Dynamic Pipe Stresses During Water Hammer: V — Applications

2003 ◽  
Author(s):  
Robert A. Leishear ◽  
Jeffrey H. Morehouse
Keyword(s):  
Nuclear Waste ◽  
Dynamic Stress ◽  
Failure Mechanisms ◽  
Water Hammer ◽  
Dynamic Stresses ◽  
Closed Form Solutions ◽  
Fluid Transient ◽  
Fluid Transients ◽  
Waste Facility ◽  
Insight Into

Theoretical equations to describe dynamic stresses during water hammer were developed in the first four parts of this series of papers, and this fifth paper applies those equations to analyze piping failures in a nuclear waste facility. The pipe failures were shown to be coincident to valve closures and pump shut downs, which caused fluid transients in the system. Magnitudes of the pressure increases during the transients were calculated and implemented in dynamic stress analyses for the piping. The maximum pipe stresses were then compared to the fatigue stresses of the pipes, and the failure mechanisms were thus established. By slowly closing valves, the effects of the fluid transient can be nearly eliminated. Using the closed from equations, the minimum time of valve closure may be calculated to prevent recurrent pipe failures. This application of the original closed form solutions provides further insight into the use and validity of the new dynamic stress equations.

Dynamic Pipe Stresses During Water Hammer: III — Complex Stress Relationships

2002 ◽  
Author(s):  
Robert A. Leishear
Keyword(s):  
Pressure Wave ◽  
Dynamic Stress ◽  
Pipe Wall ◽  
Three Dimensional ◽  
Complex Stress ◽  
Water Hammer ◽  
Dynamic Stresses ◽  
Vibration Theory ◽  
Pressure Spike ◽  
Fluid Transients

Complex three-dimensional dynamic stresses occur in a pipe following a water hammer event. Equations from vibration theory were adapted for use to describe the dynamic stresses at any point along the pipe wall. Hoop, radial, and axial dynamic stress equations are presented to approximate the stresses at a point on the pipe wall. Dynamic stress equations for beams and other simple shapes are also considered. The dynamic pipe stresses are affected principally by the types of water hammer waves or fluid transients, by the wave impacts at elbows or tees, and by the reflections of the waves from these elbows or tees. The three fluid transients considered are a moving step pressure wave, a ramp pressure, and a moving pressure spike. Approximate techniques are presented for evaluating the effects on piping due to the impingement of these transients on an elbow. For an equivalent pressure in a long pipe, application of the step pressure created the largest stress increases of the three transients considered. The vibration equations also prompt a solution to reduce water hammer effects. To this end, slow closing valves are frequently employed. Vibration theory may be applied to quantify the stress reductions afforded by these valves. Pipe stress equations may be manipulated to reduce pipe stresses for a linearly increasing, or ramp, pressure wave traveling along the pipe.

Application of a Dynamic Stress Theory to Pipe Leaks

2006 ◽  
Author(s):  
Robert A. Leishear
Keyword(s):  
Radioactive Waste ◽  
Failure Mechanism ◽  
Dynamic Stress ◽  
Water Hammer ◽  
Stress Theory ◽  
Fluid Transient ◽  
Cause Of Failure

Leaks in system piping used to transfer radioactive waste were attributed to water hammer. Ball valves leaked on several occasions and the cause of failure was not obvious. Facility records were used to determine the facility status at the time the leaks occurred. For one particular leak, valve manipulations controlling flow were shown to be coincident to the time of leak. The fluid transient pressures were calculated, and once the maximum pressures were established, the stresses on the equipment could be discerned. Water hammer was concluded to be the failure mechanism. To eliminate this failure mechanism, procedural and equipment modifications were made and further leaks have been eliminated.

Failure mechanisms in two-layer undrained slopes

2020 ◽  
Vol 57 (10) ◽  
pp. 1617-1621
Author(s):  
Shuangfeng Guo ◽  
D.V. Griffiths
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Failure Mechanism ◽  
Failure Mechanisms ◽  
Slope Angle ◽  
Strength Ratio ◽  
The Finite Element Method ◽  
Stability Analyses ◽  
Shallow Failure ◽  
Insight Into

This note presents results of stability analyses of two-layer undrained slopes by the finite element method. The study focuses on the circumstances under which either deep or shallow failure mechanisms occur, as a function of the strength ratio of the layers, slope angle, and foundation depth ratio. Improved knowledge of the location of the critical failure mechanism(s) in two-layer systems will give engineers better insight into where to focus their attention in terms or remediation or reinforcement to preserve stability.

Fluid Transients in a Pipeline With One Open End

2008 ◽  
Author(s):  
Robert A. Leishear
Keyword(s):  
Water Hammer ◽  
Atmospheric Conditions ◽  
Air Entrapment ◽  
Complex Interactions ◽  
Fluid Transients ◽  
Pipe Line ◽  
Multi Phase Flow ◽  
Time Required ◽  
Multi Phase ◽  
Transparent Tube

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.

Assessment of Aided-INS Performance

2011 ◽  
Vol 65 (1) ◽  
pp. 169-185 ◽  
Author(s):  
Itzik Klein ◽  
Sagi Filin ◽  
Tomer Toledo ◽  
Ilan Rusnak
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Navigation Systems ◽  
Inertial Navigation Systems ◽  
Closed Form Solutions ◽  
Land Vehicles ◽  
Error Covariance ◽  
Model Dependency ◽  
Error State ◽  
Insight Into

Aided Inertial Navigation Systems (INS) systems are commonly implemented in land vehicles for a variety of applications. Several methods have been reported in the literature for evaluating aided INS performance. Yet, the INS error-state-model dependency on time and trajectory implies that no closed-form solutions exist for such evaluation. In this paper, we derive analytical solutions to evaluate the fusion performance. We show that the derived analytical solutions manage to predict the error covariance behavior of the full aided INS error model. These solutions bring insight into the effect of the various parameters involved in the fusion of the INS and an aiding sensor.

A Method of Structural Analysis For Small Items in A Random Vibration Environment, Part I.

1987 ◽  
Vol 30 (3) ◽  
pp. 38-44
Author(s):  
Hilary Allen
Keyword(s):  
Dynamic Stress ◽  
Cost Effective ◽  
Variable Stiffness ◽  
Element Model ◽  
Equivalent Stiffness ◽  
Dynamic Stresses ◽  
Single Degree Of Freedom ◽  
Critical Design ◽  
Effective Manner ◽  
Beam Method

To perform engineering analyses in the most cost-effective manner, engineers must eliminate noncritical design items from a detailed analysis program and concentrate on the marginal and critical design items. This paper shows an approach to accomplishing this objective through the use of a rapid single-degree-of-freedom analysis. Part I develops equations for determining dynamic stresses on structural items modeled as simple beams and presents a nondimensional method for determining the equivalent spring rate of a variable-stiffness beam. Part II presents a step-by-step example that provides the deflection, equivalent stiffness, frequency, and dynamic stress on two different beam configurations with their predicted times-to-failure. In addition, the deflection and frequency results from a finite-element-model analysis of two tapered brackets are compared with the results from the nondimensional variable stiffness beam method developed previously.

A Method of Structural Analysis for Small Items in a Random Vibration Environment, Part II

1987 ◽  
Vol 30 (4) ◽  
pp. 33-38
Author(s):  
Hilary Allen
Keyword(s):  
Dynamic Stress ◽  
Cost Effective ◽  
Variable Stiffness ◽  
Equivalent Stiffness ◽  
Dynamic Stresses ◽  
Single Degree Of Freedom ◽  
Critical Design ◽  
Effective Manner ◽  
Beam Method ◽  
Dimensional Variable

To perform engineering analyses in the most cost-effective manner, engineers must eliminate non-critical design items from a detailed analysis program and concentrate on the marginal and critical design items. This paper shows an approach to accomplishing this objective through the use of a rapid single-degree-of-freedom analysis. Part I develops equations for determining dynamic stresses on structural items modeled as simple beams and presents a non-dimensional method for determining the equivalent spring rate of a variable-stiffness beam. Part II presents a step-by-step example that provides the deflection, equivalent stiffness, frequency and dynamic stress on two different beam configurations with their predicted times-to-failure. In addition, the deflection and frequency results from a finite-elementmodel analysis of two tapered brackets are compared with the results from the non-dimensional variable-stiffness beam method developed previously.

Finite Element Modeling of the Dynamic Response of a Steel Pipe During Water Hammer

2012 ◽  
Author(s):  
Juan C. Suárez ◽  
Paz Pinilla ◽  
Javier Alonso
Keyword(s):  
Finite Element ◽  
Wall Thickness ◽  
Pipe Wall ◽  
Element Model ◽  
Water Hammer ◽  
Steel Pipe ◽  
Dynamic Stresses ◽  
Rate Dependent ◽  
Simple Step ◽  
Von Mises

Water hammer imposes a steep rise in pipe pressure due to the rapid closure of a valve or a pump shutdown. Transversal strain waves propagate along the pipe wall at sonic velocities, and dynamic stresses are developed in the material, which can interact with discontinuities and contribute to an unexpected failure. Pressure increase has been modeled as a simple step front in a finite element model of a short section of a steel pipe. Boundary conditions have been considered to closely resemble the conditions of longer pipe behavior. The shock traveling along the length of the fluid-filled pipe causes a vibration response in the pipe wall. Dynamic strains and stresses follow the water hammer event with a certain delay, as is shown from the results of the FEA. Response of the material is strain rate dependent and dynamic peak stresses are substantially larger than the expected from the static pressure loads. Damping of the waves, neither by the material of the pipe nor by the interaction fluid-pipe, has not been considered in this simple model. Hoop, axial, radial, and Von Mises equivalent stresses have been evaluated both for the overshooting and the following phase of decompression of a pipe without discontinuities. However, dynamic stresses can be enhanced in the presence of discontinuities such as laminations, thickness losses in the pipe wall due to corrosion, changes in the wall thickness in neighboring pipe sections, dents, etc. These dynamic effects are able to explain how certain discontinuities that were reported as passing an Engineering Critical Assessment can eventually cause failure to the integrity of the structure. Deflections in the pipe wall can be altered by the welded transition from a pipe with a certain thickness to another with a smaller thickness, and wavelength changes of one order of magnitude can be expected. This can result in different approaches towards the risk assessment for discontinuities in the proximity of changes in wall thickness.

A Finite Element Approach to Dynamic Stresses of Helical Gear Pairs Considering Tip Relief and Crowning Modifications

2013 ◽  
Vol 284-287 ◽  
pp. 577-581
Author(s):  
Kuo Jao Huang ◽  
Ching Ya Su
Keyword(s):  
Finite Element ◽  
Dynamic Stress ◽  
Helical Gear ◽  
Dynamic Responses ◽  
High Quality ◽  
Dynamic Stresses ◽  
Dynamic Finite Element ◽  
Bending Stresses ◽  
Element Approach ◽  
Maximum Stresses

A dynamic finite element (FE) approach to contact and fillet bending stresses of helical gear pairs (HGPs) is presented. Using derived tooth profiles, high quality elements of HGPs can be efficiently constructed. The resulted maximum stresses of elements on teeth are 3D illustrated. Design of relief and profile modifications is also condisered. The effect of tooth modifications on HGP dynamic responses including misalignment errors is discussed. It shows adequate modification of tip relief and crowning can reduce dynamic stress peaks of HGPs.

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