Valve Design for Extracting Response Functions from Hydraulic Systems Using Pseudorandom Binary Signals

The analysis of the dynamic response of a pressurized water pipeline system is important for the design and also the integrity monitoring of these systems. An efficient method for summarizing the behavior of a pipeline system is through the determination of their system response functions. These functions can be extracted by injecting a pressure signal with a wide bandwidth that persists over the length of a pipeline system. Unlike electrical and mechanical systems, generating such signals in pressurized water systems is difficult. Valves capable of generating a signal against the system back-pressure often lack the necessary maneuverability to ensure the signal is sharp (and hence with high-frequency content) and the generated transient is often large in amplitude, risking damage to the system. A method for generating a small amplitude transient signal with a wide band of frequencies is desirable. This paper presents the design for a side discharge valve for generating a pseudorandom binary sequence of pressure changes that are of a small magnitude in relation to the steady state head of the pipeline. The pseudorandom pressure sequence is used to provide an estimate of the system response function. The continuous form of the signal allows the amplitude of each individual pulse within the signal to be small while maintaining the same signal bandwidth. The valve has been tested experimentally and was found to provide a good match with the theoretical response of the pipeline. The method provides a practical alternative to frequency sweeping using sinusoidal signals or sharp valve closures for the extraction of the response functions. Once determined, the system response function can be utilized to detect system faults such as leaks and blockages.     

Leak Detection in Pipelines using the Damping of Fluid Transients

Leaks in pipelines contribute to damping of transient events. That fact leads to a method of finding location and magnitude of leaks. Because the problem of transient flow in pipes is nearly linear, the solution of the governing equations can be expressed in terms of a Fourier series. All Fourier components are damped uniformly by steady pipe friction, but each component is damped differently in the presence of a leak. Thus, overall leak-induced damping can be divided into two parts. The magnitude of the damping indicates the size of a leak, whereas different damping ratios of the various Fourier components are used to find the location of a leak. This method does not require rigorous determination and modeling of boundary conditions and transient behavior in the pipeline. The technique is successful in detecting, locating, and quantifying a 0.1% size leak with respect to the cross-sectional area of a pipeline.     

Fluid Flow in a Tundish Optimized through Genetic Algorithms

The fluid flow in a continuous casting tundish is computed for an optimum parameter setting such that the stresses produced at the walls get minimized. This optimization task is carried out using a Genetic Algorithms based procedure that worked in tandem with a 3‐D transient Navier‐Stokes equation solver. The fluid flow equations are iteratively solved by using a pressure‐based finite volume method, according to the SIMPLER algorithm. The k‐ε model is used for achieving the turbulence closure. The numerical simulations reveal how the Genetic Algorithm can be effectively used for optimizing the fluidic design of the tundish.     

Heat-transfer enhancement using weakly ionized, atmospheric pressure plasma in metallurgical applications

Experimental measurements and computational analysis of heat transfer in atmospheric pressure, midtemperature range (1200 to 1600 K) plasma flow over an aluminum cylinder have been carried out. A comparison of transient temperature measurements for the aluminum cylinder under convective unionized air flow and those with convective plasma flow shows significantly higher heat transfer from plasma flow compared to air flow under identical temperature and flow conditions. A heattransfer problem is computationally modeled by using available experimental measurements of temperature rise in the cylinder to determine the degree of ionization in the plasma flow. The continuity, momentum, and energy conservation equations, as well as conservation equations for electrons and ions, and the Poisson’s equation for self-consistent electric field are solved in the plasma by a finite volume method. The conjugated transient heat transfer in the cylinder and in the plasma is obtained by simultaneous solution of the transient energy conservation equations. It is shown that the enhancement of heat transfer in plasma flow is due to the energy deposited by charged species during recombination reaction at the solid surface. An important finding is that even a small degree of ionization (<1 pct) provides significant enhancement in heat transfer. This enhancement in heat transfer can lead to a productivity increase in metallurgical applications.     

Axisymmetric Stress Analysis of a Thick Conical Shell with Varying Thickness under Nonuniform Internal Pressure

A mathematical approach based on the perturbation theory has been used for axisymmetric stress analysis of a thick conical shell with varying thickness under nonuniform internal pressure. The equilibrium equations have been derived using the energy principle and considering the second-order shear deformation theory (SSDT), which includes shear deformation effects. This system of ordinary differential equations with variable coefficients has been solved analytically using the matched asymptotic expansion method of the perturbation theory. A comparison of the results with the finite-element method and the first-order shear deformation theory shows that the SSDT can predict the displacements and stresses of the shell for a wide range of thicknesses as well with less calculations than other analytical methods such as the Frobenius series method.     

Computer and Experimental Models of Transient Flow in a Pipe Involving Backflow Preventers

Transient flow in a pipe was studied using both experimental and computer models. In the present study, three different numerical models: The method of characteristics model, the axisymmetrical model, and the implicit scheme model are utilized and compared. Experiments for transient flow in a simple pipeline have been conducted to verify the results from the computer models. It was found that head loss coefficient for the 1D models, such as the method of characteristics model and the implicit scheme model, should be much bigger than the Darcy-Weisbach frictional coefficient. Experiments for transient flow with the backflow preventer in a pipe were conducted. Results show that backflow preventer serves as a strong damper to the water hammer generated by the hydraulic transients. Numerical investigation simulating a backflow preventer in transient flow has been performed in this study. It was found that different values of head loss coefficient should be applied for the upstream and downstream of backflow preventer. All of the numerical models were compared with the experiments. The results of different computer models developed in the present study agree well with the experimental data.     

Explicit Integration Method for Extended-Period Simulation of Water Distribution Systems

Extended-period simulation of incompressible and inertialess flow in water distribution systems is normally done using numerical integration techniques, although regression methods are also sometimes employed. A new method for extended-period simulation, called the explicit integration (EI) method, is proposed. The method is based on the premise that a complex water distribution system can be represented by a number of simple base systems. The simple base systems are selected in such a way that their dynamic equations can be solved through explicit integration. In this paper a simple base system consisting of a fixed-head reservoir feeding a tank through a single pipeline is analyzed. It is then illustrated how a complex water distribution system can be decoupled into simple base systems and its dynamic behavior simulated using a stepwise procedure. The EI method is compared to the commonly used Euler numerical integration method using two example networks. It is shown that the accuracy of the EI method is considerably better than that of the Euler method for the same computational effort.     

Multilayer Averaged and Moment Equations for One-Dimensional Open-Channel Flows

A model is developed to account for the vertical distribution of velocity and nonhydrostatic pressure in one-dimensional open-channel flows. The model is based on both classical multilayer models and depth-averaged and moment equations. The establishment of its governing equations and the flow simulation are performed over a number of flow layers as in classical multilayer models. However, the model also allows for vertical distributions within a flow layer by including both Boussinesq terms and effective stress terms due to depth-averaging operations. These terms are evaluated on the basis of vertically linearly approximated profiles of velocity and pressure. The resulting additional coefficients can be solved by the moment equations for the relevant layers. Three verifications demonstrate satisfactory simulations for water surface profile, as well as vertical distributions for horizontal velocity, vertical velocity, and nonhydrostatic pressure. Sensitivity analysis shows that the model can be applied with fewer flow layers, more flexibility of layer division, and less computational cost than classical multilayer models, without a remarkable compromise in accuracy.     

New Elastic Model of Pipe Flow for Stability Analysis of the Governor-Turbine-Hydraulic System

A higher-order elastic model of the flow in long pressurized pipelines is expected to be utilized for stability analysis of the governor-turbine-hydraulic system in hydropower stations. Because traditional elastic models are limited in lower order application because of their difficult decoupling in addition to the rigid model, a new linear elastic model of the flow in pressurized pipelines is derived on the basis of the equations of hydraulic vibration, in which each oscillatory flow with a different order has been obtained with ordinary differential equations in decoupling form. For water conveyance systems with branching pipes or parallel pipes in hydropower stations, the state equations to describe hydraulic characteristics of the governor-turbine-hydraulic system are established with the application of this new elastic model for diversion pipeline flow or tail tunnel flow. The influence of the elastic models with different order on a system’s stability are revealed in detail by two cases that illustrate that an elastic model with proper order should be used for the flow in pressurized pipelines of hydropower stations, according to their length, to improve the accuracy of stability analysis.     

Numerical Modeling of Local Scour below a Piggyback Pipeline in Currents

Local scour below a piggyback pipeline in steady currents is investigated numerically. A piggyback pipeline comprises two pipelines that are arranged in the so-called piggyback configuration with the small pipeline being located directly above the large pipeline. The Reynolds-averaged Navier–Stokes equations and the transport equation for suspended sediment concentration are solved using a finite element method. The bed scour profile is determined through solving sediment mass conservation equation. The numerical model is validated against experimental data available in literature on scour below a single pipeline. Computations are carried out for the diameter ratio [the small pipe diameter (d) to the larger one (D)] of 0.2 and the gap (G, between the two pipelines) to the large diameter ratio G/D ranging from 0.0 to 0.5. It is found that the flow and the scour profiles are influenced significantly by the gap ratio.     

Range of Validity of the Transient Damping Leakage Detection Method

In a recent paper, an elegant, efficient, and easy to apply transient-based leakage detection method was proposed. The method exploits the fact that friction and leakage damp the modes of transient waves in a different manner. The method involves six major assumptions. These are: (1) the periodic motion in time of each mode is linearly independent of all other modes; (2) the amplitude of the induced transient is small; (3) the magnitude of the leak is small in comparison with the flow rate; (4) the wall friction can be represented by the Darcy–Weisbach equation; (5) the transient is initiated by an instantaneous small amplitude disturbance; and (6) the pipe system is a simple reservoir–pipe–valve type system or reservoir–pipe–reservoir type system. These six assumptions are relaxed and the validity of the transient damping method is assessed. The analysis shows that the first four assumptions do not pose any serious restriction to the applicability of the damping rate method provided that the mathematical model, used to generate the transient head trace in the leak-free pipe, accurately represents the frictional damping in the system. On the other hand, Assumptions (5) and (6) restrict the applicability of the method to systems that do not involve internal boundary conditions, such as junctions and pumps, and to transients triggered by impulses whose duration is smaller than the wave travel time. Extension of this method to complex pipe systems requires that the linearized waterhammer equations are solved under more general initial and boundary conditions. In addition, more investigation in relation to the frequency content of the input signal and its importance in leakage detection is warranted. The general framework used to derive the damping rate method has led to an efficient and direct algorithm for identifying leaks and future research should seek ways to adapt this framework to more complex pipe systems.     

基于管道流体信号的自振射流特性检测方法

提出基于管道流体信号的自振射流特性检测方法, 将压力传感器从高压罐内移至高压罐外, 布置在高压罐外的前端管路上, 从而避开高围压环境影响; 通过双压力传感器拾取管道流体压力脉动信号, 并运用信号处理技术有效抑制干扰噪声, 提高有用信号强度, 准确获取射流的压力脉动信息.试验表明, 管道流体压力信号的频谱特征与喷嘴腔内检测法具有一致性, 且与理论计算较为吻合, 充分表征了射流的压力振荡特性; 其声功率谱与高压罐内水听器检测结果相一致, 较好地表述了射流的空化作用特性.由此认为基于管道流体信号的检测法用于自振射流特性的检测是完全可行的, 具有先进性, 为高围压下自振射流的研究提供了新手段.      

Water Table Profiles and Discharges for an Inclined Ditch-Drained Aquifer under Temporally Variable Recharge

This paper presents the solution of the linearized Boussinesq equation for an inclined, ditch-drained aquifer, with a temporally varying recharge rate. Water-table profiles and flow rates into the ditches are calculated. As an initial condition the steady-state profile for a constant recharge rate is used, and the linearized Boussinesq equation is solved for a different recharge rate. Then, at a specified time, the transient water table profile is used as initial condition for the Boussinesq equation with a new recharge rate. The transient solution at a new specified time is then used as the initial condition for the Boussinesq equation with a different recharge rate, and so on. Using the Darcy equation, analytical expressions for the flow rates into the ditches can be obtained. The solution allows the calculation of the transient behavior of the groundwater table and its flow rates due to temporally variable recharge rates.     

Junction and Drop-Shaft Boundary Conditions for Modeling Free-Surface, Pressurized, and Mixed Free-Surface Pressurized Transient Flows

A junction and drop-shaft boundary conditions (BCs) for one-dimensional modeling of transient flows in single-phase conditions (pure liquid) are formulated, implemented and their accuracy are evaluated using two computational fluid dynamics (CFD) models. The BCs are formulated in the case when mixed flows are simulated using two sets of governing equations, the Saint-Venant equations for the free-surface regions and the compressible water hammer equations for the pressurized regions. The proposed BCs handle all possible flow regimes and their combinations. The flow in each pipe can range from free surface to pressurized flow and the water depth at the junction or drop shaft can take on all possible levels. The BCs are applied to the following three cases: (1) a three-way merging flow; (2) a three-way dividing flow; and (3) a drop shaft connected to a single-horizontal pipe subjected to a rapid variation of the water surface level in the drop shaft. The flow regime for the first two cases range from free surface to pressurized flows, while for the third case, the flow regime is pure pressurized flow. For the third case, laboratory results as well as CFD results were used for evaluating its accuracy. The results suggest that the junction and drop-shaft BCs can be used for modeling transient free-surface, pressurized, and mixed flow conditions with good accuracy.     

Approximate Solutions for Forchheimer Flow to a Well

An exact solution for transient Forchheimer flow to a well does not currently exist. However, this paper presents a set of approximate solutions, which can be used as a framework for verifying future numerical models that incorporate Forchheimer flow to wells. These include: a large time approximation derived using the method of matched asymptotic expansion; a Laplace transform approximation of the well-bore response, designed to work well when there is significant well-bore storage and flow is very turbulent; and a simple heuristic function for when flow is very turbulent and the well radius can be assumed infinitesimally small. All the approximations are compared to equivalent finite-difference solutions.     

Flow Modeling in Pressurized Systems Revisited

Assuming 1D flow in pressurized systems, transient analyses can be performed using a number of well-established models. In the short-term timescale, practical problems are solved using either elastic or rigid models, whereas in the long-term scale a quasi-static model is more convenient. These models can be obtained by simplifying the general equations for flow of an elastic fluid. A brief overview of these models is presented, with the major emphasis being on the use of dimensionless parameters to define the range of their applicability for simple hydraulic systems. Guidelines for applicability are presented in the form of graphs and equations. The effects of resistance, inertia, and elasticity may vary in relative importance under different circumstances. The present analysis provides a unified approach to represent each of these effects using a different parameter.     

Modeling Sediment Transport Using Depth-Averaged and Moment Equations

A 1D mathematical model to calculate bed variations in alluvial channels is presented. The model is based on the depth-averaged and moment equations for unsteady flow and sediment transport in open channels. Particularly, the moment equation for suspended sediment transport is originally derived by the assumption of a simple vertical distribution for suspended sediment concentration. By introducing sediment-carrying capacity, suspended sediment concentration can be solved directly from sediment transport and its moment equations. Differential equations are then solved by using the control-volume formulation, which has been proven to have good convergence. Numerical experiments are performed to test the sensitivity of the calibrated coefficients α and k in the modeling of the bed deposition and erosion. Finally, the computed results are compared with available experimental data obtained in laboratory flumes. Comparisons of this model with HEC-6 and other numerical models are also presented. Good agreement is found in the comparisons.     

Quantifying Linearization Error When Modeling Fluid Pipeline Transients Using the Frequency Response Method

The unsteady mass and momentum equations for pipe flow can be solved in the frequency domain and provides additional insight into the behavior of fluid transients. Additionally, this approach has significant computational advantages compared to the method of characteristics because it is not based on a rigid time-space grid. Despite its advantages, the frequency domain approach must be used with care as it uses linearized forms of the steady friction and orifice equations—which can deviate significantly from the true nonlinear solution. The conditions in which the frequency response method can be accurately used are currently unknown. This paper investigates and quantifies the error in the frequency-domain method, via comparison to a highly discretized time-domain model that uses the method of characteristics, and describes situations where the frequency response method can be used with accurate results. A reservoir-pipe-valve system was used in this study with transients generated by perturbation of the valve. The error consists of errors from two sources: the linear approximations of the steady friction and the steady orifice equations. The frequency response method was shown to produce identical results to the method of characteristics when these two sources of error are minimized. The error in the frequency-domain model was quantified as functions of the perturbation magnitude, frequency, and system parameters. The results indicate that errors are significant when the perturbation size is more than 25% of the steady-state condition and this error is frequency dependent with the largest errors occurring at the harmonic peaks of the system.     

Efficient Treatment of the Vardy–Brown Unsteady Shear in Pipe Transients

An accurate, simple, and efficient approximation to the Vardy–Brown unsteady friction equation is derived and shown to be easily implemented within a one-dimensional characteristics solution for unsteady pipe flow. For comparison, the exact Vardy–Brown unsteady friction equation is used to model shear stresses in transient turbulent pipe flows and the resulting waterhammer equations are solved by the method of characteristics. The approximate Vardy–Brown model is more computationally efficient (i.e., requires one-sixth the execution time and much less memory storage) than the exact Vardy–Brown model. Both models are compared with measured data from different research groups and with numerical data produced by a two-dimensional turbulence waterhammer model. The results show that the exact Vardy–Brown model and the approximate Vardy–Brown model are in good agreement with both laboratory and numerical experiments over a wide range of Reynolds number and wave frequencies. The proposed approximate model only requires the storage of flow variables from a single time step while the exact Vardy–Brown model requires the storage of flow variables at all previous time steps and the two-dimensional model requires the storage of flow variables at all radial nodes.