Turbulent Pipe Flow Research Articles

The similarity theory of free turbulent shear flows of viscoelastic fluids

A new theory is formulated for the description of the conformation state of the polymer chains in free turbulent shear flows of viscoelastic fluids. Using self-similarity arguments and new scaling relations for the turbulent flux of conformation tensor we show the existence of minimum and maximum solvent dissipation reduction asymptotes, and four different polymer deformation regimes. The similarities with the maximum drag reduction asymptote of turbulent pipe flow is discussed and new scaling laws are obtained for all components of the mean conformation tensor at each deformation regime. Analytical solutions for the self-similar transverse profiles of the conformation tensor components are also obtained, providing the complete solution for the mean flow problem at the far field. The analysis is developed for both planar jets and wakes and covers the two limits of shear flows, with large and small velocity differences, respectively. Comparisons of the new theoretical results with several direct numerical simulations employing the FENE-P rheological model show excellent agreement.

Experimentally trained hybrid machine learning algorithm for predicting turbulent particle-laden flows in pipes

A hybrid learning algorithm consisting of a preprocessor, a k-nearest neighbors regressor, a noise generator, and a particle–wall collision model is introduced for predicting features of turbulent single-phase and particle–liquid flows in a pipe. The hybrid learning algorithm has the ability to learn and predict the behavior of such complex fluid dynamic systems using experimental dynamic databases. Given a small amount of typical training data, the algorithm is able to reliably predict the local liquid and particle velocities as well as the spatial distribution of particle concentration within and without the limits of the range of training data. The algorithm requires an order of magnitude less training data than a typical full set of experimental measurements to give predictions on the same level of accuracy (typically, 20 cf. 100 trajectories for phase velocity distribution and 40 cf. 500 trajectories for phase concentration distribution), thus leading to huge reductions in experimentation and simulation. A feature importance analysis revealed the effects of the different experimental variables on the particle velocity field in a two-phase particulate flow, with particle–liquid density ratio and particle vertical radial position being the most influential and particle concentration the least. The algorithm is amenable to extension by using more complex databanks to address a much more comprehensive range of flow situations.

Investigating Reynolds number effects in turbulent concentric coaxial pipe flow using stochastic one‐dimensional turbulence modeling

AbstractThe present study numerically investigates turbulent momentum transfer in concentric coaxial (annular) pipe flow with small radius ratios . To model the flow, a stochastic one‐dimensional turbulence (ODT) model formulated for cylindrical geometry is used that provides full‐scale resolution along a representative radial coordinate. The present investigation extends the model validation by Tsai et al. (PAMM, 22:e202200272, 2023), to radius ratios smaller than 0.1 and addresses boundary layers with strong spanwise curvature effects. The focus is on the assessment and analysis of statistical flow features in the vicinity of the inner cylinder wall, particularly in cases with small radius ratios. Following Boersma & Breugem (Flow Turbul. Combust., 86:113–127, 2011), classical boundary‐layer and mixing‐length theory is utilized to analyze the model predictions. The results demonstrate that the ODT model captures leading‐order curvature and mixing‐length effects by its physics‐compatible construction. Utilizing the model for extrapolation to high Reynolds numbers inaccessible to conventional high‐fidelity numerical approaches shows that curvature effects persist and nonlocally affect the entire boundary layer. The model results provide support for a spanwise‐curvature‐modified wall function.

Developed log-wake law and turbulent behaviour of flow along a stepped spillway

Abstract The log-wake law for turbulent current has been developed and tested with laboratory data on turbulent flow in smooth pipes. However, flow with turbulence and vortices in a stepped spillway have not been described. Therefore, in this study, a log-wake law has been developed for use in stepped spillway systems. It can be divided into three parts. The first part, a logarithmic equation, describes the effect of shear stress between the flow layers with a von Kármán constant of 0.41. The second part, a third-degree polynomial, describes the effect of the shear stress on the wall. The last part, a fourth-degree polynomial, describes the effect of changing the flow pressure distribution, similar to the wall-free shear stress. Calibration tests (68 datasets) are used with a flow rate between 0.0233 and 3.285 m3/s, a spillway slope of 14–30°, and a step height of 0.0380–0.610 m. The developed log-wake law characterized the flow in a stepped spillway well. The limitation of the equation is a maximum flow velocity of 4 m/s; the accuracy of this equation decreases as the step height increases.

Anisotropy and relaminarisation of the turbulent flow near a rotating cylindrical cavity wall

AbstractRotor internal cooling is a new concept for high power density electric vehicle drives. A turbulent pipe flow is injected into a cylindrical cavity in the rotor shaft of the motor. The flow is deflected in the cavity, accelerated in circumferential direction by the rotor wall and exits through an annular duct with the outer wall rotating. Due to the opposing effects of rotation on turbulence, a complex transitional flow develops. The strong shear layer in the jet region causes high turbulence production. On the other hand, these fluctuations are damped by the centrifugal forces due to the flow rotation. To investigate the influences of the rotation on the turbulence properties and the mean flow, highly resolved large eddy simulations are performed. It is shown that the turbulence production and attenuation due to rotation affect different components of the Reynolds shear stress tensor. This results in highly anisotropic turbulence. In certain areas, where the turbulence attenuation is strongest, the flow even relaminarises. Since the cooling efficiency depends on the turbulent heat transfer of the flow, the local turbulence characteristics are key quantities for the cooling application.

Reynolds number dependence of azimuthal and streamwise pipe flow structures

This paper revisits the study by Baileyet al.(J. Fluid Mech., vol. 615, 2008, pp. 121–138), adopting a higher-fidelity calibration approach to reveal subtle flow variations with Reynolds numbers that were not discernible previously. The paper aims therefore to provide insights into the characteristics of azimuthal and streamwise pipe flow structures adopting two-point joint statistics and spectral analysis for shear Reynolds numbers in the range$2\times {10^3}\le {Re_\tau }\le {16\times {10^3}}$, where${Re_\tau }$is based on the wall friction velocity$u_{\tau }$, the pipe radius$R$, and the fluid kinematic viscosity$\nu$. The streamwise velocity fluctuations were measured at four wall-normal locations,$0.1\le {x_{{2}}/R}\le {0.7}$, covering the logarithmic and core regions of fully developed turbulent pipe flow based on 35–41 azimuthal probe separations using, simultaneously, two single hot-wire probes. A uniquein situcalibration approach for both probes was adopted where a potential flow was insured, resulting in consistent and precise pipe flow data. The azimuthal velocity correlation, the cross-power spectral density and the coherence function of the streamwise velocity fluctuations are discussed, revealing a clear dependence of the azimuthal scales of the large and very large flow motions on the wall-normal location, the azimuthal separation, the streamwise wavenumber and the Reynolds number. Along the logarithmic region, a linear growth of the azimuthal scales of the large- and very-large-scale structures was observed; however, they do scale nonlinearly and reach their maximum sizes in the core region, i.e. near the centreline of the pipe. Additionally, the streamwise very-large- and large-scale motions were evaluated using the premultiplied energy spectra, showing wavelengths${\approx }{18R}$and${\approx }{3R}$for${Re_{\tau }}\approx {16\times {10^3}}$at half of the pipe radius, respectively.

Particle behavior in a turbulent pipe flow with a flat bed

Particle behavior in a turbulent pipe flow with a flat bed

Wave spectrum characterization in turbulent stratified air-water flows in a large diameter pipe

This study presents an analysis of interfacial waves in turbulent stratified air-water pipe flow in a 10 cm diameter pipe at atmospheric conditions. Interface elevation measurements are performed by means of conductance probes at a high sampling rate. In particular, the frequency spectra are characterized and the wave structure is assessed through the analysis of the power spectral density (PSD) and its important features, such as dominant frequencies, peak densities and dissipation region. The influence of both gas and liquid superficial velocities is assessed. For the range of superficial velocities investigated (USL = 0.08-0.15 m/s, USG = 1.0-4.5 m/s), dominant frequencies of approximately 7-8 and 3-4 Hz are observed in the wave growth and saturation regimes, respectively, defined by Ayati & Carneiro (2018). A transition from wave growth to wave saturation regime was observed to occur in the range of USG = 1.0-2.0 m/s, for the current conditions studied. In the saturation regime, a secondary peak is observed in the frequency spectra at approximately 7-8 Hz. A scaling analysis is performed to support the interpretation of results and parameterization of spectral parameters, as an indication of the wave structures. In the saturation regime, the high frequency region of the frequency spectra (spectral tail) displays a nearly monotonic decay, and the data supports in general a power law of the form F−n, n ∼ 4-4.5, as evidenced by the non-dimensional analysis covering the full range of conditions tested in this work. This is in accordance with the power law expression derived by Phillips (1985) and supports recent interpretation of air-flow separation and micro-breaking as wave dissipation mechanisms (Ayati, 2018). Power-laws of the form S(F0) ∼(F0) -5 for the peak densities in the PSDs are also found to represent well the current data set for the envelope curve of the spectral peaks. Particularly for the wave saturation regime. For the waves analyzed in the current work, a direct relation between the dominant frequencies and the mean liquid depth is shown to hold.

Simulation of multiphase flow in pipes with simplified models of deposited beds

Turbulent particle-laden flows in pipes can result in particle deposition leading to the formation of solid beds. The presence of such beds modifies the flow field, resulting in secondary motions in the plane of the pipe cross-section, which in turn impact particle transport. In this work turbulent pipe flows with equal mass flow rates and solid beds of height Hb = 0 (full pipe), 0.5R (three-quarter pipe), and R (half pipe) are predicted using direct numerical simulation, with the beds represented simplistically as flat surfaces. The particulate phase is one-way coupled to the flow at a volume fraction of 10−3 and particle motion is solved for using a Lagrangian point-particle approach. The Reynolds numbers computed based on bulk velocity and equivalent pipe diameter for the full, ¾ and, ½ pipes are 5,300, 5,909 and 7,494, respectively. The same particle size is used in all the simulations and their respective Stokes numbers, based on the shear timescale, are 0.5, 1.2 and 1.9, respectively. The results for flows with beds show that the fluid flow exhibits secondary vortices and an increase in the mean streamwise vorticity caused by corners in the cross-sectional plane of the pipes, with their intensity near the upper curved wall increasing with Hb. However, the upper vortices remain relative weak compared to those in lower regions of the pipes. The increase in mean streamwise vorticity in the half pipe is larger than that in the three-quarter pipe near the upper curved wall, while similar near the flat pipe floor due to the resistance of the curved wall to secondary motions. The movement of the particles in the cross-sectional plane is consistent with that of the secondary flows, but with slightly lower velocities. In regions near the wall away from the pipe corners, particle concentration in the half pipe is lower than in the three-quarter pipe, most likely due to its thinner boundary layer. This is reversed for concentration maxima near the pipe corners because of the magnitude of the secondary flows. Finally, the secondary flow changes the deposition or resuspension rate of the particles, particularly near the pipe corners, but these are always less than equivalent rates in the full pipe flow, which is likely caused by the magnitude of the wall unit.

Micellar aggregation of poly(acrylamide-co-styrene): Towards ‘self-removing’ polymers from solution

Polymer drag reducing agents (DRAs) are used in hydraulic fracturing processes to reduce frictional drag developed in fully turbulent pipe-flows. The drag reduction lowers energy consumption required to pump fluids. Removal and/or recovery of DRAs from the fracking fluids remains challenging causing environmental issues. We used model aqueous hydraulic fracturing fluids containing poly(acrylamide-co-styrene) P(AAm-co-St) as DRA and demonstrate an approach to ‘self-remove’/recover the P(AAm-co-St) copolymers by up to 55%. This approach involves foaming of P(AAm-co-St) solutions by sparging gas into fluid (at application relevant conditions) resulting in copolymer enrichment in a generated foam phase and subsequent removal from solution. Our observations suggest a simple method to remove or recover DRAs after drag reduction applications from fracking fluids. Liquid foams containing the P(AAm-co-St) copolymer were dried and redissolved in water offering the potential to be reused for further drag reduction applications or, in case of waste, explored for other applications as emulsifier or in macroporous materials.

Self-sustained azimuthal aeroacoustic modes. Part 1. Symmetry breaking of the mean flow by spinning waves

In this paper, we study the aeroacoustic instability which occurs in a deep axisymmetric cavity in a turbulent pipe flow. This phenomenon is the axisymmetric counterpart of the classical whistling of a rectangular deep cavity subject to a grazing flow. The whistling of such axisymmetric cavity originates from the interaction of the coherent fluctuations of the vorticity at the cavity's opening with one of its trapped azimuthal or radial acoustic modes. We focus here on the situation involving the first pure azimuthal mode, which is trapped in the cavity. As a consequence of the rotational symmetry of the configuration, azimuthal modes are actually pairs of degenerate eigenmodes, or almost degenerate in the presence of small asymmetries. Therefore, the aeroacoustic instabilities exhibit more complex mechanisms than in the case of a rectangular deep cavity. In particular, we show that self-sustained spinning modes induce a symmetry breaking of the mean flow and we will elucidate the details of this phenomenon. To that end, simultaneous acoustic and time-resolved stereoscopic particle image velocimetry (PIV) measurements are performed. They reveal that when large-amplitude aeroacoustic waves spin around the cavity, a quasi-steady mean flow starts whirling slowly in the opposite direction to the wave propagation. A linear perturbation analysis around an axisymmetric mean flow confirms the experimental observations: although the incoming pipe flow is not swirling, the hydrodynamic component of the aeroacoustic wave induces such whirling motion of the mean flow because of the forcing from the steady part of the coherent Reynolds stress tensor.

Self-similar, spatially localized structures in turbulent pipe flow from a data-driven wavelet decomposition

This study aims to extract and characterize structures in fully developed pipe flow at a friction Reynolds number of $\textit {Re}_\tau = 12\,400$ . To do so, we employ data-driven wavelet decomposition (DDWD) (Floryan & Graham, Proc. Natl Acad. Sci. USA, vol. 118, 2021, e2021299118), a method that combines features of proper orthogonal decomposition and wavelet analysis in order to extract energetic and spatially localized structures from data. We apply DDWD to streamwise velocity signals measured separately via a thermal anemometer at 40 wall-normal positions. The resulting localized velocity structures, which we interpret as being reflective of underlying eddies, are self-similar across streamwise extents of 40 wall units to one pipe radius, and across wall-normal positions from $y^+=350$ to $y/R=1$ . Notably, the structures are similar in shape to Meyer wavelets. Projections of the data onto the DDWD wavelet subspaces are found to be self-similar as well, but in Fourier space; the bounds of self-similarity are the same as before, except streamwise self-similarity starts at a larger length scale of $450$ wall units. The evidence of self-similarity provided in this study lends further support to Townsend's attached eddy hypothesis, although we note that the self-similar structures are detected beyond the log layer and extend to large length scales.

Turbulence suppression by cardiac-cycle-inspired driving of pipe flow.

Flows through pipes and channels are, in practice, almost always turbulent, and the multiscale eddying motion is responsible for a major part of the encountered friction losses and pumping costs1. Conversely, for pulsatile flows, in particular for aortic blood flow, turbulence levels remain low despite relatively large peak velocities. For aortic blood flow, high turbulence levels are intolerable as they would damage the shear-sensitive endothelial cell layer2-5. Here we show that turbulence in ordinary pipe flow is diminished if the flow is driven in a pulsatile mode that incorporates all the key features of the cardiac waveform. At Reynolds numbers comparable to those of aortic blood flow, turbulence is largely inhibited, whereas at much higher speeds, the turbulent drag is reduced by more than 25%. This specific operation mode is more efficient when compared with steady driving, which is the present situation for virtually all fluid transport processes ranging from heating circuits to water, gas and oil pipelines.

Prediction of pulsating turbulent pipe flow by deep learning with generalization capability

The spatiotemporal development of turbulent pipe flows with various conditions of pulsation is predicted by deep learning. In the present model, convolutional autoencoder (CAE) extracts the spatial features of the input as latent space vectors and long short-term memory (LSTM) evolves them in time. Time-delay neural network (TDNN) is accompanied by LSTMs to treat general unsteady variations of the spatial mean pressure gradient of the pulsatile flows. Temporal evolution is processed in a sequence-to-sequence manner. Note that the pulsating turbulent pipe flows are statistically unsteady flows for which the spatiotemporal development has been seldom predicted by the deep learning technique. The flow field obtained by direct numerical simulation (DNS) was used to train the model. When the pulsating parameters for the training and prediction are the same, several model parameters are validated. To examine further generalization capability, the present model was trained by data from four pulsation conditions. The model was tested afterward by test data from twenty different pulsation conditions of which the range of parameters is either within or out of the range covered by the training data. The model successfully predicts the various pulsating flow fields with reasonable accuracy. The change in the period yields a larger influence on prediction accuracy than the change in the amplitude. The degradation of the prediction accuracy of the bulk velocity for the case with a long period and large amplitude is not caused by the latent space vectors themselves, but by the decoder which reconstructs the flow field from the latent space vectors.

Near-wall model for compressible turbulent boundary layers based on an inverse velocity transformation

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al., Proc. Natl Acad. Sci., vol. 118, 2021, p. 34) and an algebraic temperature–velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows and boundary layers (48 cases, with edge Mach numbers in the range 0.77–11, and semi-local friction Reynolds numbers in the range 170–5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range 0.7–4 and friction Reynolds numbers in the range 320–1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two, and has a computational cost and implementation complexity similar to that of the commonly used ODE model.

Experiments on large-scale structures in fully developed turbulent pipe flow

The experimental results reported in present paper represent contributions from the Cottbus large pipe facility to DFG-priority program SPP 1881: Turbulent Superstructures. Fundamental questions regarding turbulence statistics and structures in fully developed turbulent pipe flow were addressed, utilizing thermal and optical measuring techniques integrated into the pipe facility. The facility enables unique in-situ calibration for the hot-wire probe and it has full optical access that allows performing Particle Image Velocimetry and 3D Lagrangian Particle Tracking measurements, resulting in consistent and accurate pipe flow data. A streamwise-spanwise field of view up to ≈20×2 pipe radii has been set for both optical techniques with 4–8 high resolution cameras for a friction Reynolds number range of 8⋅102≤R+≤18⋅103. The setup enabled field of measurements with an unprecedented dynamic range in turbulent pipe flow at high Reynolds numbers with spatial resolution better than 1 vector/mm. Proper Orthogonal Decomposition and Shake-The-Box algorithm were used, highlighting energy contents of the large-scale motions in fully developed turbulent pipe flow regime.

Experimental and numerical investigation of cylinder rising in co-current turbulent air pipe flow: Application in pneumatic ice drilling

Air-reverse-circulation drilling into ice sheets is a promising clean technology for fast and safe ice sample recovery in the polar regions. However, a few studies in the literature explore an ice cylinder's rising from rest in tubing filled by co-current air flow. This study builds an experimental setup as well as uses the computational fluid dynamics (CFD) method to characterize the process of ice cylinder rising from being seated at bottom. Variations of the drag coefficient when a cylinder starts to rise and the critical velocity, i.e., the minimum air injection velocity to raise a cylinder, are investigated with the experiments and simulations. Reynolds number is found to have a marginal effect on the drag coefficient and critical velocity while ice-cylinder-pipe geometry can influence the two factors. Wall effect resulting from the existence of pipe lateral wall can enhance the drag coefficient and accordingly, reduce critical velocity. Decreasing the clearance between cylinder and pipe or increasing cylinder length is observed to strengthen the wall effect, but enlarging the cylinder diameter surprisingly weakens the wall effect. A mathematical correlation is developed to quantify the interplay between cylinder-pipe geometry and critical velocity by using parameters like sphericities and diameter ratio. When a cylinder continues to rise off bottom, its drag coefficient would first increase quickly and then decrease gradually to a value where terminal velocity is achieved.

Large-eddy-simulation-informed resolvent-based estimation of turbulent pipe flow

Large-eddy-simulation-informed resolvent-based estimation of turbulent pipe flow

Drag Reduction by Complex Mixtures in Turbulent Pipe Flows

Drag Reduction by Complex Mixtures in Turbulent Pipe Flows

Backflow structures in turbulent pipe flows at low to moderate Reynolds numbers

The statistical characteristics and the evolution of the backflow structures are investigated in wall-bounded flows at Reynolds numbers up to $Re_{\tau }=1000$ . The backflow is caused by the joining of large-scale high- and low-speed structures in the vicinity of the wall and is formed at the tail tip of the low-speed structure. The distribution density of the backflow structures and the percentage area of the backflow region on the wall both increase with the Reynolds number. The backflow structures have an average lifespan of 8 wall units which is found to be slightly longer in the pipe than the channel, and they are convected downstream at the average velocities of the buffer region of approximately 10 wall units, similar to Cardesa et al. (J. Fluid Mech., vol. 880, 2019, R3). The backflow structures occasionally split and merge, and can form detached from the wall. Evidence shows that the split, merged and wall-detached backflow structures are caused by the near-wall structures. The split backflow structures are on average, larger and more spanwise-elongated which are split due to the spanwise shearing of the near-wall streaks. A backflow structure is formed detached from the wall when the trailing end of its carrier low-speed structure ‘sits’ on the near-wall high-speed streaks. The wall-detached backflow structures tend to become wall-attached by approaching the wall when undergoing a similar life cycle to the normal backflow of growth and decay with spanwise elongation because the backflow region at the tail of the low-speed structure is continuously pressed down to the wall by the high-speed structure driven by persistent vortical structures in the buffer region.