Subcritical spatial transition of swept Hiemenz flow

It is known from experimental investigations that the leading-edge boundary layer of a swept wing exhibits transition to turbulence at subcritical Reynolds numbers, i.e. at Reynolds numbers which lie below the critical Reynolds number predicted by linear stability theory. In the present work, we investigate this subcritical transition process by direct numerical simulations of a swept Hiemenz flow in a spatial setting. The laminar base flow is perturbed upstream by a pair of stationary counter-rotating vortex-like disturbances. This perturbation generates high- and low-speed streaks by a non-modal growth mechanism. Further downstream, these streaky structures exhibit a strong instability to secondary perturbations which leads to a breakdown to turbulence.The observed transition mechanism has strong similarities to by-pass transition mechanisms found for two-dimensional boundary layers. It can be shown that transition strongly depends on the amplitude of the primary perturbation as well as on the frequency of the secondary perturbation.     

Experimental study and large eddy simulation for the turbulent flow around four cylinders in an in-line square configuration

The turbulent flows around four cylinders in an in-line square configuration with different spacing ratios of 1.5, 2.5, 3.5 and 5.0 have been investigated experimentally at subcritical Reynolds numbers from 11,000 to 20,000. The mean and fluctuating velocity distributions were obtained using the laser Doppler anemometry (LDA) measurement. The digital particle image velocimetry (DPIV) was employed to characterize the full field vorticity and velocity distributions as well as other turbulent quantities. The experimental study indicated that several distinct flow patterns exist depending on the spacing ratio and subcritical Reynolds number for turbulent flow. The three-dimensional numerical simulations were also carried out using the large eddy simulation (LES) at Reynolds number of 15,000 with the spacing ratio of 1.5 and 3.5. The results show that the LES numerical predictions are in good agreement with the experimental measurements. Therefore, the three-dimensional vortex structures and the full field instantaneous and mean quantities of the flow field such as velocity field, vorticity field, etc., which are very difficult to obtain experimentally, can be extracted from the simulation results for the deepening of our understanding on the complex flow phenomena around four cylinders in in-line configuration.     

亚临界雷诺数下圆柱绕流的大涡模拟

本文应用Smagorinsky涡粘性模式和二阶精度的有限体积法对圆柱绕流的流场进行大涡模拟．求解了非正交曲线坐标系下的N-S方程,对雷诺数为100和20000的工况进行了计算．计算结果与实验及动力涡粘性模式的结果进行了比较,表明计算对于层流及高亚临界雷诺数的湍流流动是合理的     

LES-based Study of the Roughness Effects on the Wake of a Circular Cylinder from Subcritical to Transcritical Reynolds Numbers

This paper investigates the effects of surface roughness on the flow past a circular cylinder at subcritical to transcritical Reynolds numbers. Large eddy simulations of the flow for sand grain roughness of size k/D = 0.02 are performed (D is the cylinder diameter). Results show that surface roughness triggers the transition to turbulence in the boundary layer at all Reynolds numbers, thus leading to an early separation caused by the increased momentum deficit, especially at transcritical Reynolds numbers. Even at subcritical Reynolds numbers, boundary layer instabilities are triggered in the roughness sublayer and eventually lead to the transition to turbulence. The early separation at transcritical Reynolds numbers leads to a wake topology similar to that of the subcritical regime, resulting in an increased drag coefficient and lower Strouhal number. Turbulent statistics in the wake are also affected by roughness; the Reynolds stresses are larger due to the increased turbulent kinetic energy production in the boundary layer and separated shear layers close to the cylinder shoulders.     

A reformulated synthetic turbulence generation method for a zonal RANS–LES method and its application to zero-pressure gradient boundary layers

A synthetic turbulence generation (STG) method for subsonic and supersonic flows at low and moderate Reynolds numbers to provide inflow distributions of zonal Reynolds-averaged Navier–Stokes (RANS) – large-eddy simulation (LES) methods is presented. The STG method splits the LES inflow region into three planes where a local velocity signal is decomposed from the turbulent flow properties of the upstream RANS solution. Based on the wall-normal position and the local flow Reynolds number, specific length and velocity scales with different vorticity content are imposed at the inlet plane of the boundary layer. The quality of the STG method for incompressible and compressible zero-pressure gradient boundary layers is shown by comparing the zonal RANS–LES data with pure LES, pure RANS, and direct numerical simulation (DNS) solutions. The distributions of the time and spanwise wall-shear stress, Reynolds stress distributions, and two point correlations of the zonal RANS–LES simulations are smooth in the transition region and in good agreement with the pure LES and reference DNS findings. The STG approach reduces the RANS-to-LES transition length to less than four boundary-layer thicknesses.     

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i     

Prediction of unsteady,separated boundary layer over a blunt body for laminar,turbulent, and transitional flow

The focus of this paper is to study the ability of unsteady RANS‐based CFD to predict separation over a blunt body for a wide range of Reynolds numbers particularly the ability to capture laminar‐to‐turbulent transition. A perfect test case to demonstrate this point is the cylinder‐in‐crossflow for which a comparison between experimental results from the open literature and a series of unsteady simulations is made. Reynolds number based on cylinder diameter is varied from 10⁴ to 10⁷ (subcritical through supercritical flow). Two methods are used to account for the turbulence in the simulations: currently available eddy–viscosity models, including standard and realizable forms of the k–ε model; and a newly developed eddy–viscosity model capable of resolving boundary layer transition, which is absolutely necessary for the type and range of flow under consideration. The new model does not require user input or ‘empirical’ fixes to force transition. For the first time in the open literature, three distinct flow regimes and the drag crisis due to the downstream shift of the separation point are predicted using an eddy–viscosity based model with transition effects. Discrepancies between experimental and computational results are discussed, and difficulties for CFD prediction are highlighted. Copyright © 2004 John Wiley & Sons, Ltd.     

Comparison of velocity and temperature measurements with simulations in a hypersonic wake flow

A hypersonic shock-tunnel flow around an axisymmetric model of a planetary entry probe is analyzed. Planar laser-induced fluorescence is applied to measure both the velocity and the rotational temperature everywhere in the central plane of the flow field. The experimental test case is compared to simulations using the direct simulation Monte Carlo (DSMC) method. While the Mach 9.7 flow at a freestream Reynolds number based on the model diameter of 35,000 is chemically frozen, effects of thermal non-equilibrium and localized rarefaction cannot be neglected. DSMC and measurements agree well within the outer wake, but disagree close to the centerline, where in particular the measured velocity is higher than values predicted by the simulations. The experimental results indicated a shorter recirculation region and increased local fluctuations in the free shear layer upstream of the wake recompression shock when compared to the simulation. These effects are attributed to incipient transition, which is not observed in the simulations, as the simulations did not model the effects of freestream fluctuations. Furthermore, measured and simulated vorticities are compared with theoretical predictions.     

A PIV study of the laminar axisymmetric sudden expansion flow

The laminar flow through an axisymmetric sudden expansion was investigated experimentally using real-time digital particle image velocimetry. An expansion ratio (downstream-to-upstream pipe diameter ratio) of 2 was selected for the study. The measurements covered the regions of separation, reattachment and re-development. Two dimensional velocity maps were obtained on the vertical center plane for six Reynolds numbers between 20 and 211, based on the upstream pipe diameter and bulk velocity. The stream function distributions are calculated and presented from the streamwise and radial velocity maps. The dependence of reattachment length, redevelopment length and recirculating flow strength on the Reynolds number are determined. Results show that not only the reattachment length but also the redevelopment length downstream of reattachment is a linear function of the Reynolds number. The recirculation eddy strength, on the other hand, has a non-linear dependence on the Reynolds number which becomes weaker as the Reynolds number is increased. The results indicate no instability- or buoyancy-driven flow asymmetry in the range 20?Re? 211.     

Instability threshold of a negatively buoyant fountain

Experimental simulations were carried out to investigate the onset of instability in negatively buoyant fountains by injecting glycerin–water mixtures into silicon oil. The transition from a stable to an unstable fountain structure is primarily governed by the Richardson number, and to a lesser extent, Reynolds number, viscosity ratio, Weber number and vent geometry. Transition nominally occurs at a Ri = 1.0. For a fountain issuing from a cylindrical pipe, the major effect of the Reynolds number is in determining whether or not the fountain is laminar or turbulent. The Reynolds number effect can be largely accounted for by basing a corrected Richardson number on the root mean square of the mean velocity. Viscosity ratio deviating from unity has the effect of stabilizing the flow structure and thereby reducing the transition Richardson number. Similarly, interfacial tension stabilizes the flow pattern resulting in a trend of increasing transition Richardson number with increasing Weber number. The results are valid in rectangular vents if the Richardson number and Reynolds number are based on the hydraulic diameter.     

Asymmetric flows in planar symmetric channels with large expansion ratio

A continuation method has been used with a finite element grid and a geometric perturbation to compute two successive symmetry breaking flow transitions with increasing Reynolds number in flow of generalized Newtonian fluids through a sudden planar expansion. With an expansion ratio of 16, the onset Reynolds number is particularly sensitive to small geometric asymmetry and the critical Reynolds numbers for the two successive flow transitions are found to be very close. These transitions are delayed to higher onset Reynolds numbers by increasing the degree of pseudoplasticity. This trend is observed experimentally as well in this work and may be attributed to the competing effects of shear thinning and inertia on the size of the corner vortex before the symmetry breaking flow transition. After the second transition with an expansion ratio of 16, the two large staggered vortices on opposite walls occupy most of the transverse dimension so that the core flow between the vortices appears as a thin jet oscillating along the flow direction. This is more pronounced for the pseudoplastic liquid. After the second transition, the degree of flow asymmetry at a given location downstream of the expansion plane is larger for the pseudoplastic liquid than for the Newtonian liquid at comparable Reynolds numbers. The last feature is also evident in the experimentally observed velocity profiles. Copyright © 2002 John Wiley & Sons, Ltd.     

An experimental study of nonrheometric flows of viscoelastic fluids: II. Flow in a liquid jet exiting from a vertical tube

A laser anemometer has been used to study the region of accelerating shear flow near the exit of a vertical tube. It is in this region that the transition between steady laminar shear flow in the upstream tube and elongational flow in the downstream liquid jet takes place.Downstream velocity profiles were measured for solutions of 0.9% polyacrylamide in 85% glycerol/water and 0.9% polyacrylamide in water. Reynolds numbers (based on wall conditions in the fully developed upstream flow) ranged from 45 to 310 and Froude numbers from 0.294 to 4.11. Tubes, having sharpedged and rounded exit corners, with diameters of 1.25 cm and 1.90 cm were usedUpstream velocity profiles were measured for a solution of 0.9% polyacrylamide in water. Reynolds numbers ranged from 16 to 670. Only tubes having sharp-edged exit corners were used.It was found that the transition region did not extend upstream into the tube but was confined to the downstream jet. The transition took place over a distance of about 3–5 tube diameters depending upon the value of the Froude number. The axial distance downstream from the tube exit plane at which the velocity profile first became flat increased with increasing Froude number. The magnitude of the jet velocity at this point decreased with increasing Froude number.The condition of the tube exit corner was found to influence the flow in the transition region. Downstream velocity profiles obtained using tubes having rounded exit corners initially develop more slowly than, but soon catch up with and eventually overtake, the corresponding profiles obtained using tubes with sharp-edged exit corners.Downstream velocity profiles obtained for the 0.9% polyacrylamide in 85% glycerol/water solution were found to develop smoothly. The transition from steady shear flow in the tube to elongational flow in the jet took place through the combined processes of acceleration of the outer layers of the jet due to radial transfer of momentum with adjacent inner layers, the process spreading steadily inwards with increasing axial distance from the tube exit plane, and acceleration of the whole due to gravity. However, the velocity profiles obtained for the 0.9% polyacrylamide in water solution did not always develop so smoothly. At a Reynolds number of 310 and Froude number of 2.06 the radial momentum transfer process was restricted to a narrow outer region of the jet until a downstream axial distance of about 2 tube diameters was reached. Thereafter, the transition to a flat profile took place smoothly.     

Side‐wall effects on the bifurcation of the flow through a sudden expansion

Three‐dimensional computations have been performed to study the flow through a symmetric sudden expansion with an expansion ratio of 3 at low Reynolds numbers. The aspect ratio of the flow channel is allowed to vary within a wide range to examine its influence on the flow which bifurcates from a symmetric state to an asymmetric state. The results reveal that the critical Reynolds number of the symmetry‐breaking bifurcation increases while the aspect ratio is reduced. The flow behaviour near the side walls is illustrated by using limiting streamlines. The origin of the singular points identifiable on the side wall can be traced back to the recirculating flows and the relevant reattachment/separation points in the core of the channel. It is seen that the determination of the exact critical Reynolds number is not trivial because it depends on how to define asymmetric flow. Computations have also been conducted to show that a slight asymmetry in the channel geometry causes a smooth transition from symmetric to non‐symmetric states. Copyright © 2007 John Wiley & Sons, Ltd.     

Unsteady force measurements in sphere flow from subcritical to supercritical Reynolds numbers

The flow over a smooth sphere is examined in the Reynolds number range of 5.0 × 10⁴ < Re < 5.0 × 10⁵ via measurements of the fluctuating forces and particle image velocimetry measurements in a planar cut of the velocity field. Comprehensive studies of the statistics and spectra of the forces are presented for a range of subcritical and supercritical Reynolds numbers. While the subcritical lateral force spectra are dominated by activity corresponding to the large-scale vortex shedding frequency at a Strouhal number of approximately 0.18, there is no such peak apparent in the supercritical spectra, although resolution effects may become important in this region. Nor does the large-scale vortex shedding appear to have a significant effect on the drag force fluctuations at either sub- or super-critical Reynolds numbers. A simple double spring model is shown to capture the main features of the lateral force spectra. The low-frequency force fluctuations observed in earlier computational studies are shown to have important implications for statistical convergence, and in particular, the apparent mean side force observed in earlier studies. At least one thousand dimensionless time units are required for reasonable estimates of the second and higher moments below the critical Reynolds number and even more for supercritical flow, stringent conditions for computational studies. Lastly, investigation of the relationship between the motion of the instantaneous wake shape, defined via the local position where the streamwise velocity is equal to half the freestream value, and the in-plane lateral force for subcritical flow reveals a significant negative correlation throughout the near wake, which is shown to be related to a structure inferred to arise from the large-scale vortex shedding convecting downstream at 61% of the freestream velocity. In addition to its utility in understanding basic sphere flow, the apparatus is also a testbed that will be used in future studies, examining the effect of both static and dynamic changes to the surface morphology.     

DNS of viscoelastic turbulent channel flow with rectangular orifice at low Reynolds number

Direct numerical simulations of turbulent viscoelastic-fluid flow in a channel with a rectangular orifice were performed to investigate the influence of viscoelasticity on turbulence statistics and turbulent structures downstream of the orifice. The geometry considered is periodic rectangular orifices with 1:2 expansion. The constitutive equation follows the Giesekus model, valid for polymer (or surfactant) solutions, which are generally capable of reducing the turbulent frictional drag in a smooth channel. The friction Reynolds number and the Weissenberg number were set to 100 and 20-30, respectively. A drag reduction of about 20% was achieved in the viscoelastic flows. The onset Reynolds number for the transition from a symmetric to an asymmetric state was found to be shifted to higher values than that for the Newtonian flow. In the viscoelastic flow, the turbulent kinetic energy was decreased and fewer turbulent eddies were observed, as the Kelvin-Helmholtz vortices were quickly damped. Away from the orifice, quasi-streamwise vortices in the viscoelastic flow were sustained for a longer period, accompanied by energy exchange from elastic energy of the viscoelastic fluid to kinetic energy.     

Direct Numerical Simulation of the Three-Dimensional Transition to Turbulence in the Transonic Flow around a Wing

The three-dimensional transition to turbulence in the transonic flow around a NACA0012 wing of constant spanwise section has been analysed at zero incidence and within the Reynolds number range [3000, 10000], by performing the direct numerical simulation. The successive stages of the 2D and 3D transition beyond the first bifurcation have been identified. A 2D study has been carried out near the threshold concerning the appearance of the first bifurcation that is the von-Kármán instability. The critical Mach number associated with this flow transition has been evaluated. Three other successive stages have been detected as the Mach number further increases in the range [0.3, 0.99]. Concerning the 3D transition of this nominally 2D flow configuration, the amplification of the secondary instability has been studied within the Reynolds number range of [3000, 5000]. The formation of counter-rotating longitudinal vorticity cells and the consequent appearance of a large-scale spanwise wavelength have been obtained downstream of the trailing-edge shock. A vortex dislocation pattern is developed as a consequence of the shock-vortex interaction near the trailing edge. The subcritical nature of the present 3D transition to turbulence has been proven by means of the DNS amplification signals and the Landau global oscillator model.     

Laminar flow performance of a heated body in particle-laden water

The effects of small uniformly sized spherical particles seeded into the freestream flow of a water tunnel on the delayed transition of a heated laminar flow control body is examined experimentally. In separate trials, four different mean diameter particle seedings were added to the flow and the approach flow velocity was cycled from subcritical to supercritical conditions at three different body heating conditions. The transition Reynolds number based on the body arc length and the approach flow velocity decreases monotonically with increasing d/ ^*, where d is the particle diameter and ^* is the displacement thickness at a critical location. The location of initial turbulent spot formation defines the critical location, and, within the range of experimental conditions reported here, is independent of particle size, heating condition and the approach velocity. For the high unit Reynolds numbers considered (Re ^u 1.88 × 10⁷ per metre), there is no observed critical particle diameterbased Reynolds number threshold; all sizes of particles considered in the experiments (d = 37 to 218 m) have some effect on transition. In a second set of experiments, particles were injected into the laminar boundary layer from a small orifice located at the forward stagnation point. These injected particles have no observable effect on the laminar layer or transition, which suggests that the injected particles fail to produce wakes or vorticity within the laminar layer that may lead to turbulent spot production.Also with the Graduate Program in Acoustics, Penn State UniversityThis work has been supported by the Applied Research Laboratory of The Pennsylvania State University under contracts with the Office of Naval Research and the Naval Sea Systems Command. The authors are particularly indebted to Professor Ron Blackwelder and his colleagues for sharing their yet unpublished findings from particle-induced transition experiments being conducted at the University of Southern California.     

An investigation of turbulent developing flow at the entrance to a smooth pipe

An attempt is made to explain the flow regimes at the entry region of a pipe. Developing turbulent flow was examined and three theoretical models were evolved to explain the three most important regimes: the region of flat plate flow, the region of transition from flat plate to pipe flow, and the region of boundary layer interaction. The model for the flat plate flow was based on the velocity power law but experimental data showed that the exponent was not constant as generally assumed. There was good agreement between the theoretical models and the experimental data for the boundary layer development.

A simple empirical formula was obtained from which it is possible to predict the length of the entry region. The onset of the increase in turbulence intensity at the core, which marks the start of transition from flat plate flow to pipe flow, seems to occur at a particular Reynolds number, based on distance into pipe, of about 3.15×10⁶. This figure may vary with inlet flow condition.     

Large-eddy simulation of counter-rotating Taylor–Couette flow: The effects of angular velocity and eccentricity

In the present work, turbulent flow in the annulus of a counter-rotating Taylor-Couette (CRTC) system is studied using large-eddy simulation. The numerical methodology employed is validated, for both the mean and second-order statistics, with the direct numerical simulation (DNS) data available in the literature, for a range of Reynolds numbers from 500 to 4000. Thereafter, turbulent flow occurring in this system at Reynolds numbers of 8000 and 16000 are studied, and the results obtained are analyzed using mean and second-order statistics, vortical structures, velocity vector plots and power energy spectra. Further, the spatio-temporal variation of azimuthal velocity, extracted near the inner cylinder, shows the existence of herringbone like patterns similar to that observed in the previous studies. The effect of eccentricity of the inner cylinder with respect to the outer cylinder is studied, on the turbulent flow in the CRTC system, for two different eccentricity ratios of 0.2 and 0.5 and for two different Reynolds numbers of 1500 and 4000. The results of the eccentric CRTC are analyzed using contours of pressure, mean and second-order statistics, velocity vectors, vortical structures, and turbulence anisotropy maps. It is observed from the eccentric CRTC simulations that the smaller-gap region seems to contain higher amplitude fluctuations and more vortical structures when compared with the larger-gap region. The mean turbulent kinetic energy contours do not change qualitatively with the Reynolds number, however, quantitatively a higher turbulent kinetic energy is observed in the higher Reynolds number case of 4000.     

PIV measurements of a turbulent jet issuing from round sharp-edged plate

An experimental investigation is presented of a turbulent jet issuing from a round sharp-edged orifice plate (OP) into effectively unbounded surroundings. Planar measurements of velocity were conducted using Particle Image Velocimetry (PIV) in the near and transition regions. The Reynolds number, based on the jet initial diameter and velocity, is approximately 72,000. The instantaneous and mean velocities, Reynolds normal and shear stresses were obtained. The centerline velocity decay and the half-velocity radius were derived from the mean velocity. It is revealed that primary coherent structures occur in the near field of the OP jet and that they are typically distributed asymmetrically with respect to the nozzle axis. Comparison of the present PIV and previous hot-wire measurements for the OP jet suggests that high initial turbulence intensity leads to reduced rates of decay and spread of the mean flow field and moreover a lower rate of variation of the turbulence intensity. Results also show that self-similarity of the mean flow is well established from the transition region while the turbulent statistics are far from self-similar within the measured range to 16 diameters.