As Arris Tijsseling

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

Fluid-structure interaction in piping systems (FSl) 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. lDept. of Civil and Environmental Engineering, Michigan State University, East Lansing, MI48824 2Dept. of Applied Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513,5600 MB Eindhoven, The Netherlands

Parameters affecting water-hammer wave attenuation, shape and timing—Part 1: Mathematical tools

This two-part paper investigates key parameters that may affect the pressurewaveform predicted by the classical theory ofwater-hammer. Shortcomings in the prediction of pressure wave attenuation, shape and timing originate from violation of assumptions made in the derivation of the classical waterhammer equations. Possible mechanisms that may significantly affect pressure waveforms include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction (FSI) effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Engineers should be able to identify and evaluate the influence of these mechanisms, because first these are usually not included in standard water-hammer software packages and second these are often “hidden” in practical systems. Part 1 of the two-part paper describes mathematical tools for modelling the aforementioned mechanisms. The method of characteristics transformation of the classical water-hammer equations is used herein as the basic solution tool. In separate additions: a convolution-based unsteady friction model is explicitly incorporated; discrete vapour and gas cavity models allow cavities to form at computational sections; coupled extended water-hammer and steel-hammer equations describe FSI; viscoelastic behaviour of the pipe-wall material is governed by a generalised Kelvin–Voigt model; and blockages and leakages are modelled as end or internal boundary conditions

Fluid-structure interaction in liquid-filled piping systems

Fluid-structure interaction in liquid-filled piping systems is modelled by extended waterhammer theory for the fluid, and beam theory for the pipes. All basic coupling mechanisms (Poisson, junction and friction coupling) are modelled. Two different solution procedures are presented. In the first procedure the governing set of equations is solved by the method of characteristics (MOC). In the second procedure the fluid equations are solved by the method of characteristics, while the pipe equations are solved by the finite element method in combination with a direct time integration scheme (MOC-FEM). The two procedures are compared with each other for a straight pipe problem. The MOC-FEM procedure is also verified against a solution procedure in which the pipe equations are solved by modal superposition. The mathematical model is validated by simulation of two experiments known fromliterature: a straight pipe experiment and an experiment with one freely moving elbow. A provisional guideline is formulated which states when interaction is of importance.

Parameters affecting water-hammer wave attenuation, shape and timing—Part 2: Case studies

This two-part paper investigates parameters that may significantly affect water-hammer wave attenuation, shape and timing. Possible sources that may affect the waveform predicted by classical water-hammer theory include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Part 1 of this two-part paper presents the mathematical tools needed to model these sources. Part 2 of the paper presents a number of case studies showing how these modelled sources affect pressure traces in a simple reservoir-pipeline-valve system. Each case study compares the obtained results with the standard (classical) water-hammer model, from which conclusions are drawn concerning the transient behaviour of real systems

Waterhammer with fluid-structure interaction

The classical theory of waterhammer is a well-known and accepted basis for the prediction of pressure surges in piping systems. In this theory the piping system is assumed not to move. In practice however piping systems move when they are loaded by severe pressure surges, which for instance occur after rapid valve closure or pump failure. The motion of the piping system induces pressure surges which are not taken into account in the classical theory. In this article the interaction between pressure surges and pipe motion is investigated. Three interaction mechanisms are distinguished: friction, Poisson and junction coupling. Numerical experiments on a single straight pipe and a liquid loading line show that interaction highly influences the extreme pressures during waterhammer occurrences.

Fluid-Structure Interaction With Cavitation in Transient Pipe Flows

The interactions between axial wave propagation and transient cavitation in a closed pipe are studied. Definitive experimental results of the phenomenon are produced in a novel apparatus. The apparatus is characterized by its simplicity and its capability of studying transient phenomena in a predictable sequence. The influence due to friction is small and the representations of the boundary conditions are straightforward. Measurements with different severity of cavitation are provided to enable other researchers in the area to compare with their theoretical models. A new cavitating fluid/structure interaction cavitation model is proposed. The measurements are compared with the column separation model of Tijsseling and Lavooij (1989) and the new model to validate the experimental results.

Detection of Distributed Deterioration in Single Pipes Using Transient Reflections

A number of different methods that use signal processing of fluid transients (water hammer waves) for fault detection in pipes have been proposed in the past two decades. However, most of them focus solely on the detection of discrete deterioration, such as leaks or discrete blockages. Few studies have been conducted on the detection of distributed deterioration, such as extended sections of corrosion and extended blockages. This is despite the fact that they commonly exist and can have a severe negative impact on the operation of pipelines. The research reported here proposes a method of detecting distributed deterioration by investigating the time-domain water hammer response trace from a single pipe with a deteriorated section. Through wave analysis using a step pressure input, a theoretical square-shaped perturbation is found to exist in the transient pressure trace as a result of distributed deterioration. The hydraulic impedance of this section can be derived from the magnitude of the reflected pressure perturbation, while the location and length of the corresponding deteriorated section can be determined by using the arrival time and duration of the perturbation. The proposed method has been validated by analyzing experimental data measured from a pipe with a section of wall thickness change.

Experimental investigation on rapid filling of a large-scale pipeline

This study presents the results from detailed experiments of the two-phase pressurized flow behavior during the rapid filling of a large-scale pipeline. The physical scale of this experiment is close to the practical situation in many industrial plants. Pressure transducers, water-level meters, thermometers, void fraction meters, and flow meters were used to measure the two-phase unsteady flow dynamics. The main focus is on the water-air interface evolution during filling and the overall behavior of the lengthening water column. It is observed that the leading liquid front does not entirely fill the pipe cross section; flow stratification and mixing occurs. Although flow regime transition is a rather complex phenomenon, certain features of the observed transition pattern are explained qualitatively and quantitatively. The water flow during the entire filling behaves as a rigid column as the open empty pipe in front of the water column provides sufficient room for the water column to occupy without invoking air compressibility effects. As a preliminary evaluation of how these large-scale experiments can feed into improving mathematical modeling of rapid pipe filling, a comparison with a typical one-dimensional rigid-column model is made.

Numerical simulation of pulse-tube refrigerators

A new numerical model has been developed for simulating oscillating gas ??ow and heat transfer in the tube section of a pulse-tube refrigerator. Pulse-tube refrigerators are among the newest types of cryocoolers. They work by the cyclic compression and expansion of gas, usually helium. Introduced in 1963, pulse-tube refrigerators typically reached temperatures of about 120 K. By the end of the 1990s temperatures below 2 K had been reached. The practical use of pulse-tube cryocoolers is still at an early stage. However, they are beginning to replace the older types of cryocoolers in a wide variety of applications: military, aerospace and medical industries. Advantages such as simplicity, low cost and reliability, combined with high performance, have resulted in an extensive study of pulse tubes in recent years. The ??rst and second laws of thermodynamics have been major tools to investigate pulse-tube refrigerators theoretically. However, a clearer understanding of the ??uid dynamical properties is necessary if one wishes to make quantitative improvements in pulse tube performance. In this study we concentrate solely on the tube section of the pulse-tube refrigerator to identify undesired effects that occur in the tube and reduce the ef??ciency of the coolers. The developed mathematical model is based on the conservation of mass, momentum and energy, and the equation of state. The conservation equations for compressible viscous unsteady ??ow are written in differential form using primitive variables. One-dimensional and two-dimensional cylindrical axisymmetrical cases are considered. According to dimensional analysis, the tube conveys a low-Mach-number compressible ??ow. Therefore, we expanded all relevant variables in terms of powers of M2, a parameter related to the Mach number. This asymptotic consideration reveals several key features of pulse tube ??ow. Two physically distinct roles of pressure are to be distinguished: one as thermodynamic variable and one as hydrodynamic variable. The thermodynamical pressure appears in the energy equation and in the equation of state. It is spatially uniform, thus a function of time only, and is responsible for the global compression and expansion. The hydrodynamical pressure appears in the momentum equations and is induced by inertia and viscous forces. The acoustic pressure does not play a role in pulse tubes. Due to the non-linearity of the resulting system of equations, general analytical solutions are not available. Therefore numerical modelling has been applied. For the numerical solution of the resulting system of equations ??nite difference methods are used. The energy equation for the temperature is a convection-diffusion equation, mostly of a convective nature. It is solved with state-of-the-art ??ux-limiter schemes in an attempt to preserve the steep temperature gradients in a pulse tube. When large gradients are present, either internally or adjacent to a boundary, more accurate solutions can be obtained by grid re??nement. Re??ning a grid throughout the entire computational domain can be expensive, particularly in multi-dimensions. Instead of applying non-uniform locally re??ned grids, we use several uniform grids with different mesh sizes that cover different parts of the domain. One coarse grid covers the entire domain. The mesh size of this global grid is chosen according to the smoothness of the solution outside the high-activity regions. Besides the global grid, ??ne local grids are used which are also uniform. They cover only parts of the domain and contain the high-activity regions. The mesh size of each of these grids follows the activity of the solution. The solution is approximated on the composite grid which is the union of the uniform subgrids. This re??nement strategy is known as local uniform grid re??nement (LUGR). To deal with the problem of pressure-velocity coupling in the ??ow computation, we employ a pressure correction method. It is specially designed for low-Mach-number compressible ??ows. Combining the continuity equation and the energy equation, we derive an expansion equation or velocity divergence constraint. Our pressure correction scheme is based on this expansion equation and not on the continuity equation, which is different from the common approach in the simulation of compressible ??ows. The simulation tool, based on the proposed model, is constructed and tested on classic problems with known analytical solutions. Finally, the model was applied to a typical pulse-tube refrigerator. Results of one-dimensional and two-dimensional axisymmetrical simulations are presented and interpreted. The proposed model is more accurate and versatile than the widely used harmonic analysis and computationally less expensive than a full three-dimensional simulation with commercially available codes. It can be used for practical simulations, for calculating optimal values of the real system design parameters and for investigating different physical effects in the pulse tube.

Emptying of large-scale pipeline by pressurized air

AbstractEmptying of an initially water-filled horizontal PVC pipeline driven by different upstream compressed air pressures and with different outflow restriction conditions, with motion of an air-water front through the pressurized pipeline, is investigated experimentally. Simple numerical modeling is used to interpret the results, especially the observed additional shortening of the moving full water column due to formation of a stratified water-air “tail.” Measured discharges, water-level changes, and pressure variations along the pipeline during emptying are compared using control volume (CV) model results. The CV model solutions for a nonstratified case are shown to be delayed as compared with the actual measured changes of flow rate, pressure, and water level. But by considering water-column mass loss due to the water-air tail and residual motion, the calibrated CV model yields solutions that are qualitatively in good agreement with the experimental results. A key interpretation is that the long air...