channel entrance, wall slip, non-Newtonian fluid, surface roughness, viscous dissipation and turbulence effects on the friction factor are discussed. The experimental findings are classified into three groups. Group I emphasizes 'flow instabilities' and group II points out 'viscosity changes' as the causes of deviations from the conventional flow theory for macrochannels. Group III caters to studies that did not detect any measurable differences between micro- and macroscale fluid flow behaviors. Based on numerical friction factor analyses, the entrance effect should be taken into account for any microfluidic system. It is a function of channel length, aspect ratio and the Reynolds number. Non-Newtonian fluid flow effects are expected to be important for polymeric liquids and particle suspension flows. The wall slip effect is negligible for liquid flows in microconduits. Significant surface roughness effects are a function of the Darcy number, the Reynolds number and cross-sectional configurations. For relatively low Reynolds numbers, Re < 2000, onset to turbulence has to be considered important because of possible geometric non-uniformities, e.g., a contraction and/or bend at the inlet to the microchannel. Channel-size effect on viscous dissipation turns out to be important for conduits with Dh < 100 µm.
TL;DR: An experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in the Reynolds number Re indicates that the amplitude of perturbation required to cause transition scales as O(Re-1).
Abstract: We report the results of an experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in the Reynolds number Re. A novel scaling law is uncovered using a systematic experimental procedure which permits contact to be made with modern theoretical thinking. The principal result we uncover is a scaling law which indicates that the amplitude of perturbation required to cause transition scales as O(Re–1).
TL;DR: Experimental measurements and flow visualiza- tion of synthetic jets and continuous jets with matched Reynolds numbers are described in this article, where the synthetic jets are wider and slower than matched continuous jets.
Abstract: Experimental measurements and flow visualiza- tion of synthetic jets and continuous jets with matched Reynolds numbers are described. Although they have the same profile shape, synthetic jets are wider and slower than matched continuous jets. The synthetic jets are ex- amined at higher Reynolds numbers than previously studied and over a large range of dimensionless stroke lengths. Nomenclature b cross-stream location where velocity is 0.5Ucl h slot width f driving frequency L0 stroke length = R T=2 0 u0 t ðÞ dt Q volume flux Q0 U0h for synthetic jet, and Q0 = Uaveh for con- tinuous jet Reh Reynolds number of continuous jet=Uaveh/m ReU0 Reynolds number of synthetic jet=U0h/m t time (with zero at start of blowing stroke) T driving period=1/f u measured instantaneous velocity U time-averaged velocity Uave time-averaged slot velocity for continuous jet Ucl time-averaged centerline velocity u0(t) centerline or cross-stream-averaged velocity at x=0 for synthetic jet umax maximum of u0(t) U0 L0f x streamwise coordinate y cross-stream coordinate m kinematic viscosity
Dissertation•
01 Jan 2003
TL;DR: In this paper, a phenomenological set of transport equations has been set up for the steady state of non-Newtonian flow in porous granular media, which is naturally non-homogeneous, and two possible mechanisms have been identified: compressibility coupled to the pressure field and compressibility associated with the fluctuations in the flow.
Abstract: Non-Newtonian flow in heterogeneous media is of enormous theoretical and industrial importance. This phenomenon is studied to reveal macroscopic effects that arise due to the interaction between the non-linear flow behaviour and the spatial variation of the medium through which it is forced to move. The heterogeneity is achieved by using porous granular media, which is naturally non-homogeneous.
The non-Newtonian properties of the fluid may have many causes and is an intrinsic property of the fluid that is used:
One way of achieving it is by studying dense slurries of neutral particles or naturally occurring magmatic flows.
Another way is to study the case where the flow is dominated by its ionic content and where the double layer thickness (the effective size of the ionic entities) is of the order of magnitude of the pore size.
All cases studied in this thesis pertain to slow flow (low Reynolds number), though the fluid may be compressible.
The variations in the flow are calculated in first order and these turn out to be coupled to the spatial variations in the porous medium. In this way structure formation is predicted. The structures may be either aligned with or may be perpendicular to the mean flow direction. 'Experiments to decide on which regime is relevant have been conducted. The genesis of structure formation is studied as a temporal development by considering a compressible flow. The constitutive equation that is required to couple the compressibility to the flow parameters is investigated. Two possible mechanisms have been identified: compressibility coupled to the pressure field and compressibility associated with the fluctuations in the flow. Using linear analysis the structure formation patterns associated with these two mechanisms are established for the steady state.
Flow of ionically laden fluids has also been studied. Experiments done at Loughborough University (Department of Chemical Engineering) on electrowashing of filter cakes has been used to prove a major macroscopic effect. This effect takes place when the ionic diameter (which is approximately twice the double layer thickness) is of the order of magnitude of the pore size.
A phenomenological set of transport equations has been set up. These contain coefficients, such as transition probabilities and mean ionic flow rates, that can be obtained from experiments by doing a first order solution of the equations for short times. A more involved numerical solution is also supplied and confirms the initial analytical estimates.
TL;DR: In this article, a simulation of two-dimensional flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers has been numerically investigated, using the immersed boundary method, in the ranges of 40 ⩽Re⩽160 and g*<5, where Re and g * are, respectively, the Reynolds number and the spacing between the two cylinder surfaces divided by the cylinder diameter.
Abstract: Two-dimensional flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers has been numerically investigated in this study. For the study, numerical simulations are performed, using the immersed boundary method, in the ranges of 40⩽Re⩽160 and g*<5, where Re and g* are, respectively, the Reynolds number and the spacing between the two cylinder surfaces divided by the cylinder diameter. Results show that a total of six kinds of wake patterns are observed over the ranges: antiphase-synchronized, in-phase-synchronized, flip-flopping, deflected, single bluff-body, and steady wake patterns. It is found that the characteristics of the flow significantly depend both on the Reynolds number and gap spacing, with the latter much stronger than the former. Instantaneous flow fields, time traces, flow statistics and so on are presented to identify the wake pattern and then to understand the underlying mechanism. Moreover, the bifurcation phenomena where either of two wake patterns can occur ...
TL;DR: In this paper, the authors investigated the effect of polymer additives on turbulent drag reduction in a channel using direct numerical simulation, where the dilute polymer solution is expressed with an Oldroyd-B model that shows a linear elastic behaviour.
Abstract: Turbulent drag reduction by polymer additives in a channel is investigated using direct numerical simulation. The dilute polymer solution is expressed with an Oldroyd-B model that shows a linear elastic behaviour. Simulations are carried out by changing the Weissenberg number at the Reynolds numbers of 4000 and 20 000 based on the bulk velocity and channel height. The onset criterion for drag reduction predicted in the present study shows a good agreement with previous theoretical and experimental studies. In addition, the flow statistics such as the r.m.s. velocity fluctuations are also in good agreement with previous experimental observations. The onset mechanism of drag reduction is interpreted based on elastic theory, which is one of the most plausible hypotheses suggested in the past. The transport equations for the kinetic and elastic energy are derived for the first time. It is observed that the polymer stores the elastic energy from the flow very near the wall and then releases it there when the relaxation time is short, showing no drag reduction. However, when the relaxation time is long enough, the elastic energy stored in the very near-wall region is transported to and released in the buffer and log layers, showing a significant amount of drag reduction.
TL;DR: In this article, the role of three-dimensionalality and unsteadiness with respect to the existence, mode selection, and internal structure of vortex breakdown, in terms of the two governing parameters and the Reynolds number, is addressed.
Abstract: Vortex breakdown of nominally axisymmetric, swirling incompressible flows with jet- and wake-like axial velocity distributions issuing into a semi-infinite domain is studied by means of direct numerical simulations. By selecting a two-parametric velocity profile for which the steady axisymmetric breakdown is well-studied (Grabowski & Berger 1976), issues are addressed regarding the role of three-dimensionality and unsteadiness with respect to the existence, mode selection, and internal structure of vortex breakdown, in terms of the two governing parameters and the Reynolds number. Low Reynolds numbers are found to yield flow fields lacking breakdown bubbles or helical breakdown modes even for high swirl. In contrast, highly swirling flows at large Reynolds numbers exhibit bubble, helical or double-helical breakdown modes, where the axisymmetric mode is promoted by a jet-like axial velocity profile, while a wake-like profile renders the flow helically unstable and ultimately yields non-axisymmetric breakdown modes. It is shown that a transition from super- to subcritical flow, as defined by Benjamin (1962), accurately predicts the parameter combination yielding breakdown, if applied locally to flows with supercritical inflow profiles. Thus the basic form of breakdown is axisymmetric, and a transition to helical breakdown modes is shown to be caused by a sufficiently large pocket of absolute instability in the wake of the bubble, giving rise to a self-excited global mode. Two distinct eigenfunctions corresponding to azimuthal wavenumbers have been found to yield a helical or double-helical breakdown mode, respectively. Here the minus sign represents the fact that the winding sense of the spiral is opposite to that of the flow.
TL;DR: The effect of surface roughness on pressure drop and heat transfer in circular tubes has been extensively studied in literature as discussed by the authors, and a detailed experimental study is undertaken to investigate the roughness effects in small diameter tubes.
Abstract: The effect of surface roughness on pressure drop and heat transfer in circular tubes has been extensively studied in literature. The pioneering work of Nikuradse [1] established the sand grain roughness as a major parameter in defining the friction factor during laminar and turbulent flows. Recent studies have indicated a transition to turbulent flows at Reynolds number values much below 2300 during single-phase flow in channels with small hydraulic diameters. In the present work, a detailed experimental study is undertaken to investigate the roughness effects in small diameter tubes. The roughness of the inside tube surface is changed by etching it with an acid solution. Two tubes of 1.032 mm and 0.62 mm inner diameter are treated with acid solutions to provide three different roughness values for each tube. The Reynolds number range for the tests is 500-2600 for 1.067 mm tube and 900-3000 for 0.62 mm tube.
TL;DR: In this paper, an interfacial rheometer for both stress and strain-controlled measurements of shear rheological properties at liquid/liquid and gas/liquid interfaces is presented, based on a rotating or oscillating biconical bob design in combination with a low friction electronically commutated motor system.
Abstract: An interfacial rheometer for both stress- and strain-controlled measurements of shear rheological properties at liquid/liquid and gas/liquid interfaces is presented. The device is based on a rotating or oscillating biconical bob design in combination with a low friction electronically commutated motor system. The interfacial shear stress, viscosity, and dynamic moduli are obtained by solving the Stokes equations (low Reynolds number) along with the Boussinesq–Scriven interfacial stress tensor, which is used for the boundary conditions at the interface. An improved and simple numerical method for the calculation of the velocity distribution in the measuring cell is presented. The scope and limitations of the rheometer are discussed. Results from steady shear and oscillatory experiments as well as creep recovery and stress relaxation tests at both oil/water and air/water interfaces with adsorbed films of a globular protein (ovalbumin) and spread films of a surfactant (sorbitan tristearate) are presented.
TL;DR: In this article, the dynamics of quasi-horizontal motions in a stably stratified fluid have been simulated for Froude numbers of order 1, so that flows are strongly affected by the stable density stratification, and for a range of Reynolds numbers.
Abstract: The dynamics of quasi-horizontal motions in a stably stratified fluid have been simulated for Froude numbers of order 1, so that the flows are strongly affected by the stable density stratification, and for a range of Reynolds numbers. It is found that the horizontal scales of the motion grow continuously in time. The vertical scales decrease and the vertical shearing increases with time, maintaining the Richardson number of order 1, as suggested by Lilly [J. Atmos. Sci. 40, 749 (1983)] and Babin et al. [Theor. Comput. Fluid Dyn. 9, 223 (1997)]. Small-scale instabilities and turbulent-like motions are observed to occur in the high shearing regions, while the larger-scale motions appear to evolve somewhat independently of the Reynolds number. The results suggest that the larger-scale, quasi-horizontal motions would be a continuous source of smaller-scale turbulence until the local Reynolds number drops below a critical value, which is estimated. Finally, a Froude number based upon a vertical differential scale and used in previous scaling arguments and theories is estimated in terms of other parameters.
TL;DR: In this paper, a similarity formulation is proposed to describe the streamwise turbulence intensity across the entire smooth-wall zero-pressure-gradient turbulent boundary layer, which is an extension of the Marusic, Uddin and Perry [Phys. Fluids 9, 3718 (1997)] formulation that was restricted to the outer region of the boundary layer.
Abstract: A similarity formulation is proposed to describe the streamwise turbulence intensity across the entire smooth-wall zero-pressure-gradient turbulent boundary layer. The formulation is an extension of the Marusic, Uddin, and Perry [Phys. Fluids 9, 3718 (1997)] formulation that was restricted to the outer region of the boundary layer, including the logarithmic region. The new formulation is found to agree very well with experimental data over a large range of Reynolds numbers varying from laboratory to atmospheric flows. The formulation is founded on physical arguments based on the attached eddy hypothesis, and suggests that the boundary layer changes significantly with Reynolds number, with an outer flow influence felt all the way down to the viscous sublayer. The formulation may also be used to explain why the empirical mixed scaling of DeGraaff and Eaton [J. Fluid Mech. 422, 319 (2000)] appears to work.
TL;DR: In this paper, the authors describe extensions of the Spalart-allmaras model to surface roughness, developed independently by Boeing and ONERA, which yield similar predictions, and are in fair agreement with experiments.
TL;DR: In this article, the spatial evolution of vortices and transition to 3D in the wake of a square cylinder have been numerically studied and the results for the square cylinder are in good accordance with the threedimensional modes of transition that are well-known in the circular cylinder wake.
TL;DR: In this article, the aerodynamic characteristics of two circular cylinders in a tandem arrangement were investigated experimentally in a uniform flow at a Reynolds number of 6.5 × 10 4, which is within the range in which fluid forces acting on a single cylinder are comparatively insensitive to change in the Reynolds number.
TL;DR: In this article, a Fourier-Chebyshev Petro-Galerkin spectral method is described for high-accuracy computation of linearized dynamics for flow in an infinite circular pipe.