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.     

Controlling spatio-temporal evolution of natural and excited square jets via inlet conditions

The paper presents numerical investigations of square jets in a wide range of Reynolds numbers with varying inlet turbulence characteristics. The research focuses on flow characteristics depending on inflow turbulent length/time scales and excitation frequencies in case of excited jets. It is found that the parameters of inlet turbulence affect the solutions qualitatively when the Reynolds number is sufficiently low. In these cases the impact of varying the turbulent time scale is considerably larger than changing the turbulent length scale. It was also observed that at sufficiently high Reynolds numbers the jets become quite independent of the inlet turbulence characteristics. This confirms findings of Xu et al. (Phys. Fluids, 2013) concerning weak/strong dependence of the jet evolution on inflow conditions. In case of excited jets the excitation frequencies play an important role and influence the jet behaviour most strongly at lower values of the Reynolds number. For some forcing frequencies a bifurcation occurs at sufficiently large forcing amplitudes. This phenomenon turned out to be independent of the assumed length and time scales of the turbulent fluctuations, both in terms of robustness as well as amplitude.     

Comparison of turbulent channel and pipe flows with varying Reynolds number

Single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ Re _τ ≤ 3,000. A total of 27 velocity profile measurements were taken with a systematic variation in the inner-scaled hot-wire sensor length l ⁺ and the hot-wire length-to-diameter ratio (l/d). It was observed that for constant l ⁺ = 22 and l/d >~200l/d \gtrsim 200, the near-wall peak in turbulence intensity rises with Reynolds number in both channels and pipes. This is in contrast to Hultmark et al. in J Fluid Mech 649:103–113, (2010), who report no growth in the near-wall peak turbulence intensity for pipe flow with l ⁺ = 20. Further, it was found that channel and pipe flows have very similar streamwise velocity statistics and energy spectra over this range of Reynolds numbers, with the only difference observed in the outer region of the mean velocity profile. Measurements where l ⁺ and l/d were systematically varied reveal that l ⁺ effects are akin to spatial filtering and that increasing sensor size will lead to attenuation of an increasingly large range of small scales. In contrast, when l/d was insufficient, the measured energy is attenuated over a very broad range of scales. These findings are in agreement with similar studies in boundary layer flows and highlight the need to carefully consider sensor and anemometry parameters when comparing flows across different geometries and when drawing conclusions regarding the Reynolds number dependency of measured turbulence statistics. With an emphasis on accuracy, measurement resolution and wall proximity, these measurements are taken at comparable Reynolds numbers to currently available DNS data sets of turbulent channel/pipe flows and are intended to serve as a database for comparison between physical and numerical experiments.     

On the effect of Reynolds number on von Kármán’s constant

Fully developed turbulence measurements in pipe flow were made in the Reynolds number ranging from 10×10³ to 350×10³ with a hot-wire anemometer and a Pitot tube. Comparisons were made with the experimental results of previous work. The mean velocity profile and the turbulent intensity in the experiments indicate that for the mean velocity profile, in the fully developed turbulent pipe flow, von Kármán's constant κ is a function of Reynolds number, i.e. κ increases slowly with the Reynolds number. The empirical relationships could not be considered to be accurate enough to describe the fully developed turbulence over the whole Reynolds number range in pipe flow. The project supported by the Deutscher Akademische Austauschdienst (DAAD)     

Effects of inlet guide-vane number on flowfields in a side-dump combustor

The flowfields of a side-dump combustor with various number of side-inlet guide-vane are measured using laser-Doppler velocimetry (LDV). The Reynolds number based on the bulk mean velocity and combustor diameter was 2.6×10⁴. Quantities such as mean velocity, turbulence intensity, turbulent kinetic energy, vorticity, friction factor, and wall static pressure oscillation are used to characterize the fluid flow. In the dome region of the inlet-jet plane, there is one pair of counter-rotating vortices for the no-vane, one-vane, and two-vane cases and two pairs of counter-rotating vortices for the three-vane case, respectively. This trend is reversed in the impinging plane. The combustor flowfield downstream of the X_c^*=2.5 station is found to be insensitive to the variation of inlet guide-vane number. In addition, the guide-vane number which provides the least pressure loss and the lowest pressure oscillation is identified for the first time. Based on the presented data, a better guide-vane number for practical reference is suggested.     

Effect of free-stream turbulence on surface friction in a turbulent boundary layer

The combined effect of the turbulence intensity , the turbulence scaleL, and the Reynolds number Re^** on the surface friction coefficientc _f in a turbulent boundary layer is studied. The dependence of the relative friction increment on the equivalent turbulence level _cq, which takes into account the simultaneous variation in ,L and Re^**, is determined. The threshold value _cq ^* below which the value ofc _f does not depend on _cq is found.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 65–75, March–April, 1995.     

Evolution of turbulence characteristics from straight to curved pipes

Fully developed, statistically steady turbulent flow in straight and curved pipes at moderate Reynolds numbers is studied in detail using direct numerical simulations (DNS) based on a spectral element discretisation. After the validation of data and setup against existing DNS results, a comparative study of turbulent characteristics at different bulk Reynolds numbers Re_b = 5300 and 11,700, and various curvature parameters κ = 0, 0.01, 0.1 is presented. In particular, complete Reynolds-stress budgets are reported for the first time. Instantaneous visualisations reveal partial relaminarisation along the inner surface of the curved pipe at the highest curvature, whereas developed turbulence is always maintained at the outer side. The mean flow shows asymmetry in the axial velocity profile and distinct Dean vortices as secondary motions. For strong curvature a distinct bulge appears close to the pipe centre, which has previously been observed in laminar and transitional curved pipes at lower Re_b only. On the other hand, mild curvature allows the interesting observation of a friction factor which is lower than in a straight pipe for the same flow rate.All statistical data, including mean profile, fluctuations and the Reynolds-stress budgets, is available for development and validation of turbulence models in curved geometries.     

Experimental and numerical study of turbulent flow and heat transfer inside hexagonal duct

Flow and heat transfer characteristics in transition and turbulent regions are studied experimentally and numerically in a horizontal smooth regular hexagonal duct under constant wall temperature boundary condition covering a range of Reynolds number from 2.3 × 10³ to 52 × 10³. Two types of k-omega (standard and shear stress transport (SST)) and three types of k-ε (standard, renormalization (RNG), and realizable) turbulence model are employed for transition and turbulent regions, respectively. Both average and fully developed Darcy friction factor and Nusselt number are presented as a function of Reynolds number. It is seen that k-omega SST and k-ε realizable turbulence models gave the best agreement with the experimental data in transition and turbulent regions, respectively. All the experimental results are correlated within an accuracy of ±13 % and ±7 % for Nusselt number and Darcy friction factor, respectively. Results obtained in this study are compared with circular duct results using hydraulic diameter.     

Effects of wall permeability on turbulence

In order to understand the effects of the wall permeability on turbulence near a porous wall, flow field measurements are carried out for turbulent flows in a channel with a porous bottom wall by a two-component particle image velocimetry (PIV) system. The porous media used are three kinds of foamed ceramics which have almost the same porosity (0.8) but different permeability. It is confirmed that the flow becomes more turbulent over the porous wall and tends to be turbulent even at the bulk Reynolds number of Re_b=1300 in the most permeable wall case tested. Corresponding to laminar to turbulent transition, the magnitude of the slip velocity on the porous wall is found to increase drastically in a narrow range of the Reynolds number. To discuss the effects of the wall roughness and the wall permeability, detailed discussions are made of zero-plane displacement and equivalent wall roughness for porous media. The results clearly indicate that the turbulence is induced by not only the wall roughness but the wall permeability. The measurements have also revealed that as Re_b or the wall permeability increases, the wall normal fluctuating velocity near the porous wall is enhanced due to the effects of the wall permeability. This leads to the increase of the turbulent shear stress resulting in higher friction factors of turbulence over porous walls.     

Polymer Induced Drag Reduction in a Turbulent Pipe Flow Subjected to a Coriolis Force

The skin friction factor f in a turbulent wall-bounded flow can be greatly reduced by using polymer solutions. In this paper we discuss experimental results on the effect of the Coriolis force on turbulent drag reduction. To study this, a horizontal smooth-walled pipe with internal diameter 25?mm is placed on a horizontal table rotating about its vertical axis. The rotation is made non-dimensional with friction velocity and pipe diameter, to form the Rotation number Ro. For a range of bulk Rotation number (Ro _b ) between 0 and 0.6 for two different Reynolds numbers (Re _b = 15 & 30 × 10³), the pressure drop is measured, from which the average friction factor f is obtained. Additionally the effect of four different polymer concentrations has been investigated. The single-phase results show that the friction factor increases monotonic but gradual with Rotation. With polymer additives a drag reduction is found that increases with concentration, but which is not affected by the rotation.     

Vortex shedding in cylinder flow of shear-thinning fluids: I. Identification and demarcation of flow regimes

An experimental study on the flow of non-Newtonian fluids around a cylinder was undertaken to identify and delimit the various shedding flow regimes as a function of adequate non-dimensional numbers. The measurements of vortex shedding frequency and formation length (l_f) were carried out by laser-Doppler anemometry in Newtonian fluids and in aqueous polymer solutions of CMC and tylose. These were shear thinning and elastic at weight concentrations ranging from 0.1 to 0.6%. The 10 and 20 mm diameter cylinders (D) used in the experiments had aspect ratios of 12 and 6 and blockage ratios of 5 and 10%, respectively. The Reynolds number (Re^*) was based on a characteristic shear rate of U_∞/(2D) and ranged from 50 to 9×10³ thus encompassing the laminar shedding, the transition and shear-layer transition regimes. Increasing fluid elasticity reduced the various critical Reynolds numbers (Re_etr^*, Re_lf^*, Re_bbp^*) and narrowed the extent of the transition regime. For the 0.6% tylose solution the transition regime was even suppressed. On the other end, pseudoplasticity was found to be indirectly responsible for the observed reduction in Re_otr^*: it increases the Strouhal number which in turn increases the vortex filaments, precursors of the transition regime. Elasticity was better quantified by the elasticity number Re′/We than by the Weissenberg number. This elasticity number involves the calculation of the viscosity at a high characteristic shear rate, typical of the boundary layer, rather than at the average value (U_∞/(2D)) used for the Reynolds number, Re^*.     

Universal threshold of the transition to localized turbulence in shear flows

Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows. By scaling analysis of a disturbed-flow model, this paper proposes a local Reynolds number Re_M to characterize the threshold of transition triggered by finite-amplitude disturbances. The Re_M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion. The lower critical Re_M observed in experiments of plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow are all close to 323, indicating the uniformity of mechanism governing the transition to localized turbulence.     

Effect of the pattern of initial perturbations on the steady pipe flow regime

The influence of the inlet flow formation mode on the steady flow regime in a circular pipe has been investigated experimentally. For a given inlet flow formation mode the Reynolds number Re* at which the transition from laminar to turbulent steady flow occurred was determined. With decrease in the Reynolds number the difference between the resistance coefficients for laminar and turbulent flows decreases. At a Reynolds number approximately equal to 1000 the resistance coefficients calculated from the Hagen-Poiseuille formula for laminar steady flow and from the Prandtl formula for turbulent steady flow are equal. Therefore, we may assume that at Re > 1000 steady pipe flow can only be laminar and in this case it is meaningless to speak of a transition from one steady pipe flow regime to the other. The previously published results [1–9] show that the Reynolds number at which laminar goes over into turbulent steady flow decreases with increase in the intensity of the inlet pulsations. However, at the highest inlet pulsation intensities realized experimentally, turbulent flow was observed only at Reynolds numbers higher than a certain value, which in different experiments varied over the range 1900–2320 [10]. In spite of this scatter, it has been assumed that in the experiments a so-called lower critical Reynolds number was determined, such that at higher Reynolds numbers turbulent flow can be observed and at lower Reynolds numbers for any inlet perturbations only steady laminar flow can be realized. In contrast to the lower critical Reynolds number, the Re* values obtained in the present study, were determined for given (not arbitrary) inlet flow formation modes. In this study, it is experimentally shown that the Re* values depend not only on the pipe inlet pulsation intensity but also on the pulsation flow pattern. This result suggests that in the previous experiments the Re* values were determined and that their scatter is related with the different pulsation flow patterns at the pipe inlet. The experimental data so far obtained are insufficient either to determine the lower critical Reynolds number or even to assert that this number exists for a pipe at all.     

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.     

Reynolds Number Effects on Statistics and Structure of an Isothermal Reacting Turbulent Wall-Jet

Three-dimensional direct numerical simulation (DNS) is used to investigate the effects of changing the Reynolds number on dynamics of a reacting turbulent wall-jet. The flow is compressible and a single-step isothermal global reaction is considered. At the inlet, fuel and oxidizer enter the domain separately in a non-premixed manner. In this study, the bulk Reynolds number of the flow, in terms of the inlet quantities, varies from Re = 2000 to Re = 6000, which results in a comparable change in friction Reynolds numbers. The DNS database in Pouransari et al. (Phys. Fluids 23(085104), 2011) is used for the lower Reynolds number case and for the higher Reynolds number case, a new DNS is performed. One of the main objectives of this study is to compare the influences of changing the Reynolds number of the isothermal flow with the heat-release effects caused by the chemical reaction, that we studied earlier in Pouransari et al. (Int. J. Heat Fluid Flows 40, 65–80, 2013). While, both turbulent and flame structures become finer at the higher Reynolds number, the effect of decreasing the Reynolds number and adding the combustion heat release are compared with each other and found to be similar for some aspects of the flow, but are not always the same.     

Transient growth and bypass transition in stenotic flow with a physiological waveform

A direct analysis method is applied to compute optimal transient growth initial conditions for physiologically relevant pulsatile flows in a smooth axisymmetric stenosis with 75% occlusion. The flow waveform employed represents phase-average measurements obtained in the human common carotid artery. Floquet analysis shows that the periodic flow is stable to infinitesimal eigenmodal-type perturbations that would grow from one cycle to the next at the Reynolds numbers considered. However, the same flows display explosive transient growth of optimal disturbances, with our analysis predicting disturbance energy growths of order 10²⁵ within half a pulse period at a mean bulk flow Reynolds number Re = 300, which is significantly lower than the physiological value of Re = 450 at this location. Direct numerical simulation at Re = 300 shows that when the base flow is perturbed a small amount with the optimal growth initial condition, the disturbance grows rapidly in time in agreement with the linear analysis, and saturates to provide a locally turbulent state within half a pulse period. This transition resulting from non-normal growth mechanisms shows the flow exhibits bypass transition to turbulence. Our analysis suggests that this route to localized turbulent states could be relatively common in human arterial flows.     

The effect of Reynolds number on a turbulent far-wake

The turbulent far-waked generated by a circular cylinder is investigated for two values (1350 and 4600) of the Reynolds number Re _θ (based on the free stream velocity and the momentum thickness). Two arrays of sixteen X-wires, eight in the (x,?y)-plane and eight in the (x,?z)-plane, are used to capture the main features of the large-scale motion in two orthogonal planes. Both the magnitude of the measured Reynolds stresses and the size of the two-point velocity and vorticity correlation contours increase with Reynolds number. The probability density function and spectra of the velocity signals also exhibit differences with Re _θ. A comparison of centerline turbulence intensities with those in the literature suggests that the Reynolds number dependence may disappear for Re _θ?5000.     

Eine asymptotische Analyse des Wärmeüberganges im Einlaufbereich von turbulenten Kanal- und Rohrströmungen

The basic equations for turbulent entrance flow are deduced from an asymptotic expansion of the Navier-Stokes equations and the thermal energy equation forRe→∞. Together with a turbulence model they can be solved numerically. Solutions are independent of the Reynolds and Prandtl number. Based on theses solutions, the skin friction and heat transfer as well as velocity and temperature profiles can be determined for finite Reynolds numbers and Prandtl numbersO (1).     

Turbulent flow in a circular separationless diffuser at Reynolds numbers smaller than 2000

The results of experimental and numerical investigation of flow in a circular conical diffuser with a small conicity angle ensuring separationless flow are presented. The measurements are carried out in an air flow with the Reynolds number Re₂ in the diffuser exit section ranging from 600 to 3000. A considerable effect of the channel expansion on the flow pattern is found to exist. It is shown that, as distinct from a tube, in which only laminar flow can be realized as steady for Re < 2000, in the exit section of a diffuser with the generator slope of 0.3° and a length equal to 70 entry diameters a developed turbulent flow is formed for Re₂ > 1000. For Re₂ > 1300 this flow is steady, that is, almost independent of the turbulence level at the entry, and is determined by the Reynolds number Re₂ in the exit section. For Re₂ ≈ 1000 the turbulent flow continuously goes over into a laminar flow. The flow parameters measured at the diffuser exit correspond to calculations in accordance with the threeequation turbulence model.     

LES and RANS for Turbulent Flow over Arrays of Wall-Mounted Obstacles

Large-eddy simulation (LES) has been applied to calculate the turbulent flow over staggered wall-mounted cubes and staggered random arrays of obstacles with area density 25%, at Reynolds numbers between 5 × 10³ and 5 10⁶, based on the free stream velocity and the obstacle height. Re = 5 × 10³ data were intensively validated against direct numerical simulation (DNS) results at the same Re and experimental data obtained in a boundary layer developing over an identical roughness and at a rather higher Re. The results collectively confirm that Reynolds number dependency is very weak, principally because the surface drag is predominantly form drag and the turbulence production process is at scales comparable to the roughness element sizes. LES is thus able to simulate turbulent flow over the urban-like obstacles at high Re with grids that would be far too coarse for adequate computation of corresponding smooth-wall flows. Comparison between LES and steady Reynolds-averaged Navier-Stokes (RANS) results are included, emphasising that the latter are inadequate, especially within the canopy region.