A simple approach to the prediction of waterhammer transients in a pipe line with entrapped air

The pressure histories within entrapped air bubbles in a pipe line during a waterhammer transient are treated theoretically. A convenient integral method is introduced, which takes full account of air/water interface movement and liquid compressibility. The significance of the method is that it provides a simple equation set for approximating, with good accuracy and with a small degree of conservatism, the solution to a problem that otherwise involves coupled partial differential equations on time dependent domains with non-linear boundary conditions. The accuracy of the method is defined by its comparison with available numerical-solution-predictions and measurements of the pressure within an entrapped-air-bubble at a dead end in a pipe. The method is shown to be a computationally simple and efficient way of assessing the impact of liquid compressibility on pressure rise when multiple water columns and air pockets are present in a pipe line.     

Modelling the fluid structure interaction produced by a waterhammer during shutdown of high-pressure pumps

Measurements of an experiment in a pipe system with pump shutdown and valve closing have been performed in the nuclear power plant KRB II (Gundremmingen, Germany). Comparative calculations of fluid and structure including interaction show an excellent agreement with the measured results. Theory and implementation of the fluid structure interaction (FSI) and the results of the comparison are described. The following measurements have been compared with calculations: (1) experiments in Delft, Netherlands to analyse the FSI; and (2) experiment with pump shutdown and valve closing in the nuclear power plant KRB II has been performed. It turns out, that the consideration of the FSI is necessary for an exact calculation of ‘soft’ piping systems. It has significant application in current waterhammer problems. For example, water column closure, vapour collapse, check valve slamming continues to create waterhammers in the energy industry. An important consequence of the FSI is mostly a significant increase of the effective structural damping. This mitigates—so far in all KED’s calculations the FSI has taken into account—an amplification of pipe movements due to pressure waves in resonance with structural eigenvalues. To investigate the integrity of pipe systems pipe stresses are calculated. Taking FSI into account they are reduced by 10–40% in the actual case.     

Void fraction measurement by a gamma-ray densitometer under instantaneous pipe rupture

A high-response gamma-ray densitometer was developed for the measurement of void fraction caused by the flashing vaporization of high-pressure and -temperature water under an instantaneous pipe break accident of a boiling water reactor, BWR. The initial conditions of the water were 6.86 MPa in pressure and saturation temperature. In order to prove the reliability and accuracy, the calibration test by dropping the acrylic void simulators and the air injection test into the cold water filled in the pipe were conducted.The following results are obtained in the experiments: (1) the cone slit method is very useful to increase the measuring accuracy, (2) it is clearly observed that the apparent increase of the void fraction occurs after the rarefaction wave passes, (3) the first maximum of the void fraction occurs with some delay time after break. Secondly, the minimum void fraction concurs with the maximum pressure in the pressure recovering process.     

Investigations on stressing and failure of pipe bends under complex loading

Investigations on stressing and failure of pipe bends under complex loading are done. First, the tests themselves will be noted shortly. Further, the deformation behaviour and the failure of ferritic and austenitic elbows is described. Finally some remarks are given on the components safety.     

Creep of a straight pipe under combined bending and internal pressure

Several analyses are presented for the isothermal creep behaviour of a thin, constant thickness, circular crosssection cylindrical shell under the action of conbined bending and internal pressure loading. Results are presented in a way that should be helpful for general pipework design. Previous analyses are summarised and discussed.     

Experimental studies of 4-inch pipe whip test under BWR loca conditions

Pipe whip tests or jet discharge tests have been performed at the Japan Atomic Energy Research Institute, which simulate the instantaneous circumferential guillotine break of primary coolant piping in nuclear power plants. The present paper describes the results of the pipe whip tests using test pipes of 4 inch diameter, under the BWR LOCA conditions, which were performed from 1979 to 1981. The tests were carried out at an initial pressure of about 6.8 MPa and an initial temperature of about 285°C.The test pipe was 114.3 mm (4 in) in diameter, 8.6 mm in thickness and 4500 mm in length. The four pipe whip restraints used in the tests were the U-bar type of 8 mm in diameter and fabricated from Type 304 stainless steel. The experimental parameters were the clearance (30, 50 and 100 mm) and the overhang length (250, 400, 550 and 1000 mm).The main purpose of these tests is to investigate the effects of the clearance and the overhang length on the pipe whip behavior. It has been clarified from the test results that a smaller clearance and a shorter overhang length causes the deformation of the pipe and restraints to be minimized, and the test pipe collapses near the setting point of the restraints with the overhang length of 1000 mm.     

Experimental and analytical studies of pipe whip tests under PWR LOCA conditions

A series of pipe rupture tests has been performed at the Japan Atomic Energy Research Institute (JAERI) to demonstrate the safety of primary coolant circuits in the event of pipe rupture in nuclear power plants. Pipe whip tests and jet discharge tests have been conducted under boiling water reactor (BWR) and pressurized water reactor (PWR) loss-of-coolant accident (LOCA) conditions. The present paper describes the experimental and analytical results of the pipe whip tests performed under PWR LOCA conditions using 4, 6 and 8-inch test pipes. The tests were carried out at an initial pressure and temperature of 15.7 MPa and 325°C, respectively. Moreover, a dynamic analysis of pipe whip tests was carried out using the general purpose finite element program ADINA.     

Lower bound limit load of a circumferentially cracked pipe under combined mechanical loading

In a study on extension of the reference stress method, for J simplified assessment, to a three dimensional (3D) configuration under combined loading, lower bound limit analysis has been developed by J. Desquines. In the present paper the limit load for cracked pipe, with a 3D circumferential flaw, under pressure, tension and bending is detailed. The limit load is explicitly defined as a yield surface is the 3D space loading. A simple algorithm is proposed to solve the non linear problem associated to the reference stress calculation. Moreover, the lower bound solution is compared with Elastic Compensation Method (ECM) results computed on a 3D finite element mesh of the cracked pipe. The lower bound yield surface underestimates the numerical limit loads with a discrepancy lower than 20%.     

Analysis of potential waterhammer at the Ignalina NPP using thermal–hydraulic and structural analysis codes

The RBMK (Russian acronym for ‘channeled large power reactor’)-1500 reactors at the Ignalina nuclear power plant (NPP) have a series of check valves in the main circulation circuit (MCC) that serve the coolant distribution in the fuel channels. In the case of a hypothetical guillotine break of pipelines upstream of the group distribution headers (GDH), the check valves and adjusted piping integrity is a key issue for the reactor safety during the rapid closure of check valve. An analysis of the waterhammer effect (i.e. the pressure pulse generated by the valves slamming closed) is needed. The thermal–hydraulic and structural analysis of waterhammer effects following the guillotine break of pipelines at the Ignalina NPP with RBMK-1500 reactors was conducted by employing the RELAP5 and PipePlus codes. Results of the analysis demonstrated that the maximum values of the pressure pulses generated by the check valve closure following the hypothetical accidents remain far below the value of pressure of the hydraulic tests, which are performed at the NPP and the risk of failure of the check valves or associated pipelines is low. Sensitivity analysis of pressure pulse dependencies on calculation time step and check valve closure time was performed. Results of RELAP5 calculations are benchmarked against waterhammer transient data obtained by employing structural mechanics code BOS fluids.     

Fracture mechanics study of a pipe bend with a longitudinal crack under static loading

The regulating norms for nuclear power plant component are based on the assumption that the components have no defects. Therefore it is of major interest to find what values the fracture mechanics parameters assume when a loading which produces in an unflawed elbow stresses which are acceptable according to the regulatory guides is applied to an elbow with cracks. It could be shown that with small flaws ( of arc length, ) calculations assuming linear-elastic behavior give results almost identical as when elastic-plastic behavior is assumed. If the cracks are small and the loading is according to the regulatory guides the initiation value J₁ for stable crack growth is not reached.     

Relaxation of elastic stresses under the action of neutron irradiation

In the article, the author discusses the results of investigations on the influence of neutron irradiation on the relaxation of elastic stresses in flat springs made of uranium alloyed with molybdenum and on the relaxation of microstresses caused by broadening of the x-raylines of drawn uranium. The theoretical notions appearing in [1] are developed further, and the results of analysis are compared with the experimental data.     

Simplified analysis of shrinkage in pipe to pipe butt welds

Generally some shrinkage is typical of butt welding of pipes. Shrinkage due to butt welding could be more pronounced and significant in thin wall stainless steel pipes because the thermal expansion coefficient is roughly one and half times that of carbon steel. An axisymmetric finite element evaluation of hoop shrinkage associated with circumferential butt welds in thin wall stainless steel pipes was performed. Actual shrinkage data for a larger (24 in. diameter, 0.375 in. wall thickness) pipe and a smaller (4 in. diameter, 0.237 in. wall thickness) pipe were utilized. The results indicate that very localized residual stresses in excess of yield strength produced during cooldown of metal in the weld and heat affected zones cause redistribution of the stresses. A simplified elastic–plastic analysis approach was developed with adjustments for section modulus and Poisson’s ratio, and the strains due to radial shrinkage were calculated for inside and outside surfaces of the pipe at the weld center line. From the strain point of view, the strain values in the circumferential direction were about 1.4% for the larger size pipe and 3.4% for the smaller size pipe. The strain values in the axial direction were 2.5% for the larger pipe and 5.9% for the smaller pipe. It is concluded that these levels of strains are not detrimental in nature. However, for the smaller pipe they are on the high side and it is recommended not to use the pipe for elevated temperature service. Residual stresses were also calculated for inside and outside surfaces of the pipe at weld center line using a simplified elastic–plastic approach and a bilinear stress–strain curve and compared with published data indicating a general agreement.     

Formation of porosity in uranium under the action of thermal cycling

In accelerated thermal cycling with a cycle of 50 sec period, considerable changes appear in uranium after 50–1000 cycles, depending upon the temperature range of the cycle. Cycling in the temperature range of the -phase (with heating up to between 550 and 600 °C) produces in texturcd uranium (containing about 0.1% carbon) a directional deformation and porosity, accompanied by a drop in density. After 5000 cycles, the drop in density amounts to 8% Thermal cycling with = ß = -transformations produces a pronounced distortion of the original shape of uranium speclmens and intense porosity formation, with a considerable drop in density, which attains 30% after 1000 cycles.