Turbulent Pipe Flow Research Articles

Drag increase and turbulence augmentation in two-way coupled particle-laden wall-bounded flows

The exact regularized point particle method is used to characterize the turbulence modulation in two-way momentum-coupled direct numerical simulations of a turbulent pipe flow. The turbulence modification is parametrized by the particle Stokes number, the mass loading, and the particle-to-fluid density ratio. The data show that in the wide region of the parameter space addressed in the present paper, the overall friction drag is either increased or unaltered by the particles with respect to the uncoupled case. In the cases where the wall friction is enhanced, the fluid velocity fluctuations show a substantial modification in the viscous sub-layer and in the buffer layer. These effects are associated with a modified turbulent momentum flux toward the wall. The particles suppress the turbulent fluctuations in the buffer region and concurrently provide extra stress in the viscous sub-layer. The sum of the turbulent stress and the extra stress is larger than the Newtonian turbulent stress, thus explaining the drag increase. The non-trivial turbulence/particles interaction turns out in a clear alteration of the near-wall flow structures. The streamwise velocity streaks lose their spatial coherence when two-way coupling effects are predominant. This is associated with a shift of the streamwise vortices toward the center of the pipe and with the concurrent presence of small-scale and relatively more intense vortical structures near the wall.

Predicting mean profiles in compressible turbulent channel and pipe flows

A robust modular iterative method is proposed to predict the mean profiles in compressible channel and pipe turbulence by solving a nonlinear system using the perfect gas assumption, Sutherland's viscosity law, the variable-property scaling models for compressible wall turbulence, the incompressible velocity law of the wall, and the temperature-velocity relation.

Comparison of Mean Properties of Turbulent Pipe and Channel Flows at Low-to-Moderate Reynolds Numbers

We focus on the fully developed turbulent flow in circular pipes and channels. We provide a comparison of the mean velocity profiles, and we compute the values of the global indicators, such as the skin friction, the mean velocity, the centerline velocity, the displacement thickness, and the momentum thickness. The comparison is done at low-to-moderate Reynolds numbers. For channel flow, we deduced the mean velocity profiles using an indirect turbulent model; for pipe flow, we extracted the needed information from a direct numerical simulation database available in the open literature. A one-to-one comparison of these values at identical Reynolds numbers provides a deep insight into the difference between pipe and channel flows. This line of reasoning allows us to highlight some deviations among the mean velocity profiles extracted from different pipe databases.

An experimental study on friction reducing polymers in turbulent pipe flow

An experimental study was conducted to search the reduction of friction in fully developed turbulent pipe flow using different types of polyacrylamides as friction reducing polymers. Pressure drop measurements determined the friction reduction. Three different polymer types Superfloc A110, Superfloc A130 and Superfloc A150 were used to examine the effect of polymer concentration, Reynolds number and polymer type on friction reduction. The Darcy friction factor was obtained for each polymer type at the polymer concentration ranging from 0 to 500 wppm and a Reynolds number range of 10000-80000.It was observed that friction factor decreased with increment in polymer concentration and Reynolds number for each polymer. Higher molecular weight polymers are more effective at reducing friction. With increasing concentration of polymer, the measured data approaches the Virk asymptote, which represents the maximum friction reduction limit by the polymers. The percentage of friction reduction increased with increasing concentration of polymer up to 100 wppm for each polymer type and then began to decrease for polymer concentrations higher than 100 wppm. An empirical formula was obtained to calculate the Darcy friction factor as a function of Reynolds number and polymer concentration for Superfloc A110.

Pulsating Turbulent Flows through a Square Pipe

Pulsating turbulent flows in a square pipe are studied numerically. The flow dominance regime in which the fluid flow rate remains positive in all phases of the oscillatory cycle is considered. The flows are studied at several oscillation frequencies. The results are compared with oscillating laminar flows and a steady turbulent flow in a square pipe, as well as with pulsating turbulent flows in a round pipe. The integral and fluctuating characteristics of turbulence and their dependence on the oscillation frequency are determined. In particular, it is found that at the considered Reynolds number Re = 2200 the friction coefficient in pulsating flows turns out to be lower than that in the stationary flows. The drag reduction increases with growth of the oscillation period and reaches 14.7%. A distinctive feature of turbulent flows in pipes of rectangular cross-section is the occurrence of secondary flows of Prandtl’s 2nd kind. The details of secondary flows under the pulsating flow conditions are studied at length.

Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow

AbstractSimultaneous momentum and passive scalar transfer in weakly heated pressure‐driven turbulent concentric annular pipe flow is numerically investigated using the cylindrical formulation of the stochastic one‐dimensional turbulence (ODT) model, which is utilized here as standalone tool. In the present study, we focus on the model calibration for heated annular pipes based on recent reference direct numerical simulations (DNS) from Bagheri and Wang (Int. J. Heat Fluid Flow 86, 108725, 2020; Phys. Fluids 33, 055131, 2021). It is shown that the model is able to individually capture scalar and momentum transfer, but not both equally well at the same time. We attribute this to less dissimilar scalar and momentum transport in the model at the low Reynolds number investigated. It is argued that the model prefers a fully developed turbulent state due to its construction. Nevertheless, it is demonstrated that ODT is able to reasonably capture the radial inner‐outer asymmetry of the scalar and momentum boundary layers which yields better predictive capabilities than wall‐function‐based approaches.

Use of recirculation theory and reduced dimensionality for efficient calculation of jet flow in cylindrical combustors

This work evaluates use of a dimensionally adaptive (DA) meshing technique to speed CFD modeling of non-reacting pressurized flow in a cylindrical geometry with a center jet and non-axisymmetric secondary jets. The DA-capable approach incorporates an a priori dimensional boundary location and extension of 3-D RANS flow solvers. Recirculation zone length, not flow asymmetry, was the limiting factor in placement of the dimensional boundary between 3-D and axisymmetric meshes. Boundary placement was based on confined turbulent jet theory, which suggests jet attachment is a linear function of cylinder radius, L, expressed as 5.85L. CFD results for a turbulent axial pipe flow showed that as the dimensional boundary was moved upstream, computational time dropped quadratically with the reduction in mesh cells. Further simulations of a 0.2032-m diameter, 1.5-m long reactor with turbulent center primary jet and outer radius secondary jets placed the dimensional boundary at 0.7 m. Results for pressures of 20, 10, and 5 bar and mass flow rates of 75% and 50% of baseline demonstrated two key results. First, flow similarity was preserved across all cases and the predicted jet attachment location was approximately 0.61 m, compared with the theoretical value of 0.594 m. Second, runtime reductions of 79% (pressure) and 82% (flow rate) were seen for the DA meshes compared with fully 3-D meshes. Differences in average exit axial velocities between DA and fully 3-D meshes were 2–4% for the pressure cases and 0.7–1.5% for the flow rate cases. Lastly, comparison with 3-D quarter-geometry calculations showed the DA approach to be ∼10% faster with exit axial velocities within 3–5% of 3-D velocities.

Particle transport in a turbulent pipe flow: direct numerical simulations, phenomenological modelling and physical mechanisms

In particle-laden turbulent wall flows, transport of particles towards solid walls is phenomenologically thought to be governed by the wall-normal turbulence intensity supporting the underlying particle–eddy interactions that are usually modelled by a combination of turbophoresis and turbulent diffusion. We estimate the turbophoretic and turbulent diffusive coefficients as a function of wall-normal coordinate directly from a generated direct numerical simulation (DNS) database of low volume fraction point particles in a turbulent pipe flow. These coefficients are then used in an advection–diffusion equation to estimate the particle concentration as a function of wall-normal distance and time, with favourable comparison against DNS for smaller Stokes number ( $St^+$ ) particles suggesting a limitation of the common gradient diffusion hypothesis for larger $St^+$ particles. Using DNS we explore the non-trivial effects of $St^+$ , pipe wall condition (particle absorbing or elastic) as well as the influence of drag and lift force on the velocity and particle statistics giving rise to different particle concentrations. We then appraise various Eulerian-based models of turbophoretic and turbulent diffusive coefficients and, finally, use physical insights from Lagrangian correlation times, conditional quadrant analysis and flow topology to shed further light on the particle transport as a function of various parameters and the limits of gradient diffusion hypothesis.

Numerical study on conjugate heat transfer in a liquid-metal-cooled pipe based on a four-equation turbulent heat transfer model

Conjugate heat transfer between liquid metal and solid is a common phenomenon in a liquid-metal-cooled fast reactor's fuel assembly and heat exchanger, dramatically affecting the reactor’s safety and economy. Therefore, comprehensively studying the sophisticated conjugate heat transfer in a liquid-metal-cooled fast reactor is profound. However, it has been evidenced that the traditional Simple Gradient Diffusion Hypothesis (SGDH), assuming a constant turbulent Prandtl number (Prt, usually 0.85 - 1.0), is inappropriate in the Computational Fluid Dynamics (CFD) simulations of liquid metal. In recent decades, numerous studies have been performed on the four-equation model, which is expected to improve the precision of liquid metal’s CFD simulations but has not been introduced into the conjugate heat transfer calculation between liquid metal and solid. Consequently, a four-equation model, consisting of the Abe k−ε turbulence model and the Manservisi kθ−εθ heat transfer model, is applied to study the conjugate heat transfer concerning liquid metal in the present work. To verify the numerical validity of the four-equation model used in the conjugate heat transfer simulations, we reproduce Johnson’s experiments of the liquid lead-bismuth-cooled turbulent pipe flow using the four-equation model and the traditional SGDH model. The simulation results obtained with different models are compared with the available experimental data, revealing that the relative errors of the local Nusselt number and mean heat transfer coefficient obtained with the four-equation model are considerably reduced compared with the SGDH model. Then, the thermal-hydraulic characteristics of liquid metal turbulent pipe flow obtained with the four-equation model are analyzed. Moreover, the impact of the turbulence model used in the four-equation model on overall simulation performance is investigated. At last, the effectiveness of the four-equation model in the CFD simulations of liquid sodium conjugate heat transfer is assessed. This paper mainly proves that it is feasible to use the four-equation model in the study of liquid metal conjugate heat transfer and provides a reference for the research of conjugate heat transfer in a liquid-metal-cooled fast reactor.

RANS-Based Modelling of Turbulent Flow in Submarine Pipe Bends: Effect of Computational Mesh and Turbulence Modelling

Pipe bend is a critical integral component, widely used in slurry pipeline systems involving various engineering applications, including natural gas hydrate production. The aim of this study is to assess the capability of RANS-based CFD models to capture the main features of the turbulent single-phase flow in pipe bends, in view of the future investigation of the hydrate slurry flow in the same geometry. This is different from the available literature in which only a few accounted for the effects of a combination of computational mesh, turbulence model, and near-wall treatment approach. In this study, three types of mesh configuration were adopted to carry out the computations, namely unstructured mesh and two structured meshes with a uniform and nonuniform inflation layer, respectively. To explore the influence of the turbulence model, standard k-ε, low-Reynolds k-ε, and nonlinear eddy viscosity turbulence model were selected to close RANS equations. Pressure coefficient, mean axial velocity, turbulence intensity, secondary flow velocity, and magnitude of secondary flow were regarded as the critical variables to make a comprehensive sensitivity analysis. Predicted results suggest that turbulent kinetic energy is the most sensitive variable to the computational mesh while others tend to stabilize. The largest difference of turbulence kinetic energy was around 26% between unstructured mesh and structured mesh with a nonuniform inflation layer. Additionally, a fully resolved boundary layer can reduce the sensitivity of mesh on turbulent kinetic energy, especially for a nonlinear turbulence model. However, the large gradient and peak value of turbulence intensity near the inner wall of the bend was not captured by the case with a fully resolved boundary layer, compared with that of the wall function used. Furthermore, it has been confirmed that the same rule was detected also for different curvature ratios, Reynolds numbers, and dimensionless wall distance y+.

Direct numerical simulations of turbulent pipe flow up to

Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius $R$ and axial length $10{\rm \pi} R$ at friction Reynolds numbers up to $Re_\tau =5200$ using the pseudo-spectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor $\lambda$ overshoots by $2\,\%$ and undershoots by $0.6\,\%$ the Prandtl friction law at low and high $Re$ ranges, respectively. In addition, $\lambda$ in our results is slightly higher than in Pirozzoli et al. (J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichi et al. (Phys. Fluids, vol. 27, issue 9, 2015, 095108). The log-law indicator function, which is nearly indistinguishable between pipe and channel up to $y^+=250$ , has not yet developed a plateau farther away from the wall in the pipes even for the $Re_\tau =5200$ cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with $Re_\tau$ – are lower in the pipe than in the channel, but the difference decreases with increasing $Re_\tau$ . While the wall value is slightly lower in the channel than in the pipe at the same $Re_\tau$ , the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defect-power laws if the coefficients are properly chosen. The one-dimensional spectrum of the axial velocity fluctuation exhibits a $k^{-1}$ dependence at an intermediate distance from the wall – also seen in the channel. In summary, these high-fidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.

Long-term degradation of high molar mass poly(ethylene oxide) in a turbulent pilot-scale pipe flow

The long-term drag reduction capability of poly(ethylene oxide) with a nominal molar weight of Mw=4×106 g/mol dissolved in water was investigated in a pilot-scale pipe flow device (inner diameter of test section 26 mm) at a Reynolds number of 105. A total loss of the initially high (75%) drag reduction capability was observed over a flow distance of several ∼10 km while the molar weight of the polymer was still Mw∼5×105 g/mol. Mechanical degradation in the turbulent flow as well as ageing of the polymer dissolved in water caused this loss in drag reduction capability. A simple ansatz of two independent, statistical polymer chain scission mechanisms was used to describe the polymer degradation empirically using a modified Brostow model. This empirical description was applied successfully and suggested that the polymer exhibited at least 15 cleavage points for mechanical degradation.

Characterization of interfacial waves in stratified turbulent gas-liquid pipe flow using Particle Image Velocimetry and controlled disturbances

The work reports an experimental investigation on stratified gas-liquid pipe flow characteristics in the presence of controlled interfacial waves. Studies of this flow regime with controlled interfacial waves are scarce in the literature. Here, the disturbances are excited at the liquid interface by an oscillating paddle. The waves are synchronized with image acquisitions, enabling the utilization of phase-locked measurements and ensemble averaging techniques. Off-axis Particle Image Velocimetry (PIV) and Shadowgraph techniques were applied to provide information about mean and wave-induced modifications on the velocity fields. Results show that mean flow velocities in the liquid and gas phases close to the pipe walls adhere well to the single-phase flow log-law profile. In the liquid layer, this agreement was observed up to half of the water depth. Controlled disturbances enabled the estimation of the wave amplitude thresholds for the appearance of relevant nonlinear wave effects on the flow field. Results suggest that such a threshold can be fairly represented by a constant value of the non-dimensional parameter proposed in the work of Kirby (2008). Within the non-linear wave regimes investigated, noticeable changes in the flow field were observed close to the interface. However, near the wall the flow was weakly affected by the presence of waves, suggesting that interfacial wave effects are weakly coupled with near-wall disturbances and might be modelled independently. Moreover, contributions to interfacial shear stress due to the presence of waves were obtained experimentally. The results presented here are useful for validation and improvement of models used to predict flow characteristics in stratified flows. In addition, they contribute to shed further light on the physical mechanisms involved in the phenomenon.

Numerical simulations of mass transfer in turbulent pipe flow at high schmidt numbers

Numerical simulations of mass transfer in turbulent pipe flow at high schmidt numbers

Heat and Mass Transfers in a Two-Phase Stratified Turbulent Fluid Flow in a Geothermal Pipe with Chemical Reaction

This research focused on the study of heat and mass transfers in a two-phase stratified turbulent fluid flow in a geothermal pipe with chemical reaction. The derived non-linear partial differential equations governing the flow were solved using the Finite Difference Method. The effects of various physical parameters on the concentration, skin friction, heat, and mass transfers have been determined. Analysis of the results obtained indicated that the coefficient of skin friction decreased with an increase in Reynolds number and solutal Grasholf number, the rate of heat transfer increased with an increase in Eckert number, Prandtl number, and angle of inclination, and the rate of mass transfer increased with increase in Reynolds number, Chemical reaction parameter and angle of inclination. The findings would be useful to engineers in designing and maintaining geothermal pipelines more effectively.

Decay of secondary motion downstream bends in turbulent pipe flows

Decay of secondary motion downstream 180° pipe bends is investigated using large-eddy simulations for the bend radii of 1≤rB/dh≤3.375 at a Reynolds number of Reh=10 000. The velocity and turbulence characteristics are validated against experimental data for a straight pipe section as well as against experimental and direct numerical simulations data for a 90° pipe bend. As the bend radius decreases, a larger magnitude of turbulence intensity is induced immediately downstream of the bend, and for the largest magnitude, the highest gradient of the decay turbulence intensity is observed. As a result, the recovery length needed to reestablish the velocity profile downstream of the pipe bend decreases. Turbulence is transported at a higher rate, indicating that the recovery of the velocity profile is driven by turbulence transport. Secondary motions are induced by the curvature of the pipe bend, and as the bend radius decreases, the magnitude of the secondary motion increases. The results show how the secondary motion decay in magnitude as the flow moves downstream the pipe bend. At the outlet of the bend, secondary motions are dominating at the walls and within the bulk flow. As the fluid moves further downstream, the secondary flows dominate close to the walls, and at a length of x/dh=5, a negligible difference in secondary motion is observed for the different bend radii.

A New Approach to Correlate Heat Transfer Data for Turbulent Flow in Smooth Pipes Based on Generalization of Reynolds Number

A New Approach to Correlate Heat Transfer Data for Turbulent Flow in Smooth Pipes Based on Generalization of Reynolds Number

Theoretical Aspects of Turbulent Flows in Pipeline

Abstract The paper presents the results of theoretical studies on turbulent water motion in pipelines, obtained by the analysis of experimental data regarding hydraulic patterns of turbulent flows. The authors suggest to evaluate the relevant parameters on the basis of the molecular and turbulent viscosity indicators, with the introduction of the conditional relative thickness of the boundary layer on the pipeline walls into the calculations. On this basis, the authors specified semi-empirical relationships for the distribution of averaged velocities in the pipe cross-sections, and revealed new theoretical relationships between the main parameters of turbulent pipe flows. The research confirmed the adequacy of these relationships given the good agreement of the calculated averaged velocity values with the experimental data which formed a basis for the current standards for hydraulic calculations of water supply pipes. For hydraulically smooth pipes, the authors derived an explicit dependence of the hydraulic friction coe cient on the Reynolds number, which almost completely corresponds to the well-known Prandtl-Colebrook equation that has an implicit form. The presented research allowed to determine numerical values and analytical relationships between parameters, which enabled evaluating turbulent flows in hydraulically smooth pipes in a new way.

Status, perspectives, and added value of high fidelity simulations for safety and design

With the increase in computational power, High Fidelity (HiFi) simulations become increasingly important to nuclear thermal hydraulics for fundamental understanding of turbulent flow and heat transfer phenomena and for further development and validation of engineering CFD models. We consider Direct Numerical Simulations (DNS) and Large Eddy Simulation (LES) as HiFi analyses. In this paper, we present an overview of single-phase and two-phase flow DNS simulations relevant for nuclear reactor safety and design purposes. In order to limit the scope, this overview has a focus on DNS simulations of fully turbulent non-reacting incompressible flows. LES approaches are briefly mentioned in certain areas, where LES-to-DNS upgrade is expected to happen in the near future.We first explain the concept of DNS and related concepts like Under-resolved DNS (UDNS) and quasi-DNS (q-DNS). Subsequently, we present the numerical methods which are generally used for HiFi simulations. A wider span of numerical methods can be observed in single-phase flow simulations than in two-phase flow simulations, where the later require additional algorithms for tracking of the interfaces between the two phases. Consequently, two-phase DNS simulations are not immune to modelling errors, and are much more complex than their single-phase counterparts. Next, an overview is given of single-phase flow DNS simulations. We start with basic cases like turbulent channel and pipe flows, which are mainly useful for development and validation of less detailed engineering CFD models. We continue with more recent and more complex cases like, e.g., flows in a rod bundle and a pebble bed, which are directly applicable in nuclear engineering. Next, an overview of two-phase flow HiFi simulations is presented in a similar fashion. The importance of the availability of the presented HiFi simulations is explained by addressing their role for further development and validation of engineering CFD models which are used for the eventual industrial applications. The importance of HiFi simulation data, complementary to experimental data, for uncertainty quantification and machine learning is explained. Finally, future challenges for HiFi simulations, especially for two-phase flow, are elucidated.

Modulation of turbulence by dispersed charged particles in pipe flow

Turbulent gas–solid two-phase flow with electrostatic effects is studied. The turbulent pipe flow is treated using large-eddy simulation, while the particles are tracked using a Lagrangian approach. Simulations are carried out with one-way coupling, two-way coupling, and two-way coupling taking account of electrostatics, and the results are compared. The bulk Reynolds number is Reb = 44 000, and the Stokes number is St = 3.9 (dp = 5 μm). The results show that the maximum electrostatic field strength in the saturated state is found near, but not at, the wall. The electrostatic effect increases the particle concentration in the viscous sublayer (0 ≤ y+ ≤ 5) and the particle dispersion in the buffer layer (5 ≤ y+ ≤ 30). Owing to the electrostatic effect, the feedback effect of particles on the fluid is increased, which leads to increase in the average fluid velocity in the buffer layer and in the velocity fluctuations. In addition, the electrostatic effect is found to increase the turbulent kinetic energy near the wall, while this trend decreases with distance away from the wall. The areas of high- and low-speed streaks near the wall are increased by the electrostatic effect. Therefore, it can be concluded that electrostatics changes not only the particle behavior, but also the flow field.