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.     

Wind tunnel simulation of wind loading on a solid structure of revolution

The wind tunnel simulations of wind loading on a solid structure of revolution with one smooth and five rough surfaces were conducted using wind tunnel tests. Timemean and fluctuating pressure distributions on the surface were obtained, and the relationships between the roughness Reynolds number and pressure distributions were analyzed and discussed. The results show that increasing the surface roughness can significantly affect the pressure distribution, and the roughness Reynolds numbers play an important role in the change of flow patterns. The three flow patterns of subcritical, critical and supercritical flows can be classified based on the changing patterns of both the mean and the fluctuating pressure distributions. The present study suggests that the wind tunnel results obtained in the supercritical pattern reflect more closely those of full-scale solid structure of revolution at the designed wind speed.     

Study of fracture permeability using Lattice Gas Automata

We study the problem of flow permeability of fracture joints using Lattice-Gas Automata simulations. We model the fracture as a rough channel bounded by a self-affine surface. Changing the surface roughness exponent, rough walls having different microstructures are obtained. Different relative roughnesses — defined as the height of the largest surface asperity divided by the mean aperture — are obtained pulling apart the two surfaces that constitute the rough walls of the channel. We calculate the macroscopic variables volume flow rate and pressure difference using microscopic balances. In the low Reynolds number regime the pressure difference and the flow rate are linearly related (the behavior is described by Darcy's law). In this regime, we study the effect of geometry on the permeability. We have found that permeability is independent of the surface roughness exponentH and it is fully determined in terms of the relative roughness and mean aperture of the fracture joint. For larger Reynolds numbers a transition to a regime in which pressure difference and flow rate are not longer linearly related is observed. This transition is observed in a domain of Reynolds numbers for which the behavior in a smooth channel remains linear. We discuss this transition.     

An experimental investigation of the combined effects of surface curvature and streamwise pressure gradients both in laminar and turbulent flows

Flow and heat transfer characteristics over flat, concave and convex surfaces have been investigated in a low speed wind tunnel in the presence of adverse and favourable pressure gradients (k), for a range of –3.6 × 10^–6 ≤ k ≤ +3.6 × 10^–6. The laminar near zero pressure gradient flow, with an initial momentum thickness Reynolds number of 200, showed that concave wall boundary layer was thinner and heat transfer coefficients were almost 2 fold of flat plate values. Whereas for the same flow condition, thicker boundary layer and 35% less heat transfer coefficients of the convex wall were recorded with an earlier transition. Accelerating laminar flows caused also thinner boundary layers and an augmentation in heat transfer values by 28%, 35% and 16% for the flat, concave and convex walls at k = 3.6 × 10^–6. On the other hand decelerating laminar flows increased the boundary layer thickness and reduced Stanton numbers by 31%, 26% and 22% on the flat surface, concave and convex walls respectively. Turbulent flow measurements at k = 0, with an initial momentum thickness Reynolds number of 1100, resulted in 30% higher and 25% lower Stanton numbers on concave and convex walls, comparing to flat plate values. Moreover the accelerating turbulent flow of k = 0.6 × 10^–6 brought about 29%, 30% and 24% higher Stanton numbers for the flat, concave and convex walls and the decelerating turbulent flow of k = –0.6 × 10^–6 caused St to decrease up to 27%, 25% and 29% for the same surfaces respectively comparing to zero pressure gradient values. An empirical equation was also developed and successfully applied, for the estimation of Stanton number under the influence of pressure gradients, with an accuracy of better than 4%.     

Experiment on smooth,circular cylinders in cross-flow in the critical Reynolds number regime

Experiments were conducted for 2D circular cylinders at Reynolds numbers in the range of 1.73 × 10⁵–5.86 × 10⁵. In the experiment, two circular cylinder models made of acrylic and stainless steel, respectively, were employed, which have similar dimensions but different surface roughness. Particular attention was paid to the unsteady flow behaviors inferred by the signals obtained from the pressure taps on the cylinder models and by a hot-wire probe in the near-wake region. At Reynolds numbers pertaining to the initial transition from the subcritical to the critical regimes, pronounced pressure fluctuations were measured on the surfaces of both cylinder models, which were attributed to the excursion of unsteady flow separation over a large circumferential region. At the Reynolds numbers almost reaching the one-bubble state, it was noted that the development of separation bubble might switch from one side to the other with time. Wavelet analysis of the pressure signals measured simultaneously at θ = ±90° further revealed that when no separation bubble was developed, the instantaneous vortex-shedding frequencies could be clearly resolved, about 0.2, in terms of the Strouhal number. The results of oil-film flow visualization on the stainless steel cylinder of the one-bubble and two-bubble states showed that the flow reattachment region downstream of a separation bubble appeared not uniform along the span of the model. Thus, the three dimensionality was quite evident.     

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.     

Drag measurements on V-grooved surfaces on a body of revolution in axial flow

In water flows with velocities of up to 9 m/s the friction drag of a body of revolution in axial flow was investigated for dependence on the body surface structure. This was done for different types of riblet film fixed on the surface with the riblet direction aligned with the flow. The lateral spacing between the triangular shaped riblets varied between 0.033 mm and 0.152 mm. In all cases the riblet spacing was equal to the riblet height. For comparison a smooth reference film was used.Depending on the Reynolds number and the non-dimensional riblet spacings ⁺, a turbulent drag reduction of up to 9% could be achieved with riblets in comparison with the flow over a smooth surface.In the region of transition to turbulent flow and with non-dimensional riblet spacings ofs ⁺10–15 drag reductions of up to 13% were obtained. It is therefore conjectured, that in addition to hampering the near wall momentum exchange, the riblets can delay the development of initial turbulent structures in time and space.     

Investigation of the influence of the unit Reynolds number on the transition of a boundary layer on a sharp cone

To establish the influence of the unit Reynolds number on the transition of a boundary layer on the side surface of a cone, the transition was investigated on a model of a sharp cone with half-angle = 7.5 ° and lengths from 150 to 400 mm. The experiments were made in a shock tube at Mach number M = 6.1 in the wide range of Reynolds numbers Re_eL = 1.3·10⁶-5.5·10⁷. The position of the transition region was determined from the results of measurement of the local heat flux by calorimetric thermocouple converters. Data were obtained on the influence on the transition of the unit Reynolds number at large values. It was also shown that under the investigated conditions the base region does not influence the transition of the boundary layer on the surface of the cone.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 32–38, July–August, 1982.     

On the onset of instability in the wake of super-hydrophobic spheres

We report an experimental investigation of free falling super-hydrophobic (SH) spheres in glycerine-water mixtures over a wide range of Reynolds number. SH coatings have the ability to reduce the contact area between the surrounding liquid and the solid surface by entrapping an air layer in the surface roughness. We investigate the effect of this air plastron on the hydrodynamic performance of spheres, focusing our attention on the onset of wake instabilities. Our results emphasise the key role of the surface roughness properties on the triggering of wake instabilities. It is shown that, unlike what was reported in previous numerical studies on SH bluff-bodies, local deformation of the interface may act as a by-pass mechanism promoting earlier transition, yielding a decrease of the critical Reynolds number at which the wake becomes unstable. A scenario coupling the hydrodynamic instabilities (scaling with the Reynolds number) and the interface deformation (scaling with the roughness-based Weber number) is proposed to describe the different transition mechanisms in presence of SH surfaces. It is found that the promotion of wake instabilities over SH surfaces occurs when the roughness-based Weber number is larger than a critical threshold. These findings are of primary importance for guiding the design of resilient and efficient SH surfaces.     

Effects of riblet bends on pipe flows

Four riblet bends were tested to investigate the effects of riblets on pipe flows including the secondary flow on the Reynolds numbers; Re _D =6×10³–4×10⁴. The pressure gradients on the smooth pipe downstream from the riblet bends were measured, and also the pressure losses of the bends only were measured. All riblet bends reduced the pressure gradient on the smooth pipe downstream from them, which means a drag reduction. Two of the riblet bends showed the maximum drag reduction of about 4 percent at Re _D = 6500; this reduction rate was significant considering the uncertainty of the present experiments. Since the pressure losses of these two riblet bends were almost identical to that of the smooth bend at Re _D = 6500, they could cause a net drag reduction of about 4 percent on the piping system including these bends at that Reynolds number. Furthermore, the velocity profiles measured by LDV indicated that the secondary flow becomes weaker downstream from the riblet bends when a drag reduction is recognized there.Nomenclature D pipe diameter - D ₀ the distance from the valley to the valley passing through the pipe center - H height of groove - P nondimensional static pressure (p/it/(U ₀ ² ):p is gauge pressure) - dP/dX nondimensional pressure gradient - Rc curvature of bend - Re _D Reynolds number based on bulk velocity and pipe diameter - s spacing of groove - U mean streamwise velocity along the horizontal diameter - U ₀ bulk velocity - V mean vertical velocity along the horizontal diameter - x streamwise direction along the pipe axis (see Fig. 1) - X nondimensionalx (=x/D) - y radial direction in the horizontal plane which is perpendicular to the plane including the bend (see Fig. 1) - yUV swirl intensity (nondimensional swirl intensity:yUV/(DU ₀ ² ))     

SOME EXPERIMENTS ON FLOW-INDUCED VIBRATION OF A CIRCULAR CYLINDER WITH SURFACE ROUGHNESS

Aeroelastic instability of a circular cylinder with surface roughness was experimentally studied by free-oscillation tests in a wind tunnel. Flows at high Reynolds numbers could be simulated at relatively low wind velocities, by introducing surface roughness, so as to reduce the value of the critical Reynolds number. The response amplitudes of a roughened cylinder oscillating in the transverse (cross-flow) direction in the flow were measured. The measured range of reduced velocity is about 1·5–8, which includes the critical velocity. The value of a reduced mass-damping parameter (the Scruton number) is constant at about 6. For the aeroelastic instability in the transverse direction, it was found that the oscillation of the roughened cylinder induced by a vortex-excitation is damped down in a small velocity range covering the critical Reynolds number. At Reynolds numbers higher than the critical value, a roughened cylinder vibrates with a large amplitude again, associated with a lock-in phenomenon due to the coincidence of the wake-frequency and the natural frequency of the oscillating cylinder.     

Drag measurements on planar riblet surfaces at high subsonic speeds

This paper presents the results of an investigation of riblet performance at high subsonic Mach numbers, and Reynolds numbers of about 20 000 based on the momentum thickness, in both zero and adverse pressure gradient boundary layers. The maximum length Reynolds number of the ribbed section was 3.4×10⁷ so the results were directly relevant to flight applications on the engine nacelles of civil airliners. Seven different sizes of riblets with heights h (equal to spacing s) ranging from 0.0007 (0.0178mm) to 0.006 (0.1524 mm) have been studied, covering a range of h+, s+ from 10 to 106. The maximum percentage skin friction reduction, as deduced from velocity profiles measured at the downstream end of the riblet surfaces, under nominally zero pressure gradient conditions was 5.5±1; rather less than that recorded in low speed studies, but consistent with a recent theoretical analysis of the effect of Reynolds number. The values of h+ required for maximum and zero skin friction reduction agreed closely with other data. In addition subsequent floating element drag balance measurements revealed little effect of yaw angles up to 15°, again in line with other findings, and also suggested that the extent of the initial development length on, and recovery length behind, the riblets was approximately 5. The adverse pressure gradient studies indicated that riblet performance was essentially unaffected by mild gradients (=0.25), but diminished to zero in a more severe gradient (=0.5).     

Computation of high Reynolds number flow around a circular cylinder with surface roughness

Incompressible high-Reynolds-number flows around a circular cylinder are analyzed by direct integration of the Navier-Stokes equations using finite-difference method. A generalized coordinate system is used so that a sufficient number of grid points are distributed in the boundary layer and the wake. A numerical scheme which suppresses non-linear instability for calculations of high-Reynolds-number flows is developed. The computation of an impulsively started flow at Re = 1200 is compared with corresponding experimental observations, and excellent agreements are obtained.A series of computations are carried out on the flow around a circular cylinder with surface roughness. The height of the roughness in these computations is 0.5% of the diameter. The range of Reynolds numbers is from 10³ to 10⁵; no turbulence model is employed. Sharp reduction of drag coefficient is observed near Re = 2 × 10⁴, which indicates that the critical Reynolds number is captured in the present computation.     

Riblet modelling using a second-moment closure

A low Reynolds number second-moment closure has been used to calculate a turbulent boundary layer which develops over a riblet surface with zero pressure gradient. The calculated mean velocity distributions compare favourably with measurements. Calculated Reynolds stresses away from the riblet surface region are also in agreement with measurements. In the vicinity of the riblets, the model reflects the increased anisotropy of the Reynolds stress tensor inadequately. Possible reasons for this shortcoming are discussed and suggestions for improving the model are made.     

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.     

Effect of longitudinal riblets on the aerodynamic characteristics of a straight wing

The results of balance aerodynamic tests on model straight wings with smooth and ribbed surfaces at an angle of attack =–4°–12°, Mach number M=0.15–0.63, and Reynolds number Re=2.4·10⁶–3.5·10⁶ are discussed. The nondimensional riblet spacings ⁺, which determines the effect of the riblets on the turbulent friction drag, and the effect of riblets on the upper and/or lower surface of a straight wing on its drag, lift, and moment characteristics are estimated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 33–38, March–April, 1995.     

Parametric Study on a Sinusoidal Riblet for Drag Reduction by Direct Numerical Simulation

The direct numerical simulation of fully developed turbulent channel flow with a sinusoidal riblet surface has been carried out at the friction Reynolds number of 110. Lateral spacing of adjacent walls in a sinusoidal riblet is varied sinusoidally in the streamwise direction. The average lateral spacing of a sinusoidal riblet is larger than the diameter of a quasi-streamwise vortex and its wetted area is smaller than that of ordinary straight-type riblets. We investigate the effect of sinusoidal riblet design parameters on the drag reduction rate and flow statistics in this paper. The parametric study shows that the maximum total drag reduction rate is approximately 9.8% at a friction Reynolds number of 110. The riblet induces downward and upward flows in the expanded and contracted regions, respectively, which contribute to periodic Reynolds shear stress. However, the random Reynolds shear stress decreases drastically as compared with the flat surface case, resulting in the reduction of total drag owing to the sinusoidal riblet. We also performed vortex tracking to discuss the motion of the vortical structure traveling over the sinusoidal riblet surface. Vortex tracking and probability analysis for the core of the vortical structure show that the vortical structure is attenuated owing to the sinusoidal riblet and follows the characteristic flow. These results show that the high skin-friction region on the channel wall is localized at the expanded region of the riblet walls. In consequence, the wetted area of the riblet decreases, resulting in the drag-reduction effect.     

Experimental study of the laminar-turbulent transition on a blunt cone

Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M _∞ = 6, and unit Reynolds number in the interval Re _∞,1 = 5.79 · 10⁶–5.66 · 10⁷ m^?1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re _∞,R ≈ 1.3 · 10⁵ beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.     

Numerical study of mixed convection and conduction in a 2-D square ventilated cavity with an inlet at the vertical glazing wall and outlet at the top surface

A steady state numerical study of combined laminar mixed convection and conduction heat transfer in a ventilated square cavity is presented. The air inlet gap is located at the bottom of a vertical glazing wall and air exits the cavity via a gap located at the top surface. Three locations for the opening at the top surface: left (case a), center (case b) and right side (case c) are considered. All the remaining surfaces are considered adiabatic. The mass, momentum and energy conservation equations were solved using the finite volume method for different Rayleigh numbers in the interval of 10⁴ < Ra < 10⁶ and Reynolds number in the interval of 100 < Re < 700. Temperature, flow field, and heat transfer rates are analyzed. The effect of the interaction between ambient conditions outside the glazing and the air inlet gap at the bottom for different air outlet gap positions at the top surface modifies the flow structure and temperature distribution of the air inside the cavity. The Nusselt number as a function of the Reynolds number was determined for the three cases. It was found that configuration for case (a) removes a higher amount of heat entering the cavity compared to cases (b) and (c). This is due to the short distance between the main stream and the glass wall surface. Thus, the forced airflow entering the cavity is assisted by the buoyancy forces, and most of the cavity remains at the inlet flow temperature, which should be appropriate for warm climates. These results may provide useful information about the heat transfer and fluid flow for future studies.