MUAP-10022-NP, Revision 2, 'Evaluation on Jet Impingement ...
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD.
US-APWR
Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture
Non-Proprietary Version
May 2012
Ⓒ2012 Mitsubishi Heavy Industries, Ltd.
All Rights Reserved
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD.
REVISION HISTORY
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD.
© 2012
MITSUBISHI HEAVY INDUSTRIES, LTD.
All Rights Reserved
This document has been prepared by Mitsubishi Heavy Industries, Ltd. (“MHI”) in connection with the U.S. Nuclear Regulatory Commission’s (“NRC”) licensing review of MHI’s US-APWR nuclear power plant design. No right to disclose, use or copy any of the information in this document, other that by the NRC and its contractors in support of the licensing review of the US-APWR, is authorized without the express written permission of MHI.
This document contains technology information and intellectual property relating to the US-APWR and it is delivered to the NRC on the express condition that it not be disclosed, copied or reproduced in whole or in part, or used for the benefit of anyone other than MHI without the express written permission of MHI, except as set forth in the previous paragraph.
This document is protected by the laws of Japan, U.S. copyright law, international treaties and conventions, and the applicable laws of any country where it is being used.
MITSUBISHI HEAVY INDUSTRIES, LTD. 16-5, Konan 2-chome, Minato-ku
Tokyo 108-8215 Japan
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD.
ABSTRACT
Pipe rupture protection design is implemented to conform to Title 10 Code of Federal Regulations Part50, Appendix-A, General Design Criteria 4. The evaluation requirements and design policy described in this report are based on a defense-in-depth approach. The calculation method for the thrust force and jet impingement force are described in a Technical Report “MUAP-10017”. This report describes blast wave, jet pressure oscillation, and jet reflection calculation methodology.
The steam break blast wave is evaluated using CFD analysis with an instantaneous pipe break assumption. In the US-APWR, the term “steam piping” refers to the piping connected to the pressurizer upper head. Analysis, including consideration of plant layout, indicates that the blast wave does not impact the stress intensity of the SSCs and has no impact on the protection design. The change of layout in the future is considered, the evaluation methodology for blast wave is also provided.
Jet pressure oscillation is unlikely at the US-APWR operating pressures because the large jet flow expansion and large Mach Disk produce a stable downstream condition. Under such conditions, feedback from a disturbance at an impingement wall is unlikely. However, It is conservatively assumed that a jet pressure oscillation occurs through full blowdown process. The evaluation for jet pressure oscillation is provided.
When jet flow impinges on a wall, the impinging jet flow is redirected along the surface of the wall forming what is called the zone of influence (ZOI). Inside the ZOI, the impingement pressure includes effect of pressure due to flow parallel to the wall. Loads due to jet impingement reflection inside the ZOI are negligible. This report considers jet impingement on a parallel wall and the more likely case of an oblique.
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. i
TABLE OF CONTENTS
LIST OF TABLES ............................................................................................................ iii
LIST OF FIGURES .......................................................................................................... iv
LIST OF ACRONYMS ..................................................................................................... vi
1.0 OVERVIEW................................................................................................................1
2.0 BLAST WAVE ............................................................................................................2
2.1 BLAST WAVE OF STEAM PIPING...........................................................................2
2.1.1 Free Blast Wave..................................................................................2
2.1.2 Reflection of Blast Wave ......................................................................7
2.2 BLAST WAVE OF SUB-COOLED WATER PIPING ...................................................14
2.3 BLAST WAVE ASSESSMENT IN US-APWR .........................................................16
2.3.1 Pressureizer Upper Piping Structure Integrity ....................................16
2.3.2 Instrument Piping Structure Integrity ..................................................17
2.3.3 Reflection Amplification ......................................................................17
2.3.4 Reflection Repitation ..........................................................................17
2.4 BLAST WAVE EVALUATION ................................................................................24
2.4.1 Scope of Evaluation ...........................................................................26
2.4.2 Load of Blast Wave ............................................................................26
3.0 JET PRESSURE OSCILLATION .............................................................................27
3.1 STEAM PIPING .................................................................................................27
3.2 SUB-COOLED WATER PIPING ...........................................................................34
3.3 EFFECT OF SOURCE CONDITION CHANGE.........................................................36
3.4 EVALUATION OF JET PRESSURE OSCILLATION ..................................................39
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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3.4.1 Scope of Evaluation ...........................................................................41
3.4.2 Jet Load of Jet Pressure Oscillation Evaluation .................................42
3.4.3 Modeling.............................................................................................46
3.4.4 Acceptance Criteria ............................................................................46
4.0 JET REFLECTION ...................................................................................................48
4.1 JET REFLECTION EVALUATION...........................................................................52
4.1.1 Scope of Evaluation ...........................................................................54
4.1.2 Load of Reflection Jet.........................................................................57
5.0 REFERENCES........................................................................................................59
APPENDIX
Appendix1 Simplified Blast Wave Model ................................................................... A1-1
Appendix2 Convergence Condition ........................................................................... A2-1
Appendix3 Outline of Blowdown Analysis ................................................................. A3-1
Appendix4 Simple Beam Methodology in Consideration of Resonating
High Frequency Mode ............................................................................. A4-1
Appendix5 Frequency of Jet Pressure Oscillation .................................................... A5-1
Appendix6 Example of Structural Analysis for Jet Pressure Oscillation .................... A6-1
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. iii
LIST OF TABLES
Table 2-1 Comparison between Simplified Model and CFD 7Table 2-2 Piping Specification 19Table 3-1 Table 3-2 (1/4)
Maximum Pressure of Single Phase Steam at Interval Stage Magnification Factor of Natural Frequency 5 Hz of Piping
3839
Table 3-2 (2/4) Magnification Factor of Natural Frequency 10 Hz of Piping 39Table 3-2 (3/4) Magnification Factor of Natural Frequency 15 Hz of Piping 40Table 3-2 (4/4) Magnification Factor of Natural Frequency 20 Hz of Piping 40Table 3-3 Design Criteria and Load Combination 53
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. iv
LIST OF FIGURES
Figure 2-1 Blast Wave Simplified Model 3Figure 2-2 Analysis Model 4Figure 2-3 Blast Wave Pressure Contour 5Figure 2-4 Blast Wave Static Pressure Distribution along Jet Axis 5Figure 2-5 Blast Wave Pressure Attenuation by Distance 6Figure 2-6 Relation between Incident Pressure Ratio and Reflection
Amplification Factor 9
Figure 2-7 Front Reflection Analysis Model Outline 9Figure 2-8 Distribution of Incident Pressure ps and Reflection
Pressure pr for Front Reflection 10
Figure 2-9 Distribution of Reflection Amplification Factor for Front Reflection
10
Figure 2-10 Corner Reflection Analysis Model 11Figure 2-11 Blast Wave Contour for Case of Reflection at Corner in
Static Pressure 12
Figure 2-12 Relation between r/d and Peak Pressure 13Figure 2-13 Relation between r/d and Reflection Amplification Factor 13Figure 2-14 Sound Speed of Liquid-Gas Two Phase Flow 15Figure 2-15 Piping Layouts at Upper Portion of Pressurizer 18Figure 2-16 Case of Closest Distance between Break &Target Points 19Figure 2-17 Figure 2-18 Figure 2-19 Figure 2-20
Piping Analysis Stress Model Load Application Image Example of Time History of Pressure Load(Piping Center Part) Time History of Piping Stress (Piping Center)
202021
21Figure 2-21 Instrument Piping in Pressurizer Compartment 22Figure 2-22 Closest Location from Break Point to Wall 23Figure 2-23 Internal Size of Pressurizer Compartment 23Figure 2-24 Evaluation Process of Blast Wave 25Figure 2-25 Load image of Blast Wave 26 Figure 3-1 Relationship between Distance from Nozzle to
Impingement Wall and Pressure Distribution at Impingement Wall
29
Figure 3-2 Pressure Distribution of Flat-Plate Impingement (D = nozzle diameter d)
30
Figure 3-3 Mechanizum of Generating Re-Circulation Flow 31Figure 3-4 Relationship between Concave-Type Pressure
Distribution Range and Pressure Oscillation Range(Reference 6-10)
32
Figure 3-5 Time-Freeze Planar Laser-induced Fluorescence(PLIF) Images of Jet
33
Figure 3-6 Flow Velocity Contour under PWR Condition with Sub-Cooling: 20°C
35
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 3-7 Steam Piping (Single Phase Flow) 35Figure 3-8 Impingement Jet and Wall Pressure Distribution of
Pressurized Hot Water (D = nozzle diameter d) 36
Figure 3-9 Jet Pressure after Blowdown in 8-inch Break Blowdown 37Figure 3-10 Evaluation Process of Jet Pressure Oscillation 40
Figure 3-11 Load Time Histories of Jet Pressure Oscillation 45
Figure 4-1 Behavior of Jet Flow Impinging on a Perpendicular Surface
49
Figure 4-2 Front Reflection Analysis Model Outline 49Figure 4-3 Expansion of Steam Jet 50Figure 4-4 Speed Distribution of Flow Jet 50Figure 4-5 Density of Flow Jet 50Figure 4-6 Speed Distribution in Jet Flow Radiating along Wall at a
Cross Section Parallel to Wall 51
Figure 4-7 Radial Force in Jet Flow Radiating along Wall 51Figure 4-8 Evaluation Process of Jet reflection 53
Figure 4-9 Reflection Jet Expansion Model 55Figure 4-10 Evaluation Range (Bird–Eye View) 56Figure 4-11 Reflection Jet Model 58Figure 4-12 Reflection Jet Model (Bird–Eye View)
58
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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LIST OF ACRONYMS
The following list defines the acronyms used in this document. MHI Mitsubishi Heavy Industries, Ltd. NRC U.S. Nuclear Regulatory Commission CFR Code of Federal Regulations GDC General Design Criteria CFD Computer Fluid Dynamic RCL Reactor Coolant Loop PLIF Planar Laser-induced Fluorescence ZOI Zone of Influence RCL Reactor Coolant Loop RCPB Reactor Coolant Pressure Boundary
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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1.0 OVERVIEW
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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2.0 BLAST WAVE
2.1 Blast Wave of Steam Piping
2.1.1 Free Blast Wave
2.1.1.1 Blast Wave Simplified Model
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-1 Blast Wave Simplified Model
2.1.1.2 CFD Analysis
a. Model Outline
b. Result
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-2 Analysis Model
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-3 Blast Wave Pressure Contour
Figure 2-4 Blast Wave Static Pressure Distribution along Jet Axis
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-5 Blast Wave Pressure Attenuation by Distance
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Table 2-1 Comparison between Simplified Model and CFD
2.1.2 Reflection of Blast Wave
2.1.2.1 Front Wall Reflection
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2.1.2.2 Front and Side Wall Reflection
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-6 Relation between Incident Pressure Ratio and Reflection Amplification Factor
Figure 2-7 Front Reflection Analysis Model Outline
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-8 Distribution of Incident Pressure ps and Reflection Pressure pr for Front Reflection
Figure 2-9 Distribution of Reflection Amplification Factor for Front Reflection
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-10 Corner Reflection Analysis Model
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-11 Blast Wave Contour for Case of Reflection at Corner in Static Pressure
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-12 Relation between r/d and Peak Pressure
Figure 2-13 Relation between r/d and Reflection Amplification Factor
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2.2 Blast Wave of Sub-cooled Water Piping
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Figure 2-14 Sound Speed of Liquid-Gas Two Phase Flow
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2.3 Blast Wave Assessment in US-APWR
2.3.1 Pressureizer Upper Piping Structure Integrity
2.3.1.1 Structral Analysis
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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2.3.2 Instrument Piping Structure Integrity
2.3.3 Reflection Amplification
2.3.4 Reflection Repitation
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Figure 2-15 Piping Layouts at Upper Portion of Pressurizer
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-16 Case of Closest Distance between Break &Target Points
Table 2-2 Piping Specification
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-17 Piping Analysis Stress Model
Figure 2-18 Load Application Image
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
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Figure 2-19 Example of Time History of Pressure Load (Piping Center Part)
Figure 2-20 Time History of Piping Stress (Piping Center)
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Figure 2-21 Instrument Piping in Pressurizer Compartment
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Figure 2-22 Closest Location from Break Point to Wall
Figure 2-23 Internal Size of Pressurizer Compartment
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2.4 Blast Wave Evaluation
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Figure 2-24 Evaluation Process of Blast Wave
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2.4.1 Scope of Evaluation
2.4.2 Load of Blast Wave
Figure 2-25 Load Image of Blast Wave
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3.0 JET PRESSURE OSCILLATION
3.1 Steam Piping
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Figure 3-1 Relationship between Distance from Nozzle to Impingement Wall and Pressure Distribution at Impingement Wall
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Figure 3-2 Pressure Distribution of Flat-Plate Impingement (D = nozzle diameter d)
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Figure 3-3 Mechanism of Generating Re-Circulation Flow
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Figure 3-4 Relationship between Concave-Type Pressure Distribution Range
and Pressure Oscillation Range(Reference 6-10)
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Figure 3-5 Time-Freeze Planar Laser-Induced Fluorescence (PLIF) Images of Jet
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3.2 Sub-Cooled Water Piping
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Figure 3-6 Flow Velocity Contour under PWR Condition with Sub-Cooling: 20°C
Figure 3-7 Steam Piping (Single Phase Flow)
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Figure 3-8 Impingement Jet and Wall Pressure Distribution of Pressurized Hot Water
(D = nozzle diameter d)
3.3 Effect of Source Condition Change
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Figure 3-9 Jet Pressure after Blowdown in 8-inch Break Blowdown
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Table 3-1 Maximum Pressure of Single Phase Steam at Interval Stage
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3.4 Evaluation of Jet Pressure Oscillation
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Figure 3-10 Evaluation Process of Jet Pressure Oscillation
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3.4.1 Scope of Evaluation
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3.4.2 Jet Load of Jet Pressure Oscillation Evaluation
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Table 3-2 (1/4) Magnification Factor of Natural Frequency 5Hz of Piping
Table 3-2 (2/4) Magnification Factor of Natural Frequency 10 Hz of Piping
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Table 3-2 (3/4) Magnification Factor of Natural Frequency 15 Hz of Piping
Table 3-2 (4/4) Magnification Factor of Natural Frequency 20 Hz of Piping
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Figure 3-11 Load Time Histories of Jet Pressure Oscillation
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3.4.3 Modeling
3.4.4 Acceptance Criteria
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Table 3-3 Design Criteria and Load Combination
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4.0 JET REFLECTION
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Figure 4-1 Behavior of Jet Flow Impinging on a Perpendicular Surface
Figure 4-2 Front Reflection Analysis Model Outline
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Figure 4-3 Expansion of Steam Jet
Figure 4-4 Speed Distribution of Flow Jet Figure 4-5 Density of Flow Jet
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Figure 4-6 Speed Distribution in Jet Flow Radiating along Wall
at a Cross Section Parallel to Wall
Figure 4-7 Radial Force in Jet Flow Radiating along Wall
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4.1 Jet Reflection Evaluation
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Figure 4-8 Evaluation Process of Jet Reflection
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4.1.1 Scope of Evaluation
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Figure 4-9 Reflection Jet Expansion Model
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iii) ZOI of Jet Reflection
Figure 4-10 Evaluation Range (Bird-Eye View)
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4.1.2 Load of Reflection Jet
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Figure 4-12 Reflection Jet Model (Bird-Eye View)
Figure 4-11 Reflection Jet Model
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5.0 REFERENCES
1-1 P.D.Smith, J.G.Hetherington, ”Blast and Ballistic Loading of Structures”, Butterworth Heinemann, pp.44-47, 1994.
1-2 T. Ito, ”Acoustic Engineering”, CORONA PUBLISHING CO.,LTD, 1976, (Revision 11)
1-3 Japanese Ministry of Technology and Industries, “Technology and Law to Prevent Pollution”, 2000, (Revision5)
1-4 Japan Society of Mechanical Engineers, “Revised Handbook for Liquid-Gas Two Phase Flow”, Page 378, 2006.
1-5 NRC Letter (ADAMS Accession No.NRR-106) dated March 31,2010 related to Generic Safety Issue-191.
1-6 H. Utsuno, M. Akamatsu, and T. Morii, H. Okada, and A. Minato,“Application of Compressible Two-Fluid Mode Code to SupersonicTwo-Phase Jet Flow Analysis”, The 13th International Topical Meetingon Nuclear Reactor Thermal Hydraulics (NURETH-13), September,2009.
2-1 Masuda, F., Nakatogawa, T., Kawanishi, K. and Isono, M., Experimental Study on an Impingement High-Pressure Steam Jet, Nuclear Engineering and Design 67-2, pgs 273-285, 1982.
2-2 F. S. Alvi, J. A. Ladd, W. W. Bower,“Experimental and Computational Investigation of Supersonic Impinging Jets”,AIAA JOURNAL, Vol. 40, No. 4, April 2002
2-3 K. Kitade, T. Nakatogawa, H. Nishikawa, K. Kawanishi, T.Tsuruto, “Free Jet and Jet Impingement of High Pressure Steam”, Journal of Atomic Energy Society of Japan, Vol. 22, No.9, pp634-640. (In Japanese)
2-4 H.Ashkenas and F.S. Sherman, “Rarefied Gas Dynamics, Vol II”, Academic press, New York, pp 84-105, 1966.
2-5 S. I. Kim, S. O. Park, “Oscillatory Behavior of Super Sonic Impinging Jet Flows Shock Waves”, 14(4), pp. 259-272, 2005
2-6 C. Y. Loh,“Computation of Tone Noise From Supersonic Jet Impinging on Flat Plates”, NASA CR—2005-213426, AIAA–2005–0418 .March,2005
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2-7 A. Krothapalli, E. Rajkuperan, F. Alvi, L.Lourenco, “Flow field and noise characteristics of a supersonic impinging jet”, J.Fluid Mech.(1999), vol.392, pp.155-181, 1999
2-8 B. Henderson, “An Experimental Investigation into the Sound Producing Characteristics of Supersonic Impinging Jets”, AIAA Paper 2001-2145, 2001
2-9 T. Yasunobu, T. Matsuoka, M. Tagami, “Pressure Fluctuation on Self Induce Flow Oscillation Caused by Under-Expanded Super Sonic Impinging Jet”, The japan Society of Mechanical Enjineers,No.028-1,pp.141-142, 2002
2-10 A. (Wilkes) Inman, P M. Danehy, R J. Nowak, and D W. Alderfer, “Fluorescence Imaging Study of Impinging Underexpanded Jets”, Extended abstract to be submitted to:46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 7-10 January 2008
2-11 kada, H. and Minato, A., the Japan Nuclear Energy Safety (JNES) paper titled “Application of Compressible Two-Fluid Mode Code to Supersonic Two-Phase Jet Flow Analysis”, The 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-13) N13P1368 Kanazawa City, Ishikawa Prefecture, Japan, September 27-October 2, 2009.
2-12 Kitade, K., Nakatogawa, T., Nishikawa, H., Kawanishi, K., and Tsuruto, C., Experimental Study of Pipe Reaction Force and Jet Impingement Load at the Pipe Break, Trans. 5th Int. Conf. on SMiRT, F6/2, 1979.
3-1 N. Rajaratonam, TUBULENT JETS, Elsevier Scientific Publishing Company, Amsterdam,1976
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Appendix 1
Simplified Blast Wave Model
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TABLE OF CONTENTS
LIST OF FIGURES ..................................................................................................... A1-3
1.0 SYMLIFIED BLAST WAVE MODEL.................................................................... A1-4
1.1 THE STEAM BALL ....................................................................................... A1-5
1.2 THE SHOCKED GAS REGION....................................................................... A1-6
1.3 BLAST CONFINED TO UNIFORM AREA PROGRESSION................................... A1-7
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LIST OF FIGURES
FigureA1-1-1 SIMPLIFIED BLAST WAVE MODEL A1-4
FigureA1-1-2 SHOCK CONFINED TO UNIFORM AREA A1-7
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1.0 SYMLI FIED BLAST WAVE MODEL
FigureA1-1-1 Simplified Blast Wave Model
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1.1 The Steam Ball
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1.2 The Shocked Gas Region
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1.3 Blast Confined to Uniform Area Progression
Figure A1-1-2 Shock Confined to Uniform Area
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Appendix 2
Convergence Condition
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TABLE OF CONTENTS LIST OF TABLES ....................................................................................................... A2-3
LIST OF FIGURES ..................................................................................................... A2-4
1.0 ANSYS FLUENT................................................................................................ A2-5
1.1 CONVERGENCE CONDITION ....................................................................... A2-5
1.1.1 Implicit Time Integration................................................................ A2-5
1.1.2 Max Iterations/Time Step.............................................................. A2-5
1.1.3 Judging Convergence................................................................... A2-5
1.2 ALGORITHM................................................................................................ A2-6
1.2.1 The Pressure-Based Coupled Algorithm ...................................... A2-7
1.2.2 QUICK Schem .............................................................................. A2-8
1.2.3 PRESTO! Schem.......................................................................... A2-9
2.0 ANSYS AUTODYN .......................................................................................... A2-10
2.1 INTRODUCTION......................................................................................... A2-10
2.2 MULTI-MATERIAL EULER SOLVER USED IN BLAST WAVE CALUCULATION...... A2-10
2.3 CALUCULATION ALGORITHMS .................................................................... A2-10
2.3.1. Convergence Calculation............................................................ A2-10
2.3.2. Basic Physical Equations of the Euler Code............................... A2-10
2.3.3. Multi-Material Interface Tracking ................................................ A2-13
2.3.4. Pressure Calculation................................................................... A2-13
2.3.5. Computation Cycle of Multi-Material Euler ................................. A2-14
2.4 TIME STEP ............................................................................................... A2-14
3.0 REFERENCES ................................................................................................ A2-16
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LIST OF TABLES
Table A2-2-1 Multi-Material Euler Solver Used in ANSYS AUTODYN A2-10
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LIST OF FIGURES
FigureA2-1-1 Example of Convergence Residual Calculation Results A2-6FigureA2-1-2 Overview of the Pressure-Based Solution Methods A2-7FigureA2-1-3 One-Dimensional Control Volume A2-8FigureA2-2-1 Computation Cycle of Multi-Material Euler A2-14
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1.0 ANSYS FLUENT
1.1 Convergence Condition
1.1.1 Implicit Time Integration
1.1.2 Max Iterations/Time Step
1.1.3 Judging Convergence
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Figure A2-1-1 Example of Convergence Residual Calculation Results
1.2 Algorithm
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1.2.1 The Pressure-Based Coupled Algorithm
Figure A2-1-2 Overview of the Pressure-Based Solution Methods ( The Right Hand Figure is Coupled Solver )
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1.2.2 QUICK Schem
Figure A2-1-3 One-Dimensional Control Volume
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1.2.3 PRESTO! Schem
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2.0 ANSYS AUTODYN
2.1 Introduction
2.2 Multi-Material Euler Solver Used in Blast Wave Caluculation
TabelA2-2-1 Multi-Material Euler Solver Used in ANSYS AUTODYN
2.3 Caluculation Algorithms
2.3.1 Convergence Calculation
2.3.2 Basic Physical Equations of the Euler Code
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2.3.3 Multi-Material Interface Tracking
2.3.4 Pressure Calculation
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2.3.5 Computation Cycle of Multi-Material Euler
FigA2-2-1 Computation Cycle of Multi-Material Euler
2.4 Time Step
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3.0 REFERENCES
1-1 ANSYS, Inc., “ANSYS FLUENT 12.0 Theory Guide”,2009
1-2 ANSYS, Inc., ANSYS FLUENT 12.0 User’s Guide, April 2009 2-1 S. Hancock, “Finite Difference Equations for PISCES-2DELK”, TCAM-76-2, Physics
International, 1976. 2-2 B. Van Leer, “Towards the Ultimate Conservative Difference Scheme.IV. A new Approach
to Numerical Convection”, J. Comp. Phys. 23, pp.276-299, 1977
2-3 B. Van Leer. “Towards the Ultimate Conservative Difference Scheme.V. A second-order sequel to Godunov's method”, J. Comp. Phys. 23, pp.276-299, 1977
2-4 W. F. Noh and P. R. Woodward. “SLIC, Simple Line Interface Calculation”, Proc. of the 5th Int. Symp. on the Numerical Method in Fluind Dynamics, 1976
2-5 O. Yu Vorobiev and I. N. Lomov, "Numerical simulation of gas-solid interfaces with large deformations," Advances in Computational Engineering & Sciences 2000, Vol. 1, pp.922-927, 2000
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Appendix 3
Outline of Blowdown Analysis
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TABLE OF CONTENTS
LIST OF FIGURES .....................................................................................................A3-3
LIST OF TABLES .......................................................................................................A3-4
1.0 OUTLINE OF BLOWDOWN ANALYSIS ........................................................... A3-5
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LIST OF FIGURES Figure A3-1 RHRS Hot Leg Branch Line off RCS(Hot Leg 10-inch Break - B
Loop)
A3-8
Figure A3-2 RHRS Hot Leg Branch Line off RCS(Hot Leg 10-inch Break - A,
C, D Loop)
A3-9
Figure A3-3 RHRS Cold Leg Branch Line off RCS(Cold Leg 8-inch Break - B
Loop)
A3-10
Figure A3-4 RHRS Cold Leg Branch Line off RCS(Cold Leg 8-inch Side
Break - A, C, D Loop)
A3-11
Figure A3-5 Pressurizer Spray Line(Cold Leg 6-inch Break - B Loop)
A3-12
Figure A3-6 Pressurizer Spray Line(Cold Leg 6-inch Break - C Loop)
A3-13
Figure A3-7 Charging Line(Cold Leg 4-inch Break - A Loop) A3-14
Figure A3-8 Letdown Line(Cross Over Leg 3-inch Break
- D Loop)
A3-15
Figure A3-9 Loop Drain/Excess Letdown Line(Cross Over Leg 2-inch Break
- A, C Loop)
A3-16
Figure A3-10 Loop Drain (Cross Over Leg 2-inch Break - B Loop) A3-17
Figure A3-11 Pressurizer Safety Valve Line (Pressurizer 6-inch Break)
A3-18
Figure A3-12 Pressurizer Safety Depressurization Valve Line
(Pressurizer 4-inch Break)
A3-19
Figure A3-13 Pressurizer Safety Depressurization Valve Line
(Pressurizer 8-inch Break)
A3-20
Figure A3-14 Seal Injection Line (RCP 1.5-inch Break) A3-21
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LIST OF TABLES Table A3-1 Blowdown Analysis Results A3-6
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1.0 Outline of Blowdown Analysis
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Table A3-1 Blowdown Analysis Results (1/2)
Figure No.
System Subsystem NominalDiameter(Inches)
Loop Break
Location
Single Phase Steam Start Time(s)/
Pressure(lb/in2)
Single Phase Steam End Time(s)/
Pressure(lb/in2)
A3-1 RCS Residual Heat Removal System (RHRS) Hot Leg
Branch Line off RCS 10 B Hot Leg
A3-2 RCS RHRS Hot Leg
Branch Line off RCS 10 A, C, D Hot Leg
A3-3 RCS RHRS Cold Leg Branch Line
off RCS 8 B Cold Leg
A3-4 RCS
RHRS Cold Leg Branch Line off RCS
8 A, C, D Cold Leg
A3-5 RCS Pressurizer Spray Line 6 B Cold Leg
A3-6 RCS Pressurizer Spray Line 6 C Cold Leg
A3-7 CVS Charging Line 4 A Cold Leg
A3-8 CVS Let Down Line 3 D Crossover Leg
A3-9 RCS Loop Drain/Excess
Letdown Line 2 A, C Crossover Leg
A3-10 RCS Loop Drain 2 B Crossover Leg
A3-11 RCS Pressurizer Safety Valve Line 6 B PZR
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Table A3-1 Blowdown Analysis Results (2/2)
Figure No.
System Subsystem NominalDiameter(Inches)
Loop Break
Location
Single Phase Steam Start Time(s)/
Pressure(lb/in2)
Single Phase Steam End Time(s)/
Pressure(lb/in2)
A3-12 RCS Pressurizer Safety
Depressurization Valve Line4 B PZR
A3-13 RCS Pressurizer Safety
Depressurization Valve Line8 B PZR
A3-14 CVS Seal Injection Line 1.5 B RCP
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Figure A3-1 RHRS Hot Leg Branch Line off RCS (Hot Leg 10-inch Break - B Loop)
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Figure A3-2 RHRS Hot Leg Branch Line off RCS (Hot Leg 10-inch Break - A, C, D Loop)
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Figure A3-3 RHRS Cold Leg Branch Line off RCS (Cold Leg 8-inch Break - B Loop)
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Figure A3-4 RHRS Cold Leg Branch Line off RCS (Cold Leg 8-inch Side Break - A, C, D Loop)
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Figure A3-5 Pressurizer Spray Line (Cold Leg 6-inch Break - B Loop)
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Figure A3-6 Pressurizer Spray Line (Cold Leg 6-inch Break - C Loop)
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Figure A3-7 Charging Line (Cold Leg 4-inch Break - A Loop)
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Figure A3-8 Let down Line (Cross Over Leg 3-inch Break - D Loop)
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Figure A3-9 Loop Drain/Excess Letdown Line (Cross Over Leg 2-inch Break - A, C Loop)
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Figure A3-10 Loop Drain (Cross Over Leg 2-inch Break - B Loop)
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Figure A3-11 Pressurizer Safety Valve Line (Pressurizer 6-inch Break)
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Figure A3-12 Pressurizer Safety Depressurization Valve Line (Pressurizer 4-inch Break)
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Figure A3-13 Pressurizer Safety Depressurization Valve Line (Pressurizer 8-inch Break)
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Figure A3-14 Seal Injection Line (RCP 1.5-inch Break)
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Appendix 4
Simple Beam Methodology in consideration of
Resonating High Frequency Mode
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TABLE OF CONTENTS
LIST OF FIGURES .....................................................................................................A4-3
LIST OF TABLES .......................................................................................................A4-4
1.0 SIMPLE MODE MODEL RESONATING WITH A JET OSCILLATION .............. A4-5
1.1 JET LOAD .................................................................................................... A4-5
1.2 ONE ANTI-NODE SPAN MODEL ................................................................... A4-6
1.3 EFFECTIVE LOAD FOR HIGH FREQUENCY MODE............................................ A4-7
1.4 NUMBER OF ANTI-NODE............................................................................. A4-10
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LIST OF FIGURES Figure A4-1-1 Vibration Mode of a Pipe Resonating with the Jet Oscillation A4-6
Figure A4-1-2 Equivalent Partial Model of a Pipe Subjected to a Dynamic
Distributed Lload that Excites the Vibration Mode
A4-6
Figure A4-1-3 Lumped Mass Vibration System (under loading conditions that
excite vibration modes)
A4-8
Figure A4-1-4 Lumped Mass Vibration System (under actual loading
conditions)
A4-8
Figure A4-1-5 Effective Load in the Resonance Model A4-9
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LIST OF TABLES
Appendix 4 has no tables
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1.0 SIMPL E MODE MODEL RESONATING WITH A JET OSCILLATION
1.1 Jet Load
1)
2)
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1.2 One Anti-Node Span Model
Figure A4-1-1 Vibration Mode of a Pipe Resonating with the Jet Oscillation
Figure A4-1-2 Equivalent Partial Model of a Pipe Subjected to a Dynamic Distributed load that Excites the Vibration Mode
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1.3 Effective Load for High Frequency Mode
6)
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Figure A4-1-3 Lumped Mass Vibration System (under loading conditions that excite vibration modes)
(7)
9)
Figure A4-1-4 Lumped Mass Vibration System (under actual loading conditions)
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Figure A4-1-5 Effective Load in the Resonance Model
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1.4 Number of Anti-Node
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Appendix 5
Frequency of Jet Pressure Oscillation
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TABLE OF CONTENTS
LIST OF FIGURES ..................................................................................................... A5-3
LIST OF TABLES ....................................................................................................... A5-4
1.0 CONSIDERATION FROM KIM’S PAPER .......................................................... A5-5
2.0 CONSIDERATION FROM TAM’S PAPER.......................................................... A5-9
3.0 REFERENCES.................................................................................................. A5-12
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LIST OF FIGURES
Figure A5-1-1 Correlation of the Oscillation Frequency with the First Shock
Cell, Shock Wave Distance and Pipe Diameter
A5-5
Figure A5-1-2 Contour Diagrams Obtained by Free-jet Analysis A5-7
Figure A5-1-3 Results of Oscillation Frequency Calculation (Specific Heat Ratio:
1.3)
A5-8
Figure A5-2-1 Type 1 Bessel Function Graph A5-10
Figure A5-2-2 Velocity Contour from Free-Jet Analysis (Results of Analysis
Under Actual Operating Conditions)
A5-10
Figure A5-2-3 Results of the Calculation of the Oscillation Frequency A5-12
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LIST OF TABLES
Table A5-1-1 Calculation Conditions A5-6
Table A5-2-1 Results of Calculation of Minimum Oscillation Frequency (Jet
Diameter :8D)
A5-11
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A5-5
1.0 CONSIDERA TION FROM KIM’S PAPER
Figure A5-1-1 Correlation of the Oscillation Frequency with the First Shock Cell, Shock Wave Distance and Pipe Diameter
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A5-6
Table A5-1-1 Calculation Conditions
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A5-7
Figure A5-1-2 Contour Diagrams Obtained by Free-Jet Analysis
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A5-8
Figure A5-1-3 Result s of Oscillation Frequency Calculation (Specific Heat Ratio: 1.3)
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A5-9
2.0 Consideration from Tam’s Paper
ω
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A5-10
Figure A5-2-1 Type 1 Bessel Function Graph
Figure A5-2-2 Velocity Contour from Free-Jet Analysis (Results of Analysis Under
Actual Operating Conditions)
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A5-11
Table A5-2-1 Results of Calculation of Minimum Oscillation Frequency (Jet Diameter :8D)
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A5-12
Figure A5-2-3 Result s of the Calculation of the Oscillation Frequency
3.0 REFERENCES
A5-1 Kim, S.I and Park, S.O., “Oscillatory behavior of supersonic impinging jet flows”, 2005
A5-2 Tam,C.K.W and Ahuja,K. K. ,”Theoretical Model of Distance Tone Generation by
Impinging Jets”, 1990
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A6-1
Appendix 6
Example of Structural Analysis
for
Jet Pressure Oscillation
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-2
TABLE OF CONTENTS
LIST OF FIGURES .....................................................................................................A6-3
LIST OF TABLES .......................................................................................................A6-4
1.0 CALUCULATION EXAMPLE OF SIMPLE BEAM (HAND CALCULATION)....... A6-5
1.1 CALCULATION CONDITIONS......................................................................... A6-5
1.2 CALCULATION RESULTS.............................................................................. A6-7
2.0 ANALYSIS EXAMPLE OF 3D BEAM MODEL FOR PIPING SYSTEMS.......... A6-14
2.1 ANALYSIS CONDITIONS............................................................................. A6-14
2.2 ANALYSIS RESULTS .................................................................................. A6-17
3.0 ANALYSIS EXAMPLE OF FEM MODEL FOR JET BARRIER......................... A6-23
3.1 ANALYSIS CONDITIONS............................................................................. A6-23
3.2 ANALYSIS RESULTS .................................................................................. A6-26
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A6-3
LIST OF FIGURES
Figure A6-1-1 Jet Impingement Model Image A6-5
Figure A6-1-2 Jet Load of Calculation Model A6-8
Figure A6-1-3 Calculation of Maximum Moment A6-9
Figure A6-1-4 Calculation Model of Resonance A6-11
Figure A6-2-1
Figure A6-2-2
The Load Time Histories of Pressure Oscillation
Analysis Load Set Image
A6-15
A6-16
Figure A6-2-3 Piping System Model A6-18
Figure A6-2-4 46th Mode Shape A6-19
Figure A6-2-5 (1/3) Moment of X- Direction Time Histories A6-20
Figure A6-2-5 (2/3) Moment of Y - Direction Time Histories A6-21
Figure A6-2-5 (3/3) Moment of Z - Direction Time Histories A6-22
Figure A6-3-1 Simplified Jet barrier model A6-24
Figure A6-3-2 Boundary conditions of the analytical model A6-25
Figure A6-3-3 FE model of Jet barrier A6-26
Figure A6-3-4 1st Mode Shape (overturning of whole body
[240Hz])
A6-27
Figure A6-3-5 2nd Mode Shape (twist of pillar [316Hz]) A6-27
Figure A6-3-6 Transient response maximum stress (Max stress
13.4MPa / Time=0.0216 s)
A6-28
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-4
LIST OF TABLES
Table A6-1-1 Break Piping Specification A6-6
Table A6-1-2 Jet Impinged Piping Specification A6-6
Table A6-1-3 Jet Characteristics A6-6
Table A6-2-1 Impinged Piping Specification A6-14
Table A6-2-2 Jet Characteristics A6-15
Table A6-2-3 Maximum Moment and Stress A6-17
Table A6-3-1 Specification of jet barrier model A6-23
Table A6-3-2 Analytical model input list
A6-25
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-5
1.0 CALCULATION EXAMPLE OF SIMPLE BEAM (HAND CALCULATION)
1.1 Caluculation Conditions
Figure A6-1-1 Jet Impingement Model Image
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A6-6
Table A6-1-1 Break Piping Specification
Table A6-1-2 Jet Impinged Piping Specification
Table A6-1-3 Jet Characteristics
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A6-7
1.2 Calculation Results
1.2.1 Calculation for Pipe Stress from Static Steam Jet Load
)
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-8
Figure A6-1-2 Jet Load of Calculation Model
)
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-9
Figure A6-1-3 Calculation of Maximum Moment
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-10
1.2.2 Calculation for pipe stress from resonance with the piping 1) Amplification factor (Af):
2) Load :
3) Moment (part center of piping):
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-11
4) Stress:
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-12
5) Number of anti-node:
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-13
1.2.3 Pipe Stress by jet pressure oscillation
)
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-14
2.0 ANALYSIS EXAMPLE OF 3D BEAM MODEL FOR PIPING SYSTEMS
2.1 Analysis Conditions
Table A6-2-1 Impinged Piping Specification
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-15
Table A6-2-2 Jet Characteristics
Figure A6-2-1 The Load Time Histories of Pressure Oscillation
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-16
Figure A6-2-2 Analysis Load Set Image
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-17
2.2 Analysis Results
Table A6-2-3 Maximu m Moment and Stress
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-18
Figu
re A
6-2-
3 P
ipin
g Sy
stem
Mod
el
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A6-19
Figu
re A
6-2-
4 4
6th
Mod
e Sh
ape
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-20
Figu
re A
6-2-
5 (1
/3)
Mom
ent o
f X- D
irect
ion
Tim
e H
isto
ries
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-21
Figu
re A
6-2-
5 (2
/3)
Mom
ent o
f Y -
Dire
ctio
n Ti
me
His
torie
s
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-22
Figu
re A
6-2-
5 (3
/3)
Mom
ent o
f Z -
Dire
ctio
n Ti
me
His
torie
s
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-23
3.0 ANALYSIS EXAMPLE OF FEM MODEL FOR JET BARRIER
3.1 Analysis Conditions
Table A6-3-1 Specification of jet barrier model
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-24
Figure A6-3-1 Simplified Jet barrier model
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-25
Figure A6-3-2 Boundary conditions of the analytical model
Table A6-3-2 Analytical model input list
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A6-26
Figure A6-3-3 FE model of Jet barrier
3.2 Analysis Results
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022-NP (R2)
Mitsubishi Heavy Industries, LTD. A6-27
Figure A6-3-4 1 st Mode Shape (overturning of whole body [240Hz])
Figure A6-3-5 2 nd Mode Shape (twist of pillar [316Hz])
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Evaluation on Jet Impingement Issues Associated with Postulated Pipe Rupture MUAP-10022- NP (R2)
Mitsubishi Heavy Industries, LTD. A6-28
Figure A6-3-6 Transient response maximum stress (Max stress 13.4MPa / Time=0.0216 s)