Time-dependent drag reduction and ageing in aqueous solutions of a cationic surfactant

The turbulent pipe flow of a highly dilute aqueous cationic surfactant solution is investigated by means of a pulsed ultrasound Doppler method with special emphasis on the wall boundary layer. The velocity profiles are recorded for several Reynolds numbers at varying ages of the solution. The wall shear stress velocities u _τ used for the normalization of the velocity profiles are determined by fitting the measured profiles to the universal linear velocity profile in the viscous sublayer. The theoretical pressure loss is then calculated from the numerical values of u _τ and compared to the experimental values. Two different scaling methods are discussed for the velocity fluctuations concerning the correlation of the root-mean square values with the effect and the amount of drag reduction. It is shown that outer scaling with the mean velocity is appropriate for the detection of drag reduction in surfactant solutions, rather than inner scaling with the wall shear stress velocity, which is common practice in investigations of 'usual' turbulent flows.     

Direct numerical simulation of turbulent flows through concentric annulus with circumferential oscillation of inner wall

Periodic wall oscillations in the spanwise or circumferential direction can greatly reduce the friction drag in turbulent channel and pipe flows. In a concentric annulus, the constant rotation of the inner cylinder can intensify turbulence fluctuations and enhance skin friction due to centrifugal instabilities. In the present study, the effects of the periodic oscillation of the inner wall on turbulent flows through concentric annulus are investigated by the direct numerical simulation (DNS). The radius ratio of the inner to the outer cylinders is 0.1, and the Reynolds number is 2 225 based on the bulk mean velocity U_m and the half annulus gap H. The influence of oscillation period is considered. It is found that for short-period oscillations, the Stokes layer formed by the circumferential wall movement can effectively inhibit the near-wall coherent motions and lead to skin friction reduction, while for long-period oscillations, the centrifugal instability has enough time to develop and generate new vortices, resulting in the enhancement of turbulence intensity and skin friction.     

Surfactant systems for drag reduction: Physico-chemical properties and rheological behaviour

The first part of the work presents an overview of the physical chemistry of surfactants which in aqueous solutions reduce the frictional loss in turbulent pipe flow. It is shown that these surfactants form rodlike micelles above a characteristic concentraionc _t. The experimental evidence for rodlike micelles are reviewed and the prerequisites that the surfactant system must fulfill in order to form rodlike micelles are given. It is demonstrated by electrical conductivity measurements that the critical concentration for the formation of spherical micelles shows little temperature dependence, whereasc _t increases very rapidly with temperature. The length of the rodlike micelles, as determined by electric birefringence, decreases with rising temperature and increases with rising surfactant concentration. The dynamic processes in these micellar systems at rest and the influence of additives such as electrolytes and short chain alcohols are discussed.In the second part, the rheological behaviour of these surfactant solutions under laminar and turbulent flow conditions are investigated. Viscosity measurements in laminar pipe and Couette flow show the build-up of a shear induced viscoelastic state, SIS, from normal Newtonian fluid flow. A complete alignment of the rodlike micelles in the flow direction in the SIS was verified by flow birefringence. In turbulent pipe flow, drag reduction occurs in these surfactant systems as soon as rodlike micelles are present in the solution. The extent and type of drag reduction, i.e. the shape of the friction factor versus Reynolds number curve, depends directly on the size, number and surface charge of the rodlike micelles. The friction factor curve of each surfactant investigated changes in the same characteristic way as a function of temperature. For each surfactant, independent of concentration, an upper absolute temperature limit,T _L, for drag reduction exists which is caused by the micellar dynamics.T _L is influenced by the hydrophobic chain length and the counter-ion of the surfactant system. A first attempt is made to explain the drag reduction of surfactants by combining the results of these rheological measurements with the physico-chemical properties of the micellar systems.     

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.     

Effects of Synthetic jets on a D-Shaped Cylinder wake at a Subcritical Reynolds Number

Effects of synthetic jets on the wake of a D-shaped cylinder is investigated experimentally at a Reynolds number Re_H= 47,000, based on incoming free-stream velocity and the cylinder height (H). The synthetic jets are introduced immediately from the upper and lower trailing edges of the cylinder. The upper and lower synthetic jets are operated in an in-phase or anti-phase mode, and at a momentum ratio C_μ= 1.0% and perturbation frequency St_A= 0.11 ?0.37. The cylinder wake with perturbation is examined in detail and compared with that without, based on smoke-wire flow visualization, pressure transducer and hotwire rake measurements, and data analyses of spectra, tempo-spatial cross-correlation and proper orthogonal decomposition (POD). Large-scale vortical structures in the cylinder wake are significantly modified by the synthetic jets perturbations, exhibiting symmetric or asymmetric patterns, depending on the perturbation frequency and phase relationship of the synthetic jets. These observations are internally correlated with the drag force variations.     

Low Reynolds number effects in open-channel turbulent boundary layers

The present study reports measurements of a turbulent boundary layer in an open-channel flow using fiber-optic laser Doppler anemometry. The Reynolds numbers based on momentum thickness and depth of flow are in the range 750≤Re _θ ≤2,400 and 15,300≤Re _h ≤54,200, respectively. It is shown that an accurate estimate of the wall shear stress can be made by fitting a fifth-order polynomial to the near-wall data. The effect of Reynolds number on the mean turbulence intensity and triple correlation is examined using both conventional scaling laws and the recent scaling laws proposed by George and Castillo. The present results show that different scaling laws lead to different conclusions on low Reynolds number effects.     

Numerical Simulation of the Negative Magnus Effect of a Two-Dimensional Spinning Circular Cylinder

Based on the finite volume method, the flow past a spinning circular cylinder at a low subcritical Reynolds number (Re =1 × 10 ⁵), high subcritical Reynolds number (Re =1.3 ×10 ⁵), and critical Reynolds number (Re =1.4 ×10 ⁵) were each simulated using the Navier-Stokes equations and the γ-Re _?? transition model coupled with the SST k?ω turbulence model. The system was solved using an implicit algorithm. The freestream turbulence intensity decay was effectively controlled by the source term method proposed by Spalart and Rumsey. The variations in the Magnus force as a function of the spin ratio, α were obtained for the three Reynolds numbers, and the flow mechanism was analyzed. The results indicate that the asymmetric transitions induced by spin affect the asymmetric separations at the top and bottom surfaces of the circular cylinder, which further affects the pressure distributions at the top and bottom surfaces of the circular cylinder and ultimately result in a negative Magnus force, whose direction is opposite to that of the classical Magnus force. This study is the first to use a numerical simulation method to predict a negative Magnus force acting on a spinning circular cylinder. At the low subcritical Reynolds number, the Magnus force remained positive for all spin ratios. At the high subcritical Reynolds number, the sign of the Magnus force changed twice over the range of the spin ratio. At the critical Reynolds number, the sign of the Magnus force changed only once over the range of the spin ratio. For relatively low spin ratios, the Magnus force significantly differed by Reynolds number; however, this variation diminished as the spin ratio increased.     

Experimental study on flow control of the turbulent boundary layer with micro-bubbles

The effect of micro-bubbles on the turbulent boundary layer in the channel flow with Reynolds numbers (Re) ranging from \(0.87\times 10 ^{5}\) to \(1.23\times 10^{5}\) is experimentally studied by using particle image velocimetry (PIV) measurements. The micro-bubbles are produced by water electrolysis. The velocity profiles, Reynolds stress and instantaneous structures of the boundary layer, with and without micro-bubbles, are measured and analyzed. The presence of micro-bubbles changes the streamwise mean velocity of the fluid and increases the wall shear stress. The results show that micro-bubbles have two effects, buoyancy and extrusion, which dominate the flow behavior of the mixed fluid in the turbulent boundary layer. The buoyancy effect leads to upward motion that drives the fluid motion in the same direction and, therefore, enhances the turbulence intense of the boundary layer. While for the extrusion effect, the presence of accumulated micro-bubbles pushes the flow structures in the turbulent boundary layer away from the near-wall region. The interaction between these two effects causes the vorticity structures and turbulence activity to be in the region far away from the wall. The buoyancy effect is dominant when the Re is relatively small, while the extrusion effect plays a more important role when Re rises.     

Flow and heat transfer characteristics of drag reducing surfactant solution in a helically coiled pipe

The reduction characteristic of turbulent drag and heat transfer of drag reduction surfactant solution flowing in a helically coiled pipe were experimentally investigated. The drag reduction surfactant used in the present study was the amine oxide type nonionic surfactant of oleyldihydroxyethylamineoxide (ODEAO, C₂₂H₄₅NO₃=371). The zwitterion surfactant of cetyldimethylaminoaciticacidbetaine (CDMB, C₂₀H₄₁NO₂=327) was added by 10% to the ODEAO solution in order to avoid the chemical degradation of ODEAO by ionic impurities in a test tape water. The experiments of flow drag and heat transfer reduction were carried out in the helically coiled pipe of coil to pipe diameter ratio of 37.5 and the helically coiled pipe length to pipe diameter of 1180.5 (pipe diameter of 14.4 mm) at various concentrations, temperatures and flow velocities of the ODEAO surfactant solution. The ODEAO solution showed a non-Newtonian behavior at high concentration of the ODEAO. From the experimental results, it was observed that the friction factor of the ODEAO surfactant solution flowing through the coiled pipe was decreased to a great extent in comparison with water as a Newtonian fluid in the turbulent flow region. Heat transfer measurements for water and the ODEAO solution were performed in both laminar and turbulent flow regions under the uniform heat flux boundary condition. The heat transfer coefficients for the ODEAO solution flow were the same as water flow in the laminar region. On the other hand, heat transfer reduction of the ODEAO solution flow was remarkedly reduced as compared with that of the water flow in the turbulent flow region.     

Taguchi design of three dimensional simulations for optimization of turbulent mixed convection in a cavity

This study discusses the application of Taguchi method in assessing maximum heat transfer rate for the turbulent mixed convection in an enclosure embedded with rotating isothermal cylinder. The simulations were planned based on Taguchi’s L16 orthogonal array with each trial performed under different conditions of position of the cylinder, Reynolds number (Re) and Rayleigh number (Ra). The thermal lattice Boltzmann based on D3Q19 methods without any turbulent submodels was purposed to simulate the flow and thermal fields. A relaxation time method with the stability constants is introduced to solve turbulent natural convection problems. Signal-to-noise ratios (S/N) analysis were carried out in order to determine the effects of process parameters and optimal factor settings. Finally, confirmation tests verified that Taguchi method achieved optimization of heat transfer rate with sufficient accuracy.     

Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier–Stokes Equations Near the Two Dimensional Couette Flow

In this work we study the long time inviscid limit of the two dimensional Navier–Stokes equations near the periodic Couette flow. In particular, we confirm at the nonlinear level the qualitative behavior predicted by Kelvin’s 1887 linear analysis. At high Reynolds number Re, we prove that the solution behaves qualitatively like two dimensional Euler for times \({{t \lesssim Re^{1/3}}}\), and in particular exhibits inviscid damping (for example the vorticity weakly approaches a shear flow). For times \({{t \gtrsim Re^{1/3}}}\), which is sooner than the natural dissipative time scale O(Re), the viscosity becomes dominant and the streamwise dependence of the vorticity is rapidly eliminated by an enhanced dissipation effect. Afterwards, the remaining shear flow decays on very long time scales \({{t \gtrsim Re}}\) back to the Couette flow. When properly defined, the dissipative length-scale in this setting is \({{\ell_D \sim Re^{-1/3}}}\), larger than the scale \({{\ell_D \sim Re^{-1/2}}}\) predicted in classical Batchelor–Kraichnan two dimensional turbulence theory. The class of initial data we study is the sum of a sufficiently smooth function and a small (with respect to Re^?1) L² function.     

Predicting Turbulent Spectra in Drag-reduced Flows

In the present work we describe how turbulent skin-friction drag reduction obtained through near-wall turbulence manipulation modifies the spectral content of turbulent fluctuations and Reynolds shear stress with focus on the largest scales. Direct Numerical Simulations (DNS) of turbulent channels up to Re _τ = 1000 are performed in which drag reduction is achieved either via artificially removing wall-normal turbulent fluctuations in the vicinity of the wall or via streamwise-travelling waves of spanwise wall velocity. This near-wall turbulence manipulation is shown to modify turbulent spectra in a broad range of scales throughout the whole channel. Above the buffer layer, the observed changes can be predicted, exploiting the vertical shift of the logarithmic portion of the mean streamwise velocity profile, which is a classic performance measure for wall roughness or drag-reducing riblets. A simple model is developed for predicting the large-scale contribution to turbulent fluctuation and Reynolds shear stress spectra in drag-reduced turbulent channels in which a flow control acts at the wall. Any drag-reducing control that successfully interacts with large scales should deviate from the predictions of the present model, making it a useful benchmark for assessing the capability of a control to affect large scales directly.     

Direct numerical simulation of Taylor–Couette turbulent flow controlled by a traveling wave-like blowing and suction

In wall turbulence, a traveling wave-like control is known to decrease the skin-friction drag and induce the relaminarization phenomenon. Because it is noteworthy to investigate the control effect in other canonical flows, direct numerical simulations of fully developed turbulent Taylor–Couette flows are performed. The Reynolds number, based on the wall velocity of a rotating inner cylinder and the radius of a centerline between cylinders, is set to 84,000. The traveling wave-like blowing and suction is imposed on the inner or outer cylinder wall, and the control effect is parametrically investigated. In the inner cylinder control, the torque reduction is obtained when the wave travels in the co-rotating direction with the inner cylinder, and its wavespeed is faster than the rotation. In the outer cylinder control, in contrast, the torque reduction is obtained when the wave propagates in the opposite direction. While the control is imposed on one side wall (i.e., inner or outer cylinder), the control affects the entire flow region. The Taylor vortex remains, while the traveling wave affects its strength. The three-component decomposition analysis shows that the traveling wave creates the coherent contribution on the torque, while the random contribution on it is reduced. Accordingly, a major factor of the torque reduction in the Taylor–Couette flow is the reduction of the random contribution. In addition, for the faster wavespeed cases with the small wavenumber (i.e., the long wavelength), the drag reduction larger than 60% is obtained and the relaminarization occurs in these cases.     

Experimental Control of Turbulent Boundary Layers with In-plane Travelling Waves

The experimental control of turbulent boundary layers using streamwise travelling waves of spanwise wall velocity, produced using a novel active surface, is outlined in this paper. The innovative surface comprises a pneumatically actuated compliant structure based on the kagome lattice geometry, supporting a pre-tensioned membrane skin. Careful design of the structure enables waves of variable length and speed to be produced in the flat surface in a robust and repeatable way, at frequencies and amplitudes known to have a favourable influence on the boundary layer. Two surfaces were developed, a preliminary module extending 152 mm in the streamwise direction, and a longer one with a fetch of 2.9 m so that the boundary layer can adjust to the new surface condition imposed by the forcing. With a shorter, 1.5 m portion of the surface actuated, generating an upstream-travelling wave, a drag reduction of 21.5% was recorded in the boundary layer with Re _τ =?1125. At the same flow conditions, a downstream-travelling produced a much smaller drag reduction of 2.6%, agreeing with the observed trends in current simulations. The drag reduction was determined with constant temperature hot-wire measurements of the mean velocity gradient in the viscous sublayer, while simultaneous laser Doppler vibrometer measurements of the surface recorded the wall motion. Despite the mechanics of the dynamic surface resulting in some out-of-plane motion (which is small in comparison to the in-plane streamwise movement), the positive drag reduction results are encouraging for future investigations at higher Reynolds numbers.     

Swirling-strength based large eddy simulation of turbulent flow around single square cylinder at low Reynolds numbers

In view of the fact that large scale vortices play the substantial role of momentum transport in turbulent flows, large eddy simulation(LES) is considered as a better simulation model. However, the sub-grid scale(SGS) models reported so far have not ascertained under what flow conditions the LES can lapse into the direct numerical simulation. To overcome this discrepancy, this paper develops a swirling strength based the SGS model to properly model the turbulence intermittency, with the primary characteristics that when the local swirling strength is zero, the local sub-grid viscosity will be vanished. In this paper, the model is used to investigate the flow characteristics of zero-incident incompressible turbulent flows around a single square cylinder(SC)at a low Reynolds number range Re ∈ [103, 104]. The flow characteristics investigated include the Reynolds number dependence of lift and drag coefficients, the distributions of time-spanwise averaged variables such as the sub-grid viscosity and the logarithm of Kolmogorov micro-scale to the base of 10 at Re = 2 500 and 104, the contours of spanwise and streamwise vorticity components at t = 170. It is revealed that the peak value of sub-grid viscosity ratio and its root mean square(RMS) values grow with the Reynolds number. The dissipation rate of turbulent kinetic energy is larger near the SC solid walls.The instantaneous factor of swirling strength intermittency(FSI) exhibits some laminated structure involved with vortex shedding.     

Transition from vortex to wall driven turbulence production in the Taylor–Couette system with a rotating inner cylinder

Axisymmetrically stable turbulent Taylor vortices between two concentric cylinders are studied with respect to the transition from vortex to wall driven turbulent production. The outer cylinder is stationary and the inner cylinder rotates. A low Reynolds number turbulence model using the k‐ω formulation, facilitates an analysis of the velocity gradients in the Taylor–Couette flow. For a fixed inner radius, three radius ratios 0.734, 0.941 and 0.985 are employed to identify the Reynolds number range at which this transition occurs. At relatively low Reynolds numbers, turbulent production is shown to be dominated by the outflowing boundary of the Taylor vortex. As the Reynolds number increases, shear driven turbulence (due to the rotating cylinder) becomes the dominating factor. For relatively small gaps turbulent flow is shown to occur at Taylor numbers lower than previously reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Separation zones in the flow near a small-angle convex corner

On the basis of an asymptotic analysis of the Navier-Stokes system of equations for large Reynolds numbers (Re → ∞), the plane incompressible fluid flow near a surface having a convex corner with a small angle 2θ* is investigated. It is shown that for θ* = O(Re^?1/4), in addition to the known solution that describes a separated flow completely localized in a thin “viscous” sublayer of the interaction region near the corner point, another solution corresponding to a flow with a developed separation zone is possible. For θ ₀ = Re^1/4 θ* = O(1), the longitudinal dimension of this zone varies from finite values up to values of the order of Re^?3/8. The nonuniqueness of the solution is established on a certain range of variation of the parameter θ ₀. The dependence of the drag coefficient on the angle θ* is found.     

The effect of polymer additives on transition in pipe flow

Summary Small amounts of long chain water soluble polymers have a marked effect on turbulent flow resulting in an appreciable reduction of turbulent friction. The maximum reduction in pipe flow resistance is obtained at such low concentrations that the density and viscosity are not altered appreciably. The minimum friction curve varies as Re ^–2/3 and appears to be the same for all effective additives tested. The transition process is affected by these additives. Quantitative results are presented showing a reduction in the intensity of the turbulent flashes and the fraction of the time the flow is turbulent at a given Reynolds number.     

Local measurements of turbulent angular momentum transport in circular Couette flow

We report on velocity fluctuations and the fluctuation-driven radial transport of angular momentum in turbulent circular Couette flow. Our apparatus is short (cylinder height to gap width ratio Γ ~ 2) and of relatively high wall curvature (ratio of cylinder radii η ~ 0.35). Fluctuation levels and the mean specific angular momentum are found to be roughly constant over radius, in accordance with previous studies featuring narrower gaps. Synchronized dual beam Laser Doppler Velocimetry (2D LDV) is used to directly measure the r − θ Reynolds stress component as a function of Reynolds number (Re), revealing approximate scalings in the non-dimensional angular momentum transport that confirm previous measurements of torque in similar flows. 2D LDV further allows for a decomposition of the turbulent transport to assess the relative roles of fluctuation intensity and r − θ cross-correlation. We find that the increasing angular momentum transport with Re is due to intensifying absolute fluctuation levels accompanied by a slightly weakening cross-correlation.