Stress Analysis of Pipeline Subjected to Differential Frost Heave

Frost heave must be considered in cases where pipelines are laid in permafrost in order to protect the pipelines from overstress and to maintain the safe operation. In this paper, a finite element model for stress/strain analysis in a pipeline subjected to differential frost heave was presented, in which the amount of frost heave is calculated using a segregation potential model and considering creep effects of the frozen soil. In addition, a computational method for the temperature field around a pipeline was proposed so that the frozen depth and temperature variation gradient could be obtained. Using the procedure proposed in this paper, stress/strain can be calculated according to the temperature on the surface of soil and in a pipeline. The result shows the characteristics of deformation and loading of a pipeline subjected to differential frost heave. In general, the methods and results in this paper can provide a reference for the design, construction and operation of pipelines in permafrost areas.

Aneurysm No-Linear Unsteady Dynamic: Mathematical Modeling

A second order no-linear partial differential equation is worked out to describe the interaction of the flow with an elastic shell in large deformation domain. The model intends to describe the vibration of an aneurysm in arteries and veins. Two models are presented in this work. In the first one, the shell is inserted in otherwise rigid plane channel and in the second model the shell is inserted in otherwise rigid tube. In order to allow large displacement, the shell motion is described by Lagrangian variables. The steady version of the governing equation is a second order no-linear differential equation. A formal solution of the steady no-linear equation is obtained for plane channel model. It is shown that a steady solution exists only for some values of the dimensionless parameters ϕ and λ where ϕ is the ratio of transmural pressure to the elasticity coefficient and λ is the ratio of volume flux to the elasticity coefficient. The critical curve in the plan (ϕ,λ) for some control parameters are computed. Then, an unsteady solution of the no-linear unsteady equation is obtained numerically. It is found that the time signal prescribed by the unsteady no-linear solution depends strongly on the numerical values of the rheological parameters of the system. It is suggested that these signals could be used as a non invasive method in the diagnostic of the aneurysm when its vibration could be detected by a non invasive method. The linear analysis of the cylindrical geometry model shows that the aneurysm structure can be locked with heart pulse in a resonance frequency when the wall of the aneurysm becomes soft leading eventually to its rupture.

A Method for Extracting the Time Delay From the Unsteady and Quasi-Steady Fluidelastic Forces in Two-Phase Flow

The time delay is a key parameter for modeling fluidelastic instability, especially the damping controlled mechanism. It can be determined experimentally by measuring directly the time lag between the tube motion and the induced fluid forces. The fluid forces may be obtained by integrating the pressure field around the moving tube. However, this method faces certain difficulties in two-phase flow since the high turbulence and the non-uniformity of the flow may increase the randomness of the measured force. To overcome this difficulty, an innovative method for extracting the time delay inherent to the quasi-steady model for fluidelastic instability is proposed in this study. Firstly, experimental measurements of unsteady and quasi-static fluid forces (in the lift direction) acting on a tube subject to two-phase flow were conducted. The unsteady fluid forces were measured by exciting the tube using a linear motor. These forces were measured for a wide range of void fraction, flow velocities and excitation frequencies. The experimental results showed that the unsteady fluid forces could be represented as single valued function of the reduced velocity (flow velocity reduced by the excitation frequency and the tube diameter). The time delay was determined by equating the unsteady fluid forces with the quasi-static forces. The results given by this innovative method of measuring the time delay in two-phase flow were consistent with theoretical expectations. The time delay could be expressed as a linear function of the convection time and the time delay parameter was determined for void fractions ranging from 60% to 90%. Fluidelastic instability calculations were also performed using the quasi-steady model with the newly measured time delay parameter. Previously conducted stability tests provided the experimental data necessary to validate the theoretical results of the quasi-steady model. The validity of the quasi-steady model for two-phase flow was confirmed by the good agreement between its results and the experimental data. The newly measured time delay parameter has improved significantly the theoretical results, especially for high void fractions (90%). However, the model could not be verified for void fractions lower or equal to 50% due to the limitation of the current experimental setup. Further studies are consequently required to clarify this point. Nevertheless, this model can be used to simulate the flow induced vibrations in steam generators’ tube bundles as their most critical parts operate at high void fractions (≥ 60%).

Simulation of Low-Reynolds Number Flow Around a Circular Cylinder Following a Slender Elliptical Path

Two-dimensional flow around a circular cylinder forced to follow an elliptical path at low Reynolds numbers is investigated numerically using a thoroughly tested in-house code based on the finite difference method. Time-mean (TM) and rms values of lift, drag and base pressure coefficients are investigated within the lock-in region against the transverse oscillation amplitude for Reynolds number Re = 150 at frequency ratios of 0.8, 0.9 and 1.0 while the ratio of in-line and transverse cylinder oscillation amplitudes is kept at six different values yielding slender elliptical cylinder paths. The objective of the paper is to investigate the effect of the shape of the path, or amplitude ratio, on force coefficients. Findings show that for the cases investigated the rms of lift and TM of drag and base pressure are hardly affected by the amplitude ratio, while its effects are pronounced on the TM of lift and rms of drag and base pressure.

Commissioning Tests for an Experimental Study of Steam Generator Tube Loading During Blowdown

The goal of this research is to improve our understanding of the effects of a postulated Main Steam-Line Break on the transient loading of nuclear steam generator tubes. The analysis of this problem deals with the complex coupling of rapid transient two-phase flow dynamics and fluid-structural loading processes. A main concern of nuclear reactor safety is to ensure that radioactive materials produced by nuclear fission are safely contained. This type of accident produces a ‘blowdown’ in which the pressurised water in the steam generator is boiled off in a few seconds. The resulting transient loading on the steam generator tubing could lead to their rupture, resulting in the release of radioactive materials out of containment. A better understanding of this phenomenon will permit the development of improved design tools to ensure steam generator safety in the event of such an accident. This paper presents a work in progress, describing the purpose-built experimental facility and a summary of commissioning results, including an evaluation of the instrumentation and data collection methodology. The final results of this research will provide physical insights and guidance for the development of predictive modelling tools.

Fluid Transient Analysis for Safety Valve Vent Stack Using S-RELAP5 Code

This paper is to present a fluid transient analysis for the safety valve vent stack which is an open discharge system using the AREVA in-house thermal hydraulic code S-RELAP5. S-RELAP5 was developed by AREVA to perform thermal hydraulic analyses. It is a RELAP5-based thermal-hydraulic system code which incorporates features of the NRC RELAP5/MOD2 and RELAP5/MOD3 as well as other improvements. S-RELAP5 deals with one-dimensional two-phase, two-fluid, non-equilibrium hydrodynamic model with a non-condensable gas field. ASME B31.1-2010 Non-mandatory Appendix II provides formulas for hand calculation of blow down forces at elbow exit and vent pipe. In general, this approach generates only steady state forces. To more accurately calculate forcing functions, S-RELAP5 is a good tool to achieve this task. The purpose of this S-RELAP5 application is to show that the usage of BRANCH and other components in the S-RELAP5 code can effectively simulate the safety valve open system discharge. This is a first-of-a-kind application of the code. Furthermore, this method provides an alternative to the ASME Appendix II hand calculation. In this paper a sample problem from ASME Appendix II is utilized to generate the time history forcing functions to demonstrate the versatility of S-RELAP5. These forcing functions can then be used for the subsequent piping dynamic analysis.

Application of the Transfer Matrix Method to the Analysis of Hydro-Mechanical Vibration of NPP Piping

The transfer matrix method (TMM) was used for description of harmonic vibrations of piping with transported medium. Apart from 12 well-known mechanical parameters which characterize the state of piping system in each cross section two additional parameters that characterize the vibration of the medium, namely its translation and pressure pulsations were considered. The solution of these equations, which take into account the Poisson contraction of the pipe wall, in the form suitable for the transfer matrix method application was derived. The biggest uncertainty in the analytical modeling is to adopt the boundary conditions for above mentioned 2 parameters for the considered piping section. To solve this problem of identification of the most probable induced frequency we developed the technique of choosing such boundary conditions at which the maximum of energy is confined within the considered piping section. The validity of the approach was tested on some analytical examples. This method was used to analyze the forced vibration of the second circuit loop of unit 1 Zaporizhia Nuclear Power Plant (ZNPP) with VVER-1000 (from Russian: Vodo-Vodyanoi Energetichesky Reactor; Water-Water Power Reactor) arising from turbulent eddies in the flow of steam. Natural frequencies and forms of mechanical, hydrodynamic, and related hydro-mechanical vibration were found, a number of recommendations were given to reduce the vibration levels.

Acoustic Resonance of a Steam Line Gate Valve

A pure tone phenomenon has been observed at 460 Hz on a piping steam line of a power plant. The source has been identified to be generated in a gate valve and to be of cavity noise type. This paper presents the investigations carried out on experimental models in order to analyze the problem. 2D and 3D axisymmetric models are used and lock-in situations between shear layer modes and acoustic duct modes are proven to give rise to powerful tones. Some counter measures are also tested with the objective of lowering the amplitude of pressure oscillations.

Condensation Induced Waterhammer in District Steam Distribution Systems

Condensation induced waterhammer in district steam distribution systems can cause catastrophic rupture of piping and inflict severe damage to personnel, property, and environment. On July 18, 2007, a 20-in. diameter underground steam pipe in New York City ruptured at 5:56 p.m. at the intersection of 41st Street and Lexington Avenue in midtown Manhattan. At the time of rupture, the steam system was in service delivering steam to the customers at an operating pressure of approximately 160 psig and a steam temperature of approximately 370°F. The incident opened a large cavity measuring approximately 32 ft × 32 ft × 18 ft deep at the intersection of 41st Street and Lexington Avenue. The pipe rupture released steam, condensate, water, pipe insulation and various construction materials to the environment. Consolidated Edison Co. of New York, Inc. (Con Edison) and LPI (Lucius Pitkin, Inc.) investigated the event. Based on detailed metallurgical and engineering evaluations of the steam system configuration and operating conditions, it was concluded that the steam pipe ruptured as a result of excessive pressure caused by condensation-induced waterhammer. This paper presents a summary of the engineering evaluation, root cause, and conditions leading to the pipe rupture and provides measures which can be taken to reduce the likelihood of such a failure and enhance public safety.