Water Flow Problems Research Articles

예조건화 HLLC 기법을 이용한 저 마하수 축소-확대 노즐의 준 1차원 이상유동 해석

In this paper, quasi-one-dimensional two-phase flows through converging-diverging nozzles are simulated using a preconditioned HLLC method applied to a compressible two-pressure, one-velocity two-phase flow model. An efficient method estimating a reference Mach number used in the preconditioned scheme has been newly proposed. The developed code has been validated by the benchmark problems of a single-phase liquid water flow and a two-phase water-air flow through a linear nozzle. The computed results are good agreement with the previous one. It is noted that the present computations for the volume fraction profile show somewhat more accurate results than the previous one. The developed code can be used for solving the cavitation problem in water flows through nozzles and hydrofoils.

A New Derivative‐Free Linear Approximation for Solving the Network Water Flow Problem With Convergence Guarantees

AbstractAddressing challenges in urban water infrastructure systems, including aging infrastructure, supply uncertainty, extreme events, and security threats, depends highly on water distribution networks modeling emphasizing the importance of realistic assumptions, modeling complexities, and scalable solutions. In this study, we propose a derivative‐free, linear approximation for solving the network water flow problem. The proposed approach takes advantage of the special form of the nonlinear head loss equations, and, after the transformation of variables and constraints, the water flow problem reduces to a linear optimization problem that can be efficiently solved by modern linear solvers. Ultimately, the proposed approach amounts to solving a series of linear optimization problems. We demonstrate the proposed approach through several case studies and show that the approach can model arbitrary network topologies and various types of valves and pumps, thus providing modeling flexibility. Under mild conditions, we show that the proposed linear approximation converges. We provide sensitivity analysis and discuss in detail the current limitations of our approach and suggest solutions to overcome these. All the codes, tested networks, and results are freely available on Github for research reproducibility.

Distributionally Robust Stochastic Optimal Water Flow and Risk Management

We present a computationally efficient framework to solve a multi-stage optimal water flow (OWF) problem with stochastic water demands. The proposed framework explicitly considers the feedback control policies and adjustable water flow with forecast errors over a planning horizon. The objective is to find an optimal operation schedule of controllable devices (e.g., pumps and valves) to trade off operational performance, such as economic efficiency, safety, and smoothness, and risk of constraint violations. We compute feedback policies that are robust to forecast errors in order to accommodate the fluctuating water demands. Given a probabilistic description of forecast errors, our formulations provide two broad approaches based on Conditional Value-at-Risk (CVaR) and distributionally robust optimization (DRO) that offer alternatives to the existing stochastic OWF formulations based on chance-constrained and robust optimization. Numerical case studies on a three-tank water network demonstrate that the proposed framework achieves effective and explicitly adjustable trade offs between operational efficiency and constraint violation risk.

Measurement of xylem water pressure using High-Capacity Tensiometer and benchmarking against Pressure Chamber and Thermocouple Psychrometer

The response of the shallow portion of the ground (vadose zone) and of earth structures is affected by the interaction with the atmosphere. Rainwater infiltration and evapotranspiration affect the stability of man-made and natural slopes and cause shallow foundations and embankments to settle and heave. Very frequently, the ground surface is covered by vegetation and, as a result, transpiration plays a major role in ground-atmosphere interaction. The soil, the plant, and the atmosphere form a continuous hydraulic system, which is referred to as Soil-Plant-Atmosphere Continuum (SPAC). The SPAC actually represents the ‘boundary condition’ of the geotechnical water flow problem. Water flow in soil and plant takes place because of gradients in hydraulic head triggered by the negative water pressure (water tension) generated in the leaf stomata. To study the response of the SPAC, (negative) water pressure needs to be measured not only in the soil but also in the plant. The paper presents a novel technique to measure the xylem water pressure based on the use of the High-Capacity Tensiometer (HCT), which is benchmarked against conventional techniques for xylem water pressure measurements, i.e. the Pressure Chamber (PC) and the Thermocouple Psychrometer (TP).

The role of the Rankine-Hugoniot relations in staggered finite difference schemes for the shallow water equations

The purpose of this work is to point out the relevance of the Rankine-Hugoniot jump relations regarding the numerical solution of the inviscid shallow water equations. To arrive at physically relevant solutions in rapidly varied flow, it is of crucial importance that continuity of mass flux and momentum flux across a steady discontinuity is fulfilled at the discrete level. By adopting this viewpoint, finite difference schemes can be studied that may be well suited to solve shallow water flow problems involving discontinuities, while they are not based on a characteristic decomposition of the governed hyperbolic equations. Three schemes on staggered grids with either the water level or the water depth at the cell centre and the flow velocity or the depth-integrated velocity at the cell interface are examined. They differ in (1) the character of the transport velocity to bias the discretization of the advective acceleration term in the upwind direction, and (2) the determination of the water depth at the cell face with which the depth-integrated velocity must be linked to the flow velocity. A detailed analysis is provided and aimed at highlighting the necessity of fulfilling the Rankine-Hugoniot jump conditions for preventing the odd-even decoupling problem. The accuracy and robustness of three selected schemes is assessed by means of convergence tests, three idealized 1D test problems with exact solutions and a 1D laboratory experiment of the breaking, runup and rundown of a solitary wave on a sloping beach. Numerical results reveal that schemes satisfying exactly the jump conditions display improved performance over schemes which do not share this property. Also, these results support strong evidence on the link between not fulfilling the jump conditions and the appearance of odd-even oscillations.

Experimental study on characteristics of a dual temperature control valve in the chilled water system of an air-conditioning unit

The excess flow of water increases the energy consumption of water pumps in the chilled water systems of air-conditioning units. This paper proposes a strategy to control the chilled water flow rate of a fan coil unit (FCU) using a control valve. A physical simulation test bench was built to verify valve control and energy-saving effects. Results showed that the control valve could effectively regulate the flow rate of chilled water, improve the temperature difference (delta-T) between supply and return water, and reduce the energy consumption of the chilled water pump. With a supply water temperature of 7 C and low (325 m3⋅h−1), medium (500 m3⋅h−1), and high (600 m3⋅h−1) FCU air velocity levels, the average delta-T values were 4.79 °C, 4.39 °C, and 4.97 °C, respectively, and the energy consumption of the chilled water pump decreased by 12.20%, 11.31%, and 10.66%, respectively. With medium air velocity and supply water temperatures of 7 °C, 8 °C, and 9 °C, the average delta-T between supply and return water was 4.39 °C, 3.56 °C, and 3.33 °C, respectively, and the energy consumption of the chilled water pump decreased by 11.31%, 5.10%, and 7.80%, respectively. These research results provide useful insights in relation to the problem of excess chilled water flow identified above.

Fast and accurate simulations of shallow water equations in large networks

We present a fast and accurate method for solving shallow water flows in large networks. The governing equations consist of the one-dimensional shallow water equations including friction forces. A class of first-order coupling conditions are implemented at the water intersections. Two-dimensional counterparts for simple water networks are also considered for comparison. As a numerical solver for shallow water equations we employed the discontinuous Galerkin method in one and two space dimensions. The method is simple, highly accurate and exhibits enhanced stability properties in the vicinity of sharp gradients which are often present in the solution of shallow water flow problems. The method belongs to a class of locally conservative finite element methods whose approximate solutions are discontinuous across inter-element boundaries. The performance of the proposed techniques is assessed on several applications for shallow water flows in networks. The aim of such a method compared to the conventional two-dimensional simulations is to solve shallow water flows in large networks efficiently and with an appropriate level of accuracy.

Simultaneous estimation of hydro-dipersive parameters using a new modified levenberg-marquardt algorithm

Determination of soil hydrodynamic parameters at field scale is of great importance for modeling soil water dynamics and for agricultural water management. The direct estimation of those parameters is time-consuming and afflicted with serious uncertainties. Inverse modeling is known to get efficient technique for solving non-linear problems in hydrology. Levenberg–Marquardt (LM) algorithm is a gradient-based method, which has been widely used for solving inverse soil water flow problems. In the LM algorithm, sensitivity coefficients are mainly evaluated by numerical differentiation methods. However, sensitivity coefficients are difficult to be precisely calculated by numerical differentiation methods, if transient states and non-linearities are involved. In this paper, a new approach is proposed for sensitivity analysis using the complex variabledifferentiation method (CVDM) to estimate simultaneously the hydraulic and dispersive properties of unsaturated soil from in-situ experiments. In this approach, the sensitivity coefficients can be determined in a more accurate way than the traditional finite difference method. The results show that the new inverse analysis method in the present work has high accuracy, validity, uniqueness and higher inversion efficiency, compared with the previous least-squares method. The simulated and measured water contents and tracer concentration were generally close. Overall, it was concluded that the CVDM is a promising method to estimate hydro-dispersive parameters in the unsaturated zone.

Energy-Optimal Pump Scheduling and Water Flow

This paper focuses on the optimal operation of water supply networks. We model water supply networks using hydraulic constraints, and formulate a joint optimal pump scheduling and water flow problem (OWF) using the hydraulic characteristics of variable speed pumps. OWF is a mixed-integer nonlinear program . This problem is nonconvex, and hence NP-hard. To compute an exact solution of OWF, we first focus on the feasibility region of OWF, and propose a mixed-integer second-order cone relaxation for the feasibility region of OWF. We prove that the proposed relaxation is exact for several relevant network topologies. We then focus on the objective function in OWF, and show that for some energy metrics, OWF can be transformed into a mixed-integer second-order cone program . Furthermore, we propose an ADMM-based algorithm to compute suboptimal solutions to OWF and lower bounds on the optimal value of the objective in OWF when the objective function is nonconvex. Finally, we consider a real-world water network, and demonstrate the effectiveness of the proposed relaxation in computing the optimal pump schedules and water flows.

RBFPUM with QR Factorization for Solving Water Flow Problem in Multilayered Soil

Abstract We discuss the numerical modeling of infiltration in variably-saturated porous media. Richards’ equation is used to describe the infiltration towards the water table. It is difficult to accurately approximate its solution especially when we deal with layered soil due to its highly nonlinear fact. In this work, the nonlinearity is handled by using Gardner model. In the case of homogeneous soil, the linearized equation is solved using radial basis function partition of unity method (RBFPUM) with the introduction of QR factorization of Gaussian in order to enhance the numerical solution for small values of the so-called “shape parameter.” In the case of layered soil, domain decomposition principle is introduced. It is based on decomposing the general problem into many subproblems. The latter are solved by RBFPUM-QR and patched by using the Steklov–Poincaré equation. Infiltration towards water table in homogeneous and layered soil is considered as a numerical test.

Mechanism and Remediation of Water and Sand Inrush Induced in an Inclined Shaft by Large-Tonnage Vehicles

In August 2016, multiple large-tonnage transport vehicles passed through the inclined shaft of the Jinjitian coal mine, Yulin, China, over a short period of time, resulting in fracturing of the floor, bearing capacity reduction, liquefaction of the underlying sand layer, and a serious water and sand inrush. The inrush and its sand content increased rapidly, with flows up to 72 m3/h, with up to 16% sand. Fractures appeared in the walls of the shaft and nine subsidence pits formed on the ground surface. As the distance between the shaft roof and floor continued to shorten, the mine faced the risk of flooding. Four remedial measures were rapidly taken. First, where the roof and floor was seriously fractured, cribs were constructed to effectively stop the convergence of the roof and floor. Second, grouting was carried out on the periphery of the shaft sides to seal and block the inrush ducts, reducing the inrush by 52% and eliminating the sand content. Then, the cribs were replaced with arched steel supports for permanent support. Finally, the shaft wall behind the sand layer was reinforced with grout, which reduced the water inrush from 34.8 to 2.5 m3/h. After adoption of these measures, the inclined shaft withstood the transport of large-tonnage coal-mining equipment for two work faces without an increase in water flow, floor fracturing, sand inrush, or other similar problems, indicating that the damaged shaft was well remediated. The measures taken provide a good reference for control of similar disasters.

Performance Study of MUSCL Schemes Based on Different Numerical Fluxes

The numerical flux is an important element in the numerical model for solving shallow water flow problems in MUSCL scheme. It is used to determine the normal transport through the boundary of the control body. With the TVD numerical flux, because of the simple form of Lax–Friedrichs, it is adopted in many articles. In fact, there are many different numerical fluxes based on exact Riemann solutions or approximate Riemann solutions, and these numerical fluxes can be combined with the MUSCL scheme. For the one-dimensional and two-dimensional shallow water equations, starting from the accuracy and discontinuous capture ability, a series of numerical examples are simulated based on the six different numerical fluxes with MUSCL scheme. Through the result analysis, the paper find out the numerical fluxes which are more suitable for shallow water flow combined with MUSCL scheme.

Numerical Simulation of Two Dimensional Flows in Yazidang Reservoir

This paper studied the problem of water flow in the Yazid Ang reservoir. It built 2-D RNG turbulent model, rated the boundary conditions, used the finite volume method to discrete equations and divided the grid by the advancing-front method. It simulated the two conditions of reservoir flow field, compared the average vertical velocity of the simulated value and the measured value nearby the water inlet and the water intake. The results showed that the mathematical model could be applied to the similar industrial water reservoir.

Application of the DIDAS program for the design and scheduling of drip irrigation

The DIDAS software package assists in drip-irrigation system design and irrigation scheduling. It is based on analytical solutions of the linearized water flow equation. The problem of water flow and uptake is described by superposing solutions for positive sources (on-surface or subsurface emitters) and negative sinks (root systems). Steady water flow is assumed in the design module and unsteady flow in the irrigation-scheduling module. The design tool, based on the relative water-uptake rate (RWUR) criterion, assesses the effects on water-use efficiency of geometrical attributes: distances between emitters along drip lines, separation between drip lines, depth of subsurface emitters, and size and depth of root systems. For design purposes, it is assumed that there is no plant-atmosphere resistance to water uptake, i.e., roots are assumed to apply maximum suction and water-uptake rate depends only on the soil's ability to conduct water from sources to sinks. The RWUR computations require only three parameters describing soil texture, root-zone size, and potential evaporation. The optimizing tool for irrigation scheduling is based on a relative water-uptake volume (RWUV) criterion. The RWUV computations for a given drip-irrigation design require additional information on the diurnal pattern of plant resistance to water uptake and soil hydraulic conductivity. DIDAS also contains a diurnal pattern module to evaluate diurnal water-uptake patterns; it assumes quasi-steady flow, accounts for diurnal variations in plant-atmosphere resistance and evaporation, and serves for fine-tuning the design and in preliminary evaluation of scheduling scenarios. DIDAS was programmed in Delphi, runs on a PC under the Windows operating system, and requires no further software. The drip-irrigation scenario is constructed via a few GUI windows, which also contain a library of the required soil input parameters, and a best-fitting procedure to determine them. The computed RWURs and RWUVs are displayed graphically and the tabulated output results can be exported to, e.g., Microsoft Excel for further processing. An updated DIDAS version can be downloaded freely from http://app.agri.gov.il/didas. From March 2014 through July 2016, 877 people from 94 countries downloaded the first or second DIDAS versions (1.0.1 and 1.1.1, respectively). We briefly introduce drip irrigation and other available programs for its design and scheduling, outline the major DIDAS concepts, and illustrate the operation of the main software modules.

STUDY THE PERFORMANCE OF THE TWO WAVELET-BASED ADAPTATION SCHEMES FOR THE SHALLOW WATER FLOW MODELLING

This work proposed a new adaptive method which avails from the wavelets theory for transforming the local single resolution information into multiresolution information. This information became accessible and by deactivating or activating them, the spatial resolution adaptation was achieved. The adaptive technique was combined with two standard numerical modelling schemes (i.e. finite volume and discontinuous Galerkin schemes) to produce two new adaptive schemes for modelling one dimensional shallow water flows so-called the Haar wavelets finite volume (HWFV) and multiwavelet discontinuous Galerkin (MWDG) schemes. Both adaptive schemes were tested using hydraulic test cases. The results demonstrated that the proposed adaptive technique could serve as the foundation on which to construct complete adaptive schemes for simulating the real problems of shallow water flow.

DIDAS – User-friendly software package for assisting drip irrigation design and scheduling

The DIDAS software package, based on analytical solutions of linearized water flow and uptake problems, assists in drip-irrigation system design and irrigation scheduling. Water flow is described by superposition of solutions for positive sources (on-surface or subsurface emitters) and negative sinks (root systems). Steady water flow is assumed in the design module and unsteady flow in the irrigation scheduling module. The design tool, based on relative water uptake rate (RWUR) criterion, assesses the effects on water use efficiency of geometrical attributes: distances between emitters along drip lines; separation between drip lines; depth of subsurface emitters; and size and depth of root systems. Evaluation of the maximum possible RWUR assumes no plant–atmosphere resistance to water uptake, i.e., the roots are assumed to apply maximum suction and the water uptake rate depends only on the soil capability to conduct water from sources to sinks. The RWUR computations require only three parameters describing the soil texture, the root zone size, and the potential evaporation, in accounting also for evaporation from the soil surface. The optimizing tool for irrigation scheduling is based on a relative water uptake volume (RWUV) criterion. The computations of diurnal variations of water uptake rates and RWUV for a given irrigation scenario require additional information on the diurnal pattern of plant resistance to water uptake and on the soil hydraulic conductivity. DIDAS also contains a diurnal pattern module for evaluating diurnal water-uptake patterns; it assumes quasi-steady flow and accounts for the diurnal variations of plant–atmosphere resistance and evaporation in fine-tuning the design and in preliminary evaluation of scheduling scenarios. DIDAS was programmed in Delphi, runs on a PC under the Windows operating system, and requires no further software. The drip irrigation scenario is constructed via a few GUI windows, which contain also a library of the required soil input parameters, and a best-fitting procedure for determining them. The computed RWURs and RWUVs are displayed graphically and the tabulated output results can be exported to, e.g., Microsoft Excel for further processing. An updated DIDAS version can be downloaded freely from http://app.agri.gov.il/didas.

Partition of unity methods for approximation of point water sources in porous media

Several partition of unity methods (PUM) are compared on the problem of steady water flow in an aquifer-well system. In order to improve the approximation of a singular behavior of the pressure near the wells, the standard finite element space is enriched with a cut-off fundamental solution to a Laplace problem with a point source on the whole R2 space. The optimal order of convergence of PUM in terms of L2 norm of the error is demonstrated. The error of adaptive integration is analysed and a new adaptive strategy is proposed. The influence of the choice of the enriched domain is investigated and its impact on the error is demonstrated numerically.

A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains

Numerical manifold method (NMM) is a numerical method known for analyzing continuous and discontinuous mechanical processes in a unified mathematical form. In this study we developed a new second-order NMM model to solve the nonlinear problem of water flow with the free surface priori unknown and the difficulty of modeling drains which could dramatically increase the meshing load. Our study consist of: (1) deriving two forms of NMM second-order approximation; (2) constructing the total potential energy for water flow by our energy-work seepage model considering Dirichlet, Neumann and material boundaries uniformly; (3) locating free surface nodes in two forms of second-order approximation; (4) tracking the free surface with an efficient iteration scheme without re-meshing; (5) deriving velocity and tunnel flux by second-order approximation. We developed a new code and demonstrate our model and code with examples including confined drainage tunnel and free surface flow through a dam. We compare the results such as tunnel flux or free surface with linear NMM, analytical or other available numerical solutions. We prove that: the two forms of second-order NMM (1) yield consistent results; (2) for modeling drains involving local intensive change, could achieve accurate result of tunnel flux calculation and dramatically save computation load with linear velocity distribution in coarse mesh; (3) for free surface iteration, are efficient with fast convergence to accurate results and with rather coarse mesh. As a result, our second-order NMM model is applicable to free surface flow with inner drains for free surface locating and flux calculation, and seepage stability analysis, laying a solid foundation for extending to coupled hydro-mechanical analysis.

Erratum to: “a variational principle for problems of steady-state ground water flow with a free surface” [Fluid Dynamics 50, 543 (2015)

Erratum to: “a variational principle for problems of steady-state ground water flow with a free surface” [Fluid Dynamics 50, 543 (2015)

A variational principle for problems of steady-state ground water flow with a free surface

The problem of steady-state free surface ground water flow through a porous medium is represented in the form of a variational principle for a functional dependent on the flow domain. It is proved that on the region to be found this functional takes a minimum value. This variational principle is generalized to include the flow models that allow the presence of partially saturated zones in the medium. On simple examples it is shown how the variational formulation can be used for proving the existence or absence of solutions.