Robert A. Leishear

Dynamic Pipe Stresses During Water Hammer: A Finite Element Approach

Water hammer is defined as a sudden increase in pipe pressure, which results in pressure waves that travel along the pipe at sonic velocities. In the wake of the pressure wave, dynamic stresses are created in the pipe wall, which contribute to pipe failures. A finite element analysis computer program was used to determine the three-dimensional dynamic stresses that result from pipe wall vibration at a distance from the end of a pipe, during a water-hammer event. The analysis was used to model a moving shock wave in a pipe, using a step pressure wave. Both aluminum and steel were modeled for an 8 NPS pipe, using ABAQUS®. For either material, the maximum stress was seen to be equal when damping was neglected. At the time the maximum stress occurred, the hoop stress was equivalent to twice the stress that would be expected if an equivalent static stress was applied to the inner wall of the pipe. Also, the radial stress doubled the magnitude of the applied pressure.

BLENDING TIME AND VELOCITY VARIATIONS DURING BLENDING IN A TANK USING DUAL OPPOSING JETS

Blending times are required for many process industries, and statistical analysis of the measured blending times was used to determine a relationship between CFD (computational fluid dynamics) predictions and experiments. A 95% blending time occurs when tank contents are sufficiently blended to ensure that concentration throughout the tank is within ±5% of the total change in concentration. To determine 95% blending times, acid and base tracers were added to an eight foot diameter tank, and the pH data were recorded to monitor blending. The data for six pH probes located throughout the tank were normalized to a range of 0 to 1. Then the blending time was established when the pH converged between 0.95 and 1.05 on the normalized graphs. Evaluation of results from 79 different tests concluded that the maximum blending time occurred randomly at any one of the six pH probes. The research then considered the calculated 95% blending times, which had uncertainties up to more than 100% at a 95% confidence level. However, this uncertainty is considered to be an actual variation in blending time, rather than an experimental error. Not only were there significant variations in the blending times, but there were significant variations in the velocities measured at different points in the blending tank.Copyright

Bubble Formation in a Large Scale System

The complexities of bubble formation in liquids increase as the system size increases, and a photographic study is presented here to provide some insight into the dynamics of bubble formation for large systems. Air was injected at the bottom of a 28 feet tall by 30 inch diameter column. Different fluids were subjected to different air flow rates at different fluid depths. The fluids were water and non-Newtonian, Bingham plastic fluids, which have yield stresses requiring an applied force to initiate movement, or shearing, of the fluid. Tests showed that bubble formation was significantly different in the two types of fluids. In water, a field of bubbles was formed, which consisted of numerous, distributed, 1/4 to 3/8 inch diameter bubbles. In the Bingham fluid, large bubbles of 6 to 12 inches in diameter were formed, which depended on the air flow rate. This paper provides comprehensive photographic results related to bubble formation in these fluids.Copyright

A Hydrogen Ignition Mechanism for Explosions in Nuclear Facility Piping Systems

Hydrogen explosions may occur simultaneously with water hammer accidents in nuclear facilities, and a theoretical mechanism to relate water hammer to hydrogen deflagrations and explosions is presented herein. Hydrogen and oxygen generation due to the radiolysis of water is a recognized hazard in pipe systems used in the nuclear industry, where the accumulation of hydrogen and oxygen at high points in the pipe system is expected, and explosive conditions may occur. Pipe ruptures in nuclear reactor cooling systems were attributed to hydrogen explosions inside pipelines, i.e., Hamaoka, Nuclear Power Station in Japan, and Brunsbuettel in Germany. Prior to these accidents, an ignition source for hydrogen was not clearly demonstrated, but these accidents demonstrated that a mechanism was, in fact, available to initiate combustion and explosion. A new theory to identify an ignition source and explosion cause is presented here, and further research is recommended to fully understand this explosion mechanism.

Mass Transfer Coefficients for a Bingham Fluid and Water With and Without Anti-Foam Agents

The equations describing mass transfer coefficients are rather concise, but experimental data is required to determine the coefficients. Here, mass transfer rates were measured in a large scale system, which consisted of an 8.4 meter tall by 0.76 meter diameter column containing one of three fluids: water with an anti-foam agent, water without an anti-foam agent, and a Bingham plastic fluid, referred to as AZ101 simulant. The Bingham fluid differed from water since it required an applied yield stress to initiate flow. Newtonian fluids, like water, have a zero yield stress. Each of the fluids was saturated with oxygen, and the oxygen was removed from solution as air bubbled up, or sparged, through the solution from the bottom of the column. Air sparging was supplied by a single pipe which was co-axial to the column. The decrease in oxygen concentration was recorded, and the oxygen measurements were then used to determine the mass transfer coefficients to describe the rate of oxygen transfer from solution. Mass transfer data for 24 different test conditions were determined. Superficial sparging velocities of 2, 5, and 10 mm/second were applied to each of the simulants at three different column fill levels, where the superficial velocity is defined as the average volumetric flow rate divided by the liquid surface area in the column. Mass transfer coefficient test results are presented herein for each test combination of superficial velocity and fluid level.© 2008 ASME

Fluid Transients in a Pipeline With One Open End

Water hammer during multi-phase flow is rather complex, but in some cases an upper limit to the pressure surge magnitude during water hammer can be estimated. In the case considered here, a two mile long pipeline with a single high point was permitted to partially drain. Due to gravitational effects, air bubbles up through the pipe line to its highest point, but the time required for air to reach the top of the pipe is rather long. Consequently, some transients caused by valve operations are affected by air entrapment and some are not. The intent of this research was to investigate the complex interactions between air, water vapor, and liquid during water hammer in a long pipe with one end of the pipe open to atmospheric conditions. To understand the system dynamics, experimental data was obtained from a long pipeline with an open end and also from a short, transparent tube. Transient calculations were performed for valve closures and pump operations as applicable. The limitations of available calculation techniques were considered in detail.Copyright

Comparison of Experimental Results to CFD Models for Blending in a Tank Using Dual Opposing Jets

Research has been completed in a pilot scale, eight foot diameter tank to investigate blending, using a pump with dual opposing jets. The jets re-circulate fluids in the tank to promote blending when fluids are added to the tank. Different jet diameters and different horizontal and vertical orientations of the jets were investigated. In all, eighty five tests were performed both in a tank without internal obstructions and a tank with vertical obstructions similar to a tube bank in a heat exchanger. These obstructions provided scale models of several miles of two inch diameter, serpentine, vertical cooling coils below the liquid surface for a full scale, 1.3 million gallon, liquid radioactive waste storage tank. Two types of tests were performed. One type of test used a tracer fluid, which was homogeneously blended into solution. Data were statistically evaluated to determine blending times for solutions of different density and viscosity, and the blending times were successfully compared to computational fluid dynamics (CFD) models. The other type of test blended solutions of different viscosity. For example, in one test a half tank of water was added to a half tank of a more viscous, concentrated salt solution. In this case, the fluid mechanics of the blending process was noted to significantly change due to stratification of fluids. CFD models for stratification were not investigated. This paper is the fourth in a series of papers resulting from this research (Leishear, et.al. [1- 4]), and this paper documents final test results, statistical analysis of the data, a comparison of experimental results to CFD models, and scale-up of the results to a full scale tank.

Higher Mode Frequency Effects on Resonance in Machinery Structures

The complexities of resonance in multi-degree of freedom systems (multi-DOF) may be clarified using graphic presentations. Multi-DOF systems represent actual systems, such as beams or springs, where multiple, higher order, natural frequencies occur. Resonance occurs when a cyclic load is applied to a structure, and the frequency of the applied load equals one of the natural frequencies. Both equations and graphic presentations are available in the literature for single degree of freedom (SDOF) systems, which describe the response of spring-mass-damper systems to harmonically applied, or cyclic, loads. Loads may be forces, moments, or forced displacements applied to one end of a structure. Multi-DOF systems are typically described only by equations in the literature, and while equations certainly permit a case by case analysis for specific conditions, graphs provide an overall comprehension not gleaned from single equations. In fact, this collection of graphed equations provides novel results, which describe the interactions between multiple natural frequencies, as well as a comprehensive description of increased vibrations near resonance.© 2010 ASME

HYDROGEN IGNITION MECHANISM FOR EXPLOSIONS IN NUCLEAR FACILITY PIPE SYSTEMS

Hydrogen and oxygen generation due to the radiolysis of water is a recognized hazard in pipe systems used in the nuclear industry, where the accumulation of hydrogen and oxygen at high points in the pipe system is expected, and explosive conditions exist. Pipe ruptures at nuclear facilities were attributed to hydrogen explosions inside pipelines, in nuclear facilities, i.e., Hamaoka, Nuclear Power Station in Japan, and Brunsbuettel in Germany. Prior to these accidents an ignition source for hydrogen was questionable, but these accidents, demonstrated that a mechanism was, in fact, available to initiate combustion and explosion. Hydrogen explosions may occur simultaneously with water hammer accidents in nuclear facilities, and a theoretical mechanism to relate water hammer to hydrogen deflagrations and explosions is presented herein.

Stresses in a Cylinder Subjected to an Internal Shock

Hoop stresses due to a moving shock front in either a gas or liquid filled cylinder can be approximated using vibration theory. The equation of motion can be combined with hoop stress equations to describe the dynamic changes in hoop stress to provide insight into the phenomenon of flexural resonance, which creates pipe stresses significantly in excess of the stresses expected from a slowly applied, or static, pressure loading. To investigate flexural resonance, vibration equations were successfully compared to available experimental results. At shock velocities, the maximum hoop stress is related to a vibration equation for a suddenly applied load. Consideration of structural and fluid damping, as well as pipe constraints at the end of the pipe, were considered in the derivation of the vibration equations. In short, vibration equations are presented in this paper and are compared to available experimental work. The equations describe hoop stresses in a pipe when a step increase in pressure travels the bore of a pipe at sonic or supersonic velocities.