Experimental study of near-wall turbulent characteristics in an open-channel with gravel bed using an acoustic Doppler velocimeter

This experimental study investigated the mean velocity profiles, skin friction and turbulent characteristics of a gravel bed over a wide range of roughness using an acoustic Doppler velocimeter (ADV). The median diameter of bed material ranged from 2 to 40 mm, and the normalized roughness heights ranged from 47 to 4,881 mm. The flow regime was fully developed turbulence with a Reynolds number in the range of 4.2 × 10⁴–9.86 × 10⁴. All velocity curves exhibited logarithmic distributions, and the log-law region was influenced greatly by both the roughness and the Reynolds number. Moreover, the roughness of the gravel bed exerted a strong effect on Reynolds stress, and the turbulence tended towards isotropic with increasing roughness. Using statistical analyses, the third-order turbulence moments, sweep, and ejection motions were also examined. The results of this experimental analysis present a contrast to the classical wall similarity hypothesis.     

Structure of turbulent pipe flow

The problem of turbulent flow in a straight circular pipe is solved. We consider a system consisting of the equation of motion, the equation for the turbulence energy, the expression relating the turbulence coefficient with the turbulence scale, and the integral formula for determining the turbulence scale. A numerical solution is presented for this closed system of equations for turbulent flow. The results of calculations are compared with experimental data.     

Wall shear stress measurement in a turbulent pipe flow using ultrasound Doppler velocimetry

A turbulent boundary layer of a water flow is investigated by means of pulsed ultrasound Doppler velocimetry. The advantage of this method is the acquisition of complete velocity profiles along the sound propagation line within very short time intervals. The shear stress velocity, used for normalizing the velocity profiles, was determined by fitting the profiles to the universal profiles in a turbulent boundary layer obtained from Prandtl's mixing length theory. A coordinate transformation in the near-wall region is proposed to allocate the velocity data to "true" wall distances. From the experimental values of the wall shear stress velocity, the friction factors for a turbulent pipe flow are calculated and compared to the Blasius law. The overall error in measurement was estimated to NJ.4%.     

Effect of measurement volume size on turbulent flow measurement using ultrasonic Doppler method

This paper presents the results of an investigation on the effects of measurement volume size on the mean velocity profile and the Reynolds stress for fully developed turbulent pipe flows. The study employs the ultrasonic velocity profile method, which is based on the ultrasonic Doppler method. The ultrasonic Doppler method offers many advantages over conventional methods for flow rate measurement in the nuclear power plant piping system. This method is capable of measuring the instantaneous velocity profile along the measuring line and is applicable for opaque liquids and opaque pipe wall materials. Furthermore, the method has the characteristic of being non-intrusive. Although it is applicable to various flow conditions, it requires a relatively large measurement volume. The measurement volume of the present method has a disk-shape determined by the effective diameter of the piezoelectric element and the number of the wave cycles of the ultrasonic pulse. Considering this disk-shaped measurement volume and expressing the time-averaged velocity in a truncated Taylor series expansion around the value at the center of the measuring control volume, the value of the velocity can be obtained. The results are then compared with the data obtained from DNS and LDA measurements. The result shows that the effect of the measurement volume size appears in the buffer region and viscous sublayer.     

Fully developed turbulent flow in a pipe: an intermediate layer

Summary The fully developed mean turbulent pipe flow is analysed at large Reynolds number by the method of matched asymptotic expansions. From the study of various limiting processes, in the sense of Kaplun, a crucial intermediate limit is identified whose transverse dimension is of the order of geometric mean of the transverse dimensions of the classical inner and outer layers. The asymptotic expansions in the three layers (inner, intermediate and outer) are matched by the Millikan's argument leading to two overlap domains where velocity distribution is logarithmic but their slopes could be different. The measurements show that the sustantial log regions do in fact exist in the two overlap domains and the ratio of their slopes is 2.03. The present theory describes the velocity profile over a greater range when compared to the classical theory. The predictions of Reynolds stress and turbulent energy production are in remarkably good argreement with the data for almost entire turbulent flow region from the beginning of the buffer layer to the axis oj pipe.

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Voll entwickelte turbulente Rohrströmung: eine Zwischenschicht

Übersicht Die voll entwickelte turbulente Rohrströmung wird für größere Reynolds-Zahlen mit der Methode der asymptotischen Entwicklungen untersucht, wobei eine wichtige Zwischenschicht identifiziert wird. Die asymptotischen Entwicklungen für drei Schichten (innere, mittlere und äußere) werden mit Hilfe von Übergangsbedingungen nach Millikan angepaßt. Messungen zeigen, daß wesentliche logarithmische Gebiete in Wirklichkeit vorhanden sind, wobei das Verhältnis ihrer Neigungen 2.03 ist. Die vorliegende Theorie beschreibt das Geschwindigkeitsprofil über einen größeren Bereich als die klassische Theorie.

     

Hierarchical structures in a turbulent pipe flow

A hierarchical structure (HS) analysis (β-test and γ-test) is applied to a fully developed turbulent pipe flow. Velocity signals are measured at two cross sections in the pipe and at a series of radial locations from the pipe wall. Particular attention is paid to the variation of turbulent statistics at wall units 10<y⁺<3000. It is shown that at all locations the velocity fluctuations satisfy the She–Leveque hierarchical symmetry (Phys. Rev. Lett. 72 (1994) 336). The measured HS parameters, β and γ, are interpreted in terms of the variation of fluid structures. Intense anisotropic fluid structures generated near the wall appear to be more singular than the most intermittent structures in isotropic turbulence and appear to be more outstanding compared to the background fluctuations; this yields a more intermittent velocity signal with smaller γ and β. As turbulence migrates into the logarithmic region, small-scale motions are generated by an energy cascade and large-scale organized structures emerge which are also less singular than the most intermittent structures of isotropic turbulence. At the center, turbulence is nearly isotropic, and β and γ are close to the 1994 She–Leveque predictions. A transition is observed from the logarithmic region to the center in which γ drops and the large-scale organized structures break down. We speculate that it is due to the growing eddy viscosity effects of widely spread turbulent fluctuations in a similar way as in the breakdown of the Taylor vortices in a turbulent Couette–Taylor flow at high Reynolds numbers.     

Optimal transient growth in turbulent pipe flow

The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the subspace spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth amplification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n=1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δ_v are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.     

Direct numerical simulation of turbulent pipe flow

Fully developed turbulent pipe flow at low Re-number is studied by means of direct numerical simulation (DNS). In contrast to many previous DNS's of turbulent flows in rectangular geometries, the present DNS code, developed for a cylindrical geometry, is based on the finite volume technique rather than being based on a spectral method. The statistical results are compared with experimental data obtained with two different experimental techniques. The agreement between numerical and experimental results is found to be good which indicates that the present DNS code is suited for this kind of numerical simulations.     

Swirling turbulent flow through a curved pipe

An experimental study of swirling turbulent flow through a curved bend and its downstream tangent has been carried out. This study reports on the recovery from swirl and bend curvature and relies on measurements obtained in the downstream tangent and data reported in Part 1 to assess the recovery. Unlike the nonswirling flow case, the present measurements show that the cross-stream secondary flow is dominated by the decay of the solid-body rotation and the total wall shear stress measured at the inner and outer bend (furthest away from the bend center of curvature) is approximately equal. The shear distribution is fairly uniform, even at 1 D downstream of the bend exit. At 49D downstream of the bend exit, the mean axial velocity has recovered to its measured profile at 18D upstream of the bend entrance. Furthermore, the mean tangential velocity is close to zero everywhere and the turbulent shear and normal stresses take another 15D to approximately approach their stationary straight pipe values. Therefore, complete flow recovery from swirl and bend curvature takes a total length of about 85D from the bend entrance. This compares with a recovery length of about 78D for bend curvature alone. The recovery length is substantially shorter than that measured previously in swirling flow through straight pipes and is a consequence of the angular momentum decreasing by approximately 74% across the curved bend. Consequently, the effect of bend curvature is to accelerate swirl decay in a pipe flow.List of symbols C _f total skin friction coefficient, = 2 _w / w ₀ ² - D pipe diameter, = 7.62 cm - De Dean number, = ^1/2 Re = 13,874 - M angular momentum - N _s swirl number, = D/2 W ₀ = 1 - r radial coordinate - R mean bend radius of curvature, = 49.5 cm - Re pipe Reynolds number, = DW ₀ /v= 50,000 - S axial coordinate along the upstream (measured negative) and downstream (measured positive) tangent - U, V, W mean velocities along the radial, tangential and axial directions, respectively - u, v, w mean fluctuating velocities along the radial, tangential and axial directions, respectively - u, v, w root mean square normal stress along the radial, tangential and axial directions, respectively - W ₀ mean bulk velocity, 10 m/s - w total wall friction velocity, = _w / - (w ) _s total wall friction velocity measured as S/D = -18 - turbulent shear stresses - pipe-to-bend radius ratio, = D/2R = 0.077 - axial coordinate measured from bend entrance - fluid kinetic viscosity - fluid density - _w total wall shear stress - azimuthal coordinate measured zero from pipe horizontal diameter near outer bend - angular speed of the rotating section     

Swirling turbulent flow through a curved pipe

An experimental study of a swirling turbulent flow through a curved pipe with a pipe-to-mean-bend radius ratio of 0.077 and a flow Reynolds number based on pipe diameter and mean bulk velocity of 50,000 has been carried out. A rotating section, six pipe diameters long, is set up at six diameters upstream of the curved bend entrance. The rotating section is designed to provide a solid-body rotation to the flow. At the entrance of the rotating section, a fully-developed turbulent pipe flow is established. This study reports on the flow characteristics for the case where the swirl number, defined as the ratio of the pipe circumferential velocity to mean bulk velocity, is one. Wall static pressures, mean velocities, Reynolds stresses and wall shear distribution around the pipe are measured using pressure transducers, rotating-wires and surface hot-film gauges. The measurements are used to analyze the competing effects of swirl and bend curvature on curved-pipe flows, particularly their influence on the secondary flow pattern in the crossstream plane of the curved pipe. At this swirl number, all measured data indicate that, besides the decaying combined free and forced vortex, there are no secondary cells present in the cross-stream plane of the curved pipe. Consequently, the flow displays characteristics of axial symmetry and the turbulent normal stress distributions are more uniform across the pipe compared to fully-developed pipe flows.List of symbols B calibration constant - e bridge voltage - e ₀ bridge voltage at zero flow - C _f total skin friction coefficient, = 2 _w/ W ₀ ² - D pipe diameter, = 7.62 cm - De Dean number, = ^1/2 Re - M angular momentum - n calibration constant - N _s swirl number, = D/2 W ₀ - r radial coordinate - R mean bend radius of curvature, = 49.5 cm - Re pipe Reynolds number, = DW ₀/ - S axial coordinate along the upstream (measured negative) and downstream (measured positive) tangent - U, V, W mean velocities along the radial, tangential and axial directions, respectively - u, v, w mean fluctuating velocities along the radial, tangential and axial directions, respectively - u, v, w root mean square normal stress along the radial, tangential and axial directions, respectively - v ^{ov2}, u^{ov2} normal stress along the tangential and radial direction, respectively - W ₀ mean bulk velocity, 10 m/s - W _c W measured at pipe axis - W total wall friction velocity, - total wall friction velocity measured at S/D = -18 - ,v vw, w7#x016B; turbulent shear stresses - pipe-to-mean-bend radius ratio, = D/2 R = 0.077 - axial coordinate measured from bend entrance - fluid kinematic viscosity - fluid density - _w mean total wall shear stress - instantaneous total wall shear - azimuthal coordinate measured zero from pipe hori zontal diameter near outer bend - angular speed of the rotating section     

Drag reduction in the turbulent pipe flow of polymers

The paper concerns an experimental study of the fully developed turbulent pipe flow of several different aqueous polymer solutions: 0.25%, 0.3% and 0.4% carboxymethylcellulose (CMC), 0.2% xanthan gum (XG), a 0.09%/0.09% CMC/XG blend, 0.125% and 0.2% polyacrylamide (PAA). The flow data include friction factor vs. Reynolds number, mean velocity and near-wall shear rate distributions, and axial velocity fluctuation intensity u′ at a fixed radial location as a laminar/turbulent transition indicator. For each fluid we also include measurements of shear viscosity, first normal-stress difference and extensional viscosity. At high shear rates we find that the degree of viscoelasticity increases with concentration (0.3% CMC is an exception) for a given polymer, and in the sequence XG, CMC/XG, CMC, PAA, whilst at low shear rates the ranking changes to CMC, CMC/XG, XG, PAA. The extensional viscosity ranking is XG/CMC, XG, CMC, PAA at high strain rates and the same as that for the viscoelasticity at low shear rates. We find that the observed drag-reduction behaviour is consistent for most part with the viscoelastic and extensional-viscosity behaviour at the low shear and strain rates typical of those occurring in the outer zone of the buffer region.Although laminar/turbulent transition is practically indiscernible from the friction factor vs. Reynolds number plots, particularly for PAA and XG, the u′ level provides a very clear indicator and it is found that the transition delay follows much the same trend with elasticity/extensional viscosity as the drag reduction.     

Heat transfer characteristics of pulsated turbulent pipe flow

Heat Transfer characteristics of pulsated turbulent pipe flow under different conditions of pulsation frequency, amplitude and Reynolds number were experimentally investigated. The pipe wall was kept at uniform heat flux. Reynolds number was varied from 5000 to 29 000 while frequency of pulsation ranged from 1 to 8 Hz. The results show an enhancement in the local Nusselt number at the entrance region. The rate of enhancement decreased as Re increased. Reduction of heat transfer coefficient was observed at higher frequencies and the effect of pulsation is found to be significant at high Reynolds number. It can be concluded that the effect of pulsation on the mean Nusselt numbers is insignificant at low values of Reynolds number. Received on 29 June 1998     

Particle and droplet deposition in turbulent swirled pipe flow

In this work we study deposition of particles and droplets in non-rotating swirled turbulent pipe flow. We aim at verifying whether the capability of swirl to enhance particle separation from the core flow and the capability of turbulence to efficiently trap particles at the wall can co-exist to optimize collection efficiency in axial separators. We perform an Eulerian–Lagrangian study based on Direct Numerical Simulation (DNS) of turbulence, considering the effect of different swirl intensities on turbulence structures and on particle transfer at varying particle inertia. We show that, for suitably-chosen flow parameters, swirl may be superimposed to the base flow without disrupting near-wall turbulent structures and their regeneration mechanisms. We also quantify collection efficiency demonstrating for the first time that an optimal synergy between swirl and wall turbulence can be identified to promote separation of particles and droplets.     

Rotation effects on a fully-developed turbulent pipe flow

A fully-developed turbulent pipe flow is allowed to pass through a rotating pipe section, whose axis of rotation coincides with the pipe axis. At the exit end of the rotating section, the flow passes into a stationary pipe. As a result of the relaxation of surface rotation, the turbulent flow near the pipe wall is affected by extra turbulence production created by the large circumferential shear strain set up by the rapid decrease of the rotational velocity to zero at the wall. However, the flow in the most part of the pipe is absent of this extra turbulence production because the circumferential strain is zero as a result of the solid-body rotation imparted to the flow by the rotating pipe section. The combined effect of these two phenomena on the flow is investigated in detail using hot-wire anemometry techniques. Both mean and turbulence fields are measured, together with the wall shear and the turbulent burst behavior at the wall. A number of experiments at different rotational speeds are carried out. Therefore, the effects of rotation on the behavior of wall shear, turbulent burst at the wall, turbulence production and the near-wall flow can be documented and analysed in detail.     

Enhanced drag in pipe turbulent flow by an aqueous electrolyte: An electroviscous effect

Drag enhancement is reported for turbulent pipe flow of aqueous electrolyte solutions. No electroviscous effect was obtained with laminar flow. Nor was any unusual pressure drop observed for laminar or turbulent flow of non-electrolyte aqueous solutions such as sugar. An electroviscous theory was advanced that predicted the drag enhancement for a 1/1 electrolyte solution. The theory depended on consideration of Debye length.     

Nuclear magnetic resonance study of turbulent flow in a pipe

Results are given from an investigation of longitudinal turbulent diffusion by the nuclear magnetic tracer method, and a technique is described for determining the velocity distribution function of the fluid particles in the pipe cross section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 105–110, November–December, 1971.