Fully-developed Turbulent Pipe Flow Research Articles

Multi-fidelity uncertainty quantification of particle deposition in turbulent pipe flow

Particle deposition in fully-developed turbulent pipe flow is quantified taking into account uncertainty in electric charge, van der Waals strength, and temperature effects. A framework is presented for obtaining variance-based sensitivity in multiphase flow systems via a multi-fidelity Monte Carlo approach that optimally manages model evaluations for a given computational budget. The approach combines a high-fidelity model based on direct numerical simulation and a lower-order model based on a one-dimensional Eulerian description of the two-phase flow. Significant speedup is obtained compared to classical Monte Carlo estimation. Deposition is found to be most sensitive to electrostatic interactions and exhibits largest uncertainty for mid-sized (i.e., moderate Stokes number) particles.

Effects of radius ratio on turbulent concentric annular pipe flow and structures

The effects of radius ratio on fully-developed turbulent concentric annular pipe flow and structures are investigated using direct numerical simulations (DNS). In order to study the radius ratio effects on the flow, four radius ratios of a concentric annular pipe (for Ri∕Ro=0.1–0.7) are compared at a fixed Reynolds number. Here, Ri and Ro are the radii of the inner and outer pipes, respectively. It is observed that the radius ratio influences the interaction of two boundary layers developed over the inner and outer cylinder surfaces, and has a significant impact on the turbulent flow structures and dynamics. The characteristics of the flow field are investigated in both physical and spectral spaces, which include the analyses of the first- and second-order statistical moments, budget balance of the transport equation of Reynolds shear stress, two-point correlation coefficients, and premultiplied spectra of velocity and vorticity fluctuations.

Turbulence in a Localized Puff in a Pipe

We have performed direct numerical simulations of a spatio-temporally intermittent flow in a pipe for Rem = 2250. From previous experiments and simulations of pipe flow, this value has been estimated as a threshold when the average speeds of upstream and downstream fronts of a puff are identical (Barkley et al., Nature 526, 550–553, 2015; Barkley et al., 2015). We investigated the structure of an individual puff by considering three-dimensional snapshots over a long time period. To assimilate the velocity data, we applied a conditional sampling based on the location of the maximum energy of the transverse (turbulent) motion. Specifically, at each time instance, we followed a turbulent puff by a three-dimensional moving window centered at that location. We collected a snapshot-ensemble (10000 time instances, snapshots) of the velocity fields acquired over T = 2000D/U time interval inside the moving window. The cross-plane velocity field inside the puff showed the dynamics of a developing turbulence. In particular, the analysis of the cross-plane radial motion yielded the illustration of the production of turbulent kinetic energy directly from the mean flow. A snapshot-ensemble averaging over 10000 snapshots revealed azimuthally arranged large-scale (coherent) structures indicating near-wall sweep and ejection activity. The localized puff is about 15-17 pipe diameters long and the flow regime upstream of its upstream edge and downstream of its leading edge is almost laminar. In the near-wall region, despite the low Reynolds number, the turbulence statistics, in particular, the distribution of turbulence intensities, Reynolds shear stress, skewness and flatness factors, become similar to a fully-developed turbulent pipe flow in the vicinity of the puff upstream edge. In the puff core, the velocity profile becomes flat and logarithmic. It is shown that this “fully-developed turbulent flash” is very narrow being about two pipe diameters long.

On the computation of low-subsonic turbulent pipe flow noise with a hybrid LES/LPCE method

Aeroacoustic computation of a fully-developed turbulent pipe flow at Reτ = 175 and M = 0.1 is conducted by LES/LPCE hybrid method. The generation and propagation of acoustic waves are computed by solving the linearized perturbed compressible equations (LPCE), with acoustic source DP(x,t)/Dt attained by the incompressible large eddy simulation (LES). The computed acoustic power spectral density is closely compared with the wall shear-stress dipole source of a turbulent channel flow at Re τ = 175. A constant decaying rate of the acoustic power spectrum, f -8/5 is found to be related to the turbulent bursts of the correlated longitudinal structures such as hairpin vortex and their merged structures (or hairpin packets). The power spectra of the streamwise velocity fluctuations across the turbulent boundary layer indicate that the most intensive noise at ω + z R < 1.5).

Analyzing a turbulent pipe flow via the one-point structure tensors: Vorticity crawlers and streak shadows

Abstract Efforts to identify and visualize near-wall structures typically focus on the region y + ≳ 5 , where large-scale structures with significant turbulent kinetic energy content reside, such as the high-speed and low-speed streaks associated with sweep and ejection events. While it is true that the level of the turbulent kinetic energy drops to zero as one approaches the wall, the organization of near-wall turbulence does not end at y + ≈ 5 . Large-scale structures with significant streamwise extent and spatial organization exist even in the immediate proximity of the wall y + 5 . These coherent structures have received less attention so far, but it would be both useful and enlightening to bring them to focus in order, on one hand, to understand them, but also to analyze their interaction with the energetic structures that reside at somewhat higher distances from the wall. We have recently developed a rigorous mathematical and computational framework that can be used for the calculation of the turbulence structure tensors in arbitrary flow configurations. In this work, we use this new framework to compute, for the first time, the structure tensors in a fully-developed turbulent pipe flow. We perform Direct Numerical Simulation (DNS) at Reynolds number R e b = 5300 , based on the bulk velocity and the pipe diameter. We demonstrate the diagnostic properties of the structure tensors, by analyzing the DNS results with a focus on the near-wall structure of the turbulence. We develop a new eduction technique, based on the instantaneous values of the structure tensors, for the identification of inactive structures (i.e. large-scale structures without significant turbulent kinetic energy). This leads to the visualization of “vorticity crawlers” and “streak shadows” , large-scale structures with low energy content in the extreme vicinity of the wall. Furthermore, comparison with traditional eduction techniques (such as instantaneous iso-surfaces of turbulent kinetic energy) shows that the structure-based eduction method seamlessly captures the large-scale energetic structures further away from the wall. We then show that the one-point structure tensors reflect the morphology of the inactive structures in the extreme vicinity of the wall and that of the energy-containing large-scale structures further away from the wall. The emerging complete picture of large-scale structures helps explain the near-wall profiles of all the one-point structure tensors and is likely to have an impact in the further development of Structure-Based Models (SBMs) of turbulence.

시간에 대해 감속하는 난류 파이프 유동에 관한 연구

Direct numerical simulations (DNSs) of turbulent pipe flows with temporal deceleration were performed to examine response of the turbulent flows to the deceleration. The simulations were started with a fully-developed turbulent pipe flow at the Reynolds number, <TEX>$Re_D=24380$</TEX>, based on the pipe radius and the laminar centerline velocity, and three different constant temporal decelerations were applied to the initial flow with varying dU/dt = -0.001274, -0.00625 and -0.025. It was shown that the mean flows were greatly affected by temporal decelerations with downward shift of log law, and turbulent intensities were increased in particular in the outer layer, compared to steady flows at a similar Reynolds number. The analysis of Reynolds shear stress showed that second- and fourth-quadrant Reynolds shear stresses were increased with the decelerations, and the increase of the turbulence was attributed to enhancement of outer turbulent vortical structures by the temporal decelerations.

A spectrally accurate method for overlapping grid solution of incompressible Navier–Stokes equations

An overlapping mesh methodology that is spectrally accurate in space and up to third-order accurate in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The ability to decompose a global domain into separate, but overlapping, subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries. The methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. The overlapping mesh methodology is thoroughly validated using two-dimensional and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver. The influence of long integration times, as well as inflow–outflow global boundary conditions on the performance of the overlapping grid solver is assessed. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data. Scaling tests are presented that show near linear strong scaling, even for moderately large processor counts.

Numerical simulation of heat transfer in a pipe with non-homogeneous thermal boundary conditions

Direct numerical simulations of heat transfer in a fully-developed turbulent pipe flow with circumferentially-varying thermal boundary conditions are reported. Three cases have been considered for friction Reynolds number in the range 180–360 and Prandtl number in the range 0.7–4. The temperature statistics under these heating conditions are characterized. Eddy diffusivities and turbulent Prandtl numbers for radial and circumferential directions are evaluated and compared to the values predicted by simple models. It is found that the usual assumptions made in these models provide reasonable predictions far from the wall and that corrections to the models are needed near the wall.

Multicolor particle shadow accelerometry

This paper describes the extension of multicolor particle shadow velocimetry (CPSV) to the measurement of local acceleration in an Eulerian frame of reference. A validation experiment was conducted on a pendulous disk undergoing unsteady rigid body rotation. Angular velocity and acceleration profiles by CPSA are presented along with a comparison to recordings by an accelerometer mounted on the pendulum. CPSA is also demonstrated in a fully-developed turbulent pipe flow. Profiles of standard deviation of the local acceleration in the near wall region are compared to similar measurements by Christensen and Adrian. A favorable comparison is found between CPSA and particle image accelerometry (PIA). The effect of acceleration time delay, or the time between two velocity estimates, on local acceleration estimates is discussed.

Distinct Organizational States of Fully Developed Turbulent Pipe Flow

Organizational states of turbulence are identified through novel analysis of large scale pipe flow experiments at a Reynolds number of 35 000. The distinct states are revealed by an azimuthal decomposition of the two-point spatial correlation of the streamwise velocity fluctuation. States with dominant azimuthal wave numbers corresponding to k_{θ}=2,3,4,5,6 are discovered and their structure revealed as a series of alternately rotating quasistreamwise vortices. Such organizational states are highly reminiscent of the nonlinear traveling wave solutions previously identified at Reynolds numbers an order of magnitude lower.

Effects of Schmidt number on near-wall turbulent mass transfer in pipe flow

Large Eddy simulation (LES) of turbulent mass transfer in circular-pipe flow has been performed to investigate the characteristics of turbulent mass transfer in the near-wall region. We consider a fully-developed turbulent pipe flow with a constant wall concentration. The Reynolds number under consideration is Re τ = 500 based on the friction velocity and the pipe radius, and the selected Schmidt numbers (Sc) are 0.71, 5, 10, 20 and 100. Dynamic subgrid-scale (SGS) models for the turbulent SGS stresses and turbulent mass fluxes were employed to close the governing equations. The current paper reports a comprehensive characterization of turbulent mass transfer in circular-pipe flow, focusing on its near-wall characteristics and Sc dependency. We start with mean fields by presenting mean velocity and concentration profiles, mean Sherwood numbers and mean mass transfer coefficients for the selected values of the parameters. After that, we present the characteristics of fluctuations including root-mean-square (rms) profiles of velocity, concentration, and mass transfer coefficient fluctuations. Turbulent mass fluxes and correlations between velocity and concentration fluctuations are also discussed. The near-wall behaviour of turbulent diffusivity and turbulent Schmidt number is shown, and other authors’ correlations on their limiting behaviour towards the pipe wall are evaluated based on our LES results. The intermittent characteristics of turbulent mass transfer in pipe flow are depicted by probability density functions (pdf) of velocity and concentration fluctuations; joint pdfs between them are also presented. Instantaneous snapshots of velocity and concentration fluctuations are shown to supplement our discussion on the turbulence statistics. Finally, we report the results of octant analysis and budget calculation of concentration variance to clarify Sc-dependency of the correlation between near-wall turbulence structures and concentration fluctuation in the vicinity of the pipe wall.

Fully-developed Turbulent Pipe Flow with Heat Transfer Using a Zero-equation Model

Aim of this study is to evaluate a zero-equation turbulence model for fully-developed turbulent pipe flow with heat transfer. Uncertainty is approximated through grid-independence and model validation. Results for mean axial velocity, Reynolds stress and temperature had maximum error of 5%, while results for the friction factor and Nusselt number had negligible error. Both the mean axial velocity and normalized temperature profiles were shown to increase and extend farther in the outer layer with increasing Reynolds number, up to 10 6 . The new turbulence model is equally applicable to developing and external flows using the same constant. For wall-bounded flows, the constant is a function of wall roughness.

Fully-developed Turbulent Pipe Flow Using a Zero-Equation Model

Aim of this study is to evaluate a zero-equation turbulence model. A fully-developed turbulent pipe flow was simulated. Uncertainty was approximated through grid-independence and model validation. Results for mean axial velocity, u + and Reynolds stress had maximum error of 5%, while results for the friction factor had negligible error. The mean axial velocity was shown to increase and extend farther in the outer layer with increasing Reynolds number, up to 10 6 . There was no effect of Reynolds number on u + below wall distance, Y + , of 100. Similar to the friction velocity, peak of the Reynolds stress was shown to increase and extend farther in the outer layer with increasing Reynolds number. There was no effect of Reynolds number on Reynolds stress below wall distance of 20. The new turbulence model is equally applicable to developing and external flows using the same constant. For wall- bounded flows, the constant is a function of wall roughness.

Large-eddy simulation of accelerated turbulent flow in a circular pipe

Turbulent pipe flows subject to temporal acceleration have been considered in this study. Large-eddy simulations (LESs) of accelerated turbulent flow in a circular pipe were performed to study the response of the turbulent flow to temporal acceleration. The simulations were started with the fully-developed turbulent pipe flow at an initial Re number, and then a constant temporal acceleration was applied. During the acceleration, the Reynolds number of the pipe flow, based on the pipe diameter and the bulk-mean velocity, increased linearly from ReD=7000 to 36,000. A dimensionless response time for various flow quantities was introduced to measure the delays in the response of the near-wall turbulence to temporal acceleration. The results reveal distinctive features of the delays responsible for turbulence production, energy redistribution, and radial propagation. The conditionally-averaged flow fields associated with Reynolds shear stress producing events were analysed. In the transient flows, sweeps and ejections were closely linked to the delays of turbulence production and of turbulence propagation away from the wall. It is found that strong sweep events were related to the delayed turbulence production in the near-wall region, while ejection events were associated with the propagation of the turbulence away from the wall. The results show that the anisotropy of the turbulence was enhanced during the transient, and this would be a challenging problem to standard turbulence models.

Formulation for predicting deposition velocity of particles in turbulence

Relationships for the particle concentration and convection velocity profile has been obtained by the adaptation of the random surface renewal model [1–5] to the particle continuity and momentum equations of the nonisothermal turbulence boundary-layer flows; particle transport mechanisms of Brownian and turbulent diffusion, eddy impaction, particle inertia, and thermophoresis are included. This proposed model provides a useful framework for coupling these modeling parameters with analytical equation of the particle deposition velocity. The predictions obtained on the basis of this equation have been found to be in good agreement with experimental values of deposition velocity for fully-developed turbulent pipe flow.

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise-wall-normal plane of a 536 lm capillary over the Reynolds-number range 1,800 £ Re £ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted lami- nar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re @ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 £ Re < 3,400 reveal that transitional flows at the microscale are com- posed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture sig- nificant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non- laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger- scale interfaces that incline slightly away from the wall. The characteristics of these ''trains'' of vortices are remi- niscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non- laminar subsets at each transitional Re, including root- mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.

Numerical predictions and measurements of Reynolds normal stresses in turbulent pipe flow of polymers

An anisotropic low Reynolds number k– ε turbulence model has been developed and its performance compared with experimental data for fully-developed turbulent pipe flow of four different polymer solutions. Although the predictions of friction factor, mean velocity and turbulent kinetic energy show only slight improvements over those of a previous isotropic model [Cruz, D.O.A., Pinho, F.T., Resende, P.R., 2004. Modeling the new stress for improved drag reduction predictions of viscoelastic pipe flow. J. Non-Newt. Fluid Mech. 121, 127–141], the new turbulence model is capable of predicting the enhanced anisotropy of the Reynolds normal stresses that accompanies polymer drag reduction in turbulent flow.

Experimental Study of Wall Pressure Fluctuations in a Pipe behind a Stenosis

Wall pressure fluctuations in a pipe, pt, behind a stenotic narrowing are studied. Sharp increase of the pressure pt in a finite region immediately downstream of the stenosis and the presence of a pronounced pressure maximum upstream of the point of re-attachment of the separated flow are found. Approximate estimates both for the distance from a stenosis to the point of maximum pressure and the pressure magnitude at this point are obtained. The study of the wall pressure power spectrum, P(ω), reveals low-frequency maxima in it. They are determined by the appropriate large-scale eddies in the regions of separated and re-attached flow, and their frequencies are close to the characteristic frequencies of the eddies' formation. These maxima are the main distinguishing features of the spectrum under investigation compared to the power spectrum of the wall pressure fluctuations in a fully-developed turbulent pipe flow.

A study on signal quality of a vortex flowmeter downstream of two elbows out-of-plane

Experiments were made with a vortex meter situated downstream of two elbows out-of-plane, at Reynolds numbers between 7.8×10 4 and 2.1×10 5. Analysis on the signals obtained from a piezo-electric sensor embedded in the vortex shedder shows that the signal quality, concerned with the vortex shedding frequency component, deduced in the vicinity of 15 pipe diameters downstream is superior to that at other locations, and is remarkably better than that found in the region of fully-developed turbulent pipe flow. The vortex shedding frequencies measured in this region, in terms of the Strouhal value, fall within 0.129±0.001, that 0.129 is the reference value reduced in the fully-developed turbulent pipe flow region. Also noted, the uncertainty interval associated with the vortex shedding frequency measured in this region is smaller than that reduced in the region of fully-developed turbulent pipe flow.

Flow rate measurements in turbulent pipe flows with minimal loss of pressure using a defect-law

In the paper, a simple and very accurate measurement technique is presented to determine the volumetric or mass flow rate. It is based on the fully-developed turbulent pipe flow, a new analytical universal velocity-profile over the entire pipe section and a single-point measurement. In combination with an optimized straightener this technique has to show minimal pressure loss, very moderate costs and high measuring accuracy compared to LDA-measurements. It is possible to apply the measuring prinicple to nonisothermal gas flows, too.