Flow In Pipe Networks Research Articles

A reduced-order configuration approach for the real-time calculation of three-dimensional flow behavior in a pipe network

The real-time computation of a three-dimensional pipe network flow is crucial for both pipe design and operational maintenance. This study devises a novel reduced-order configuration approach that combines the advantages of the acceleration characteristics of the reduced-order model and the structural applicability of the configuration model. First, a configuration model is established by categorizing sub-pipes extracted from a pipe network into sets based on the sub-pipes' type. Subsequently, reduced-order configurations are realized by a reduced-order model established for each type of configuration, enabling real-time computation of individual sub-pipes. Thus, the concatenation of sub-pipes allows the computation of an entire pipe network. A complex boundary–deep learning–reduced-order configuration model and a complex boundary–deep learning–reduced-order configuration–multi-source data–reduced-order configuration model integrated with a local multi-physical–discrete empirical interpolation method and a multi-source data fusion model are devised. These models were employed for the real-time computation and prediction of a three-dimensional velocity field for 300 snapshots composed of one to four sub-pipes extrapolated from a dataset of 294 pipe network snapshots composed of one to three sub-pipes. The maximum relative errors for snapshots from the dataset were similar to the limit precision of the proper orthogonal decomposition, with more precise accuracy than the relevant studies, indicating the excellent performance of our reduced-order configuration approach.

Experimental study of rainwater grate blocking and submergence of outfall on drainage network capacity

Accurately evaluating the performance of urban underground drainage network and its influencing factors is a challenging problem, as this process is affected by many complex factors. In this study, based on an overland flow experiment considering drainage process of pipe network, a series of physical model experiments were conducted to investigate the influences of different surface slopes, rainwater grate blockage and the submergence of outfall on the performance of the drainage pipe network system. The hydrographs of surface runoff and pipe network flow were recorded in collection tanks by precise digital pressure sensors to provide comprehensive information about the characteristics of drainage performance in the pipe network. Through a series of experimental data collection and analysis, the following conclusions are drawn from this study: (1) The longitudinal slope of the road decreases the pipe drainage capacity by 1.68%–8.94%, and this reduction effect is more significant with the increase of slope. (2) The blockage of rainwater grate at different locations has different impacts on the road drainage system, the downstream rainwater grate blockage has the most obvious impact on the performance of the drainage system, which reduces the drainage capacity by 22.59%–25.38%. (3) Different submergence degrees of rainwater outlet have different impacts on the drainage system. Under different slopes, the drainage capacity of the pipe network decreases by 1.88%–23.46% with the increase of the submergence degree of the outfall. These experimental results are helpful in understanding the working conditions of urban road drainage system and the influencing factors of the system's drainage capacity, and also provide measured data for verification of relevant numerical models and coefficient calibration.

Research on intelligent control theory and strategy of gas drainage pipe network based on graph theory

To address the issues related to the working conditions of the mine gas drainage system and achieve adaptive adjustment of negative pressure during gas drainage, this study proposes a gas drainage pipe network structure model based on graph theory principles. The model is built upon the air-gas mixed flow model of the pipe network. The boundary conditions of the pipe network are determined, and both the pipe network flow model and resistance model are constructed. An assignment iterative adjustment method is used to establish the pipe network solution model, enabling the solution of the gas drainage pipe network. The mathematical model for regulating and controlling the gas drainage pipe network is formulated, considering the objective function, decision variables, and constraint conditions based on the drainage parameters. The control model, along with the flow calculation model of the gas drainage pipe network system, is employed to calculate the optimal gas control scheme. This scheme enables remote intelligent control of the control valve opening on the ground, significantly improving the safety and efficiency of the gas drainage system. The engineering application of Liuzhuang Coal Mine demonstrates the successful realization of the rational distribution of negative pressure and intelligent dynamic control of the drainage pipe network. As a result, the total gas concentration in the drainage pipe network has increased by 12%, yielding favorable outcomes. The findings of this study have significant theoretical and practical implications for the design, development, and improvement of intelligent control systems for mine drainage pipe networks.

Mesoscopic interpretation of hydraulic fracture initiation and breakdown pressure using discrete element method

The relationship between initiation pressure and breakdown pressure, two vital parameters in hydraulic fracturing operations, requires further investigation, with the explicit mechanism underlying breakdown pressure yet to be revealed. This study presents an enhanced particle discrete element model with a regular-shaped borehole, wherein the pressure-updating equation of the pipe network flow model is improved to incorporate comprehensive fluid–solid coupling. Through simulation of the mesoscopic process of hydraulic fracturing initiation and propagation, the characteristic curve of borehole fluid pressure is obtained. By comparing the curves of borehole pressure and fluid flow into the fracture, the physical meaning of breakdown pressure is explained at the mesoscopic level. The results show that the breakdown pressure fundamentally arises from the unstable propagation of the fracture, with its numerical value corresponding to the borehole fluid pressure when the fluid flow into the fracture reaches the injection rate for the first time. Additionally, employing fluid–solid coupling modeling, the impacts of fluid viscosity, injection rate, and borehole diameter on breakdown pressure are investigated. Finally, the evolution of fracture morphology under different injection rates and elastic moduli is analyzed.

Cooling Pipe Network System in the Quenching Green Equipment Design Method Based on the “Solid Contact-Fluid Heat Transfer” Mode

As a typical thin plate part, a circular saw blade matrix is prone to deformation and cracking due to uneven surface cooling rate during heat treatment. Simultaneously, the traditional quenching method is easy to produce a low product qualification rate and serious environmental severe when processing thin plate parts. The quenching device designed in this paper is to achieve the non-contact quenching between the processed parts and the quenching medium through the heat transfer of the fluid in the cooling pipe. The structure design of the internal cooling channel will directly affect the temperature field distribution of the quenching device, thus determining the microstructure and final performance of the product. Therefore, based on the microstructure transformation mechanism and pipe network flow control theory, combined with the heat transfer theory and other relevant theoretical bases, this paper established the mathematical model of internal cooling system parameters. Finally, MATLAB is applied to solve the fluid network topology model. It provides a reliable and general research method for cooling pipe networks in quenching devices based on the “Solid Contact-Fluid Heat Transfer” Mode.

Fluid transient analysis by the method of characteristics using an object-oriented simulation tool

Abstract This paper presents the development of an efficient, interactive and fully extendable computer code to analyse hydraulic transients – water hammer – using a generic object-oriented modelling and simulation (OOMS) tool to simplify and shorten the development process. OOMS tools provide continuous simulation features by means of ordinary differential equation (ODE) and differential algebraic equation (DAE) solvers, and discrete simulation features by means of event handling algorithms. Previous OOMS tool applications to simulate fluid flow in pipe networks primarily used semi-discrete methods with continuous solvers. A novel aspect of this work is the application of the method of characteristics (MOC) using the discrete simulation features of the OOMS tool. When compared to a code developed with an OOMS tool using a semi-discrete method and to commercial software that uses the MOC, the new code shows much higher accuracy and performance than the former and is similar to the latter in accuracy and calculation time. It has a graphical user interface, and its modularity makes it easily extendable with new components and algorithms. An academic version is available on github.

Mechanical Properties and Permeability Evolution of Red Sandstone Subjected to Hydro-mechanical Coupling: Experiment and Discrete Element Modelling

This paper presents the hydro-mechanical behaviors of a red sandstone from the Three Gorges reservoir area using laboratory testing and numerical modelling. A series of laboratory triaxial compression tests were performed on the red sandstone to understand the effect of confining stress and seepage pressure on the rock mechanical properties and permeability. The laboratory results show that the initial elastic modulus, Poisson’s ratio and peak strength of the red sandstone increase with confining stress, and decrease with the increase in seepage pressure. The change in the permeability of the red sandstone is slight during the initial and elastic deformation stages, but increases rapidly when approaching to the peak stress. Micromechanical insights on the sandstone’s hydro-mechanical behaviors were unveiled by implementing an improved pipe network flow model in the discrete element method. The improved pipe network model can well capture the stress–strain response and the permeability changes of the red sandstone that were consistent with the laboratory test results. The numerical results reveal that the distribution of flow rate, pore pressure, and force chains in rock is closely related to microcracking, and the permeability increases accordingly with the increase in the number of microcracks and their coalescence. The number of microcracks and the rock fracture angle with respect to the axial axis at peak stress increase with the effective confining stress. The damage process of the red sandstone during the hydro-mechanical loading is divided into three distinct stages based on the mechanical response and permeability evolution.

Rapid Blockage Diagnosis And Early Warning of Urban Drainage Pipe Network

The core of comprehensive treatment effect of water environment in river basin lies in pipe network system. The blockage of urban drainage pipe network is one of the main reasons affecting the healthy operation of urban drainage network system. So the intelligent analysis method of urban drainage pipe network blockage diagnosis can quickly find the problems of urban drainage pipe network and improve the operation and maintenance efficiency of urban drainage pipe network. In this paper, through the analysis of rainfall data, rainfall and sewage pipe network flow variation regular pattern, the change range, the essay obtains the rain and sewage pipe network blockage diagnosis threshold. Combined with the urban intelligent drainage pipe network system, through the customized setting of pipe network blockage threshold, the rapid diagnosis and early warning of the blockage problem of the drainage pipe network are realized, and the healthy operation of the urban drainage network is guaranteed.

Bayesian Update and Method of Distributions: Application to Leak Detection in Transmission Mains

AbstractWater‐hammer equations are used to describe transient flow in pipe networks. Uncertainty in model parameters, initial and boundary conditions, and location and strength of a possible leak renders deterministic predictions of this system untenable. When deployed in conjunction with pressure measurements, probabilistic solutions of the water‐hammer equations serve as a tool for detecting leaks in pipes. We use the method of distributions to obtain a probability density function (PDF) for pressure head, whose dynamics are described by the stochastic water‐hammer equations. This PDF provides a prior distribution for subsequent Bayesian data assimilation, in which data collected by pressure sensors are combined with this prior to obtain a posterior PDF of the leak location and size. We conduct a series of numerical experiments with uncertain initial velocity and measurement noise to ascertain the robustness and accuracy of the proposed approach. The results show the method's ability to identify the leak location and strength in a water transmission main.

Variability of permeability and seepage characteristics in soil landslides: a test case in the Three Gorges Reservoir Area, China

Abstract This study presents assessments of the spatial variability of a soil landslide in the Three Gorges Reservoir Area in China. The results challenge the idea that variability of permeability within a landslide is secondary. Consequently, it cannot be assessed through single representative values. It was found that its variability spans two orders of magnitude, a consequence of it being influenced by both morphology and regolith properties. Identification of zones that display comparable behavior can be done through assessment of remote-sensing images collected by drones, as growth patterns of vegetation correspond well with zones that displayed similar permeability coefficients within the landslide body. Furthermore, extensive variability of permeability was caused by a diverse range of seepage mechanisms, namely pipe network flow, interface network seepage and pore water seepage. Thus, the hydraulic behavior of large landslide bodies is remarkably complex.

Simulation of transient flow in viscoelastic pipe networks

The use of polymeric pipes such as polyethylene (PE) and polyvinyl chloride (PVC) has recently increased in water distribution networks. This necessitates the understanding of the viscoelastic behaviour of these pipes in practice and in particular for transient flow analysis. The purpose of this study is to calibrate a developed numerical model based on the experimental results of transient flow in PE pipe networks. The linear viscoelastic model parameters were calibrated using the inverse transient analysis. Comparison of numerical results with experimental data indicated that the developed viscoelastic model was able to predict both pressure wave damping and dispersion in these pipe systems. Results confirmed a negligible viscoelastic effect of single pipe and pipe network on the linear viscoelastic model. Hence, the calibrated results of a single PE pipe were used to simulate the transient flow in the pipe network. The experimental and simulation results of pipe network transient flow in this study are new and advance previous studies.

Applicability of Preissmann box scheme for calculation of transcritical flow in pipes

AbstractThe accurate computer simulation of pipe flow is of great importance in the design of urban drainage. The Preissmann box scheme is usually used to model a wide range of subcritical and supercritical flows. However, care must be taken over the modelling of transcritical flows since, unless the correct internal boundary conditions are imposed, the scheme becomes unstable. In this paper, using the scheme in conjunction with the reduced momentum equation and applying boundary condition structure inherent to subcritical flow to all regimes, is an approach that enables efficient numerical simulation of transcritical flows in pipe networks. The approach includes three steps. First, a unified mathematical model which is based on the Preissmann slot model is derived. Second, the Preissmann box scheme is used to solve the set of equations, by analyzing and discussing the origin of the invalidity of applying the scheme, and a numerical model suitable for transcritical flow is proposed by the method of changing the convection acceleration term. Third, the numerical model is assessed by comparison with analytical, experimental and numerical results. The proposed models verified that this method can make the Preissmann box scheme applicable to the computation of transcritical flow in pipes.

Optimal model switching for gas flow in pipe networks

We consider model adaptivity for gas flow in pipeline networks. For each instant in time and for each pipe in the network a model for the gas flow is to be selected from a hierarchy of models in order to maximize a performance index that balances model accuracy and computational cost for a simulation of the entire network. This combinatorial problem involving partial differential equations is posed as an optimal switching control problem for abstract semilinear evolutions. We provide a theoretical and numerical framework for solving this problem using a two stage gradient descent approach based on switching time and mode insertion gradients. A numerical study demonstrates the practicability of the approach.

Seepage simulation using pipe network flow model in a discrete element system

The pipe network flow model can simulate the seepage process with DEM conveniently because of its simple algorithm. However, whether it can recover the correct seepage process has not been verified. In this paper, the equation to update the fluid pressure is rebuilt according to the flow conservation. Through the steady seepage simulation, this algorithm is verified to be able to recover Darcy’s law, and the equation to calibrate the aperture according to macro permeability is derived. Furthermore, the modified algorithm is used to simulate the unsteady seepage process, and the results show good agreement with the analytical solutions.

Experimental calibration and validation of sewer/surface flow exchange equations in steady and unsteady flow conditions

The linkage between sewer pipe flow and floodplain flow is recognised to induce an important source of uncertainty within two-dimensional (2D) urban flood models. This uncertainty is often attributed to the use of empirical hydraulic formulae (the one-dimensional (1D) weir and orifice steady flow equations) to achieve data-connectivity at the linking interface, which require the determination of discharge coefficients. Because of the paucity of high resolution localised data for this type of flows, the current understanding and quantification of a suitable range for those discharge coefficients is somewhat lacking. To fulfil this gap, this work presents the results acquired from an instrumented physical model designed to study the interaction between a pipe network flow and a floodplain flow. The full range of sewer-to-surface and surface-to-sewer flow conditions at the exchange zone are experimentally analysed in both steady and unsteady flow regimes. Steady state measured discharges are first analysed considering the relationship between the energy heads from the sewer flow and the floodplain flow; these results show that existing weir and orifice formulae are valid for describing the flow exchange for the present physical model, and yield new calibrated discharge coefficients for each of the flow conditions. The measured exchange discharges are also integrated (as a source term) within a 2D numerical flood model (a finite volume solver to the 2D Shallow Water Equations (SWE)), which is shown to reproduce the observed coefficients. This calibrated numerical model is then used to simulate a series of unsteady flow tests reproduced within the experimental facility. Results show that the numerical model overestimated the values of mean surcharge flow rate. This suggests the occurrence of additional head losses in unsteady conditions which are not currently accounted for within flood models calibrated in steady flow conditions.

Effective Flow of Incompressible Micropolar Fluid Through a System of Thin Pipes

In this paper, we consider the incompressible micropolar fluid flowing through a multiple pipe system via asymptotic analysis. Introducing the ratio between pipes thickness and its length as a small parameter ?$\varepsilon$, we propose an approach leading to a macroscopic model describing the effective flow. In the interior of each pipe (far from the junction), we deduce that the fluid behavior is different depending on the magnitude of viscosity coefficients with respect to ?$\varepsilon$. In particular, we prove the solvability of the critical case characterized by the strong coupling between velocity and microrotation. In the vicinity of junction, an interior layer is observed so we correct our asymptotic approximation by solving an appropriate micropolar Leray's problem. The error estimates are also derived providing the rigorous mathematical justification of the constructed approximation. We believe that the obtained result could be instrumental for understanding the microstructure effects on the fluid flow in pipe networks.

Coupling constants and the generalized Riemann problem for isothermal junction flow

We consider gas flow in pipe networks governed by the isothermal Euler equations. A set of coupling conditions is required to completely specify the Riemann problem at the junction. The momentum-related condition has no obvious expression and different approaches have been used in previous work. For the condition of equal momentum flux, Colombo and Garavello [A well posed Riemann problem for the p-system at a junction, Netw. Heterog. Media 1 (2006) 495–511] proved existence and uniqueness of solutions globally in time and locally in the subsonic region of the state space. If the entropy constraint is not considered, we are able to prove existence and uniqueness globally in the subsonic region for any momentum-related coupling constant satisfying a monotonicity requirement. The previously suggested conditions of equal pressure and equal momentum flux satisfy this requirement, but in general they both fail to fulfill the entropy constraint. The classical Bernoulli invariant is a natural scalar formulation of momentum conservation under ideal flow conditions. Our analysis shows that this invariant is monotone and unconditionally leads to solutions satisfying the entropy constraint. Of the coupling constants considered, this is therefore the only choice that guarantees the unique existence of entropy solutions to the N-junction Riemann problem for all initial data in the subsonic region.

The Analysis of Efficiency and Safety of the Plan of Quantity Adjustment in Heating System

To direct at heating system when it adopts quantity adjustment. Taking a community in Zhangjiakou as an example, using the method of Graphic theory to analysis and compare these two operation schemes: adjusting parallel pump's valve in shared pipeline and adjusting parallel pump's valve in non-shared pipeline. We can know that adjusting parallel pump's valve in non-shared pipeline is energy-saving, when the flow in pipe network is bigger than 79% of the boiler's total circulating water. There is a lowest limit of system's circulating water, when adopt the method that adjusting the parallel pump's valve in non-shared pipeline, otherwise it would damage the pump.

Gas Flow in Fan-Shaped Networks: Classical Solutions and Feedback Stabilization

We analyze the subcritical gas flow through fan-shaped networks of pipes, that is, through tree-shaped networks with exactly one node where more than two pipes meet. The gas flow in pipe networks is modeled by the isothermal Euler equations, a hyperbolic PDE system of balance laws. For this system we analyze stationary states and classical nonstationary solutions locally around a stationary state on a finite time interval. Furthermore, we present a Lyapunov function and boundary feedback laws to stabilize a fan-shaped network around a given stationary state.

A new model for gas flow in pipe networks

AbstractWe introduce a new model for gas dynamics in pipe networks by asymptotic analysis. The model is derived from the isothermal Euler equations. We present the derivation of the model as well as numerical results illustrating the validity and its properties. We compare the new model with existing models from the mathematical and engineering literature. We further give numerical results on a sample network. Copyright © 2009 John Wiley & Sons, Ltd.