A Reassessment of PWR Pressure Vessel Integrity During Overcooling Accidents, Considering 3-D Flaws

1984 ◽  
Vol 106 (4) ◽  
pp. 375-382 ◽  
Author(s):  
R. D. Cheverton ◽  
D. G. Ball
Keyword(s):  
Finite Length ◽  
Three Dimensional ◽  
Crack Arrest ◽  
Mechanics Model ◽  
Pressurized Thermal Shock ◽  
Maximum Crack ◽  
Vessel Integrity ◽  
Thermal Shock Problem ◽  
Arrest Toughness ◽  
Plate Type

A continuing analysis of the pressurized-thermal-shock problem associated with PWR postulated overcooling accidents indicates that the previously accepted degree of conservatism in the fracture-mechanics model needs to be more closely evaluated, and, if excessive, reduced. One feature that was believed to be conservative was the use of two-dimensional as opposed to finite-length (three-dimensional) flaws. The degree of conservatism could not be adequately investigated because of computational limitations and a lack of knowledge regarding flaw behavior; however, that situation has changed to the extent that some cases involving finite-length flaws can be studied. A flaw of particular interest is one that is located in an axial weld of a plate-type vessel. For those vessels that suffer relatively high-radiation damage in the welds, the length of the flaw will be no greater than the length of the weld, and recent calculations indicate that a deep flaw of that length (∼2 m) is not effectively infinitely long, contrary to previous thinking. The benefit to be derived from consideration of the 2-m flaw and also a semi-elliptical flaw with length-to-depth ratio of 6/1 was investigated by analyzing several postulated transients. In doing so the sensitivity of the benefit to a specified maximum crack-arrest toughness and to the duration of the transient was investigated. Results of the analysis indicate that for some conditions the benefit in using the 2-m flaw is substantial, but it decreases with increasing pressure, and above a certain pressure there may be no benefit, depending on the duration of the transient and the limit on crack-arrest toughness.

French RPV PTS Assessment: An Overview of EDF Research and Development in Progress on Thermalhydraulic, Materials and Mechanical Aspects

2003 ◽  
Author(s):  
Dominique Moinereau ◽  
Jean-Michel Frund ◽  
Henriette Churier-Bossennec ◽  
Georges Bezdikian ◽  
Alain Martin
Keyword(s):  
Structural Integrity ◽  
Three Dimensional ◽  
Crack Arrest ◽  
Pressure Vessels ◽  
Short Description ◽  
Constraint Effect ◽  
Materials Properties ◽  
Integrity Assessment ◽  
Pressurized Thermal Shock ◽  
Reactor Pressure

A significant extensive Research & Development work is conducted by Electricite´ de France (EDF) related to the structural integrity re-assessment of the French 900 and 1300 MWe reactor pressure vessels in order to increase their lifetime. Within the framework of this programme, numerous developments have been implemented or are in progress related to the methodology to assess flaws during a pressurized thermal shock (PTS) event. The paper contains three aspects: a short description of the specific French approach for RPV PTS assessment, a presentation of recent improvements on thermalhydraulic, materials and mechanical aspects, and finally an overview of the present R&D programme on thermalhydraulic, materials and mechanical aspects. Regarding the last aspect on present R&D programme, several projects in progress will be shortly described. This overview includes the redefinition of some significant thermalhydraulic transients based on some new three-dimensional CFD computations (focused at the present time on small break LOCA transient), the assessment of vessel materials properties, and the improvement of the RPV PTS structural integrity assessment including several themes such as warm pre-stress (WPS), crack arrest, constraint effect ....

Crack Arrest Toughness of 4140, 1340 and 4340 Steel

1981 ◽  
Author(s):  
E. J. Ripling ◽  
P. B. Crosley
Keyword(s):  
Crack Arrest ◽  
4340 Steel ◽  
Arrest Toughness

Crack Arrest Toughness of Two High Strength Steels (AISI 4140 and AISI 4340)

1982 ◽  
Vol 13 (4) ◽  
pp. 657-664 ◽  
Author(s):  
E. J. Ripling ◽  
J. H. Mulherin ◽  
P. B. Crosley
Keyword(s):  
High Strength Steels ◽  
High Strength ◽  
Crack Arrest ◽  
Aisi 4140 ◽  
Arrest Toughness ◽  
Aisi 4340

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Tilting at wave beams: a new perspective on the St. Andrew’s Cross

2017 ◽  
Vol 830 ◽  
pp. 660-680 ◽  
Author(s):  
T. Kataoka ◽  
S. J. Ghaemsaidi ◽  
N. Holzenberger ◽  
T. Peacock ◽  
T. R. Akylas
Keyword(s):  
Wave Field ◽  
Finite Length ◽  
Line Source ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Resonance Phenomenon ◽  
Buoyancy Frequency ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Viscous Effects

The generation of internal gravity waves by a vertically oscillating cylinder that is tilted to the horizontal in a stratified Boussinesq fluid of constant buoyancy frequency, $N$, is investigated. This variant of the widely studied horizontal configuration – where a cylinder aligned with a plane of constant gravitational potential induces four wave beams that emanate from the cylinder, forming a cross pattern known as the ‘St. Andrew’s Cross’ – brings out certain unique features of radiated internal waves from a line source tilted to the horizontal. Specifically, simple kinematic considerations reveal that for a cylinder inclined by a given angle $\unicode[STIX]{x1D719}$ to the horizontal, there is a cutoff frequency, $N\sin \unicode[STIX]{x1D719}$, below which there is no longer a radiated wave field. Furthermore, three-dimensional effects due to the finite length of the cylinder, which are minor in the horizontal configuration, become a significant factor and eventually dominate the wave field as the cutoff frequency is approached; these results are confirmed by supporting laboratory experiments. The kinematic analysis, moreover, suggests a resonance phenomenon near the cutoff frequency as the group-velocity component perpendicular to the cylinder direction vanishes at cutoff; as a result, energy cannot be easily radiated away from the source, and nonlinear and viscous effects are likely to come into play. This scenario is examined by adapting the model for three-dimensional wave beams developed in Kataoka & Akylas (J. Fluid Mech., vol. 769, 2015, pp. 621–634) to the near-resonant wave field due to a tilted line source of large but finite length. According to this model, the combination of three-dimensional, nonlinear and viscous effects near cutoff triggers transfer of energy, through the action of Reynolds stresses, to a circulating horizontal mean flow. Experimental evidence of such an induced mean flow near cutoff is also presented.

Simulation of Plasto-Elastohydrodynamic Lubrication in Line Contacts of Infinite and Finite Length

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Tao He ◽  
Jiaxu Wang ◽  
Zhanjiang Wang ◽  
Dong Zhu
Keyword(s):  
Surface Roughness ◽  
Finite Length ◽  
3D Model ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Axial Direction ◽  
Contact Length ◽  
Line Contact ◽  
Line Contacts ◽  
3D Surface Topography

Line contact is common in many machine components, such as various gears, roller and needle bearings, and cams and followers. Traditionally, line contact is modeled as a two-dimensional (2D) problem when the surfaces are assumed to be smooth or treated stochastically. In reality, however, surface roughness is usually three-dimensional (3D) in nature, so that a 3D model is needed when analyzing contact and lubrication deterministically. Moreover, contact length is often finite, and realistic geometry may possibly include a crowning in the axial direction and round corners or chamfers at two ends. In the present study, plasto-elastohydrodynamic lubrication (PEHL) simulations for line contacts of both infinite and finite length have been conducted, taking into account the effects of surface roughness and possible plastic deformation, with a 3D model that is needed when taking into account the realistic contact geometry and the 3D surface topography. With this newly developed PEHL model, numerical cases are analyzed in order to reveal the PEHL characteristics in different types of line contact.

A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method

1998 ◽  
Vol 120 (2) ◽  
pp. 371-377 ◽  
Author(s):  
Huan Wang ◽  
Keith Williams ◽  
Wei Guan
Keyword(s):  
Finite Length ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Vibrational Modes ◽  
The Finite Element Method ◽  
Cylinder Length ◽  
Radial Thickness ◽  
Thick Cylinder

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.

Shear-Driven Flow in a Toroid of Square Cross Section

2003 ◽  
Vol 125 (1) ◽  
pp. 130-137 ◽  
Author(s):  
J. A. C. Humphrey ◽  
J. Cushner ◽  
M. Al-Shannag ◽  
J. Herrero ◽  
F. Giralt
Keyword(s):  
Cross Section ◽  
Finite Length ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Radius Of Curvature ◽  
Infinite Length ◽  
Core Flow ◽  
Reynolds Number Flow ◽  
End Wall

The two-dimensional wall-driven flow in a plane rectangular enclosure and the three-dimensional wall-driven flow in a parallelepiped of infinite length are limiting cases of the more general shear-driven flow that can be realized experimentally and modeled numerically in a toroid of rectangular cross section. Present visualization observations and numerical calculations of the shear-driven flow in a toroid of square cross section of characteristic side length D and radius of curvature Rc reveal many of the features displayed by sheared fluids in plane enclosures and in parallelepipeds of infinite as well as finite length. These include: the recirculating core flow and its associated counterrotating corner eddies; above a critical value of the Reynolds (or corresponding Goertler) number, the appearance of Goertler vortices aligned with the recirculating core flow; at higher values of the Reynolds number, flow unsteadiness, and vortex meandering as precursors to more disorganized forms of motion and eventual transition to turbulence. Present calculations also show that, for any fixed location in a toroid, the Goertler vortex passing through that location can alternate its sense of rotation periodically as a function of time, and that this alternation in sign of rotation occurs simultaneously for all the vortices in a toroid. This phenomenon has not been previously reported and, apparently, has not been observed for the wall-driven flow in a finite-length parallelepiped where the sense of rotation of the Goertler vortices is determined and stabilized by the end wall vortices. Unlike the wall-driven flow in a finite-length parallelepiped, the shear-driven flow in a toroid is devoid of contaminating end wall effects. For this reason, and because the toroid geometry allows a continuous variation of the curvature parameter, δ=D/Rc, this flow configuration represents a more general paradigm for fluid mechanics research.

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