Fluid Transients Research Articles

Detection and Location of a Partial Blockage in a Pipeline Using Damping of Fluid Transients

The effects of a partial blockage on pipeline transients are investigated analytically. A partial blockage is simulated using an orifice equation, and the influence of the blockage on the unsteady pipe flow is considered in the governing equations using a Dirac delta function. A simplified, linear dimensionless governing equation has been derived, and an analytical solution expressed in terms of a Fourier series has been developed under nonvarying boundary conditions. The linear analysis indicates that pipe friction and a partial blockage both introduce damping on fluid transients. The friction damping and blockage damping are exponential for each of the individual harmonic components. For each individual harmonic component, the blockage-induced damping depends on the blockage magnitude and position and is also independent of measurement location and the transient event. A new blockage detection method using the blockage-induced transient damping is developed based on the analytical solution. The magnitude of the blockage-induced damping rate indicates the size of the blockage, and the ratios of different damping rates can be used to locate the blockage. The proposed blockage detection method has been successfully used in detecting, locating, and quantifying a pipe blockage based on laboratory experiments.

New exact solutions for fluid transients

New exact solutions for damped fluid transients are reported. Complicated excitations are easily accommodated. Some interesting special cases are discussed in detail.

Behavior of Short Lateral Dead Ends on Pipeline Transients: A Lumped Parameter Model and an Analytical Solution

By integrating the continuity equation over a short lateral dead end, the effects of a short lateral dead end side branch on pipeline fluid transients can be lumped into a node. The analytical solution to a linearized equation shows that a pipeline transient can be expressed as a Fourier series and presence of a lateral dead end reduces the frequencies of the harmonic components. The impact of the lateral dead end on the observed transients depends on a parameter Sd, which is related to the location of the lateral dead end, the relative volume, and the wave speed of the lateral dead end with respect to the pipeline. A lumped parameter approach that can be incorporated into the method of characteristics has also been developed in this paper. It has been found that it is possible to take account of the effects of a short lateral dead end in an accurate and computational efficient manner.

Application of MATLAB Functions for Time Domain Simulation of Systems With Lines With Fluid Transients

Application of MATLAB Functions for Time Domain Simulation of Systems With Lines With Fluid Transients

Fluid transients and pipeline optimization using GA and PSO: the diameter connection

This paper describes the optimal selection of pipe diameters in a network considering steady state and transient analysis in water distribution systems. Two evolutionary approaches, namely genetic algorithms (GA) and particle swarm optimization (PSO), are used as optimization methods to obtain pipe diameters. Both optimization programs, inspired by natural evolution and adaptation, show excellent performance for solving moderately complex real-world problems which are highly nonlinear and demanding. The case study shows that the integration of GA or PSO with a transient analysis technique can improve the search for effective and economical hydraulic protection strategies. This study also shows that not only is the selection of pipe diameters crucially sensitive for the surge protection strategies but also that more global systematic approaches should be involved in water distribution system design, preferably at an early stage in the design process.

Some analytical tools for fluids management in space: Isothermal capillary flows along interior corners

Recent advances in the analysis of a class of capillary-driven flows relevant to materials processing and general fluids management in space have been made. The class of flows addressed concern spontaneous capillary flows in complex containers with interior comers. Such flows are commonplace in space-based fluid systems and arise from the particular container geometry and wetting properties of the system. Important applications for this work involve low-g liquid fill and drain operations where the container geometry is complex, possessing interior corners, and where quantitative information of fluid location, transients, flow rates, and stability is critical. Examples include the storage and handling of liquid propellants and cryogens, water conditioning for life support, fluid phase-change thermal systems for temperature control and power production, materials processing in the liquid state, and on-orbit biofluids processing. For several important problems, closed-form expressions to transient three-dimensional flows are possible that, as design tools, compliment if not replace difficult, time-consuming, and rarely performed numerical calculations. The theory is readily extended to address more complex flows. An overview of a selection of solutions in-hand is presented. Drop tower and low-g aircraft experimental results are cited to support the theoretical findings.

Development of Accurate and Practical Simulation Technique Based on the Modal Approximations for Fluid Transients in Compound Fluid-Line Systems

In the previous paper, the authors proposed a new simulation technique called the “system modal approximation” method (SMA method) for fluid transients in compound fluid-line systems. This technique was able to predict the behaviour fast and accurately, and its superiority to other existing methods was verified by simulation and experimental analysis. However, detailed considerations were limited to the cases whose transfer functions of output/input could be approximated by the second order modes alone. This paper enhances the analytical functions of the SMA method so as to be widely applicable to compound fluid-line systems with various kinds of system compositions and boundary conditions. Specifically, the calculation methods of time response of the required output variable at any points are newly proposed for case (A) whose transfer functions of output/input have to be approximated by the first order modes and derivative element besides second order modes, and (B) whose boundary conditions are given by the relation between pressure and flow-rate. Fluid transients in three kinds of compound fluid-line systems under the several different boundary conditions including the occurrence of column separation are considered. Simulation results based on the methods mentioned above are compared with both the solutions from the method of characteristics and experimental results, and then the usefulness of the generalized SMA method is verified.

A Finite Element Model and Electronic Analogue of Pipeline Pressure Transients With Frequency-Dependent Friction

A finite element model and its equivalent electronic analogue circuit has been developed for fluid transients in hydraulic transmission lines with laminar frequency-dependent friction. Basic equations are approximated to be a set of ordinary differential equations that can be represented in state-space form. The accuracy of the model is demonstrated by comparison with the method of characteristics.

複合管路系内流体過渡現象の数値的モード近似法に基づく実用的で高精度なシミュレーション法の開発 第２報 多様な境界条件に適用できる汎用ＳＭＡ法の開発

In the previous paper, the authors proposed a new simulation technique called the “system modal approximation” method (SMA method for short) for fluid transients in compound pipeline systems, which was able to predict fast and accurately, and verified superiority of this technique to other existing methods. There, however, detailed considerations were limited to the case whose transfer functions of output/input were of the form of pressure/pressure and flow-rate/flow-rate. This paper enhances the analytical functions of the SMA method so as to be widely applicable to compound pipeline systems with various kinds of boundary conditions. Specifically, the calculation methods of time response of the wanted output variables at any points are newly proposed for the case (i) whose transfer functions of output/input are of the form of pressure/flow-rate and flow-rate/pressure, and (ii) whose boundary conditions are given by the relation between pressure and flow-rate. For fluid transients in three kinds of compound pipeline systems, simulation results based on the methods mentioned above are compared with both the solutions from the method of characteristics and experimental results, and then the usefulness of the generalized SMA method is verified.

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.

Development of Accurate and Practical Simulation Technique Based on the Modal Approximations for Fluid Transients in Compound Fluid-Line Systems

AbstractNew simulation technique called the “system modal approximation” method for fluid transients in compound fluid-line systems is developed and presented. Unlike existing approaches based on the modal approximation of the input/output causality relationship of individual line element, this new method is based on the modal approximation of the frequency transfer function itself of the output (wanted variable) to the input (source) considering the dynamic characteristics of total system. This simulation technique also has the feature that only the numerical data of the frequency response of transfer matrix parameters of individual line element, which may be obtained from either theoretical model or experimental measurements, is needed and that the wanted output variable alone can be calculated selectively in the time domain by a simple algebraic expression in the form of recurrence formula. For complex fluid-line systems, the advantages of this technique over other existing modal approximation-based me...

複合管路系内流体過渡現象の数値的モード近似法に基づく実用的で高精度なシミュレーション法の開発 第１報 基本的な計算アルゴリズムの確立

A new simulation technique called the “system modal approximation” method for fluid transients in compound pipeline systems is developed and presented. Unlike existing approaches based on modal approximation of the input/ output causality of individual line elements, this new method is based on modal approximation of the frequency transfer function itself of the output (wanted variable) to the input (source), considering the total system dynamics This simulation technique also has these features only the numerical data of the frequency response of transfer matrix parameters of individual line element, which may be given from either theoretical model or experimental measurements, is needed, and the desired output variable alone can be calculated selectively in the time domain by a simple algebraic expression in the form of a recurrence formula For complex pipeline systems the superiority of this technique to other existing modal approximation-based methods in accuracy, easy applicability, flexibility, computation time, etc. is discussed with experimental comparisons.

DEVELOPMENT OF A PRACTICAL AND HIGH ACCURACY SIMULATION TECHNIQUE BASED ON NUMERICAL MODAL APPROXIMATION FOR FLUID TRANSIENTS IN COMPOUND FLUID-LINE SYSTEMS

A new simulation technique called the “system modal approximation” method for fluid transients in compound fl uid-line systems composed of many line elements is developed and presented. This new method is based on numerical modal approximation of the frequency transfer function itself of the output to the input, considering the total system dynamics. This simulation technique also has the feature that the line elements with any kinds of the dynamic characteristics can be applicable because only the numerical data of the frequency response of transfer matrix parameters of individual line element is needed, and that the computation time is very short because the output in time domain can be calculated by the simple algebraic expression in the form of a recurrence formula. Simulation results of this method for the pressure transients in typical three kinds of compound fluid-line are compared with both the solutions from the method of characteristics and experimental results, and the superiority of this technique in easy applicability, flexibility, accuracy, computation time, etc. are demonstrated.

Fluid transients and fluid-structure interaction in flexible liquid-filled piping

Fluid-structure interaction in piping systems (FSI) consists of the transfer of momentum and forces between piping and the contained liquid during unsteady flow. Excitation mechanisms may be caused by rapid changes in flow and pressure or may be initiated by mechanical action of the piping. The interaction is manifested in pipe vibration and perturbations in velocity and pressure of the liquid. The resulting loads imparted on the piping are transferred to the support mechanisms such as hangers, thrust blocks, etc. The phenomenon has recently received increased attention because of safety and reliability concerns in power generation stations, environmental issues in pipeline delivery systems, and questions related to stringent industrial piping design performance guidelines. Furthermore, numerical advances have allowed practitioners to revisit the manner in which the interaction between piping and contained liquid is modeled, resulting in improved techniques that are now readily available to predict FSI. This review attempts to succinctly summarize the essential mechanisms that cause FSI, and present relevant data that describe the phenomenon. In addition, the various numerical and analytical methods that have been developed to successfully predict FSI will be described. Several earlier reviews regarding FSI in piping have been published; this review is intended to update the reader on developments that have taken place over the last approximately ten years, and to enhance the understanding of various aspects of FSI. There are 123 references cited in this review article.

Simulation of Fluid Transients in Piping using the Optimized Finite Element Model

Simulation of Fluid Transients in Piping using the Optimized Finite Element Model

Finite Element Coupled Slosh Analysis of Rectangular Liquid Filled Laminated Composite Tanks

This paper presents the sloshing response and coupled dynamic behaviour of rectangular liquid filled laminated composite tanks under harmonic base excitation. For the numerical simulation of the problem, the finite element method is used to develop an integrated computational scheme in 3-D, which accounts for the coupling effect between liquid sloshing and the tank vibration. Dynamic responses are computed in the time domain using Newmark's predictor-multicorrector-algorithm. Both fluid transients and structural dynamics problems are dealt with separately before solving the coupled slosh problems. A computer code is developed which generates numerical data for the slosh frequency, sloshing displacement, free surface profiles, hydrodynamic pressure, deformed structural modes and the container response due to the change in the hydrodynamic pressure. The solution procedures are applied to both rigid and flexible containers to demonstrate the effect of tank flexibility on the overall slosh phenomenon and structural response. The effects of lamination scheme, free surface wave and decoupled analysis approach on the tank wall response are also investigated. To the best knowledge of the authors, the results of similar cases involving the interaction of fluid with laminated composite tanks, are not available in the open literature.

On the Use of Nonlinear Filtering, Artificial Viscosity, and Artificial Heat Transfer for Strong Shock Computations

A new artificial viscosity (Q) model, based on physical conservation corrections for momentum, and a new artificial heat transfer (H) formulation are developed for the analysis of one-dimensional compressible fluid transients in plane, cylindrical, and spherical geometries. The accuracy of these formulations is verified against various benchmark shock tube problems. A Q-induced geometric error for cylindrical and spherical geometry is defined and the benefits of the Q formulation presented are demonstrated. It is also shown that these formulations can control the total variation of the solution and have superior shock-capturing capabilities. Comparisons are made with the original Q formulations of J. von Neumann and R. D. Richtmyer (1950, J. Appl. Phys.21, 232), W. F. Noh's Q&H shock-following method (1987, J. Comput. Phys.72, 78), and the piecewise-parabolic method of P. Colella and P. R. Woodward (1984, J. Comput. Phys.54, 174). The comparisons demonstrate the advantages of the new method. Numerical examples for more realistic equations of state which show the robustness of the method are also presented.

Coupled Slosh Dynamics of Liquid-Filled, Composite Cylindrical Tanks

The present paper concerns the hydrodynamic coupling of fluid with laminated composite cylinders under small displacements. A numerical model using finite-element technique is presented to study the dynamics of inviscid, incompressible liquid inside thin-walled, flexible, composite cylindrical tanks. The finite-element equations of motion for both the tank wall and the fluid domain are formulated and numerically integrated using Newmark's predictor–multicorrector algorithm. Both fluid transients and structure dynamics problems are dealt with separately before solving for the coupled interaction problems. The solution procedures are applied to both rigid and flexible fluid-tank systems to demonstrate the effect of tank flexibility on the slosh characteristics and the structural response.

Dynamic Modeling Analysis for Control of Chemical Vapor Deposition

A nonlinear dynamic model of the chemical vapor deposition (CVD) process has been developed to aid design of a closed-loop control system. A lumped control volume analysis is used to capture important mass and fluid transients and spatial affects, while a simplified single variable equation is used to represent the complex reaction chemistry. Steady-state experimental results and model predictions are compared and the control implications of the process dynamics are discussed.

Quasi-steady friction in transient polytropic flow

An accurate method of integrating quasi-steady friction in transient polytropic flows is introduced and is justified both physically and analytically. When applied to subsonic flows, it is found to be especially informative at higher Mach numbers where existing methods of integration can lead to serious errors in mass conservation. The method is used herein to assess the accuracy of widely used finite difference representations of quasi-steady friction, attention focusing principally on solutions obtained using the method of characteristics. The new method is exact in the special case of steady flows. Of the approximate methods considered, the popular approximation V t ¦ V t − Δ t ¦Δ t is found to perform well. A modification introduced by Karney and McInnis ( Journal of Hydology Engineering, ACSE, 1992, 118(7), 1014–1030 [1]) improves the correlation for downstream characteristic lines, but has the opposite effect for upstream characteristics. A simple cubic scheme, loosely related to a more complex one used successfully by Murray ( Proceedings of the International Conference on Unsteady Flow and Fluid Transients, 29 September–1 October. Balkema, Amsterdam, 1992, pp. 143–157 [2]), illustrates difficulties in higher-order schemes. The new method is not exact in transient flows, but it gives good accuracy in slowly varying flows and it is plausible in rapidly varying flows. Using it as a benchmark, the approximation V t ¦ V t − Δ t ¦Δ t is again shown to perform well. All of the schemes considered are unreliable when the flow is about to become choked within the region of integration