Submit to Water Review for Water Propose a Special Issue

Journal Browser

► Journal Browser

Pipeline Fluid Mechanics

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Published Papers

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydraulics and Hydrodynamics".

Deadline for manuscript submissions: closed (31 August 2019) | Viewed by 59282

Share This Special Issue

Special Issue Editors

Dr. Mostafa Safdari Shadloo

E-Mail Website
Guest Editor

CORIA Lab., INSA Rouen/ CNRS (UMR 6614), Rouen, France
Interests: turbulence; computational fluid dynamics (CFD); multiphase flows; meshless methods; high performance computing (HPC)
Special Issues, Collections and Topics in MDPI journals

Dr. Ali Bakhshandeh Rostami

E-Mail Website
Guest Editor

Maritime Engineering Marine, Offshore and Subsea Technology, School of Engineering Armstrong Building, Newcastle University
Interests: fluid–structure interactions; applied fluid mechanics and hydro-aerodynamics; vortex induced motions; applied mathematics and nonlinear dynamics

Dr. Omid Mahian

E-Mail Website
Guest Editor

School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an 710049, China
Interests: solar energy systems; entropy generation and exergy analysis in energy systems; heat transfer in nanofluids; solar stills
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The fluid flow dynamics through a pipe is a basic Fluid Mechanics problem, which occurs in many industrial applications. This basic geometry is, not only found in the transportation of goods and/or materials, such as oil, gas and water, but also used as a building block to model more complex flows, such as those in teleheating systems, heat exchangers, mixing chambers, product changeover, as well as in bio-medical applications. Though simple in geometries, they possess very fundamental yet complex fluid flow physics with practical importance.

For instances for internal flow in pipes, a curvature may cause a dean flow and/or with internal perturbation/friction the flow may undergoes laminar to turbulent transition. This significantly alters the pressure head loss, mixing, as well as wall heat transfer. Alternatively, a multiphase or an aggressive fluid flow inside a pipe may cause fluid induced vibration and/or corrosion, pipe failure and as a consequence an environmental hazard. Flow around the pipelines may also cause vortex induced vibrations and affect other nearby pipes and infrastructure.

This Special Issue is dedicated to different fundamental aspects of “Pipeline Fluid Mechanics” along with their applications to engineering problems. The current Special Issue invites all original experimental, statistical, analytical and computational fluid dynamic research works in the field. This research topic also welcomes related novel inter-/multi-disciplinary works in the emerging areas of mechanical, chemical, process and energy engineering.

Prof. Mostafa Safdari Shadloo
Dr. Omid Mahian
Dr. Ali Bakhshandeh Rostami
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Water is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Pipeline engineering
Pipeline fluid transport
Fluid induced vibration (FIV)
Vortex induced vibration (VIV)
Multi-phase flow
Offshore engineering
Flow hydrodynamics
Pipeline slug flow and fatigue
Pipeline heat transfer
Waste and hazard prevention

Published Papers (14 papers)

Download All Papers

Research

Jump to: Other

13 pages, 3469 KiB

Open AccessArticle

Investigation on the Effect of Structural Parameters on Cavitation Characteristics for the Venturi Tube Using the CFD Method

by Pan Tang, Juan Manzano Juárez and Hong Li

Water 2019, 11(10), 2194; https://doi.org/10.3390/w11102194 - 22 Oct 2019

Cited by 8 | Viewed by 5297

Abstract

The venturi tube is a special kind of pipe which has been widely applied in many fields. Cavitation is one of the most important research issues for the Venturi tube. Hence, three key structural parameters (contraction angle, diffusion angle and contraction ratio) were selected to investigate the influence of different factors on cavitation characteristics, using the computational fluid dynamics (CFD) method. A series of experiments for measuring the relationship between differential pressure and flow rate were carried out to verify the accuracy of the simulation method. Results showed that the simulation results had a high accuracy and the numerical method was feasible. The average vapor volume fraction of cross-section from the throat in the axial direction increased with increasing contraction angle. The cavity length increased with increasing contraction angle. The average volume fraction in the diffusion section rapidly decreased with increasing diffusion angle. The diffusion angle had no significant effect on the cavitation characteristics in the throat section and had a significant influence in the diffusion section. The average vapor volume fraction increased with decreasing contraction ratio. The contraction ratio had no significant effect on the cavity length under the same differential pressure. The average vapor volume fraction increased with decreasing contraction ratio. However, the variation in the throat section was less than the diffusion section. Under the same inlet and outlet pressure, the cavity lengths for different contraction ratios were basically the same, which indicated that the contraction ratio had no significant effect on the cavity length. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

24 pages, 52408 KiB

Open AccessArticle

Wall Stresses in Cylinder of Stationary Piped Carriage Using COMSOL Multiphysics

by Xiaoni Yang, Juanjuan Ma, Yongye Li, Xihuan Sun, Xiaomeng Jia and Yonggang Li

Water 2019, 11(9), 1910; https://doi.org/10.3390/w11091910 - 13 Sep 2019

Cited by 10 | Viewed by 3925

Abstract

Hydraulic transportation of the piped carriage is a new energy-saving and environmentally-friendly transportation mode. There are two main states in the conveying process, stationary and moving. In the process of hydraulic transportation of the piped carriage, the study of the stress of the water flow act on the cylinder wall of the piped carriage can help to improve the design of the piped carriage structure and even the selection of piped carriage materials. The distribution of flow velocity around the stationary piped carriage and the stress distribution on the cylinder wall of the stationary piped carriage were investigated by combining numerical simulations with model experiment verification. The commercial finite element software, Comsol Multiphysics, was utilized to solve this problem using the arbitrary Lagrangian–Eulerian (ALE) method. The results showed that the simulation results were in good agreement with the experimental results. It also showed that the ALE method can well be applied for fluid-structure problems in the process of hydraulic transportation of the piped carriage. The simulation results showed that the low velocity region near the inner wall of the pipe was smaller than that near the outer wall of the piped carriage, and both regions decreased with the increase of the discharge. The maximum stress on the cylinder wall of the piped carriage appeared between the two support feet in the middle and rear sections of the cylinder. The influence of the unit discharge on wall stress increased with the increase of the discharge, that is, k₁ < k₂ < k₃. Moreover, the increase of the discharge had the greatest influence on the circumferential component of the principal stress of the cylinder, followed by the axis component, and the smallest influence on the wall shear stress of the cylinder, i.e.,

{\bar{k}}_{σ_{c}}

{\bar{k}}_{σ_{a}}

{\bar{k}}_{σ_{r}}

{\bar{k}}_{τ_{c}}

. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

16 pages, 4810 KiB

Open AccessArticle

Convective Bubbly Flow of Water in an Annular Pipe: Role of Total Dissolved Solids on Heat Transfer Characteristics and Bubble Formation

by M. M. Sarafraz, M. S. Shadloo, Zhe Tian, Iskander Tlili, Tawfeeq Abdullah Alkanhal, Mohammad Reza Safaei, Marjan Goodarzi and M. Arjomandi

Water 2019, 11(8), 1566; https://doi.org/10.3390/w11081566 - 29 Jul 2019

Cited by 22 | Viewed by 4018

Abstract

Formation of bubbles in water inside an annulus pipe in a flow boiling regime was experimentally investigated. The effect of various variables, such as total dissolved solid materials (TDS) in terms of mass fraction, flow rate of water, and applied heat flux (HF) on the heat transfer coefficient (HTC) and bubble behavior of water, was experimentally investigated. A regression formula was fitted to estimate the average bubble diameter at various TDS values, with accuracy of <4.1% up to heat flux of 90 kW/m². Results show that the presence of TDS materials can increase the contact angle of bubble and bubble diameter, and also promotes the HTC value of the system. However, flow rate of water suppressed bubble generation, and increased the heat transfer coefficient due to the renewal of the thermal boundary layer around the boiling surface. Likewise, it was identified that forced convective and nucleate boiling heat transfer mechanisms contribute to the flow of boiling water, and heat flux is a key parameter in determining the mechanism of heat transfer. In the present study, heat flux of 15 kW/m² at 50 °C was the heat flux in which onset of nucleate boiling was identified inside the annulus pipe. The contact angle of water at TDS values of 300 mg/L and 1200 mg/L was 74° and 124°, respectively, showing the improvement in heat transfer characteristics of water due to the presence of TDS materials. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Graphical abstract

22 pages, 6987 KiB

Open AccessArticle

Multi-Objective Optimization of a Pitch Point Absorber Wave Energy Converter

by Rezvan Alamian, Rouzbeh Shafaghat and Mohammad Reza Safaei

Water 2019, 11(5), 969; https://doi.org/10.3390/w11050969 - 09 May 2019

Cited by 30 | Viewed by 4009

Abstract

In this paper, a pitch point absorber wave energy converter (WEC) is selected in order to be optimized for the wave characteristics of the Caspian Sea. The optimization process is a multi-objective optimization. For achieving the optimal WEC, mean absorbed power should be maximized while the construction cost should be minimized. The submerged surface area of the WEC is selected as a cost parameter. The amount of mean absorbed power depends on the installation site and also the shape of the WEC. For optimizing the shape of the WEC, various shapes are considered which are categorized into three different sections. A multi-objective genetic algorithm is used for optimization of the model, and the NEMOH software is used to simulate the wave-body interaction. The results show that the bottom flat and upside chamfered geometry with X:Y ratio of 10:1 is the best geometry for the desired application. Comparing the results from the final optimized shape with the optimized basic parallelepipedic hull shape reveals that much more extractable power can be achieved with less cost. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

17 pages, 3576 KiB

Open AccessArticle

Effect of the Concentration of Sand in a Mixture of Water and Sand Flowing through PP and PVC Elbows on the Minor Head Loss Coefficient

by Piotr Wichowski, Tadeusz Siwiec and Marek Kalenik

Water 2019, 11(4), 828; https://doi.org/10.3390/w11040828 - 19 Apr 2019

Cited by 6 | Viewed by 4071

Abstract

The article presents the results of tests of minor head losses through PVC and PP elbows for a flow of water and mixtures of water and sand with grain sizes of up to 0.5 mm and concentrations of 5.6 g·L⁻¹, 10.84 g·L⁻¹, and 15.73 g·L⁻¹. The tests were carried out at variable flow velocities for three elbow diameters of 63 mm, 75 mm, and 90 mm. The flow rate, pressure difference in the tested cross-sections, and temperature of the fluids were measured and automatically recorded. The results of the measurements were used to develop mathematical models for determining the minor head loss coefficient as a function of elbow diameter, sand concentration in the liquid, and Reynolds number. The mathematical model was developed by cross validation. It was shown that when the concentration of sand in the liquid was increased by 1.0 g∙L⁻¹, the coefficient of minor head loss through the elbows increased, in the Reynolds number range of 4.6 × 10⁴–2.1 × 10⁵, by 0.3–0.01% for PP63, 0.6–0.03% for PP75, 1.1–0.06% for PP90, 0.8−0.01% for PVC63, 0.8–0.02% for PVC75, and 0.9–0.04% for PVC90. An increase in Re from 5 × 10⁴ to 2 × 10⁶ for elbows with diameters of 63, 75 and 90 mm caused a 7.3%, 6.8%, and 6.0% decrease in the minor head loss coefficient, respectively. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Graphical abstract

19 pages, 6133 KiB

Open AccessArticle

Numerical Modeling and Hydraulic Optimization of a Surge Tank Using Particle Swarm Optimization

by Khem Prasad Bhattarai, Jianxu Zhou, Sunit Palikhe, Kamal Prasad Pandey and Naresh Suwal

Water 2019, 11(4), 715; https://doi.org/10.3390/w11040715 - 06 Apr 2019

Cited by 7 | Viewed by 5214

Abstract

In a pressurized water conveyance system, such as a hydropower system, during hydraulic transients, maximum and minimum pressures at various controlling sections are of prime concern for designing a safe and efficient surge tank. Similarly, quick damping of surge waves is also very helpful for the sound functioning of the hydro-mechanical system. Several parameters like diameter of the surge tank, diameter of the orifice, operating discharge, working head, etc., influence the maximum/minimum surge, damping of surge waves in the surge tank, and the difference of maximum pressure head at the bottom tunnel and maximum water level in the surge tank. These transient behaviors are highly conflicting in nature, especially for different diameters of orifices (D_O) and diameters of surge tanks (D_S). Hence, a proper optimization method is necessary to investigate the best values of D_O and D_S to enhance the safety and efficiency of the surge tank. In this paper, these variables are accurately determined through numerical analysis of the system by the Method of Characteristics (MOC). Furthermore, the influence on the transient behavior with changing D_O and D_S is investigated and finally, optimum values of D_O and D_S are determined using Particle Swarm Optimization (PSO) to minimize the effects of hydraulic transients on the system without compromising the stability and efficiency of the surge tank. The obtained results show significant improvements over the contemporary methods of finding D_O and D_S for surge tank design. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

26 pages, 7921 KiB

Open AccessArticle

Hydraulic Oscillation and Instability of A Hydraulic System with Two Different Pump-Turbines in Turbine Operation

by Sunit Palikhe, Jianxu Zhou and Khem Prasad Bhattarai

Water 2019, 11(4), 692; https://doi.org/10.3390/w11040692 - 04 Apr 2019

Cited by 7 | Viewed by 4113

Abstract

Hydraulic oscillation mainly reveals the undesirable pressure fluctuations which can cause catastrophic failure of any hydraulic system. The behavior of a hydraulic system equipped with two different pump-turbines was investigated through hydraulic oscillation analysis to demonstrate severe consequences induced in turbine operation, including S-shaped characteristics. The impedance of a pump-turbine has an essential role in the determination of the instability of the hydraulic system. The conventional way to determine the instability solely using the slope of a characteristic curve was improved, including the effect of guide vane opening in pump-turbine impedance, which consequently modified the instability expression. With this pump-turbine impedance, hydraulic oscillation analysis, including free oscillation analysis and frequency response analysis, was carried out. The free oscillation analysis entails the computation of complex natural frequencies and corresponding mode shapes of the system. These computations provided necessary information about the vulnerable position of vital hydraulic components and the scenario for self-excited oscillation. Further, the analysis illustrates the significant role of guide vane opening to prevent the system from becoming unstable. Lastly, frequency response analysis was performed for the system with an oscillating guide vane to obtain the frequency response spectrum, which revealed that the resonating frequencies are consistent with natural frequencies, and it supported free oscillation results. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

12 pages, 2544 KiB

Open AccessArticle

Effects of Geometry and Hydraulic Characteristics of Shallow Reservoirs on Sediment Entrapment

by Hamidreza Zahabi, Mohammadamin Torabi, Ebrahim Alamatian, Mehdi Bahiraei and Marjan Goodarzi

Water 2018, 10(12), 1725; https://doi.org/10.3390/w10121725 - 26 Nov 2018

Cited by 39 | Viewed by 3798

Abstract

Sediment and deposition are among the main problems in dam engineering and other related fields. Because of the numerous advantages of numerical modeling, effects of different geometries of reservoirs on the flow pattern and deposition of sediments are investigated using the finite volume based Flow-3D software package. In this study, three rectangular reservoirs with different dimensional ratios are simulated using the large eddy simulation (LES) turbulence model. To validate the numerical modeling, existing experimental data is used. Results indicate that Flow-3D can accurately simulate flow and sediment deposition in the reservoirs, and the numerical data are in reasonable agreement with the experimental results. Numerical efforts showed that the amount of deposition in reservoirs is significantly dependent on the geometry. Among the modeled reservoirs, the 6 × 4 m one has the best performance. Moreover, it can be said that changing the position of the flow’s inlet and outlet of the reservoir does not have a considerable effect on increasing its efficiency. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Graphical abstract

21 pages, 2598 KiB

Open AccessArticle

An Improvement of Port-Hamiltonian Model of Fluid Sloshing Coupled by Structure Motion

by Mohammad Yaghoub Abdollahzadeh Jamalabadi

Water 2018, 10(12), 1721; https://doi.org/10.3390/w10121721 - 24 Nov 2018

Cited by 8 | Viewed by 3191

Abstract

The fluid–solid interaction is an interesting topic in numerous engineering applications. In this paper, the fluid–solid interaction is considered in a vessel attached to the free tip of a cantilever beam. Governing coupled equations of the system include the Euler–Bernoulli equation for bending of a beam, torsion of a beam, 2-D motion of the rigid vessel, and rotating shallow water equation of fluid sloshing in the vessel. As an essential portion in the numerical simulation of the vibration control of this fluid–plate system is the accurate modeling of sloshing; the partial differential equations of the system are modified by approximation of velocity profile. The suggested method is validated by experimental results of a piezoelectric actuated clamped rectangular plate holding a cylindrical vessel. These sloshing interactions with elastic test cases illustrate the mass conservative characteristics of the method as well as its stability in a prompt change of the vessel situations. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

17 pages, 2715 KiB

Open AccessArticle

Analysis of Pressure Transient Following Rapid Filling of a Vented Horizontal Pipe

by Lin Li, David Z. Zhu and Biao Huang

Water 2018, 10(11), 1698; https://doi.org/10.3390/w10111698 - 21 Nov 2018

Cited by 16 | Viewed by 4031

Abstract

Rapid filling/emptying of pipes is commonly encountered in water supply and sewer systems, during which pressure transients may cause unexpected large pressure and/or geyser events. In the present study, a linearized analytical model is first developed to obtain the approximate solutions of the maximum pressure and the characteristics of pressure oscillations caused by the pressurization of trapped air in a horizontal pipe when there is no or insignificant air release. The pressure pattern is a typical periodic wave, analogous to sinusoidal motion. The oscillation period and the time when the pressure attains the peak value are significantly influenced by the driving pressure and the initial length of the entrapped air pocket. When there is air release through a venting orifice, analysis by a three-dimensional computational fluid dynamics model using ANSYS Fluent was also conducted to furnish insights and details of air–water interactions. Flow features associated with the pressurization and air release were examined, and an air–water interface deformation that one-dimensional models are incapable of predicating was presented. Modelling results indicate that the residual air in the system depends on the relative position of the venting orifice. There are mainly two types of pressure oscillation patterns: namely, long or short-period oscillations and waterhammer. The latter can be observed when the venting orifice is located near the end of the pipe where the air is trapped. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

18 pages, 1150 KiB

Open AccessArticle

Optimal Design of Circular Baffles on Sloshing in a Rectangular Tank Horizontally Coupled by Structure

by Mohammad Yaghoub Abdollahzadeh Jamalabadi, Vinh Ho-Huu and Truong Khang Nguyen

Water 2018, 10(11), 1504; https://doi.org/10.3390/w10111504 - 24 Oct 2018

Cited by 11 | Viewed by 5473

Abstract

Parametric studies on the optimization of baffles on vibration suppression of partially filled tanks coupled by structure have been widely conducted in literature. However, few studies focus on the effect of the position of the baffles on fluid flow stratification and dampening the motion. In the present study, a numerical investigation, an engineering analysis, and optimal design study were performed to determine the effect of external flow on circular obstacle baffles performance on suppressing the vibrations of coupled structure in a closed basin. The single degree of freedom model (mass–spring–damper) is used to model the structure that holds the tank. The coupled system is released from an initial displacement without a velocity. The governing mass, turbulent Navier–Stokes momentum, volume of fluid, and one degree of freedom structure equations are solved by the Pressure-Implicit with Splitting of Operators algorithm in fluids and Newmark method in structure. Based on a detailed study of transient structure motion coupled with sloshing dynamics, the optimal baffle location was achieved. Optimal position of the baffle and its width are systematically obtained with reference to the quiescent free surface. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

42 pages, 8045 KiB

Open AccessArticle

Effects of Guide Vane Placement Angle on Hydraulic Characteristics of Flow Field and Optimal Design of Hydraulic Capsule Pipelines

by Chunjin Zhang, Xihuan Sun, Yongye Li, Xueqin Zhang, Xuelan Zhang, Xiaoni Yang and Fei Li

Water 2018, 10(10), 1378; https://doi.org/10.3390/w10101378 - 02 Oct 2018

Cited by 10 | Viewed by 3068

Abstract

With the rapid growth of agricultural trade volumes, the transportation of agricultural products has received widespread attention from society. Aiming at these problems of low transport efficiency and high transport cost in long-distance transport of agricultural products, an energy-saving and environmental-friendly transport mode of agricultural machinery—hydraulic capsule pipelines (HCPs)—was proposed. HCPs effectively solve issues like traffic congestion, energy crises, and atmospheric pollution. Published literature is mainly limited to the capsule speed and the pressure drop characteristics of the fluid within the pipelines. This research was conducted on the following four aspects of HCPs. Firstly, the structure of the carrier was improved and called a ‘piped carriage’. Secondly, a coupled solution between the structural domain of the piped carriage and the fluid domain within the pipelines was numerically investigated by using the commercial CFD software ANSYS Fluent 12.0 based on the bidirectional fluid–structure interaction methods. Thirdly, the effects of guide vane placement angle on hydraulic characteristics of the internal flow field within the horizontal pipelines transporting the piped carriage were extensively evaluated. Finally, based on least-cost principle, an optimization model of HCPs was established. The results indicated that the simulated results were in good agreement with the experimental results, which further demonstrated that it was feasible to adopt the bidirectional fluid–structure interaction methods for solving the hydraulic characteristics of the internal flow field when the piped carriage was moving along the pipelines. This article will provide an abundant theoretical foundation for the rational design of HCPs and its popularization and application. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Graphical abstract

14 pages, 4402 KiB

Open AccessCommunication

Symbolic Regression-Based Genetic Approximations of the Colebrook Equation for Flow Friction

by Pavel Praks and Dejan Brkić

Water 2018, 10(9), 1175; https://doi.org/10.3390/w10091175 - 02 Sep 2018

Cited by 20 | Viewed by 4101

Abstract

Widely used in hydraulics, the Colebrook equation for flow friction relates implicitly to the input parameters; the Reynolds number, Re and the relative roughness of an inner pipe surface, ε/D with an unknown output parameter; the flow friction factor, λ; λ = f (λ, Re, ε/D). In this paper, a few explicit approximations to the Colebrook equation; λ ≈ f (Re, ε/D), are generated using the ability of artificial intelligence to make inner patterns to connect input and output parameters in an explicit way not knowing their nature or the physical law that connects them, but only knowing raw numbers, {Re, ε/D}→{λ}. The fact that the used genetic programming tool does not know the structure of the Colebrook equation, which is based on computationally expensive logarithmic law, is used to obtain a better structure of the approximations, which is less demanding for calculation but also enough accurate. All generated approximations have low computational cost because they contain a limited number of logarithmic forms used for normalization of input parameters or for acceleration, but they are also sufficiently accurate. The relative error regarding the friction factor λ, in in the best case is up to 0.13% with only two logarithmic forms used. As the second logarithm can be accurately approximated by the Padé approximation, practically the same error is obtained also using only one logarithm. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

Other

Jump to: Research

15 pages, 2648 KiB

Open AccessTechnical Note

A Simple and Unified Linear Solver for Free-Surface and Pressurized Mixed Flows in Hydraulic Systems

by Dechao Hu, Songping Li, Shiming Yao and Zhongwu Jin

Water 2019, 11(10), 1979; https://doi.org/10.3390/w11101979 - 23 Sep 2019

Cited by 3 | Viewed by 2727

Abstract

A semi–implicit numerical model with a linear solver is proposed for the free-surface and pressurized mixed flows in hydraulic systems. It solves the two flow regimes within a unified formulation, and is much simpler than existing similar models for mixed flows. Using a local linearization and an Eulerian–Lagrangian method, the new model only needs to solve a tridiagonal linear system (arising from velocity-pressure coupling) and is free of iterations. The model is tested using various types of mixed flows, where the simulation results agree with analytical solutions, experiment data and the results reported by former researchers. Sensitivity studies of grid scales and time steps are both performed, where a common grid scale provides grid-independent results and a common time step provides time-step-independent results. Moreover, the model is revealed to achieve stable and accurate simulations at large time steps for which the CFL is greater than 1. In simulations of a challenging case (mixed flows characterized by frequent flow-regime conversions and a closed pipe with wide-top cross-sections), an artificial slot (A-slot) technique is proposed to cope with possible instabilities related to the discontinuous main-diagonal coefficients of the linear system. In this test, a slot-width sensitivity study is also performed, and the suitable slot-width ratio (ε) for the linear solver is suggested to be 0.05–0.1. Full article

(This article belongs to the Special Issue Pipeline Fluid Mechanics)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Pipeline Fluid Mechanics

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (14 papers)

Research

Other

Further Information

Guidelines

MDPI Initiatives

Follow MDPI