Flow In Rough Pipes Research Articles

Direct numerical simulation of turbulent flow in pipes with realistic large roughness at the wall

We carry out direct numerical simulation (DNS) of turbulent flow in rough pipes. Two types of irregular roughness are investigated, namely a grit-blasted and a graphite surface. A wide range of Reynolds numbers is tested, from the laminar up to the fully rough regime, attempting to replicate Nikuradse's pioneering study. Despite the large relative roughness, outer-layer similarity is achieved at high Reynolds number as hypothesised by Townsend, with deviations from the smooth wall case of 4 % for the grit-blasted surface and 13 % for the graphite surface. This makes it possible to define a roughness function and the equivalent sand-grain roughness. The results are compared with those obtained in plane channels, with small differences pointing to the residual influence of the duct cross-sectional shape in the presence of relatively large roughness. The computed friction factors behave similar to those Nikuradse's chart, with differences in terms of the friction factor in the laminar region and of the critical Reynolds number, which are partly absorbed by using the hydraulic radius as reference length scale. The distributions of the velocity fluctuations intensities point to a isotropisation of turbulence in the near-wall region resulting from the roughness, with influence of the roughness geometry. Comparison of the computed equivalent sand-grain roughness height suggest that existing correlations suffer from poor predictive power, at least for surfaces with large relative roughness.

Application of random forest-based decision tree approach for modeling fully developed turbulent flow in rough pipes

A random forest (RF) -based decision tree programming methodology was aimed for modeling fully developed turbulent flow conditions in rough pipes. In the present computational study, a flexible RF-based soft-computing strategy was applied for the estimation of the required pipe diameter (D) and Darcy–Weisbach friction factor (λ or f) obtained from the iterative solution of the implicit Colebrook–White equation for five basic pipeline design variables considered in sizing problems (Type 3) of pipe distribution systems. The prediction performance of the implemented RF-based model was assessed more than 15 different statistical goodness-of-fit parameters and useful mathematical diagrams such as box-and-whisker-plots and spread plots. The statistical metrics corroborated the superiority of the RF-based approach in predicting both the required pipe diameter (R2 = 0.9793, MAE = 0.0287 m, RMSE = 0.03833 m, SEE = 0.0326 m, IA or WI = 0.9933, CV(RMSE) or SI = 0.0595, NSE = 0.9753, LMI = 0.8482, and AIC = -1954.6438 for the testing dataset) and friction factor (R2 = 0.9576, MAE = 0.0011, RMSE = 0.0023, SEE = 0.0018, IA or WI = 0.9851, CV(RMSE) or SI = 0.0660, NSE = 0.9478, LMI = 0.8500, and AIC = -3646.7124 for the testing dataset). The descriptive statics suggested that the 25% percentile values (Q1), median values (Q2), and 75% percentile values (Q3) of RF-predicted values of D and λ and the corresponding actual values of these responses were found to be very close. The proposed RF-based model was also tested against additional some dataset obtained from the relevant literature. The validation results indicated that the applied decision tree-based method produced realistic estimations and acceptable statistics (i.e., R2 = 0.9624, MAE = 0.0598 m, and RMSE = 0.0708 m for D values, and R2 = 0.9130, MAE = 0.0043, RMSE = 0.0052 for λ values) even at extreme L values greater than 2000 m. This study demonstrated the importance and ability of the applied soft-computing strategy to accurately predict D and λ values and eliminated error-prone steps of the traditional iterative approach.

Large eddy simulations of fully developed turbulent flows over additively manufactured rough surfaces

In the last decade, with the growing demand for efficient and more sustainable products that reduce our CO2 footprint, progresses in Additive Manufacturing (AM) have paved the way for optimized heat exchangers, whose disruptive design will heavily depend on predictive numerical simulations. Typical AM rough surfaces show limited resemblance to the artificially constructed rough surfaces that have been the basis of most prior fundamental research on turbulent flow over rough walls. Hence, current wall models used in steady and unsteady three-dimensional (3D) Navier–Stokes simulations do not consider such characteristics. Therefore, a high-fidelity Large Eddy Simulation (LES) database is built to develop and assess novel wall models for AM. This article investigates the flow in rough pipes built from the surfaces created using AM techniques at Siemens based on Nickel Alloy IN939 material. We developed a code to generate the desired rough pipes from scanned planar surfaces. We performed high-fidelity LES of turbulent rough pipe flows at Reynolds number, Re = 11 700, to reveal the influence of roughness parameters on turbulence, mainly the average roughness height and the effective slope. The equivalent sand-grain roughnesses, ks, of the present AM rough surfaces are predicted using the Colebrook correlation. The main contributors to the skin friction coefficient are found to be turbulence and drag forces. In the present study, the existence of a logarithmic layer is marked even for high values of ks. The mean flow, the velocity fluctuations, and the Reynolds shear stresses show turbulence's strong dependence on the roughness topography. Profiles of turbulence statistics are compared by introducing an effective wall-normal distance defined as zero-plane displacement. The effective distance collapses the shear stresses and the velocity fluctuations outside the roughness sublayer; thus, Townsend's similarity of the streamwise mean velocity is marked for the present roughnesses. Furthermore, a mixed scaling is introduced to improve the collapse of turbulence statistics in the roughness sublayer. In addition, an attempt to investigate the impact of surface roughness on flow physics using the acquired LES results based on quadrant analysis of the Reynolds shear stresses and anisotropy of turbulence is made.

Poiseuille flow in rough pipes: linear instability induced by vortex–wave interactions

Abstract

Re-examining log law velocity profile in smooth open channel flows

A comprehensive investigation of velocity distribution is presented, and the log law is re-examined using experimental data from a smooth uniform open channel flow. It is widely reported that the coefficients of the log law in channel flows deviate from those obtained from circular pipe flows by Nikuradse (Laws of flow in rough pipes, 1933), but the mechanism is not clear and no theoretical formulae are available to express these deviations. A Laser Doppler Velocimetry system was used to measure velocity profiles at the centre of the channel. The data obtained support previous conclusions that the additive constant B of the log law in channel flows can no longer be considered to be 5.5. Interestingly, the experimental data also support Tracy and Lester’s discovery that the shear velocities on both sides of the log law are different. Better agreement can be achieved if the global shear velocity (U*1) is used to normalize the measured velocity, and the local shear velocity (U*2) is used to normalize the distance from the wall. Other researchers’ data in the literature also validates this new relationship. Based on this new relationship, a theoretical value of B is obtained, which agrees well with the observed B, thus a new form of log law for channel flow is suggested. The new relationship developed was verified with present experimental and past literature data suggesting its universality irrespective of wide or narrow open channels, or subcritical or super critical flow conditions. By using the developed relationship the large scatter associated with the additive constant B associated with the log law has been explained. It is found that the additive constant B in the log law is a function of channel aspect ratio. The developed relationship for B is validated from a wide range of data from the literature to confirm its universality.

HYDRAULIC RESISTANCE OF TURBULENT FLOWS IN ROUGH PIPES USING DRAG REDUCING AGENTS

Background Prediction of the pressure gradient and estimation of the hydraulic resistance of turbulent flows are of great industrial importance. In the literature, there are practically no studies on calculating the reduction in hydraulic resistance using polymer additives for turbulent flows in rough pipes. Aims and Objectives Calculation of hydraulic resistance of turbulent flows in rough pipes using polymer additives. Methods Mathematical modeling and numerical calculations of determining the hydraulic resistance coefficient in rough pipes using drag reducing agents. Results A review of the works on the calculation of the decrease in hydraulic resistance by polymer additives in rough pipes is carried out. A comparative analysis of calculations based on various methods of hydraulic resistance coefficient and comparison with the available experimental data in the literature are presented.

Explicit solutions for turbulent flow friction factor: A review, assessment and approaches classification

Abstract The Colebrook –white equation is widely used in many fields, like civil engineering for calculation of water distribution systems and in all fields of engineering where fluid flow can be occurred. Numerous formulas have been proposed since 1947 in order to simplify the computation of the friction factor, to avoid the iterative procedures methods and to alter the Colebrook-white equation in practice. most of the existing explicit formulas for computation of the friction factor for turbulent flow in rough pipes proposed are cited, where thirty three “33” equations have been inventoried. The goal of this paper is to assess the accuracy of each model and to propose an arrangement from the best to the lower accuracy according to a proposed method combined of three criteria which are: simplicity of the formula, maximum deviations and the coverage of the entire range of Moody diagram.

Turbulence as a Problem in Non-equilibrium Statistical Mechanics

The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent flows in rough pipes and quasi-two-dimensional soap films, showing how the data obey a two-parameter scaling law known as roughness-induced criticality, and exhibit power-law scaling of friction factor with Reynolds number that depends on the precise form of the nature of the turbulent cascade. These results hint at a non-equilibrium fluctuation-dissipation relation that applies to turbulent flows. The second part of this article concerns the lifetime statistics in smooth pipes around the transition, showing how the remarkable super-exponential scaling with Reynolds number reflects deep connections between large deviation theory, extreme value statistics, directed percolation and the onset of coexistence in predator-prey ecosystems. Both these phenomena reflect the way in which turbulence can be fruitfully approached as a problem in non-equilibrium statistical mechanics.

Hydrodynamics and heat transfer in single-phase fluid flows in artificially rough pipes

Studies on hydraulic resistance and heat transfer in pipes with artificial roughness of different profiles are reviewed; artificially rough surfaces, flow regimes, boundaries of flow regimes, and equations for calculation of the coefficients of hydraulic resistance and heat transfer during single-phase flow in rough pipes are classified. It has been ascertained that many available equations for calculation of hydraulic resistance and heat transfer for single-phase flows in artificially rough channels, however, do not allow these data to be always used, because of the many types and forms of artificial roughness. The generalized equations presented in this review mainly relate to flows in channels with sand-grain roughness. The absence of studies of the hydraulic resistance and heat transfer in single-phase flows in rough channels with flow swirling is noted, which is an effective way for intensification of heat transfer in practical applications.

English

This paper continues the recent research of the authors concerning the interaction between the micro and macro flow structure domains (further on called IPmMD). The authors propose a probabilistic type approach of the IPmMD, in plane boundary layer, channel and pipe flows. This process, purely theoretical expressed by using transformations associated to transversal coordinate, tends to ensure the equipartition of the kinetic energy and to lead to a minimum in information transmission in the space-time ensemble. Taking into account several velocity distributions as not mutually exclusive events, new distributions are obtained by a probabilistic type union of the events. These new distributions present important aspects related to the classical transition from the laminar- to-turbulent regime. In this way, as an example, the parabolic-laminar and the linear distributions lead to a velocity distribution very close to experimental data corresponding to the rough pipe flow.

Single phase flow heat transfer and pressure drop measurements in doubly enhanced tubes

Global in-tube flow heat transfer and pressure drop measurements were conducted with Water (Pr = 4.42) and Ethylene Glycol (Pr = 80.5–135.7), in the laminar-transition-turbulent flow regime (Re = 400–39,750) in double pipe heat exchangers fabricated from doubly enhanced tubes. The internal fin height to effective diameter ratio ef,i/deff varied between 0.0289 and 0.0314. The internal groove helix angles varied between 35 and 40°, while the internal fin pitch to height p/ef,i ratios varied between 3.4 and 5.36. The external fin density was 40 fins per inch (25.4 mm). In comparison to a smooth tube, tube-side (internal) heat transfer enhancements (hdeff,enhanced/hdeff,smooth) of up to 6% were measured with Ethylene Glycol in the laminar regime, while tube-side enhancement of up to 34% was measured with water in the turbulent flow regime. The overall heat transfer enhancement (UAeff)enhanced/(UAeff)smooth based on the overall heat transfer coefficients was measured as 116% with water in the turbulent flow regime. Transition to fully developed rough pipe flow was detected in the enhanced tubes after a critical Reynolds number and the corresponding Prandtl number exponent was estimated to be 0.47. At constant pumping power, the maximum tube-side heat transfer enhancement was 6% with Ethylene Glycol in the laminar regime, and 18% with water in the turbulent regime. On a constant heat duty basis, the maximum reduction in pumping power was 23% with Ethylene Glycol in the laminar regime and 54% with water in the turbulent regime. Although the inner (tube-side) heat transfer enhancement is lower than that measured in conventional micro-fin tubes (inner grooves only), the overall heat transfer enhancement suggests that these tubes will be useful for designing heat exchangers deploying fluids of similar thermal conductivity in the tube and annulus. Typical applications include, but are not limited to, design of marine oil coolers, lubricating oil coolers, and sub-cooled sections of condensers.

Implementation of Two-Fluid Model for Dilute Gas-Solid Flow in Pipes With Rough Walls

A numerical study was carried out to investigate the performance of a two-layer model for predicting turbulent gas-particle flows in rough pipes. An Eulerian–Eulerian two-fluid formulation was used to model both the gas and solid phases for turbulent gas-particle flow in a vertical tube. The stresses developed in the particle phase were calculated using the kinetic theory of granular flows while the gas-phase stresses were described using an eddy viscosity model. The two-fluid model typically uses a two-equation k-ɛ model to describe the gas phase turbulence, which includes the suppression and enhancement effects due to the presence of particles. For comparison, a two-layer model was also implemented since it has the capability to include surface roughness. The current study examines the predictions of the two-layer model for both clear gas and gas-solid flows in comparison to the results of a conventional low Reynolds number model. The paper specifically documents the effects of surface roughness on the turbulence kinetic energy and granular temperature for gas-particle flow in both smooth and rough pipes.

Optimal structure of tree-like branching networks for fluid flow

Tree-like branching networks are very common flow or transportation systems from natural evolution. In this study, the optimal structures of tree-like branching networks for minimum flow resistance are analyzed for both laminar and turbulent flow in both smooth and rough pipes. It is found that the dimensionless effective flow resistance under the volume constraint for different flows is sensitive to the geometrical parameters of the structure. The flow resistance of the tree-like branching networks reaches a minimum when the diameter ratio β∗ satisfies β∗=Nk, where, N is the bifurcation number N=2,3,4,… and k is a constant. For laminar flow, k=−1/3, which is in agreement with the existing Murray’s law; for turbulent flow in smooth pipes, k=−3/7; for turbulent flow in rough pipes, k=−7/17. These results serve as design guidelines of efficient transport and flow systems.

Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow

AbstractMeasurements of the streamwise component of the turbulent fluctuations in fully developed smooth and rough pipe flow are presented over an unprecedented Reynolds number range. For Reynolds numbers$R{e}_{\tau } \gt 20\hspace{0.167em} 000$, the streamwise Reynolds stress closely follows the scaling of the mean velocity profile, independent of the roughness, and over the same spatial extent. This observation extends the findings of a logarithmic law in the turbulence fluctuations as reported by Hultmark, Vallikivi & Smits (Phys. Rev. Lett., vol. 108, 2012) to include rough flows. The onset of the logarithmic region is found at a location where the wall distance is equal to ∼100 times the Kolmogorov length scale, which then marks sufficient scale separation for inertial scaling. Furthermore, in the logarithmic region the square root of the fourth-order moment also displays logarithmic behaviour, in accordance with the observation that the underlying probability density function is close to Gaussian in this region.

ВЗАИМНАЯ СОГЛАСОВАННОСТЬ ЗАКОНОМЕРНОСТЕЙ ТЕЧЕНИЯ И ГИДРАВЛИЧЕСКОГО СОПРОТИВЛЕНИЯ

Mutual consistency of regularities demonstrated by the flow and hydraulic resistance is analyzed in this article. It is proven that the values of friction factors of pipes, identified through the employment of traditional methods, differ from those of channels by 4 times. It is also proven that the average velocity deficit inside pipes and channels, identified by integrating velocity profiles that depend on the Karman parameter, differ by only 1.5 times. The relation between the Karman parameter and the average velocity deficit provides this parameter with a clear physical sense.The original method of reconciliation of the experimental regularity of smooth pipes against the resistance ratio formula, obtained by integrating the logarithmic velocity profile, adjusts the value of the Karman parameter and the second constant of the velocity profile, as both are slightly different from the experimental values identified by I. Nikuradze.The average velocity deficit identified for the flow in rough pipes by integrating the velocity profile coincides with the same in smooth pipes, and they both have the same dependence on the Karman parameter. The adjusted Karman parameter value is almost the same for rough and smooth pipes. The adjusted value of the second turbulence constant for rough pipes is a little higher than the experimental value identified by I. Nikuradze.Adjusted first and second constant values of turbulence for rough and smooth pipes assure more consistency between the regularities of resistance and distribution of velocities inside smooth and rough pipes.

Energy–Vorticity Turbulence Model with Application to Flow Near Rough Surfaces

Based on a more direct analogy between turbulent and molecular transport, a foundation is presented for an energy–vorticity turbulence model. Whereas traditional , , and models relate the eddy viscosity to a dissipation length scale associated with the smaller eddies having the highest strain rates, the proposed model relates the eddy viscosity to a mean vortex wavelength associated with the larger eddies primarily responsible for turbulent transport. A rigorous development of the turbulent-energy-transport equation from the Navier–Stokes equations includes exact relations for the viscous dissipation and molecular transport of turbulent kinetic energy. Application of Boussinesq’s analogy between turbulent and molecular transport leads to a transport equation, which shows neither molecular nor turbulent transport of turbulent energy to be simple gradient diffusion. The new turbulent-energy-transport equation contains two closure coefficients: a viscous-dissipation coefficient and a turbulent-transport coefficient. To help evaluate closure coefficients and provide insight into the energy–vorticity turbulence variables, fully rough pipe flow is considered. For this fully developed flow, excellent agreement with experimental data for velocity profiles and friction factors is attained over a wide range of closure coefficients, provided that a given relation between the coefficients is maintained.

Economic optimization of pipe diameter for complete turbulence

Paper deals with the model for economic optimization of pipe diameter for complete turbulence. The proposed new model for economic optimization of pipe diameter is based on simple economic balance approach. The model covers the region of complete turbulence (so called rough pipe flow). Final result estimates somewhat different pipe diameter values than the widely cited Genereaux equation for smooth pipe flow.

Turbulent flow in a machine honed rough pipe for large Reynolds numbers: General roughness scaling laws

An alternate inner wall variable, for flow over a transitional rough pipe surface, is defined as the ratio of normal coordinate measured above the mean roughness level to the wall roughness scale. The Reynolds equations for mean turbulent flow in a transitional rough pipe, in two layers (inner and outer) are considered. The predictions of the mean velocity and friction factor in fully developed turbulent flow in a rough pipe flow, presented here, covers all types of roughness. The data for a particular case of the machine honed Princeton superpipe roughness, analogous to inflectional type roughness of Nikuradse, is presented, as two expressions using our roughness scale. The velocity profile and friction factor, on a transitional rough wall, are shown to be governed by the new log laws, which are explicitly independent of the transitional wall roughness. Further, the inflectional roughness has also been connected with geometric roughness parameters; like, arithmetic mean roughness, mean peak to valley heights roughness, root mean square (rms), roughness based on texture measure; and the friction factor implicit and approximate explicit formulas have also been proposed. In entire transition region between fully smooth and fully rough wall, monotonic roughness of Colebrook (Moody Chart) over estimaton the friction factor when compared with present inlectional roughness.

Numerical modelling of unsteady turbulent flow in tubes, including the effects of roughness and large changes in Reynolds number

A method has been developed for predicting unsteady turbulent friction in smooth, transitional, and rough pipe flows. For transitional and rough pipe flows the effective viscosity at the wall is varied depending on Reynolds number and roughness. An approximation has been made for the transition region using a cubic spline for the friction factor between the smooth and rough regions. This turbulence model can be implemented readily in several types of numerical model for pipe flow, including simple lumped parameter models, finite difference/finite element methods, and the method of characteristics. An approximate method for representing changes in turbulence energy is discussed. Using this, the method is suitable for small and large changes in flow, and for short and long time scales, but further validation is needed.

Friction factor for turbulent flow in rough pipes from Heisenberg’s closure hypothesis

We show that the main results of the analysis of the friction factor for turbulent pipe flow reported by Gioia and Chakraborty [Phys. Rev. Lett. 96, 044502 (2006)] can be recovered by assuming the Heisenberg closure hypothesis for the turbulent spectrum. This highlights the structural features of the turbulent spectrum underlying the analysis of Gioia and Chakraborty.