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.     

The effect of riblets on laminar to turbulent transition

Experiments conducted on the effect of riblets on the laminar-to-turbulent transition of a flat plate in a water tunnel are reported. Transition was determined using a Laser Doppler Velocimeter (LDV). A smooth reference surface was compared to five riblet surfaces for a range of Reynolds numbers. Smooth surface transition Reynolds number was about 2.75 × 10⁶. All of the five tested riblet surfaces had lower transition Reynolds numbers. A critical roughness Reynolds number of about 6 was determined for one of the riblet surfaces. This is much lower than the generally accepted value of 25, considered safe for distributed roughness.     

Newtonian liquid jet impaction on a high-speed moving surface

In the railroad industry a friction modifying agent may be applied to the rail or wheel in the form of a liquid jet. In this mode of application the interaction between the high-speed liquid jet and a fast moving surface is important. Seven different Newtonian liquids with widely varying shear viscosities were tested to isolate the effect of viscosity from other fluid properties. Tests were also done on five surfaces of different roughness heights to investigate the effects of surface roughness. High-speed video imaging was employed to scrutinize the interaction between the impacting jet and the moving surface. For all surfaces, decreasing the Reynolds number reduced the incidence of splash and consequently enhanced the transfer efficiency. At the elevated Weber numbers of the testing, the Weber number had a much smaller impact on splash than the Reynolds number. The ratio of the surface velocity to the jet velocity has only a small effect on the splash, whereas increasing the roughness-height-to-jet-diameter ratio substantially decreased the splash threshold.     

Newtonian liquid jet impaction on a high-speed moving surface

In the railroad industry a friction modifying agent may be applied to the rail or wheel in the form of a liquid jet. In this mode of application the interaction between the high-speed liquid jet and a fast moving surface is important. Seven different Newtonian liquids with widely varying shear viscosities were tested to isolate the effect of viscosity from other fluid properties. Tests were also done on five surfaces of different roughness heights to investigate the effects of surface roughness. High-speed video imaging was employed to scrutinize the interaction between the impacting jet and the moving surface. For all surfaces, decreasing the Reynolds number reduced the incidence of splash and consequently enhanced the transfer efficiency. At the elevated Weber numbers of the testing, the Weber number had a much smaller impact on splash than the Reynolds number. The ratio of the surface velocity to the jet velocity has only a small effect on the splash, whereas increasing the roughness-height-to-jet-diameter ratio substantially decreased the splash threshold.     

Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Roughness effects in low-<Emphasis Type="Italic"> Re</Emphasis><Subscript><Emphasis Type="Italic"> θ</Emphasis></Subscript> open-channel turbulent boundary layers

This paper reports velocity measurements obtained on a smooth and two geometrically different types of rough surfaces in an open channel. The measurements were obtained using a laser-Doppler anemometer. The recent boundary layer theory proposed by George and Castillo (1997) and conventional scaling laws are used to analyze the data. The present flow shows a strong structural similarity to a canonical turbulent boundary layer in the inner layer. The results demonstrate that surface roughness increases the wake parameter. Surface roughness also enhances the levels of turbulence intensities, Reynolds shear stress and triple correlations over most of the boundary layer, but decreases the stress anisotropy.     

Hydrodynamic forces acting on a rigid fixed sphere in early transitional regimes

A spectral – spectral-element code is used to investigate the hydrodynamic forces acting on a fixed sphere placed in a uniform flow in the Reynolds number interval [10–320] covering the early stages of transition, i.e. the steady axisymmetric regime with detached flow, the steady non-axisymmetric and the unsteady periodic regimes of the sphere wake. The mentioned changes of regimes, shown by several authors to be related to a regular and a Hopf bifurcations in the wake, result in significant changes of hydrodynamic action of the flow on the sphere. In the present paper, we show that the loss of axisymmetry is accompanied not only by an onset of lift but also of a torque and we give accurate values of drag, lift and torque in the whole interval of investigated Reynolds numbers. Among other results show, moreover, that each bifurcation is accompanied also by a change of the trend of the drag versus Reynolds number dependence, the overall qualitative effect of instabilities being an increase of drag.     

The wake of falling disks at low Reynolds numbers

We visualized the wake structure of circular disks falling vertically in quiescent water.The evolution of the wake was shown to be similar to the flow patterns behind a fixed disk.The Reynolds number,Re = Ud/ν,is in the range of 40 200.With the ascension of Reynolds numbers,a regular bifurcation occurred at the first critical Reynolds number Re c 1,leading to a transition from an axisymmetric wake structure to a plane symmetric one;A Hopf bifurcation took place at the second critical Reynolds number Re c 2,as the wake structure became unsteady.Plane symmetry of the wake structure was first lost as periodic vortex shedding appeared,but recovered at higher Reynolds number.The difference between the two critical Reynolds numbers was found to be shape-dependent,as we compared our results for thin discs with those for other falling bodies,such as spheres and cones.This observation could be understood in terms of the instability mechanism of the vortical structure.     

Scalar dispersion in the near wake of a simplified model car

Experimental results on tracer gas diffusion within the near wake of a simplified model car (Ahmed model with a rear slant angle of 25°) are presented. Pollutant emission is simulated using heated air injected through a small pipe at one side of the model base. Fine cold wire thermometry is used to measure instantaneous temperature excess in the near wake. Characteristics of the temperature field over the Reynolds number range (1.3×10⁴<Re _L<7×10⁴) show strong differences as a result of transition in the wake at a critical Reynolds number Re _Lc=2.7×10⁴.     

Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.     

Stability of dispersed-particle shape at small Reynolds numbers

The results of experimental studies of the conditions of loss of stability of the shape of a single dispersed-phase inclusion (droplet and bubble) during its motion in a viscous fluid at low Reynolds numbers are presented. It is shown that in the conditions considered the deformation of an initially spherical inclusion occurs due to the development of the Rayleigh-Taylor instability, as a critical value of the Bond number is attained. It is found that the onset of deformation of the phase interface and the instability mechanism depend strongly on the particle motion regime. A range of critical Reynolds numbers, corresponding to the boundaries of the regions of the Rayleigh-Taylor and Kelvin-Helmholtz instabilities, is determined.     

Hyperbolic Approximation of the Navier-Stokes Equations for Viscous Mixed Flows

Simplified two-dimensional Navier-Stokes equations of the hyperbolic type are derived for viscous mixed (with transition through the sonic velocity) internal and external flows as a result of a special splitting of the pressure gradient in the predominant flow direction into hyperbolic and elliptic components. The application of these equations is illustrated with reference to the calculation of Laval nozzle flows and the problem of supersonic flow past blunt bodies. The hyperbolic approximation obtained adequately describes the interaction between the stream and surfaces for internal and external flows and can be used over a wide Mach number range at moderate and high Reynolds numbers. Examples of the calculation of viscous mixed flows in a Laval nozzle with large longitudinal throat curvature and in a shock layer in the neighborhood of a sphere and a large-aspect-ratio hemisphere-cylinder are given. The problem of determining the drag coefficient of cold and hot spheres is solved in a new formulation for supersonic air flow over a wide range of Reynolds numbers. In the case of low and moderate Reynolds numbers a drag reduction effect is detected when the surface of the sphere is cooled.     

介观双粗糙弹塑性流体动力润滑界面法向接触刚度模型

弹性流体动力润滑状态通常出现在机械高副零部件的点/线接触部位,如齿轮、轴承和蜗轮蜗杆等.宏观上点/线接触在介观层面表现为两粗糙表面的接触,在微观层面上则又表现为微凸体间的接触.由于在中/重载荷作用下,粗糙表面上的微凸体发生接触后会产生弹塑性/塑性变形,从而使得两粗糙表面的弹流润滑接触转变为弹塑性流体动力润滑接触.此外,界面的接触刚度决定了机械装备的整机刚度.为了精确获得弹性流体动力润滑状态下界面法向接触刚度及其主要影响因素,基于界面的法向接触刚度由固体接触刚度和润滑油膜刚度两部分构成的思想,根据固体弹塑性理论和流体动力学理论,分别对界面间微凸体侧接触及部分膜流体动力润滑进行分析,从微观入手揭示双粗糙表面弹塑性流体动力润滑接触机理,进而建立考虑微凸体侧接触弹塑性变形的流体动力润滑界面法向接触刚度模型.通过仿真分析,揭示了法向载荷、卷吸速度、表面粗糙度及润滑介质特性等因素对润滑界面法向接触刚度的影响规律.研究表明：在相同速度、粗糙度及润滑油黏度的工况下,固体接触刚度和油膜接触刚度均随着法向接触载荷的增加呈非线性增大;在相同载荷、速度及润滑油黏度的工况下,接触表面粗糙度越大,表面形貌对于润滑...     

CaCO3 scaling in AISI 316 stainless steel tubes – effect of thermal and hydraulic parameters on the induction time and growth rate

Calcium Carbonate (CaCO₃) is predominantly present in cooling water which is commonly used as a coolant in many industrial processes. It has inverse solubility characteristics i.e., it is less soluble in warm water, resulting in the deposition of scale on heat transfer surfaces. An experimental study was carried out to determine the effect of tube surface temperature, Reynolds number, tube diameter and salt concentration on the induction time of CaCO₃ scaling. It was observed that tube surface temperature, Reynolds number and tube diameter had no effect on the onset time of scaling, whereas salt concentration and tube surface roughness had a profound influence on the induction period. The data collected from the experiments were used to develop dimensionless fouling resistance models for estimation and prediction purposes. Received on 22 December 1997     

Numerical Simulation of the Flow Around an Infinitely Long Circular Cylinder in the Transition Regime

The development of three-dimensional structures and the succeeding transition to turbulence occurs in the wake of a circular cylinder at Reynolds numbers 190≤Re≤330. This regime is investigated numerically by means of a spectral element method. Earlier numerical works aimed mainly at reproducing characteristic wake patterns observed in experiments. Small sizes of computational domains and short integration times were chosen to save computational resources. Consequently, the quantitative results show a considerable scatter. Within this work, a step by step approach to highly accurate direct numerical simulations is described. Thorough studies of the effect of resolution and blockage are performed in the laminar, two-dimensional regime, resulting in Reynolds number relationships that exactly reproduce experimental data. Based on these results, a stability analysis is performed to obtain wavelengths that are unstable against spanwise perturbations and the critical Reynolds number for the onset of three-dimensionality. The most unstable wavelengths of the “mode A” and “mode B” instabilities and its multiples are used as periodicity length for direct numerical simulations. Effects of integration time, resolution in streamwise as well as spanwise directions, and periodicity length on the flow quantities are studied. Numerically obtained Reynolds number relationships of Strouhal number and base-pressure coefficients that fit accurately within measured results are given for the first time. Curves for drag and lift coefficients are provided and compared with previous numerical studies. Furthermore, physical interpretations of the wake transition are discussed. Since the separation of physical features and effects of experimental arrangements are frequently an open question, our numerical results are able to supply a contribution to the understanding of the physics of cylinder flow. Received 12 September 2000 and accepted 26 June 2001     

Surface roughness effects in a short porous journal bearing with a couple stress fluid

In this paper, a theoretical study of the effect of surface roughness in hydrodynamic lubrication of a porous journal bearing with couplestress fluid as lubricant is made. The modified Reynolds equations accounting for the couple stresses and randomized surface roughness structure are mathematically derived. The Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to study the effects of surface roughness on the static characteristics of a short porous journal bearing with couplestress fluid as lubricant. Further, it is assumed that, the roughness asperity heights are small compared to the film thickness. It is observed that, the effects of surface roughness on the bearing characteristics are more pronounced for couplestress fluids as compared to the Newtonian fluids.     

An extension of the second moment closure model for turbulent flows over macro rough walls

An advanced second moment closure for rough wall turbulence is proposed. In contrast to previously proposed models relying on an empirical correlation based on equivalent sand grain roughness, the proposed model mathematically derives roughness effects by applying spatial and Reynolds averaging to the governing equations. The additional terms in the momentum equations are the drag force and inhomogeneous roughness density terms. The drag force term is modeled with respect to the plane porosity and plane hydraulic diameter. The two-component limit pressure-strain model is applied to the additional pressure-strain term, which is related to the external force terms. An evaluation of turbulence over surfaces with randomly distributed semi-spheres confirms that the developed model reasonably reproduces the effects of roughness on mean velocity, Reynolds stress, and energy dissipation. Turbulence over rough surfaces of marine paint is also simulated to assess the predictive performance for higher Reynolds number turbulent flows over real rough surfaces. The developed model successfully reproduces the dependence of the Reynolds number on roughness effects. Moreover, qualitative agreement of the skin friction increase with the experimental data is confirmed.     

Stabilization of cylinder wakes in shallow water flows by means of roughness elements: an experimental study

Shallow wakes that occur in a wide range of natural flows tend to generate instabilities that develop into large, 2D coherent structures (2DCS). We present the results of an experimental study to stabilize shallow wakes by local, enhanced bottom roughness. Two successful stabilization strategies are compared to a base case of an unsteady bubble wake. First, localized bed roughness is placed in the lateral shear layers near the shoulders of the cylinder. Second, a local roughness element is placed at the end of the recirculation bubble, in the downstream region where large-scale vortices would normally shed. Dye visualization is used to assess the qualitative behavior of the wake, and two-component laser Doppler velocimetry (LDV) measurements are made to measure the Reynolds stress distributions and time-averaged velocity profiles. In both stabilization cases, a minimum patch size of the enhanced roughness elements is required for stabilization, which depends on the momentum thickness of the shear layers and the locations of enhanced Reynolds shear stresses. The main effect of the wake stabilization is a reduction in momentum exchange with the ambient flow due to damping of the large 2DCS. This reduction in eddy diffusivity results in a narrower wake and a slower decay of the centerline velocity deficit with downstream distance compared to the base case of an unsteady bubble wake.     

Study of a free surface in open-channel water flows in the regime from “weak” to “strong” turbulence

A liquid–air interface in an inclined open-channel water flows was studied experimentally as the flow changes from “weak” to “strong” turbulence. In this regime, the interface is highly agitated by bulk eddies and waves, but not broken. The surface deformation statistics were obtained under a variety of conditions, including different inclination angles and flow rates. The parameter space is described in terms of Reynolds, Froude, and Weber numbers. The surface-normal displacements were obtained via the time series of the fluctuating flow depth with an ultrasound transducer. Independently, the in-plane changes in surface structures were acquired with a high-speed camera. These structures are seen as surface cells. By applying a newly developed image processing technique, the cell celerity was found to agree well with the mean flow velocity. This suggests that the cells appear when a turbulent surface-renewal eddy interacts with the interface. As the flow changes to strong turbulence, the turbulence–interface interactions become dominant over the wave phenomena, and the turbulent structures at the surface become more 3D (similar to those in the bulk flow), compared to quasi-2D structures in the weak turbulence.     

Hydrodynamic instability of separated viscous flow around a circular cylinder

A uniform viscous flow around a circular cylinder is studied numerically in the Reynolds number range from 0 to 500. It is shown that the existence and the basic properties of self-oscillating regimes are specified by the evolution of their hydrodynamic instability. It is found that the vortex formation in a near wake is associated with the separation zone dynamics in the main flow. The values of critical Reynolds numbers for the four successive bifurcations of the self-oscillating regimes of flow are obtained. An interpretation of experimental data on the vortices in the near wake is discussed.