Evaluation of Thin Plate Hydrodynamic Stability through a ...

Experimental Effort
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ANL/RTR/TM-16/9
Nuclear Engineering Division, Argonne National Laboratory
G. Solbrekken, C. Jesse, J. Kennedy, J. Rivers, and G. Schnieders
Nuclear Engineering Program, University of Missouri-Columbia
May 2017
Combined Numerical Modeling and Experimental Effort
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ANL/RTR/TM-16/9
Combined Numerical Modeling and Experimental Effort i
EXECUTIVE SUMMARY
An experimental and computational effort was undertaken in order to evaluate the capability of
the fluid-structure interaction (FSI) simulation tools to describe the deflection of a Missouri
University Research Reactor (MURR) fuel element plate redesigned for conversion to low-
enriched uranium (LEU) fuel due to hydrodynamic forces. Experiments involving both flat plates
and curved plates were conducted in a water flow test loop located at the University of Missouri
(MU), at conditions and geometries that can be related to the MURR LEU fuel element. A wider
channel gap on one side of the test plate, and a narrower on the other represent the differences that
could be encountered in a MURR element due to allowed fabrication variability. The difference in
the channel gaps leads to a pressure differential across the plate, leading to plate deflection. The
induced plate deflection the pressure difference induces in the plate was measured at specified
locations using a laser measurement technique. High fidelity 3-D simulations of the experiments
were performed at MU using the computational fluid dynamics code STAR-CCM+ coupled with
the structural mechanics code ABAQUS. Independent simulations of the experiments were
performed at Argonne National Laboratory (ANL) using the STAR-CCM+ code and its built-in
structural mechanics solver. The simulation results obtained at MU and ANL were compared with
the corresponding measured plate deflections.
The initial 40 mil thick flat aluminum plate experiments and simulations provided valuable
information about the capabilities of the computational tools and the importance of accurately
describing the experimental geometry. A set of experiments were performed with average coolant
velocities ranging from 2.07 m/s to 7.78 m/s with offset channel gaps. The plate deflection was
measured at multiple locations during each experiment. When the geometry of the computational
models reflected the actual geometry of the test section, based on measurements of the channel
thickness at multiple locations, both the MU and ANL FSI simulations were shown to predict
reasonably well the deflection of the flat plate. Higher flow rates near 8 m/s proved more
challenging to model due to sensitivities to deviations from perfectly flat shapes. That is not
unexpected, since reactors curve plates ordinarily for the reason of increasing plate stability.
The MURR fuel element is comprised of curved plates, and so while the more simply fabricated
flat-plate experiments were being performed, curved-plate experiments were being fabricated.
Those experiments were developed to measure the deflection of a curved aluminum plate, with a
shape similar to, but much thinner than the widest LEU plate which is 44 mil (1.12 mm) thick.
Since curved plates have a substantially increased resistance to deflection due to the effect of the
shape on rigidity, a thinner plate was tested in order to obtain measurable deflections that could be
used to compare to simulation results. Based on initial simulations and the experimentally
achievable fluid flow velocities a plate with the thickness 15.9 mil was selected. The plate
separates two curved hydrodynamic channels that are offset so that the thicker channel is ordinarily
on the inside of the channel. With the offset, the larger channel gap averages up to about 2.5 times
the size of the thinner channel.
Experiments with average fluid velocities ranging between 2.2–4.3 m/s were performed and the
maximum deflection of the curved plate (which occurs at the inlet edge) was measured using a
laser displacement sensor. The measured plate deflection increases with the increased fluid
ANL/RTR/TM-16/9
Combined Numerical Modeling and Experimental Effort ii
velocity as expected and the maximum deflection for multiple experiments performed with an
average flow velocity near 4.3 m/s was found to range between 5.5–7.0 mil.
Due to the apparatus the plate deflection could only be measured along an azimuthally-centered
line. Therefore simulations of the curved-plate experiments were performed with two models: a
model that assumes that the channels are azimuthally uniform and a model that assumes
azimuthally varying channels. The results obtained with the azimuthally uniform model agree well
with the measured results. The azimuthally uniform model predicts a deflection of 5.6 mil for the
average coolant velocity of 4.25 m/s, which under-estimated by 8% the 6.06 mil fit of the measured
deflections at this fluid velocity. The results obtained with the azimuthally varying model provide
a measure of the sensitivity of the deflection results to the geometry of the curved plate. The
azimuthally varying model over-estimates the measured plate deflection at the leading edge by
approximately 80% for an average coolant velocity of 4.0 m/s. The measured values, even at their
upper 95% confidence limit of the best fit, remain bounded by the azimuthally non-uniform model.
Based on the modeling of experiments there are certain points to consider relative to the expected
stability of a prototypic LEU MURR fuel plate. The comparison of FSI simulation results with the
measured experimental plate deflections shows that when the plate and channel geometry are
accurately modeled, FSI simulations can reasonably predict the magnitude of the curved plate
deflections. The more straightforward azimuthally uniform model estimated the experimental
deflection within 8% (under-estimated). When significant channel geometry variations were
assumed (azimuthally varying model), the maximum modeled plate deflection was about 80%
larger than the measured deflection. The actual MURR plates the channel is fabricated to specified
dimensional tolerances even smaller than those of these experimental channels. Therefore, based
on the azimuthally uniform case, the FSI deflection predictions for the actual MURR plates are
expected to be estimated within approximately 10-20% of the actual deflection.
Simulations specifically representative of the LEU fuel element design were also performed. For
these much thicker plates which are 44-mil thick (42-mil minimum thickness), at 8.7 m/s, the
maximum calculated plate deflection, which is located at the center of the leading edge, is
0.167 mil. Using the 10-20% uncertainty estimated above leads to a maximum expected deflection
of 0.20 mil or less. The plate deflection is much less than this leading edge value over almost all
of the plate area. This maximum predicted deflection is extremely small compared to a
manufacturing channel gap thickness of 93 mil and tolerance of ±8 mil. It is also significant that
the plate deflection is towards the larger channel, which tends to enlarge the thickness of the
smaller channel. Based on these observations, and noting that the real fuel element includes a comb
at the entrance and exit, the effect of plate deflection due to FSI on the MURR LEU fuel element
thermal-hydraulic and structural performance under expected conditions is insignificant.
ANL/RTR/TM-16/9
Combined Numerical Modeling and Experimental Effort iii
TABLE OF CONTENTS
Executive Summary ......................................................................................................................... i
1.3 Reactor Core Design ........................................................................................................ 2
1.4 Fuel Plate Design ............................................................................................................. 4
1.5 Building the Fluid-Structure-Interaction (FSI) Safety Case ............................................ 6
1.6 Coupling Methodologies for Solving FSI Problems ........................................................ 7
1.6.1 Methodologies for FSI Analysis ............................................................................... 7
1.6.2 Governing Equations for the Fluid and Structural Domains .................................. 10
2. Flat Plate Experiments and Simulation Effort ...................................................................... 13
2.1 Flat Plate Experiments ................................................................................................... 13
2.1.1 Experiment Apparatus ............................................................................................ 13
2.1.2 Channel Mapping .................................................................................................... 18
2.1.3 Free-Edge Flow Testing .......................................................................................... 21
2.1.4 Pinned-Edge Flow Testing ...................................................................................... 22
2.1.5 Experiment Discussion and Conclusions ................................................................ 26
2.2 Flat Plate Simulations..................................................................................................... 26
2.2.1.1 Free Edge Simulations ..................................................................................... 27
2.2.1.2 Pinned/Combed Edge Simulations .................................................................. 28
2.2.2 As-Built Geometry Single Plate Simulations at MU .............................................. 34
2.2.3 Ideal and As-Built Single Plate Simulations at ANL .............................................. 42
2.2.4 Discussion of Simulation Results ........................................................................... 53
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Combined Numerical Modeling and Experimental Effort iv
3. Curved-Plate Experiments and Simulation Effort ................................................................ 55
3.1 Curved-Plate Experimental Work .................................................................................. 55
3.1.1 Preparation of the Experimental Test Section ........................................................ 55
3.1.2 Installation of the Curved Plate Test Section in the Flow Loop ............................. 61
3.1.2.1 Calibration of the Flow Meter ......................................................................... 62
3.1.2.1.1 Procedure ...................................................................................................... 62
3.1.2.1.2 Results .......................................................................................................... 62
3.1.2.2.1 General Procedure ........................................................................................ 63
3.1.2.2.3 Channel Gap Measurement along the Plate without Flow ........................... 66
3.1.2.2.4 Measurement of Plate Deflection at the Leading Edge with Flow ............... 68
3.2 Curve Plate Simulation Results ...................................................................................... 73
3.2.1 Ideal and As-Built Plate Simulations at MU........................................................... 73
3.2.1.1 Ideal Curved Plate Results ............................................................................... 74
3.2.1.1.1 Case 1 Results ............................................................................................... 74
3.2.1.1.2 Case 2 Results ............................................................................................... 77
3.2.1.2 As-Built Curved Plate Results ......................................................................... 80
3.2.1.2.1 Ideal Dimensions .......................................................................................... 80
3.2.2 Ideal and As-Built Plate Simulations at ANL ......................................................... 92
3.2.2.1 Ideal Single Plate Simulations at ANL ............................................................ 92
3.2.2.1.1 Ideal 26-Mil Plate ......................................................................................... 92
3.2.2.1.2 Ideal 15.9-Mil Plate ...................................................................................... 99
3.2.2.2 As-Built Simulations at ANL ........................................................................ 104
3.2.2.2.1 As-Built Total Channel Simulations ........................................................... 104
3.2.2.2.2 As-Built Azimuthally-Uniform Simulations .............................................. 107
3.2.2.2.3 As-Built Azimuthally-Non-Uniform Simulations ...................................... 113
3.2.3 Comparison of Simulation Results Obtained at MU and ANL ............................ 116
3.3 Comparison of Simulation Results with Experiment Measurements........................... 118
4. Analysis of a Prototypic MURR Plate ................................................................................ 120
4.1 Plate and Channel Geometry ........................................................................................ 120
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Combined Numerical Modeling and Experimental Effort v
4.2 Channel Velocity .......................................................................................................... 121
4.3 FSI Analysis ................................................................................................................. 121
5. Conclusions - Implications of Plate Stability Results for the MURR Safety Analysis ...... 124
Acknowledgements ..................................................................................................................... 126
References ................................................................................................................................... 127
ANL/RTR/TM-16/9
Combined Numerical Modeling and Experimental Effort vi
LIST OF FIGURES
Figure 1.1. Top View of MURR Core. ........................................................................................... 3 Figure 1.2. MURR Fuel Element. ................................................................................................... 4 Figure 1.3. MURR Fuel Element End Cap and Plates. ................................................................... 4 Figure 1.4. Cross Section Schematic of U-Al Dispersion Fuel Plate before Forming and Swaging
into a Fuel Element. ...................................................................................................... 5 Figure 1.5. Cross Section Schematic of LEU Fuel Plate before Forming and Swaging into a Fuel
Element. ........................................................................................................................ 5 Figure 1.6. Explicit and Implicit FSI Coupling Schemes. .............................................................. 8 Figure 1.7. Initial Stage of the FSI Problem and an Intermediate Stage with Mesh Morphing. .. 10
Figure 2.1. University of Missouri Hydro-Mechanical Flow Loop (HMFL). .............................. 14 Figure 2.2. Test Section Vertical Cross-Section (Not to Scale) and Front View. ........................ 15
Figure 2.3. Test Section Horizontal Cross-Section (to Scale). ..................................................... 15 Figure 2.4. Laser Channel Thickness Measurement During Mapping (Left) & During Flow
Testing (Right). ........................................................................................................... 17 Figure 2.5. Schematic Illustrating Difference between Ideal and Actual Channel Gaps. ............ 19
Figure 2.6. Color Map Showing Contour of Channel Gap Thickness. ......................................... 20 Figure 2.7. Constructed Plate Profiles from Flow Experiments. .................................................. 21 Figure 2.8. Free-Edge Centerline Plate Deflection into Larger Channel at Locations A-G. ........ 22
Figure 2.9. Free-Edge Experiment Pressure Results. ................................................................... 23 Figure 2.10. Pinned-Edge Centerline Plate Deflection into Larger Channel at Locations A-G. .. 24
Figure 2.11. Pinned-Edge Experiment Pressure Results. ............................................................. 25 Figure 2.12. FSI Geometry: Plate (Green Mesh); Background Fluid (Blue Mesh); Overset Fluid
(Red Mesh).................................................................................................................. 27
Figure 2.13. 3.43 kg/s Abaqus Deflection Profile (m) .................................................................. 29
Figure 2.14. Deflection Profiles for Ideal Geometry FSI Simulations. ........................................ 30 Figure 2.15. Channel Pressure Difference (Psmall channel – Plarge channel) Across Plate Data at 3.43
kg/s Flow. .................................................................................................................... 30
Figure 2.16. Pressure Difference (Psmall channel – Plarge channel) Across Plate for Ideal Geometry
Simulations. ................................................................................................................ 31
Figure 2.17. MURR Fuel Element Comb. .................................................................................... 31 Figure 2.18. Simulating the Test Section “Comb” in Abaqus. ..................................................... 32 Figure 2.19. Pinned vs. Combed Deflection Contours (m) .......................................................... 33 Figure 2.20. Pinned and Combed Deflection Profiles. ................................................................. 33
Figure 2.21. Deflection Profiles for As-Built Geometry FSI Simulations. .................................. 35 Figure 2.22. Axial Pressure Difference (Psmall channel – Plarge channel) Profiles for As-Built FSI
Simulations. ................................................................................................................ 36
Figure 2.23. 2.07 m/s Experiment and FSI Calculated Plate Deflection into Larger Channel
Comparison Along Plate Axial Direction. .................................................................. 36 Figure 2.24. 2.78 m/s Experiment and FSI Calculated Plate Deflection into Larger Channel
Comparison Along Plate Axial Direction. .................................................................. 37
Figure 2.25. 3.46 /s Experiment and FSI Calculated Plate Deflection into Larger Channel
Comparison Along Plate Axial Direction. .................................................................. 37 Figure 2.26. 4.57 m/s Experiment and FSI Calculated Plate Deflection into Larger Channel
Comparison Along Plate Axial Direction. .................................................................. 38
ANL/RTR/TM-16/9
Combined Numerical Modeling and Experimental Effort vii
Figure 2.27. 5.17 m/s Experiment and FSI Calculated Plate Deflection into Larger Channel
Comparison Along Plate Axial Direction. .................................................................. 38 Figure 2.28. 2.07 m/s Experiment and FSI Calculated Pressure Difference. ............................... 40 Figure 2.29 2.78 m/s Experiment and FSI Calculated Pressure Difference (Psmall channel – Plarge
channel) Profiles Along Plate Axial Direction. .............................................................. 40 Figure 2.30. 3.46 m/s Experiment and FSI Calculated Pressure Difference (Psmall channel – Plarge
channel) Profiles Along Plate Axial Direction. .............................................................. 41 Figure 2.31. 4.57 m/s Experiment and FSI Calculated Pressure Difference (Psmall channel – Plarge
channel) Profiles Along Plate Axial Direction. .............................................................. 41
Figure 2.32. 5.17 m/s Experiment and FSI Calculated Pressure Difference (Psmall channel – Plarge
channel) Profiles Along Plate Axial Direction. .............................................................. 42 Figure 2.33. Sketch of the Test Section. ....................................................................................... 43 Figure 2.34 Mesh Sketch (Element Size Along Thickness Direction: 0.2mm) ............................ 45
Figure 2.35 Mesh Sensitivity Study Based on the Aspect Ratio of the Plate (Left) Mesh
Sensitivity Study on Turbulent Models (Right) .......................................................... 45
Figure 2.36. Convergence of the Displacement Monitor in Explicitly Coupled Simulation for
Flow Velocity of V=2m/s. .......................................................................................... 46
Figure 2.37. Convergence of the Displacement Monitor in Implicitly Coupled Simulation for
Flow Velocity of V=2m/s. .......................................................................................... 47 Figure 2.38. Comparison of the Plate Deflection Within Explicit and Implicit Coupling Methods.
..................................................................................................................................... 47 Figure 2.39. Deformation of the Flat 40-Mil-Thick Perfect Plate in the 8 m/s Flow Based on
STAR-CCM+ Analysis. (Note: The figure is not to scale.) ........................................ 48 Figure 2.40.Deflection of the Middle of the Plate in the Simulations of 40-Mil-Thick Plate and 8
m/s Average Channel Flow Velocity with the Use of STAR-CCM+ Finite Volume
Solver and Co-Simulation Approach with ABAQUS. ............................................... 49
Figure 2.41. Simulated Location of the Outer Face in the 100-Mil Channel at 0 m/s velocity. ... 50 Figure 2.42. Simulated Location of the Outer Face in the 80-Mil Channel at 0 m/s velocity. ..... 50 Figure 2.43. Application of the Directed Mesher in STAR-CCM+ to Create a Mesh of the
Computational Domain. .............................................................................................. 50 Figure 2.44. Deflection of the Middle of the Plate in the As-Built Simulations of 40-Mil-Thick
Plate and 2.78 m/s Average Channel Flow Velocity as Compared to the Experimental
Data. ............................................................................................................................ 51
Figure 2.45. Deflection of the Middle of the Plate in the As-Built Simulations of 40-Mil-Thick
plate and 3.46 m/s Average Channel Flow Velocity as Compared to the Experimental
Data. ............................................................................................................................ 52 Figure 2.46. Deflection of the Middle of the Plate in the As-Built Simulations of 40-Mil-Thick
Data. ............................................................................................................................ 52 Figure 2.47. Deflection of the Middle of the Plate in the As-Built Simulations of 40-Mil-Thick
Data. ............................................................................................................................ 53 Figure 3.1. Entire Curved Plate Test Section in Test Loop. ......................................................... 56 Figure 3.2. Inner Cylinder and Curved Plate Assembly. .............................................................. 57 Figure 3.3. Bottom View of Curved Plate Test Section. .............................................................. 58 Figure 3.4. Curved Plate Assembly in Measurement and Assembly Jig. ..................................... 59
ANL/RTR/TM-16/9
Combined Numerical Modeling and Experimental Effort viii
Figure 3.5. Drawing of Curved-Plate Measurement and Assembly Jig. ...................................... 60
Figure 3.6. End View of Test Section with the Short Curved Aluminum Spacer Wedge in the
Coolant Channel between the Side Rails. ................................................................... 60 Figure 3.7. Framework for the Flow Loop Adjusted for the Curved Test Section. ...................... 61
Figure 3.8. Calibration of the MPS4218-500 Scale. ..................................................................... 62 Figure 3.9. Paddlewheel Flow Meter Calibration (Omega FP-7001A). ....................................... 63 Figure 3.10. Laser Measurement Setup Without Water in the Test Section. ................................ 64 Figure 3.11. Laser Measurement Setup with Water in the Test Section. ...................................... 64 Figure 3.12. Sketch Illustrating Parameters Used in the Calculation of Channel Gap Based on
Laser Measurements. .................................................................................................. 65 Figure 3.13. Outer Channel Gap Measurements Through Pressure Ports. (The outer cylinder is
assumed to have a 250-mil thickness.) ....................................................................... 67 Figure 3.14. Outer Channel Gap Mapping.................................................................................... 67
Figure 3.15. Cross Sectional Diagram of Curved Test Section Showing Deflection Sign. .......... 70 Figure 3.16. Channel Gap Measurements at Leading Edge – With Error Bars. ........................... 72
Figure 3.17. Channel Deflection Measurements at Leading Edge – With Error Bars.................. 72 Figure 3.18. Top View of the MURR Core with Photo of a Mock Fuel Element [15]. ............... 73
Figure 3.19. Top View of the Curved Plate FSI Model Geometry (Flow is into the page.). ........ 74 Figure 3.20. Two Distinct Cases for Curved Plate Modeling. ...................................................... 74 Figure 3.21. Case 1 Maximum Deflection vs. Average Channel Velocity. .................................. 75
Figure 3.22. Abaqus Contour Plots of Radial Deflection (m) at 25 and 40 m/s with a 0.66 mm
Plate............................................................................................................................. 76
Figure 3.23. Deflection at 25 to 40 m/s Flow Velocity with a 0.66 mm (26 mil) Plate. .............. 76 Figure 3.24. Case 2 Maximum Deflection Results vs. Average Channel Velocity. ..................... 77 Figure 3.25. Beyond-Prototypic Velocity Investigation of Deflection (m) with a 0.66 mm Thick
Plate............................................................................................................................. 78
Angles into the 2.54 mm Channel............................................................................... 79 Figure 3.27. Beyond-Prototypic Velocity Investigation of Deflection (m) into the 2.54 mm
Channel at 30 m/s........................................................................................................ 79 Figure 3.28. Deflection into the Larger Channel with Various Channel Offsets and 16 mil or 40
mil thick plates at 9 m/s. ............................................................................................. 80 Figure 3.29. Cross-Sectional View of the Curved Plate Model for a 15.9-Mil-Thick Plate with an
Outer Fluid Channel of 78 Mil and an Inner Fluid Channel of 130 Mil. .................... 81 Figure 3.30. Maximum Deflection Results for a Curved Plate with Uniform Fluid Channels with
an Outer Channel of 78 Mil and an Inner Channel of 130 Mil. .................................. 82 Figure 3.31. AB1 Model with Morphed Plate and Inner Cylinder Wall Dictated by Depth
Micrometer Measurements Taken at MU and Horizontal Leading and Trailing Edges.
..................................................................................................................................... 83 Figure 3.32. AB2 Model with Morphed Plate with Linearly Extrapolated Leading and Trailing
Edges and Inner Cylinder Wall Dictated by Depth Micrometer Measurements Taken
at MU. ......................................................................................................................... 84 Figure 3.33. AB3 Model with Morphed Plate with Linearly Extrapolated Leading and Trailing
Edges with Angled Leading Edge Face and Inner Cylinder Wall Dictated by Depth
Micrometer Measurements. ........................................................................................ 84
Combined Numerical Modeling and Experimental Effort ix
Figure 3.34. Fluid and Plate Model with Approximate Location of Pressure Taps Shown (Left)
and Azimuthal Dimensions of the Fluid Channel in the Middle of and on the Edges of
the Test Section for Uniform Azimuthal Profile. ........................................................ 86 Figure 3.35. Fluid and Plate Model with Approximate Location of Pressure Taps Shown (Left)
and Azimuthal Dimensions of the Fluid Channel in the Middle of and on the Edges of
the Test Section for Variable Azimuthal Profile......................................................... 87 Figure 3.36. Maximum Deflection Results for AB1 Plate Geometry (Figure 3.31) with
Azimuthally Uniform Channels (Solid Orange Line) and with Azimuthally Variable
Channels ((Gray Dashed Line). .................................................................................. 87
Figure 3.37. Example of Distribution of Deflection (m) on the Plate for the FSI Simulations for
AB1. ............................................................................................................................ 88 Figure 3.38. Excessive Deflection (m) into the Larger, Inner Channel for Average Velocity
Beyond 4 m/s. ............................................................................................................. 89
Figure 3.39. Maximum Deflection Results for AB2 with Uniform and Non-Uniform Azimuthal
Variation. .................................................................................................................... 90
Figure 3.40. Maximum Deflection Results for AB3 with Uniform and Non-Uniform Azimuthal
Variation. .................................................................................................................... 90
Figure 3.41. Comparison Between Modeling and Averaged Experimental FSI Results. ............. 91 Figure 3.42. Schematic of Curved 26-Mil-Thick Plate Model Geometry. ................................... 92 Figure 3.43. Face Mesh used in the Directed Mesher in Star-CCM+ to Create a Mesh of the
Computational Domain. .............................................................................................. 93 Figure 3.44. Comparison of Meshes with (Top) Constant and (Bottom) Variable Mesh Size
Around the Tip of the Plate. ........................................................................................ 93 Figure 3.45. Deflection of the Middle of the Plate in the Simulations of the 26-Mil-Thick Curved
Plate and 8m/s Average Channel Flow Velocity. ....................................................... 95
Figure 3.46. Deflection of the Middle of the Plate in the Simulations of the 26-Mil-Thick Curved
Plate and 8 m/s Average Channel Flow Velocity (Zoomed-In View). ....................... 95 Figure 3.47. Deflection of the Middle of the Plate in the Simulations of the 26-Mil-Thick Curved
Plate at Various Flow Velocities................................................................................. 96
Figure 3.48. Deflection of the Plate’s Leading Edge Tip in the Simulations of the 26-Mil-Thick
Curved Plate at Various Flow Velocities. ................................................................... 96
Figure 3.49. Deflection on the 26-Mil-Thick Plate in the Simulation with 9 m/s Average Flow
Velocity. ...................................................................................................................... 97
Figure 3.50. Schematic of Experimental Setup for the 15.9-Mil-Thick Plate. ............................. 99 Figure 3.51. Convergence of Solution in Time for Different Plate Thicknesses and Shapes. .... 100 Figure 3.52. Deflection of the Centerline of the 15.9-Mil-Thick Curved Plate for Different Flow
Velocities. ................................................................................................................. 101 Figure 3.53. Deflection of the Plate’s Leading Edge Tip in the Simulations of 15.9-Mil-Thick
Curved Plate at Various Flow Velocities. ................................................................. 102 Figure 3.54. Deflection on the 15.9-Mil-Thick Plate in the Simulation with 9 m/s Average Flow
Velocity. .................................................................................................................... 103 Figure 3.55. Convergence History of Average Pressure on the Plate. ........................................ 104 Figure 3.56. Convergence History of Average Pressure on the Plate Within Several Time Steps.
................................................................................................................................... 104 Figure 3.57. Deflection of the Centerline of the 15.9-Mil-Thick Curved Plate for Different Flow
Velocities with the Use of the Finite Volume Solver in STAR-CCM+. .................. 106
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Figure 3.58. Deflection of the Centerline of the 15.9-Mil-Thick Curved Plate for Different Flow
Velocities with the Use of the Finite Element Solver in STAR-CCM+. .................. 106 Figure 3.59. Deflection of the Tip of the Plate Computed with the Use of FV, FE, and Co-
Simulation Techniques.............................................................................................. 107
Figure 3.60. Comparison of Channel Gap Thicknesses Measured. ............................................ 108 Figure 3.61. Cross Section Through the CFD Model with Imperfections Applied to the Shape of
the Plate. .................................................................................................................... 108 Figure 3.62. Cross Section Through the CFD Model with Imperfections Applied to the Shape of
the Outer Walls. ........................................................................................................ 108
Figure 3.63. Cross Section Through the CFD Model with Imperfections Applied to the Shape of
the Plate with Sloped Leading and Trailing Edges. .................................................. 109 Figure 3.64. Deflection on the 15.9-Mil-Thick, As-Built Plate in the Simulation with 4.25 m/s
Average Flow Velocity. ............................................................................................ 110
Figure 3.65. Deflection of the Centerline of 15.9-Mil-Thick Curved Plate for Different Flow
Velocities when the Imperfections are Applied to the Initial Shape of the Plate. .... 111
Figure 3.66. Deflection of the Centerline of 15.9-Mil-Thick Curved Plate for Different Flow
Velocities when the Imperfections are Applied to the Initial Shape of the Outer Walls.
................................................................................................................................... 111 Figure 3.67. Comparison of Maximum Deflection of the Plate for As-Built Cases. .................. 112 Figure 3.68. Comparison of Maximum Deflection of the Plate for As-Built Cases Obtained with
Various Solvers. ........................................................................................................ 113 Figure 3.69. Axial Cross Sections of the Azimuthally Non-Uniform Plate with Sloped Edges. 114
Figure 3.70. Azimuthal Cross Sections of the Azimuthally Non-Uniform Plate with Sloped
Edges. ........................................................................................................................ 115 Figure 3.71. Comparison of Maximum Deflection of the Plate for As-Built Cases with
Azimuthally Uniform and Non-Uniform Cross Sections. ........................................ 116
Figure 3.72: Comparison of Maximum Deflection of the Plate for As-Built Cases Obtained at
ANL and MU ............................................................................................................ 117 Figure 3.73. Measured Deflection Data. ..................................................................................... 118
Figure 3.74: Comparison of Maximum Deflection of the Plate for As-Built Cases Obtained with
Different Solvers with the Experimental Results...................................................... 119
Figure 4.1. Maximum Deflection of the Prototypic Plate at Several Average Flow Velocities. 122 Figure 4.2. Deflection of the Middle of the Plate in the Simulations of Prototypic Plate 22. .... 123
Figure A.1. Side View of Laser Displacement Positioning for Plate Mode Change Experiments.
................................................................................................................................... 131 Figure A.2. Representative Channel Gap Measurements for Upscale Flow Velocity Sweep and
First Experiment........................................................................................................ 131 Figure A.3. Representative Fixed Channel Gap Measurements for Downscale Flow Velocity
Sweep and First Experiment. .................................................................................... 132 Figure A.4. Representative Fixed Channel Gap Measurements for Upscale Flow Velocity Sweep
After At Least One Previous Experiment. ................................................................ 133 Figure A.5. Representative Fixed Channel Gap Measurements for Downscale Flow Velocity
Sweep After At Least One Previous Experiment. .................................................... 133
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LIST OF TABLES
Table 1.1. Software Versions Used in the Analysis of MURR Plates. ......................................... 10 Table 2.1. Laser Channel Gap Measurement Location Relative to Plate Trailing Edge. ............. 16 Table 2.2. Pressure Measurement Location Relative to Plate Trailing Edge. .............................. 16
Table 2.3. Channel Thickness Summary Data. ............................................................................. 19 Table 2.4. Ideal Geometry FSI Parameters. .................................................................................. 28 Table 2.5. As-Built Geometry FSI Parameters. ............................................................................ 34 Table 2.6. Geometry Parameters of the Model. ............................................................................ 43 Table 2.7. Computational Cost Analysis for the Simulation with the Flat 40-Mil-Thick Plate. .. 46
Table 3.1. Channel Gap Thickness Measurements Taken through Outer Cylinder Pressure Tap
Locations. .................................................................................................................... 82 Table 3.2. Geometric Parameters of the Model for 26-Mil-Thick Curved Plate. ......................... 92
Table 3.3. Comparison of Performance of the Models with Different Meshes. ........................... 94 Table 3.4. Comparison of Performance of the Models with Different Meshes. ........................... 98 Table 3.5. Comparison of Performance of the Models with Different Numbers of Cells Through
the Thickness of the Domain. ..................................................................................... 98 Table 3.6. Comparison of Performance of the Models with Different Numbers of Cells Along the
Length of the Domain. ................................................................................................ 99
Table 3.7. Geometric Parameters of the Model for 15.9-Mil-Thick Curved Plate. ...................... 99 Table 3.8. Comparison of Performance of the Models with Different Numbers of Cells Through
the Thickness of the Domain. ................................................................................... 102 Table 3.9. Geometric Parameters of the Model for Updated 15.9-Mil-Thick Curved Plate. ..... 105 Table 3.10. Measurements of Outer Channel Gap Thickness in the Test Section...................... 107
Table 4.1. Geometrical Details Used for Modeling the Prototypic Plate. .................................. 121 Table 4.2. Maximum Deflection of the Prototypic Plate for Several Average Channel Flow
Velocities. ................................................................................................................. 122
Combined Numerical Modeling and Experimental Effort 1
1. INTRODUCTION
As an introduction to the content of this report, Chapter 1 provides background on the MURR
reactor and conversion as well as the safety and analysis methods. Chapter 2 describes the joint
University of Missouri and ANL flat-plate experimental and analytical effort. Similarly, Chapter
3 describes the MU/ANL curved-plate effort. Chapter 4 provides the implications of the curved
plate stability results for the MURR LEU fuel element safety case. Chapter 5 provides conclusions.
1.1 General Background
There are five U.S. high-power research and test reactors: Massachusetts Institute of Technology
Reactor (MITR), National Bureau of Standards Reactor (NBSR), University of Missouri Research
Reactor (MURR), Advanced Test Reactor (ATR), and High Flus Isotope Reactor (HFIR). Three
of these five reactors are regulated by the U.S. Nuclear Regulatory Commission (NRC) while the
other two are regulated by the U.S. Department of Energy (DOE). The University of Missouri
Research Reactor (MURR) is one of the three reactors that are regulated by NRC. The NRC
regulates 31 operating research and test reactors. These nuclear reactors are non-power reactors
i.e. they do not produce electricity. They are used primarily for research, training, and
development. They contribute to almost every field of science. [1]
All five of the U.S. high-power research and test reactors currently use highly-enriched uranium
(HEU). The primary objective of the Office of Material Management and Minimization (M3) is to
minimize, and when possible eliminate, weapons-usable nuclear materials around the world. M3
is part of the National Nuclear Security Administration (NNSA), which is within the U.S. DOE.
M3 was created to include elements of the former Global Threat Reduction Initiative (GTRI)
program. M3 accomplishes its primary objective via three subprograms – Conversion, Nuclear
Materials Removal, and Materials Disposition. A function of the Conversion subprogram is to
reduce the civilian use and demand for weapon-grade nuclear materials. [2, 3] The U.S. High
Performance Research Reactor (USHPRR) Conversion Program, as part of M3, supports the
conversion of nuclear research and test reactors from the use of highly-enriched uranium (HEU)
to low-enriched uranium (LEU).
M3 is leading the effort to convert the five U.S. high-power research and test reactors so that they
can use the LEU fuel that is currently under development. All five reactors (MITR, NBSR, MURR,
ATR, and HFIR) use flat, curved, or involute HEU fuel plates. Although the fuel plates for each
reactor are of a unique design, all use uranium fuel in an aluminum matrix and are clad in
aluminum alloy 6061. Similarly, the proposed LEU replacement fuel plates are flat, annular
curved, or involute plates, as required by each reactor. The proposed design is an alloy fuel foil
clad in aluminum alloy 6061. The alloy under qualification is uranium with 10% molybdenum (U-
10Mo) with a thin interlayer of zirconium to limit reactions between the U-10Mo and the
aluminum.
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1.2 University of Missouri Research Reactor (MURR) Background
It is important to assemble the analytical and experimental data and supporting analysis to show
that the proposed University of Missouri Research Reactor (MURR) LEU fuel elements can safely
withstand the hydrodynamic forces that are anticipated to be applied to them in the reactor during
operation. The concern here is the fluid-structural interaction (FSI) in which the forces of the
coolant flowing in the channels between the LEU fuel plates may cause fuel plates to deflect and
reduce the flow in one or more channels, which, in turn, could lead to fuel overheating and possible
failure. To a lesser degree, plate vibration and exceeding the Miller critical velocity could also be
of concern. [4] The safety case that is being developed will become part of the Preliminary Safety
Analysis Report (PSAR) for the conversion of the MURR from the use of HEU fuel to LEU fuel.
This PSAR report should eventually lead to the final Safety Analysis Report (SAR) for conversion
after fabrication and qualification of LEU elements for use in MURR
The MURR achieved its first critical state in 1966 and was initially licensed at 5 MW. In 1974 it
was uprated and licensed for operation at 10 MW. At that time the licensing report was called a
Hazards Summary Report. In 2006 the University of Missouri (MU) submitted a Safety Analysis
Report (SAR) to the U.S. Nuclear Regulatory Commission (NRC). [5] The statement that this
report describes about fuel element structural integrity is on page 4-8 and is:
The fuel plates are supported along their vertical edge by slotted aluminum side
plates. The fuel plates are permanently fastened into the side plates using a
mechanical binding procedure that provides a tensile strength of greater than 150
pounds per linear inch of the side plate joint. This ensures a rigid assembly fully
capable of withstanding the hydraulic forces imposed by the primary coolant design
velocity of 23 ft/sec (7.01 m/sec). In fact, fuel assemblies of similar construction
have withstood severe hydraulic tests at flow velocities up to 50 feet/sec (15.24
m/sec) without distortion, thus indicating an adequate design margin in this regard.
The side plates are 31.75 inches (80.65 cm) long by 3.16 inches (8.03 cm) wide and
0.15 inches (3.81 mm) thick.
The fuel assemblies of similar construction that are identified in the above quote are for the
Advanced Test Reactor (ATR). The fuel elements of this reactor are of similar design to those of
the MURR with the most notable difference being that the ATR fuel meat is 48 inches long, which
is twice that of the MURR.
1.3 Reactor Core Design
MURR continues to operate weekly operating cycles at supporting a wide range of research in life
and materials sciences research, and radiopharmaceutical production. In addition to being the
United States’ most powerful university research reactor, MURR has a proven record as one of the
most reliable and capable nuclear research facilities in the world [6]. Like most other research and
test reactors constructed during the same time period, MURR utilizes highly enriched uranium
(HEU) fuel. Over recent decades, significant progress has been made in converting these reactors
to a proliferation resistant low enriched uranium (LEU) fuel. Due to its unique requirements,
MURR is one of the few remaining reactors in the United States yet to be converted.
ANL/RTR/TM-16/9
Figure 1.1 shows the MURR core, which consists of 8 concentric fuel elements placed between an
inner and an outer pressure vessel. The pressure vessels direct and contain high-velocity water
coolant flow, which maintains the fuel plates at safe temperatures while moderating fast neutrons.
The core itself is quite compact, with the outer pressure vessel diameter measuring 29.97 cm (11.80
inches). The inner pressure vessel diameter is 13.51 cm (5.32 inches) and the fuel plates measure
64.77 cm (25.5 inches) in length.
Figure 1.1. Top View of MURR Core.
Figure 1.2 shows the design of a MURR fuel element. Each HEU fuel element has 24 fuel plates.
The fuel plates are curved and concentric, providing constant thickness coolant channels between
the plates. The plates are held in place through swage joints along the sidewalls and a support
comb which is placed radially along both the top and bottom of the fuel plates. Figure 1.3 shows
an end of the fuel element. Both the top and the bottom ends are the same and include a handling
fixture to allow for insertion into and removal from the reactor. The HEU fuel plates themselves
are nominally 1.27 mm (50 mil) thick with coolant channels of 2.032 mm (80 mil) between them.
Note that 1 mil is used to refer to 0.001 inch.
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1.4 Fuel Plate Design
In 1971 MURR transitioned from its initial uranium-aluminum alloy fuel to the uranium-aluminide
dispersion fuel still used today. This fuel allowed for an increase in U-235 loading from 650 grams
to 775 grams per element at an enrichment of 93%. The fuel meat portion of the plate is 0.508 mm
(20 mil) thick, with 0.381 mm (15 mil) of aluminum cladding on either side. The current HEU
plates are relatively thick at 1.27 mm (50 mil), curved, and have support combs at the midpoint of
the leading and trailing edges. All of these features make the plates fairly stiff and resistant to flow
induced deformation. Each HEU fuel element consists of 24 fuel plates [7].
Figure 1.2. MURR Fuel Element.
Figure 1.3. MURR Fuel Element End Cap and Plates.
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Figure 1.4. Cross Section Schematic of U-Al Dispersion Fuel Plate before Forming and Swaging into a Fuel Element.
Figure 1.5. Cross Section Schematic of LEU Fuel Plate before Forming and Swaging into a Fuel Element.
As part of the effort to convert MURR to an LEU fueled core, a new fuel element design, design
CD35 [8], was developed. The proven structural integrity of the HEU fuel element is not sufficient
to demonstrate the structural integrity of the proposed LEU fuel element largely because of
differences between the HEU and LEU fuel plate designs, which are shown schematically in Figure
1.4 and Figure 1.5. The outermost (largest arc length) LEU CD35 fuel plate is nominally 0.049
inches (1.24 mm) thick. The nominal thickness of all of the other LEU fuel plates is 0.044 inches
(1.12 mm). The HEU fuel meat is uranium particles dispersed in an aluminum matrix. Since the
cladding is also made of aluminum, the HEU fuel plate is in effect a curved aluminum plate with
particles of uranium near the middle of the plate thickness. By contract, the LEU fuel plate is
largely a five-layer sandwich, with a fuel meat layer in the middle, a zirconium layer on each side
of the fuel meat, and an aluminum layer on the outside of each zirconium layer.
Another difference is that the HEU element has 24 fuel plates and the LEU element has 23 fuel
plates. This difference, and the difference in fuel plate thicknesses, allows the nominal coolant
channel gap thickness between adjacent fuel plates to increase from the HEU value of 0.080 inches
(2.032 mm) to 0.093 inches (2.36 mm) for the outer channels of the LEU CD35 element, and to
0.092 inches (2.34 mm) for the inner 14 channels.
44 (plates 1-22) 49 mil (Plate 23)
23)
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1.5 Building the Fluid-Structure-Interaction (FSI) Safety Case
A significant change between the HEU and LEU fuel element designs is that the thinner LEU fuel
plates may make them more susceptible to bending. The tolerance on coolant channel gap
thickness between adjacent fuel plates is ±0.008 inches (±0.20 mm) for both the HEU and LEU
fuel elements. This tolerance can result in different flow velocities on either side of a fuel plate,
which, in turn, can produce pressure differences from one side of a fuel plate to the other. So even
with pressure differences analogous to those in the HEU fuel elements, the thinner LEU plates will
lead to some level of increased plate deflection. Although this has not been observed to be a
concern for HEU operations, it requires evaluation for LEU conversion in the present work.
The testing and analyses needed to qualify LEU fuel for MURR has the following two major
components: 1) irradiation testing of the new fuel including a Design Demonstration Experiment
(DDE) conducted by the Fuel Qualification pillar of the fuel US High-Power Research Reactor
(USHPRR) Conversion Program and 2) flow loop tests in the Oregon State University Hydro-
Mechanical Fuel Test Facility (OSU-HMFTF) conducted by the USHPRR Reactor Conversion
pillar. Both of these efforts rely on construction of full-size MURR LEU fuel assemblies by the
USHPRR Fuel Fabrication pillar. However, in advance of when full elements are available for
flow testing, plate-level experiments and modeling have been performed. This experimental work
in support of MURR conversion was performed at the University of Missouri Thermal
Management and Microscale Energy Conversion Research (TherM-MEC) Laboratory, and the
related modeling reported here was planned to evaluate the suitability of plates expected to later
undergo full-scale prototype qualification testing.
The DDE is a test of full-scale LEU element prototype to be irradiated in the BR2 reactor in
Belgium. Section 4.0 of Reference [9] states:
The MURR-DDE of a prototypic element is being conducted to observe how the
prototypic LEU element behaves under conditions comparable to what will be
experienced in MURR. The element will be placed in an irradiation vehicle which
will support the element in an experimental location in BR2. The irradiation vehicle
and experimental campaign of the MURR-DDE should be designed so that the
element operates at conditions comparable to those which are expected for typical
operations in the MURR. This includes the nominal plate-by-plate heat flux
profiles, temperatures, flow conditions, and discharge fission density.
The MURR-DDE is not intended to test limits of the fuel or element performance (e.g., maximum
allowable fission density).
Although the MURR-DDE element test is not conducted for flow test purposes, and is not intended
to be flow tested to limits, it will however undergo required flow testing for insertion into the BR2
reactor. Thus a successful DDE test will strengthen the safety case with regard to plate structural
stability under relevant conditions.
The focus of this report is the work being performed at the University of Missouri TherM-MEC
Laboratory and ANL as part of the flow testing, which is the second area of MURR LEU fuel
ANL/RTR/TM-16/9
qualification listed above in addition to irradiation testing. For this effort, testing alone is not as
effective as a broader effort because of the limited geometrical combinations testable. These
limitations may arise due to the differences between manufacturing tolerances, as-built
dimensions, and accuracy of measurement of quantities such as dimensions or deflection. Analysis
and simulation alone without experimental measurements would also not be effective because the
simulations may not include all effects, and because experimental data is needed for validation of
the simulations. When simulations predict experiments accurately the reliability of results is
enhanced. Thus, these experiments at MU were undertaken in order to benchmark the model
predictions used in the determination of safe performance of these LEU elements in the MURR
reactor. It should be noted that prototypic HEU fuel plates are expected to deflect so slightly that
measurements of such have not generally been practical in the past. The task here was to give an
early indication before full element testing that slight deflections remain true for the LEU plates,
which are somewhat thinner.
Besides the modeling and experimentation described in this report, an entire MURR LEU fuel
element is to be tested in the Oregon State University OSU-HMFTF facility [10]. Plans are
currently that in this demonstration test pressure drop vs. flow rate for the entire fuel element will
be measured. Also, fuel plate stability will be established through the measurement of deflection.
At OSU preparations are being made so strain may be measured via a local method on the plate.
Strain gauge rosettes or fiber optics are being tested, though a form of visual inspection could be
substituted. These measurements should enable a significant restriction in channel flow area due
to fuel plate deformation to be detected. A gauge will be used to make detailed coolant channel
gap measures before and after flow testing to assess if any plastic deformation has occurred.
Testing at limiting hydrodynamic conditions anticipated for these fuel elements when they are in
the reactor are planned to demonstrate the structural integrity of the LEU element. Other testing
may be conducted, but the fundamental demonstration testing of the element at limiting
hydrodynamic conditions is the key purpose of this experiment.
1.6 Coupling Methodologies for Solving FSI Problems
1.6.1 Methodologies for FSI Analysis
In general there are two groups of coupling solutions for FSI problems: integrated and partitioned.
The integrated approach involves solving the coupled set of equations for the fluid and structural
domain as a single problem. Although this approach may seem the most natural one, it can be more
difficult to adjust solver parameters to obtain a converged solution than with the partitioned
approach.
Historically computational fluid dynamics (CFD) software used for solving fluid flows and
computational structural mechanics (CSM) software used for solving the deformations and stresses
in solid bodies were developed independently. In recent years a number of CFD and CSM software
vendors have developed capabilities needed to solve FSI problems. Thus, structural solvers were
added to the CFD programs facilitating the analysis of FSI problems. It naturally leads to using a
partitioned approach where the equations are solved iteratively one domain at a time and coupling
boundary conditions are exchanged between the solid and fluid domains at each iteration.
ANL/RTR/TM-16/9
Otherwise implementing an integrated solution for FSI in software like STAR-CCM+ would be a
major task that would require the rewriting of a significant portion of the source code.
Depending on the magnitude of the influence of interface boundary condition changes computed
in either the solid or fluid domain on the other domain, one-way or two-way coupling may be
needed to solve the problem. If, for example, displacements of the structure due to fluid forces are
small enough so that they do not substantially influence the fluid flow, then one-way coupling
from the fluid domain to the structural domain can be used. In this case the pressure distribution
on the structure is not affected much by its motion, and therefore flow equations need to be solved
only once to obtain the load from the flow on the structure. However, for the case of thin plates
deflecting under pressure difference in surrounding channels two-way coupling is necessary. Plate
deflection significantly reduces the thickness of one channel and increases the thickness of the
other one. As a consequence of the channel thickness change the pressure distribution on both
sides of the plate changes.
Two-way coupling can be either explicit (weak) or implicit (strong). Explicit coupling is
schematically presented in Figure 1.6 (a). In a weakly coupled step n, the solution in the fluid
region, including the pressure and shear stress distribution, is found on the plate boundaries
obtained from the structural solver from the previous step n-1. This distribution is subsequently
passed to the structural solver, which will yield a solution giving the solid boundary displacement
and velocity that is subsequently passed to the CFD solver for use in time step n+1. The number
of steps and length of time steps is determined by the complexity of the physics modeled in each
solver.
ANL/RTR/TM-16/9
Figure 1.6 (b) presents a schematic of the strong coupling procedure. In this scheme the two
problems are also numerically decoupled. However, within each time step n, the CFD and CSM
solvers exchange interface conditions computed by the separate solvers during the inner iterations
to converge the time step. An updated location of the structure’s boundary in the structural step is
fed to the CFD model and a new pressure field is found. Instead of progressing to the next step,
the updated pressures are used one more time to find a different state of the structure within the
same time step. The process is repeated until convergence of user-defined criteria is achieved.
STAR-CCM+ uses the strong coupling mechanism for its own Finite Volume (FV) fluid and two
available structural solvers. When this work was started for the structural part only a Finite Volume
solver was available. However, most recent versions of STAR-CCM+, including 11.02 and 11.04,
also have a Finite Element (FE) solver available for the structural part. In fact, CD-Adapco has
recommended using the FE solver instead of the FV solver for the structure. It allows for a
significant reduction in the number of elements in the domain and it is planned to be the only
structural solver further developed by Siemens Corp. Initial releases of the FE solver in STAR-
CCM+ were not giving converged results for as-built cases of the thin plate. Thus, a majority of
the results presented here were obtained with the use of FV-to-FV strong coupling technique. A
handful of cases were successfully run with the version of STAR-CCM+ 11.04 where the FV
(fluid) solver was coupled to the internal FE (structural) solver.
Researchers at the University of Missouri used both strong and weak couplings of STAR-CCM+
with an external FE solver ABAQUS. STAR-CCM+ provides an interface facilitating the coupling
of these two separate solvers and an easy exchange of data between them running both solvers in
the memory of the computer at the same time.
COMSOL uses the Finite Element method for solving systems of PDEs for both the fluid and the
structural problems. For this reason COMSOL offers two types of solvers for fluid-structure
interaction problems. The first is the integrated solver (or fully coupled solver), and the second is
the segregated solver (or partitioned solver). For the purpose of the work presented in this report
COMSOL was only used for selected runs with the 15.9 mil as-built curved plate. The solver was
only used as a verification of the runs performed in STAR-CCM+. Version 5.2a of the software
was used in the analysis. The integrated approach was applied to solve the cases with lower average
channel velocities (below 3.0 m/s). For higher velocities (3.5 and 4.0 m/s) this approach was
diverging and the segregated approach was used.
Table 1.1 contains a list of versions of the software used and cases analyzed with it. Since the
duration of the project was well over a year several versions of STAR-CCM+ were released in that
time. Each of them brought new features and bug fixes. The FE solver for the structural part of
FSI solutions was significantly improved during that time and its use for our purposes was possible
toward the end of the project.
ANL/RTR/TM-16/9
1.6.2 Governing Equations for the Fluid and Structural Domains
This section presents a brief introduction to the mathematical description of the FSI problem.
Figure 1.7a presents a schematic of a discretized computational domain with fluid occupying space
f and solid body occupying space s.
Table 1.1. Software Versions Used in the Analysis of MURR Plates.
Software Version Solver type Cases analyzed
STAR-CCM+ 10.02 FV coupled with FV Perfect and as-built 40 mil flat plate,
perfect curved 26 and 40 mil plates
STAR-CCM+ 11.02 FV coupled with FV Perfect 15.9 mil thick curved plate
STAR-CCM+ 11.02 FV coupled with FE Perfect 15.9 mil thick curved plate
STAR-CCM+ 11.02 FV coupled with FV As-built 15.9 mil thick curved plate,
prototypic plate 22
STAR-CCM+ 11.04 FV coupled with FE As-built 15.9 mil thick curved plate
COMSOL 5.2a FE Integrated As-built 15.9 mil thick curved plate
Figure 1.7. Initial Stage of the FSI Problem and an Intermediate Stage with Mesh Morphing.
It is currently a standard approach to use the Reynolds-averaged Navier-Stokes (RANS) equations
for Newtonian incompressible fluids with a k- turbulence model to solve for the flow field and
pressure distribution on the boundaries. The conservation of momentum and mass equations
represented by the RANS equations are [11]:
fi
j
f
i
(1.2)
where is the fluid density, ui is the velocity component in the i-direction, vj is the mesh velocity
in the j-direction, p is the pressure, eff = +t is the effective viscosity, t = C k 2/ is the
turbulent viscosity, and gi is the i-direction component of the gravity vector. The standard
equations for turbulent kinetic energy, k, and dissipation rate, , are given by:
ft
jk
t
iij
(1.4)
where S = (2 Sij Sij) 1/2 is the norm of the mean strain rate tensor of the fluid, and the model constants
are C = 0.09, k = 1.0, = 1.3, C1 = 1.44, and C2 = 1.92. STAR-CCM+ contains options to
select a wide variety of variations of the RANS turbulence models. The more general realizable k-
model with a blended wall function formulation to determine the shear stresses at solid
boundaries was used for this work. Details can be found in the user guide [11]. The initial and
boundary conditions for the fluid domain are:
00
(1.7)
where ξ {ux, uy, uz, p, k, ε} and ξb and hb are known boundary values for Dirchlet, 1f
, and
Neuman, 2f , boundary conditions respectively. Information on setting consistent boundary
values for inlet, outlet, pressure, wall, and symmetric boundaries is contained in the user guide
[11]. The solid part of the domain s is governed by the following conservation equations:
ANL/RTR/TM-16/9
si
j
(1.11)
where ij are components of the stress tensor, ni are the components of the surface normal vector,
ti are components of external surface forces, and equation 1.9 requires equality of contact forces
at the interface of two solids in contact (if it occurs).
In most classical CFD problems the boundaries are fixed during the analysis, and the
computational mesh does not change. In FSI problems the fluid boundaries may be part of a
structure that will move or deform in response to surface and body forces that are determined as
part of the solution of the problem. As the boundary motion is calculated, the computational mesh
in the fluid domain has to be updated either by a morphing procedure or a complete domain remesh
process. The coupling conditions on the interface between the fluid and solid domains of an FSI
problem are:
sfsf onuu (1.12)
sfsf onnn (1.13)
where f and s are the fluid and solid side stress tensors respectively.
The CFD solution of the fluid flow equations yields the detailed distribution of fluid stress on solid
surfaces (left hand side of equation 1.11). This stress distribution is passed to the structural solver
to solve for the response of the solid bodies, and that solution yields the displacement rate
(velocity) distribution of the solid surfaces (right hand side of equation 1.10). In general, the
surface velocity distribution may include both deformation and rigid body motion.
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2. FLAT PLATE EXPERIMENTS AND SIMULATION EFFORT
2.1 Flat Plate Experiments
As part of ongoing development efforts for numerical Fluid-Structure Interaction (FSI) simulation
of fuel-coolant systems, there is a need for experimental benchmarking data. In order to generate
this data, it has been necessary to develop techniques for characterization of the experiment
geometry. Experimental geometries are challenging since among the USHPRR reactors, the ratio
of the fuel plate length to the thickness scales is on the order of 1000:1. For the LEU MURR
element, successful modeling of problems like these has not previously been reported.
Earlier comparisons between experiments and numerical simulations using models with the ideal
channel geometry – i.e. a flat plate and perfectly flat walls – showed a need for more detailed
characterization of the experiment geometry [12] [13]. The test section was constructed with two
plexiglass panels on the outside, allowing laser displacement sensors to monitor plate deflection
during flow tests. However, similar experiments conducted in 1959 showed a potential for
plexiglass to absorb water even when exposed for short periods [14]. This leads to warping of the
plexiglass, and therefore significant variability in the surface of the channels. After completing
numerous flow experiments warping became clearly visible during test section assembly and
disassembly.
In order to evaluate how the warping of the plexiglass (and the resulting irregularity of the fluid
channel thicknesses) might affect the plate deflection profile, a method was developed for mapping
the fluid channels with the laser displacement sensors. This mapping process involved moving the
lasers to about 2000 different locations in each channel and measuring the channel thickness as
described in Section 2.1.2 below. The resulting channel profile maps were used in later numerical
models to ensure close geometric matching between the numerical models and experimental setup.
In addition to mapping the channels, the lasers were used to measure the change in fluid channel
thickness (i.e. plate deflection) in each channel at a single axial location during flow testing. The
flow tests were repeated seven times with the lasers in a different location for each repetition.
Additionally, the pressure difference between the two channels was monitored at eight axial
locations during every flow test. Finally, flow rate was controlled with a bypass valve that directed
flow back to the reservoir.
Additional detail on the experimental results presented here can be found in an earlier report,
“Experimental Investigation of Deflection of Flat Aluminum Plates Under Variable Velocity
Parallel Flow,” [15].
2.1.1 Experiment Apparatus
2.1.1.1 Flow Loop
The Hydro-Mechanical Flow Loop (HMFL) at the University of Missouri was used for completing
these experiments. The flow loop includes a National Instruments data acquisition system for data
collection and flow control. User control and monitoring is accomplished with a LabVIEW
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program. The flow loop and a flow path schematic are shown in parts a and b, respectively, of
Figure 2.1.
(a) (b) Figure 2.1. University of Missouri Hydro-Mechanical Flow Loop (HMFL).
2.1.1.2 Test Section
The flow loop was designed to accommodate a wide range of test sections. The test section used
for these experiments was based on a layered sandwich structure, with two outer plexiglass panels
and interior channel spacers around an aluminum alloy 6061-T6 plate. A vertical cross-section
indicating the pressure tap locations (PT1 – PT9) and laser measurement locations is shown in
Figure 2.2, where plexiglass is labeled “Perspex”. A horizontal cross-section demonstrating the
sandwich structure of the test section is shown in Figure 2.3. The axial distances from the trailing
edge of the aluminum plate to the laser measurement locations and to the pressure tap locations
are shown in Table 2.1 and Table 2.2, respectively.
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Figure 2.2. Test Section Vertical Cross-Section (Not to Scale) and Front View.
Figure 2.3. Test Section Horizontal Cross-Section (to Scale).
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Table 2.1. Laser Channel Gap Measurement Location Relative to Plate Trailing Edge.
Location ID Axial Location
(From Plate Trailing Edge)
Table 2.2. Pressure Measurement Location Relative to Plate Trailing Edge.
Pressure Tap Distance From
Trailing Edge of Plate
PT1 64.8 mm (2.55 inches)
PT2 129.5 mm (5.10 inches)
PT3 194.3 mm (7.65 inches)
PT4 259.1 mm (10.20 inches)
PT5 323.9 mm (12.75 inches)
PT6 388.6 mm (15.30 inches)
PT7 453.39 mm (17.85 inches)
PT8 518.2 mm (20.4 inches)
PT9 582.9 mm (22.95 inches)
2.1.1.3 Laser Channel Gap Measurement
To map the thickness of the fluid channels and monitor plate deflection during a flow test, two
Keyence LK-G152 laser displacement sensors were used. The sensors work by emitting a laser
beam through the plexiglass panel and monitoring the location of the reflected signal. For mapping
the fluid channels, water was drained from the test section and the channels are filled with air.
Reflected signals were detected at the outer surface of the plexiglass, inner surface of the
plexiglass, and the surface of the plate. The channel thickness was taken as the distance between
the inner surface of the plexiglass and the plate surface. Any refractive effects resulting from the
emitted laser passing through the plexiglass are canceled when the return signal passes back
through the plexiglass.
Figure 2.4. Laser Channel Thickness Measurement During Mapping (Left) & During Flow Testing (Right).
During flow testing, the fluid channels are filled with water. Since the refractive index of water
and plexiglass are so close, the lasers are unable to detect a signal from the inner surface of the
plexiglass. This results in the measurement scenario shown in right side of Figure 2.4. The
measured signal during flow testing is the distance from the outer surface of the plexiglass to the
surface of the plate. To convert this measured signal to a usable measurement, it is therefore
necessary to subtract the laser measurement of the plexiglass thickness (points 1-2 in Figure 2.4),
and multiply by a correction factor. The correction factor is determined by dividing the real channel
gap thickness with air (points 2-3 in Figure 2.4) by the measured channel gap thickness with water.
This results in the laser calibrations equations (2.1) and (2.2).
=
= (4−5 − 1−2) ∗ (2.2)
Where:
4−5 = Measured plexiglass + gap thickness with water
1−2 = Measured thickness of Perspex
= Real gap thickness with water
During flow testing, the lasers were positioned at one of the seven locations (A-G) indicated in
Figure 2.2. Measurements of the channel gap were continuously collected at a set flow rate. After
running through all 11 flow rates, the lasers were repositioned and the process was repeated at the
new location.
2.1.1.4 Differential Pressure Measurement
In order to monitor the pressure difference between the two fluid channels during flow testing, the
test section was equipped with nine Omega PX-26 differential pressure transducers (PT1 – PT9),
as shown in Figure 2.2. The pressure transducers have been calibrated across a range of −30 kPa
to +30 kPa. The pressure measurement locations are spaced at 64.77 mm (2.55 inch) increments.
ANL/RTR/TM-16/9
There are no pressure measurements at the leading and trailing edges due to the presence of screws
for pinning the plate at those locations. Pressure measurements were always collected in the same
locations. Since the lasers had to be moved through seven locations, the pressure measurements
were essentially repeated seven times at all 11 flow rates. This data can provide a reliable measure
of the repeatability of the flow tests. Additionally, while the test section was instrumented with
nine pressure transducers, PT8 failed early in flow testing and no data was available from that
location.
Once the lasers were positioned at the desired location, calibration measurements were taken as
outlined in Eqns. (2.1 and (2.2. Then, the water was turned on and flow testing began at the lowest
flow rate. After collecting data for approximately 30 seconds, the flow rate was increased by
slightly closing the flow control valve shown in Figure 2.1. The process was repeated until data
was collected at all 11 flow rates. Upon completion of the final flow rate, the water was shut off,
the test section was drained, and the lasers were moved to the next measurement location where
the flow test was repeated. This process was completed first with the leading and trailing edges
free, and then a second time with pins at the leading and trailing edges to simulate a comb.
2.1.2 Channel Mapping
The fluid channel gaps in the test section, while targeted to be 2.032 mm (80 mil) and 2.540 mm
(100 mil), will vary from those values, as illustrated in Figure 2.5. The two primary factors
contributing to variation in the fluid channel thickness are variations in the flatness of the
plexiglass and variations in the flatness of the plate. Therefore, in order to better characterize the
geometry of the channels, the laser displacement sensors were utilized to map the thickness of the
fluid channels.
A programmable controller was used to automate the mapping process, with the lasers starting
each pass at the top of the plate, working across the plate width, and then moving down. Upon
reaching the final location at the bottom of the plate, the lasers were reset at the top edge and the
process was repeated a total of 30 times. Some locations were obstructed from view of the lasers
and no data is available in those areas. A grid of about 5 mm was used for the mapping, with a
total of 2000 locations in channel 1 and 2026 locations in channel 2 being measured. This
information is useful not only for analyzing the actual shape of the channels, but the repeated trials
of the mapping are useful for determining the error associated with repositioning of the lasers.
The average of all channel mapping passes was used to generate the color map of Figure 2.6. A
linear interpolation was used to approximate the channel thickness between measurement
locations. Through all the mapping trials, the measured thickness of channel 1 was repeatable with
a 95% uncertainty of ±0.0060 mm, and channel 2 was repeatable with a 95% uncertainty of
±0.0350 mm. The reason for the difference in the uncertainty values may be the result of
differences in tolerances in the positioning systems on each side of the test section. Summary data
for the channel gaps is shown in Table 2.3.
ANL/RTR/TM-16/9
Figure 2.5. Schematic Illustrating Difference between Ideal and Actual Channel Gaps.
Table 2.3. Channel Thickness Summary Data.
Ideal
(mm)
Minimum
(mm)
Mean
(mm)
Maximum
(mm)
2.1.2.1 Experiment Apparatus Impacts on Channel Mapping
The pump used to circulate the water in the flow loop is located between the open-pool reservoir
and the test section, as shown in Figure 2.1b. That pump location ensures that the pressure of the
water in the test section is higher than the ambient. When that pressure differential is applied across
the Perspex test-section walls, there is a potential for the test section to bow outward. Recall that
variations, such as water-related absorption into the plexiglass, occurring between tests are
accounted for via pre-measurement of the channels as described in Section 2.1. However,
preventing significant test section bowing movement during the test was a goal so that any channel
ANL/RTR/TM-16/9
gap change measured using the laser displacement sensors will correspond to changes in the plate
position. Thus, to mitigate test section bowing, metal cross-bars are attached laterally to the outside
of the test section, as can be seen in Figure 2.2.
As can be seen in Figure 2.5, the inner surface of the Perspex panel is a boundary to one flow
channel. On the other side of the plate is the second flow channel and corresponding Perspex panel.
As long as the distance between the inner surfaces of the two Perspex panels do not move relative
to one-another, changes in the channel gap measurements will indeed correspond to changes in the
plate position. The change in the channel gap thickness is assumed to correspond to the plate
deflection. Therefore, the initial channel gap thickness was subtracted from the gap thickness
observed during flow testing. It is noted that this assumption is only true if the plexiglass walls are
rigid. This assumption was investigated in [16] and found to be acceptable. Thus, for purposes of
the analysis presented here, it is assumed that any change in channel gap observed using the laser
sensors corresponds to a change in the plate position.
Figure 2.6. Color Map Showing Contour of Channel Gap Thickness.
ANL/RTR/TM-16/9
2.1.3 Free-Edge Flow Testing
Once the flow test section with the plate was installed into the flow loop fitted with a pump, the
testing commenced. It should be noted that the first investigation was performed with free (that is
unpinned) leading and trailing edges of the plates and so is here called free-edge flow testing. The
next section will cover the results of pinned-edge experimental measurements. The plot in Figure
2.7 shows the resulting plate deflection at all seven measurement locations for all flowrates. At
lower flow velocities, the deflection at, or near, the leading edge is normally larger than elsewhere
on the plate. This deflection progressively increases as flow velocities increase, until a velocity of
5.69 m/s (2.86 kg/s flow rate) was achieved.
Figure 2.7. Constructed Plate Profiles from Flow Experiments.
Figure 2.8 presents the same data plotted against the flow rate in order to more clearly illustrate
that the plate exhibits a change in the mode of deformation. This ‘mode change’ was visually
observed as a change of the shape of entire plate once a specific flowrate range is achieved. As
further discussed in Appendix A, this was reversible as the velocity is subsequently decreased, and
no plastic deformation was experienced by the plate. However, an edge constraint (plate slipping
out of the friction bond), or the non-ideal shape of the ‘flat’ plate (e.g. warping leading to a
‘snapping’ from one shape mode to another) are postulated to have led to this behavior since this
is otherwise inconsistent with simple elastic theory of structural deformation. In any event, this
mode change was repeatable, did not change the plate or channel geometry when the flow loop
was returned to rest (i.e. zero flow conditions), and occurred instantly across the entire plate so as
not to interfere with the trending of data at velocities lower than where the plate experienced this
phenomena. In the tests shown in Figure 2.7 this mode change is observed after increasing

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