Turbulent Pipe Flow Research Articles

Turbulent pipe flow and heat transfer of a binary mixture at supercritical pressure: Influences of cross-diffusion effects

Cross-diffusion effects, including Soret and Dufour effects, are enhanced around the pseudo-critical temperature (Tpc) of a binary mixture. Their influences on heat transfer at supercritical pressure have been scarcely studied. To bridge this gap, large-eddy simulations (LES) are conducted to investigate forced convective heat transfer of a CO2–ethane mixture at supercritical pressures in a circular pipe subject to a uniform heat flux. Both heating and cooling conditions, along with varying initial concentrations and thermodynamic pressures, are included in the simulations. The LES results reveal that the Soret effect causes concentration separation, resulting in a concentration boundary layer. The magnitudes of the thermodiffusion factor (kT) and the radial temperature gradient control the intensity of separation, which is more pronounced at near-critical pressure and high heat flux. Since kT is significant only around Tpc, downstream decay of the concentration separation is observed as the loci of T=Tpc migrate away from the wall so that the local radial temperature gradient diminishes. The primary factors affecting heat transfer are the variations in thermal conductivity and isobaric specific heat resulting from concentration separation. In contrast, the Dufour effect and the accompanying inter-diffusion play negligible roles. In deterioration scenarios, the bulk Nusselt number (Nub) shows a maximum relative drop of 8%, whereas in enhancement scenarios, Nub shows a maximum relative increase in 10%, with both deterioration and enhancement decaying downstream. Cross-diffusion effects have negligible impacts on density and streamwise velocity, but noticeably alter streamwise velocity fluctuation and turbulent kinetic energy.

Uniform momentum zones in turbulent channel flow

The characteristics of uniform momentum zones (UMZs) and UMZ interfaces in turbulent channel flow (TCF) at friction Reynolds number ranging from 600 to 2000 are investigated. The focus is on the Reynolds number effect and the difference among the turbulent channel flow, turbulent pipe flow (TPF), and turbulent boundary layer (TBL). The UMZ is identified using the approach of probability density histograms, a discrete approximation of the probability density function. We find that the average number of UMZs increases with the Reynolds number, similar to the findings in the TBL. The first group of UMZ in the TCF, namely the quiescent core, has a thicker thickness at a higher Reynolds number. Therefore, the UMZ closer to the channel centre significantly influences high Reynolds number wall turbulence by occupying a large portion of the channel. With increasing Reynolds number, the intensity of spanwise vorticity at the UMZ interface increases, while the thickness of the local maximum decreases. The dominance of prograde vorticity at the interface also increases with the Reynolds number. Moreover, the contortion of the UMZ interface is significantly enhanced at high Reynolds numbers than at low Reynolds numbers in both the streamwise and spanwise directions. Furthermore, the number of UMZ for a given snapshot is related to the overall velocity fluctuations in the subregion, increasing with large-scale Q2 events and decreasing with large-scale Q4 events. Comparing the three flow configurations, UMZs show similarities in their trends, along with two notable differences. First, the TPF has more UMZs compared to the TCF and TBL. Second, the innermost group in the TPF is considerably thicker than that of the higher ranks, a pattern absent in the TCF and TBL. The present findings advance the understanding of UMZs in TCF and demonstrate the similarities and differences between the cases of TCF and TBL.

Persistence of large-scale coherent structures in a turbulent pipe flow through an improved lattice Boltzmann approach

Persistence of large-scale coherent structures in a turbulent pipe flow through an improved lattice Boltzmann approach

An accurate and robust method for intensification of wastewater sludge pipe flow

Globally, environmental impacts and population growth are driving the process intensification of wastewater treatment plants (WWTPs) via transition from conventional (2–3 wt% solids) to highly concentrated (4–6 wt% solids) wastewater sludges (HCWS). This presents an industrial challenge as HCWS are complex, non-Newtonian materials whose viscosity increases nonlinearly with solids concentration. This viscosity increase is particularly relevant for sludge pipe flow as it leads to considerable pumping pressure that ultimately limits the feasibility of pipe flow transportation. Hence, process intensification demands accurate prediction of HCWS turbulent pipe flow to design and optimise pumping infrastructure and piping systems. Such prediction requires accurate rheological characterisation of HCWS and numerical prediction of HCWS turbulent pipe flow, neither of which has been achieved to date due to respective limitations associated with benchtop rheometry and numerical turbulence models. We address these challenges by first developing accurate methods for rheological characterisation of HCWS via laminar flow of digested sludge at various solids concentrations (2–5 %) in a fully instrumented pipe loop facility at a large-scale WWTP. These rheological parameters are used in direct numerical simulation (DNS) computations (that avoid turbulence models) of turbulent pipe flow of HCWS. These predictions are then validated against turbulent flow pipe loop data. This method yields accurate (2–15 % error) predictions of HCWS turbulent pipe flow, compared with up to ∼75 % error for conventional pipe flow correlations. This validation highlights the need for accurate rheological characterisation and numerical simulation to predict HCWS pipe flow and provides a sound basis for the intensification and optimisation of WWTP pipeline systems.

Turbulent pipe flow with spherical particles: Drag as a function of particle size and volume fraction

Suspensions of finite-size solid particles in a turbulent pipe flow are found in many industrial and technical flows. Due to the ample parameter space consisting of particle size, concentration, density and Reynolds number, a complete picture of the particle–fluid interaction is still lacking. Pressure drop predictions are often made using viscosity models only considering the bulk solid volume fraction. For the case of turbulent pipe flow laden with neutrally buoyant spherical particles, we investigate the pressure drop and overall drag (friction factor), fluid velocity and particle distribution in the pipe. We use a combination of experimental (MRV) and numerical (DNS) techniques and a continuum flow model. We find that the particle size and the bulk flow rate influence the mean fluid velocity, velocity fluctuations and the particle distribution in the pipe for low flow rates. However, the effects of the added solid particles diminish as the flow rate increases. We created a master curve for drag change compared to single-phase flow for the particle-laden cases. This curve can be used to achieve more accurate friction factor predictions than the traditional modified viscosity approach that does not account for particle size.

Transition from laminar to turbulent pipe flow as a process of growing material instabilities

Experiments show that a laminar pipe flow starts to change to turbulence at Reynolds numbers around 2000. However, the classical Navier-Stokes theory fails to explain such a transition; according to it the pipe flow should always be stable and laminar. In the present work, it is hypothesized that the transition to turbulence occurs due to material rather than kinematic instabilities of the flow, and the classical Navier-Stokes theory is enhanced with a description of viscous strength. Numerical simulations of the pipe flow with and without the viscous strength are performed. The results show that material instabilities due to the viscous strength gradually develop into a turbulent flow, in agreement with the experimental observations. In the absence of viscous strength, the pipe flow remains laminar in disagreement with experiments. It is concluded that the material instabilities can generally compete with the kinematic ones in the process of transition from laminar to turbulent flow.

Drag Reduction by Dried Malted Rice Solutions in Pipe Flow

In this study, the friction factor of a turbulent pipe flow for dried rice malt extract solutions was experimentally reduced to that of a Newtonian fluid. The friction factor was measured for four types of solutions at different culture times and concentrations. The results indicate that the experimental data points of the test solutions diverged from the maximum drag reduction asymptote at and above Re√f ≅ 200~250 and aligned parallel to those of Newtonian fluids. This drag reduction phenomenon differed from that observed in artificial high-molecular-weight polymer solutions, called Type A drag reduction, in which the drag reduction level is dependent on the Reynolds number in the intermediate region. This is classified as a Type B drag reduction phenomenon in biopolymer solutions and fine solid particle suspensions. The order of drag reduction corresponded to approximately 5–50 ppm xanthan gum solutions, as reported previously. Furthermore, the velocity profile in a turbulent pipe flow was predicted using a semi-theoretical equation in which the friction factors were determined using the difference between the experimental results of the tested solutions and Newtonian fluids. The results indicate considerable thickening of the viscous sublayer in the turbulent pipe flow of the test solutions compared with that of Newtonian fluids.

Improving the prediction of turbulent kinetic energy for drag reduction in turbulent viscoelastic pipe flow

Reducing turbulence in pipe flows using polymer additives is crucial for industrial applications like crude oil, water, and sewage transportation. While previous research has accurately predicted friction factor and velocity profiles, none has fully understood turbulent kinetic energy (TKE) behavior in such fluids. Authors are now focusing on exploring turbulence models to better understand the TKE behavior. In this research, we have introduced a model to improve the behavior of TKE in a modified generalized Newtonian fluid (GNF). The developed model aims to simulate the viscoelastic effects of fluids that result in drag reduction in turbulent pipe flow. The work is noteworthy as it integrates turbulence and viscoelastic components, offering a comprehensive understanding of the phenomenon. By incorporating the rheological properties of viscoelastic fluids and replacing the damping function with a non-Newtonian alternative proposed by Cruz and Pinho, the Launder–Sharma k–ε turbulence model is now suitable for simulating dilute non-Newtonian viscoelastic fluids. The viscoelastic aspect of the model employs the modified GNF model. The developed model has been subjected to simulations using the computational fluid dynamics software. The results obtained for fluid TKE demonstrate a significant improvement in comparison to our previous research and the findings of other researchers. Furthermore, the model's prediction for the Darcy friction factor has been enhanced, resulting in an average error of only 3.71% in this section. It is noteworthy that the model consistently maintains a high level of accuracy in predicting other essential flow parameters such as mean axial velocity and Reynolds stresses. The provided model advances our understanding of viscoelastic fluid behavior in turbulent pipe flow by applying the modified GNF model.

Effect of the Womersley number on transition to turbulence in pipe flow: An experimental study

The mechanisms driving the transition to turbulence in pulsatile flows are not well understood. Prior studies in this domain have noted the dynamics of this flow regime to depend on the mean Reynolds number, pulsation frequency (i.e., Womersley number), and inflow pulsatile waveform shape. Conflicting findings, particularly regarding the role of the Womersley number on the critical Reynolds number and the development of turbulence, have been reported. The discord has primarily been observed for flows, with Womersley numbers ranging from 4 to 12. Hence, in this work, we use particle image velocimetry to explore the effects of the Womersley number within this 4–12 range on the dynamics of the pulsatile transition. Eighteen test cases were captured using six mean Reynolds numbers (range 800–4200) and five Womersley numbers. Turbulent kinetic energy, turbulence intensity (TI), and phase lag were computed. Our results indicated that the critical Reynolds number was roughly independent of the Womersley number. At high Womersley numbers, the TI trend maintained lower pulsatility, and the flow was observed to mimic a steady transitional flow regime. A plateau of the TI-velocity and TI-acceleration phase lag was observed at a Womersley number of 8, highlighting that this may be the critical value where further increases to the Womersley number do not alter the transition dynamics. Furthermore, this suggests that the phase lag may provide a universal indicator of the specific influence of the Womersley number on transition for a given flow. Overall, these findings elucidate critical details regarding the role of the Womersley number in the transition to turbulence.

Polymers in turbulence: any better than dumbbells?

Polymer chains in turbulent flows are generally modelled as dumbbells, i.e. two beads joined by a nonlinear spring. The dumbbell only maps a single spatial configuration, described by the polymer end-to-end vector, thus a multi-bead FENE (finitely extensible nonlinear elastic) chain seems a natural improvement for a more accurate characterisation of the polymer spatial conformation. At a large Weissenberg number, a comparison with the more accurate Kuhn chain reveals that the multi-bead FENE chain drastically overestimates the probability of folded configurations. Surprisingly, the dumbbell turns out to be the only meaningful bead-spring model to coarse-grain a polymer macromolecule in turbulent pipe flows.

Eddy self-similarity in turbulent pipe flow

Eddy self-similarity in turbulent pipe flow

Experimental study of boiling heat transfer characteristics of multi-elbow cooling system under one-sided heating with long section for fusion divertor cooling

In this study, heat transfer experiments were conducted under one-sided heating conditions using water as the coolant and an electron gun as the heat source. To evaluate the boiling heat transfer characteristics of the swirling flow formed by a multi-elbow piping, heat flux by the electron gun is deposited on the region of 60 mm-section in the flow direction corresponding to 0.5 D (inner diameter of the flow channel) to 6.5 D from the elbow outlet, and then temperature distributions in the flow, circumferential and radial directions were measured. The experimental results showed that the wall temperature cooled by the swirling flow generated downstream of the multi-elbow was lower than that obtained in the case of turbulent flow in the straight pipe when irradiated with the same value of heat flux. Thereby, the heat fluxes at the boiling start and DNB points obtained in the multi-elbow case were higher than those in the straight pipe case. These results imply the superior cooling performance of multi-elbow system.

On the extreme wall shear stress events in a turbulent pipe flow

This study investigates the extreme wall shear stress events in a turbulent pipe flow by direct numerical simulation at a frictional Reynolds number Reτ≈500. A two-step conditional averaging scheme is implemented to identify the locations of extreme events and construct their spatial structures. Combined with the joint probability density functions of shear stresses, further evidence is provided for the argument that extreme positive events occur below an intense sweep event (Q4), and the formation of the backflow events is predominantly aided by an identifiable oblique vortex. Moreover, the conditional probability distribution of shear stress for varying thresholds used to define extreme events reveals that, when the threshold is above or below the mean, the probability distributions of the extreme positive events or the backflow events generally follow an exponential relationship, suggesting the extreme wall shear stress events are a threshold-independent process. Finally, the conditional space–time proper orthogonal decomposition is performed to extract the dominant modes and characterize the evolution of the extreme events from inception to dissipation, which exhibits morphological features of real flow structures. It is found that the observation of uθ modes can provide a basic representation of the entire variation process and the extreme values return to normal levels in a very short time.

Asymmetry and intermittency in the rheo-inertial transition to turbulence in pipe flow

Transition to turbulence in pipe has been extensively studied but is still not completely understood and even more for non-Newtonian fluids. We focus here on yield stress shear-thinning fluids and the mechanism leading to the transition in pipe, the so-called rheo-inertial transition to turbulence. An experimental setup has enabled us to identify flow regimes in a cylindrical pipe, using both flow visualizations and pressure drops measurements for a range of Reynolds numbers. We delimited the non-Newtonian specific regime in the laminar-turbulent transition triggered at a critical Reynolds number below the turbulent puffs onset. This pre-transition regime is associated with a velocity profile asymmetry in which its degree and position evolve as the Reynolds number increases. The origin for the stability of this rheo-inertial regime is discussed, as it could be due to a competition between the nonlinear contributions of rheological behavior and flow inertia. Beyond this regime, we quantified the intermittence of puff transit, revealing the delay to turbulence. We spotted for the first time a different rheo-inertial transitional behavior in the intermittency evolution vs Reynolds number, displaying a smoother transition on a broader range. Finally, the critical Reynolds numbers for different yield stresses are compared with previous works, and the novelty is the linear increase in the delay to turbulent puffs with the yield stress.

Resolvent analysis of turbulent flow laden with low-inertia particles

We extend the resolvent framework to two-phase flows with low-inertia particles. The particle velocities are modelled using the equilibrium Eulerian model. We analyse the turbulent flow in a vertical pipe with Reynolds number of $5300$ (based on diameter and bulk velocity), for Stokes numbers $St^+=0-1$ , Froude numbers $Fr_z=-4,-0.4,0.4,4$ and $1/Fr_z = 0$ (gravity omitted). The governing equations are written in input–output form and a singular value decomposition is performed on the resolvent operator. As for single-phase flows, the operator is low rank around the critical layer, and the true response can be approximated using one singular vector. Even with a crude forcing model, the formulation can predict physical phenomena observed in Lagrangian simulations, such as particle clustering and gravitational effects. Increasing the Stokes number shifts the predicted concentration spectra to lower wavelengths; this shift also appears in the direct numerical simulation spectra and is due to particle clustering. When gravity is present, there are two critical layers, one for the concentration field, and one for the velocity field. For upward flow, the peak of concentration fluctuations shifts closer to the wall, in agreement with the literature. We explain this with the aid of the different locations of the two critical layers. Finally, the model correctly predicts the interaction of near-wall vortices with particle clusters. Overall, the resolvent operator provides a useful framework to explain and interpret many features observed in Lagrangian simulations. The application of the resolvent framework to higher $St^+$ flows in combination with Lagrangian simulations is also discussed.

Karhunen–Loéve decomposition of high Reynolds number turbulent pipe flows: a Voronoi analysis

We perform the Karhunen–Loéve decomposition of the data from direct numerical simulations pertaining to incompressible turbulent pipe flow at various Reynolds numbers, in order to identify large-scale coherent structures. A novel approach based on the Voronoi diagram is introduced to estimate the energy distribution along the radial direction as a function of the geometrical properties of the modes. In contrast to previous classifications, no user-defined criterion, threshold or ad-hoc separation of the eddies is required since the two most energetic branches are inherently present as the Reynolds number increases. Details about the Voronoi analysis are provided, together with a comprehensive validation and comparison with previous classifications at low Reynolds numbers. We discuss the results and potential of the presented approach at Reτ = 180 and 5200, commenting on the two classes of coherent structures with a varying and constant size in the radial direction appearing at Reτ = 5200.

Large eddy simulations of turbulent pipe flows at moderate Reynolds numbers

Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we investigate fully developed turbulent pipe flows at moderate-to-high friction velocity Reynolds numbers (361≤Reτ≤2000), corresponding to bulk velocity-based Reynolds numbers of 11 700≤Reb≤82 500, using wall-modeled large eddy simulations (LES) in OpenFOAM. A grid convergence study is performed for Reτ=361, followed by an investigation of the accuracy of various subgrid-scale stress models for the same Reynolds number. Results show that the wall-adapting local eddy (WALE) model performs well compared to experiments and direct numerical simulations, while one-equation eddy-viscosity model and Smagorinsky are too dissipative. LES utilizing WALE is then performed for four different Reynolds numbers with gradually refined grids, revealing excellent agreement with DNS data in the outer region. However, a significant deviation from DNS data is observed in the sub-viscous layer region, indicating the need for further mesh refinement in the wall-normal direction to accurately capture the smallest-scale motions' behavior. Additional mesh sensitivity analysis uncovered that, as the Reτ value rises, it becomes crucial for a grid to adhere to the condition of Δx+≤20−25 and Δz+≤10 in order to precisely capture substantial large and small-scale fluctuations. Overall, the WALE model enables accurate numerical simulations of high-Reynolds number, wall-bounded flows at a fraction of the computational cost required for temporal and spatial resolution of the inner layer.

Predictability of decay events in transitional wall-bounded flows

Extreme events in turbulent flows are in general linked with sudden changes in the dynamics of the system. Despite the increasing interest in modelling these events, their predictability remains largely unexplored. Here we focus on the case of sudden turbulence/chaos decay in pipe flow and in a reduced-order model of shear flows (Moehlis, Faisst and Eckhardt, 2004). We study the predictability of decay events with massive ensembles of simulations. For this purpose we introduce a new pseudo-spectral GPU code to perform fast simulations of turbulent pipe flow and describe a methodology to characterize predictability of decay events using the results of the ensembles of simulations. We report the decrease of predictability as one goes back in time with respect to a decay event, and show that this decrease does not need to be monotonic.

Turbulent Pulsating Convective Flow in the Quasi-Steady and Low-Frequency Regimes

Abstract The instantaneous and time-averaged dynamics of turbulent pulsating convective pipe flow is investigated experimentally over Strouhal number, St=3.3×10−4−0.12 that falls in the quasi-steady and low-frequency regimes, pulsation amplitude, βb=0.05−0.2, and bulk Reynolds numbers, Reb=7528−10,920. The analytical expressions for pulsation amplitudes of centerline velocity, bulk velocity, and Nusselt number are derived. The time series of oscillating components of centerline velocity (Uc˜), cross-sectionally averaged bulk velocity (Ub˜), and Nusselt number (Nu˜) depicts that the phase differences between Uc˜, and Ub˜, and between Ub˜, and Nu˜ increase with St nonmonotonically with near zero phase difference at St→0. The time-averaged pulsating Nusselt number Nu¯ is invariant of St for St > 0.01. Nu¯ depends marginally on βb. The relative mean Nusselt number, Nur=Nu¯/Nus<1 for Reb≥8885 and Nur>1 for Reb = 7528. The general observations from this study is that, in the quasi-steady and low-frequency regimes, turbulent pulsating flows leads to marginal changes in the time-averaged Nusselt number Nu¯ compared to the time-averaged Nusselt number Nus in steady flow condition at any Reb.

Advanced Thermo-Hydraulic Assessment of Helical Pipes with Different Shapes of Jackets Using Single-Phase and Hybrid Nanofluids

This study investigates the efficiency and flow characteristics of helical pipes with different jacket shapes, utilizing single and hybrid nanofluids to enhance heat transfer. The research work presented here provides a unique, coherent method to enhance heat transfer efficiency by concurrently incorporating geometrical alterations and improving operating fluid efficiency. A computational framework analyzes turbulent flow in three-dimensional helical pipes with Reynolds numbers ranging from 5000 to 30,000 and a constant heat flux of 1000 W/m2. This investigation involves evaluating the thermo-hydrodynamic performance of spiral pipes with circular, triangular, and square-shaped jackets, using various volume fractions of single-phase nanofluids (water-based Al2O3 and CuO nanofluids) and a water-based hybrid nanofluid comprising Al2O3/Cu. The results indicate that using different nanofluids significantly improves the Nusselt number value and heat transfer coefficients, ranging from 36 % to 60 % compared to water in a smooth coiled pipe. The strategic design of the jacket enhances the Nusselt number values by generating vortices and increasing turbulence. The Bejan number indicates greater irreversibility in the heat transfer process, leading to substantial energy dispersion. The performance evaluation criterion (PEC) value exceeding one suggests that the modified geometries have the potential to outperform smooth channels.