ML20199B046
| ML20199B046 | |
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| Site: | 05200003 |
| Issue date: | 10/31/1997 |
| From: | Theofanous T CALIFORNIA, UNIV. OF, SANTA BARBARA, CA |
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| ML20199B025 | List: |
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Text
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VOLUME 2 ADDENDA TO DOFAD-10541, October 1997 -10503,-10504 i .
P T. G. Theofanous, et al. .
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l Advanced Reactor Severe L
N Accident Program I
Department of Energy i
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VOLUME 2 ADDENDA TO DOE /ID-10541, O '**'1887 -10503,-10504 T.G, Theofanous et al.
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Center for Risk Studies and Safety Departments of Chemical and Mechanical Engineering University of California, Santa Barbara Santa Barbara,CA 93106 Prepared for the U. S. Depanment of Energy Idaho Operaticas Office Under ANL Subcontract No. 23572401 i
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. CONTENTS-4 E- : PART !.' ADDENDA TO DOE /ID-10541 '
1,-' ADDENDUM TO CHAPTER 3 - l Additional Perspectives on Fragthty_ . . . . . . .
- . 3 ]
- 2. ADDENDUM TO CHAPTER 4 j Additional PerspecHves on Blockage Formation . . ._. . . . . . .. . . . 4 3.' ADDENDUM TO CHAPTER 5 Ad/jtional Premixing Results . . . . , . . . . . .- . . . . . . . . . .
5-13 4 /.DDENDUM TO CHAPTER 6 Additionc! Explosion Results - _ . . . . - . . . . . . . . . . . . . . - . . = . . 6 PART II. ADDENDA TO DOE /ID-10504
- 1. ADDENDUM TO SECTION 2.1.2 .
Drift Flux Relations with PM-ALPHA.L , . . .. . . , . . . . . . . . 2.1.21 -
- 2. ADDENDUM TO SECTION 2.2 3
- QUEOS Test Simulations with PM ALPHA.L , - . . . . . . . . . . . . .
2.2.3-1
- 3. ADDENDUM 1 TO APPENDIX B
! The Regimes of Premixing . . . . . . . . . . . . . . . . . . . . . . . . B-35
- 4. ADDENDUM 2 TO APPENDIX B MAGICO-2000 Test Simulations with PM-ALPHA.L . . . . . . . . . . . . B-77
- 5. ADDENDUM TO SECTION 3.1:2 Further Comparisons between the 2D and 3D Codes . . . . . . . . . . 3.1.2-1 PARTIII. ADDENDA TO DOE /ID-10503
- 1. ADDENDUM TO SECTION 2.1.2 2D Wave Dynamics with Coarse Nodalization . . . . . . . . . . . . . 2.1.2-1
- 2. ADDENDUM TO APPENDIX C-New SIGMA'-2000 Results with Steel Melt , . . . . . . . . . . . . . . . . C-29 Notei The three parts are separated by the blue inserts. The various addenda within each
< part are separated by yellow inserts.
111
- - _ _ - _ _ - - _ . _ _ . - - . - - - _ - - . . - - _ . - . . _ , - _ _ . . _ . - - _ . _ _ _ . _ ~. . _ . . . ~ . . . - . . . . . . .. . . . - . . . . . . . - ~ ~ - ~ . ~ - ~
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o PART I. ADDENDA TO DOE /ID-10541 4
i 1
9 4
3
(( ADDENDUM TO CHAPTER 3))
ADDITIONAL PERSPECTIVES ON FRAGILITY -
The purpose of this addendum is to provide results of calculations and assessments carried out in response to reviewers' questions.
- 1. Effect of actual yield strength. The quoted material strength for steel A508B is 330 MPa, while the reported value of the reactor steel (from Japan Steel Works) is 450 MPa. In all previous calculations we have used the former, to compensate for
. potential uncertainty in the rate-dependent yield strength. A calculation carried out with an imposed impulse of 0.3 MPa s on loading pattern 1+, and the 450 MPa value, reduced the fraction of the wall area strained to over 11% (void nucleation threshold) from ~40% to ~10%.
- 2. Applicability of rate dependent yield strength of mild steel to A508B.The calculetion performed in Chapter 3 utilized the strain rate dependency of yield stress as found experimentally for mild steel, since A508B has a carbon content that places it into that category, and experimental data on A508B at high strain rates do not exist. Yet a similar steel, A533B, with somewhat higher carbon content, has been found tested at high strain rates and shows much less strain rate dependence. As explained in the report, to ensure against this eventuality, we took a lower yield stress, of 330 MPa, that
.iust about compensates for the variation due to the strain rate dependency. We now have two additional calculations, carried out for reactor case C2-20, as summarized in Table 3.al. The first entry in this table is the old result. We can see that strain rate dependency is not crucial to the conclusion; however, in the absence of directly applicable data,it may not be appropriate to concede this additional safety factor.
Table 3.a1 The Interplay Between Yield Stress and Strain Rate Effects YieldStress Strain Rate Maximum Equivalent (MPa) Dependency Plastic Strain
(%)
330 Yes 0.34 330 No 0.47
'450 No 0.23 O
V 3-17
4
. 3. The use of shell elements versus continuum brick elements In ABAQUS. '
- . This addresses the effect of accounting for transverse shcar, which is mv.;elled by the brick elements and not by the shell elements. In these calculations we used a 3000-bar,2 ms triangular pulse to load pattem 1+. The results are summarized in Table 3.a2. From here, we can see that our use of thin shells is somewhat conservative.
Table 3.a2 Shells Versus Bricks Maximum Equivalent Plastic Strain
(%)
330 MPa Thin Shel! 20.6 With Strain Rate Depend. Thick Shell 21.3 450 MPa Thick Shell 42.0 No Strain Rate Depend. Brick (3D) 33.0 l
l
- 4. Refinement of Computational Mesh. The calculation for the thick shell case in Table 3.a2 was repeated with 4 times as many nodes. Computed maximum strain changed from 0.213 to 0.217.
- 5. Smaller Loading Areas. A whole series of new calculations was carried out to investig, ate response to more localized loads than previously considered. Scaled rep-resentetions of the areas, and related nomenclature, are summarized in Table 3.a3.
The ef!ective impulse scaling works well down to pattem 5, as illustrated in Figure ,
3.al. For still more localized loads, it takes extremely high pressures to produce any yield, and the results depart significantly from this sort of scaling. In this highly localh ed loading range the safety margins (for a given impulse) increase rapidly, as shown in Figure 3.a2.
- 6. New Calculations with Representative ESPROSE.m Results. As expected, from the above, these show strains limited within the elastic range.
d(3 3-18 l
l
i, 12 , , , , ,
[ , . o panem 1 x panem 2
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-A g . + panem 3
+ - panem 1+ ,
g- o panem 0 e penem o+ x-
- 0.6 - - .' a' panem P'"'* 4 ~
5 10 w/ Mrsin rate 0.6 -
} .
.$ 0.4 -
~
1 0.2
^# ' ' '
0 O 0.1 0.2 0.3 0.4 0.5 0.6 1,[MPa s)
L Figure 3.al. Peak equivalent plastic strains as functions of " effective impulse."
120 , , , ,
[ r -
V/ at 100 C
t : pattom 1
--*-- pettom 2
$ 80 pattom 3
,l -*- pattom 4
--+-- pettom 5 60 - --*-- pattom 6 - ,
uniform load U' 40 - -
T a -
-: 20 -
0 '. - t 0- 0.2 0.4 0.6 0.8 1 Impulse [MPa s)
. Figure 3.a2. Percentage of wall exceeding 11% strain as a function of impulse and loaded
" area.
3-19
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O Table 3.a3 Loading Patterns and Respective Dimensions for the U Non-Uniform Loading Runs ee$e e, m
- 9. A, 2( A, + An)
Loading di dl, As 2&
Patterns (m) (m) (m )
2 (m )
2 yp2 yp2
(%) (%)
1 0.94 1.40 0.70 0.84 2.8 6.1 2 1.40 2.00 1.54 1.60 6.1 12.5 3 2.10 3.10 3.60 4.00 13.8 29.7 1+ 1.40 -
1.54 - 6.1 -
0 0.39 0.87 0.12 0.47 0.5 2.3 0+ 0.55 0.94 0.24 0.46 1.0 2.8 4 0.81 1.33 0.52 0.87 2.0 5.5 l 5 0.61 1.09 0.29 0.64 1.2 3.7 i 6 0.38 0.61 0.11 0.18 0.4 1.1 7 0J 0.38 0.028 0.085 0.1 0.4 8 0.i4 0.31 0.015 0.075 0 06 0.36
- Based on areas,i.e. Ai = xdl/4, Ao = xdl,/4 - A4 4
\ 3-20 l
I
,f m (( ADDENDUM TO CHAPTER 4))
r 4 V ADDITIONAL PERSPECTIVES ON BLOCKAGE BEHAVIOR A number of questions were raised about the integrity of the lower blockages, and the purpose of this addendum is to provide material relevant to these questions. Specifically_
we consider in more detail the coolability and resulting radiative heat fluxes downward to the water. Also, we quantify the additional heat sink, due to the core support plate, after the water is vaporized to a level below it. Finally, we address the question, What if a blockage located at or near the bottom of the core were to fall?
- 1. Calculations were carried out with oxidic blockages of various porosities in both the bottom of the active fuel region, as well the Zr plug region. Also, calculations were carried out with metallic blockages, containing 14 o/o fuel, in the bottom of the active fuel region.
Effective volumetric powers and thermal conductivities were computed consistently, as described in the report. Relocated fuel in the blockage was taken at the average axial core power and the highest radial power factor, and released volatile fission products as in DOE /ID-10460. Fuel stubs were taken at the local power peaking at the location of the maximum radial factor and with all volatiles in them. The calculated values are shown together with the results in Tables 4.a1 through 4.a3. We find, in all cases, robust blockages.
- Also, we find that downward heat fluxes are in the range 0.1 to 0.2 MW/m2as estimated previously.
Table 4.a1 Oxidic Blockage at Bottom of Zr Plug Region Blockage Blockage Blockage Downward Blockage Porosity Power per Effective Radiative Thickness Volume Thermal Heat Flux cm 3
MW/m Conductivity MW/m2 W/(m K) 0.1 1.337 19.9 0.186 12.5 0.1 1.273 19.8 0.183 12.8 0.5 - 0.743 18.5 0.144 16.7 0.5 0.709 18.5 0.141 17.1 0.8 0.297 17.0- 0.096 25.5
- 0.8 0.283 17.0 0.094 26.9 4 29
. ,. - .. ...~ - - - -. _ ..=.. .- - .. .- . - .. - - . , . .
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- . - l Table 4.a2 - Oxidic Blockage at Bottom of Active Fuel Region ; j Blockage _ - Blockage Blockage - Down_ ward ' ; Blockage -
- Porosity . Power per Effective Radiative . Thickness Volume - Thermal Heat Flux: cm. .
2-MW/m - 3 Conductivity MW/m W/(m K) t 0.1 1.786 6.28 0.213 5.48 0.1 1.694 6.29 0.209 5.63 -
-0.51 1.192- 5.61 0.175 6.45- 4 0.5 1.128 5.60 - 0.171 6.63 0.8 0.746 5.07 0.141- .7.75 0.8 0.705 5.60 0.137 7.95
- Table 4.a3 Metallic Blockage at Bottom of Active Fuel Region Blockage - Blockage Blockage Downward Blockage Porosity Power per - Effective- Radiative Thickness Volume Thermal Heat Flux cm MW/m Conductivity MW/m 2 W/(m K)
L 0.3 0.596- 19.5 0.216 16.7 0.3 0.561 19.4 0.210 17.2-0.4 0.575 17.3 0.203 16.1 0.4 0.541 17.2 0.198 16.6 2.- The temperatures of the core support plate subjected to a heat flux of 0.20 MW/m2 at its upper surface (and an adiabatic boundary condition at the lower surface) are shown in Figure 4.al. It is clear that this heat sink provides significant further margin to the " race .
between the 100 minutes estimated to vaporize the water and the ~91 minutes to fail the core barrel. Also,it should be noted that the boiled water was taken to escape the vessel, while in reality some significant fraction of it would be expected to reflux back.
4 !
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t PN .
l MW . . . ..
.g 1 ;
' [ w.
CORE $UPPORT PLAlf UPPER SURFACE ~.
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I ul ;'803 - -
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'. Sco -1 CORE SUPPORT PLATE LoWEA SURFACE- ,
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"0 10 M 33 40 50 N 73 '
TIME, minutes 2
Figure 4.al. Heatup of the core supported plate under a heat flux of 0.2 MW/m applied to the top surface.1The emissivity of the plate was taken as 0.4 and the holes were ignored (conservative by ~25%)._.
l
- 3. It is postulated here that a blockage located at or near the bottom of the core fails releasing oxidic melt into the underlying portion of the rod structure. The configuration
~o f the fuel rods below the co're consists of an 18 centimeter (7.0 inch) high fission gas plenum and a 6.9 centimetar(.'t7 inch) long solid zirconium alloy plug at the bottom of the rod. The
~
zirconium plug region constitutes a non heat generating heat sink to freeze melt released from the assumed failure site possibly forming a complete blockage. Thus, the heat sink potential ~of the Zr plug region is examined here. An important feature of this region is
=
the lowermost space-grid located at the bottom of the plugs. The lowermost spacer grid is inconel and further restricts the flow of melt between the plugs. The obstructiors posed by the inconel grid straps could tend to break up the melt such that the melt that freezes-
- between the plugs and straps may contain porosity. It is assumed here that the grid straps
'have a thickness of 0.27 millimeter (0.0105 inch).
Table 4.a4 shows that the plugs and straps do not have enough heat sink to freeze
.the melt unless the blockage has a pomsity of 0.4 or higher. This thermal equilibration brings the plugs, straps, and oxide melt to the plug solidus temperature. Because the
- plug melting temperature exceeds that of inconel, the straps could melt but the straps 7
- correspond to only 4.2 percent of the unit cell volume.
!s M 4 31
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[d
_ ' Table 4.a4 : Heat Sink Pc.ential of Zr Alloy Plugs and Inconel Grid Spacer at Bottom of Fuel Rods - ,
- Blockage Porosity Z8.rconium Alloy Plug and Oxide Melt Enthalpy Change j Between Liquidus and Plug.
Grid Strap Heat Sink: 3
- Between Plug Melting - Melting Temperature,a- .
Temperature and 398K*, KJ
-i KJ
/
0.0 ' 3.6 - 5.8 0.1' 3.6 5.2 0.2 3.6 4.6
-0.3 3.6 4.0 0.4 3.6 3.5
' O.5 - 3.6 - 2.9
- Based upon a unit cell having a side equal to the rod pitch and a 1_ centimeter height.
Thus, it is possible for a new lower blockage to form in the Zr plug region, if the melt collecting in this region has considerable porosity. As the melt released from the postulated failure site freezes in the plug region, the flow will be diverted away from the blockage to drain do.wnward at surrounding plug locations. In this manner, the , blockage grows sidewards. The fuel rod walls in the fission gas plenum region do not have adequate heat sink to freeze melt. The gas plenum walls will therefore melt away and the oxide melt fill in the space above the Zr plugs. This is how a new blockage forms and the pool lower boundary moves downward.
As melt flows and freezes between the Zr plugs and straps, melt penetrates downward
. below the plug region. The potential for melt penetration below the plugs was estimated
.with transient freezing calculations. Freezing is modeled solely through the formation of .
a crust upon the outer surface of the 6.9 centimeter (2.7 inch) high plug. The heat sink of the grid straps is neglected; the straps only decrease the flow area available to the melt in I
the calculation. Melt is assumed to enter the plug region with 10 degrees Kelvin molten -
( superheat above the liquidus temperature. The driving potential for melt fiow is taken to -
j: : be the gravity head of a melt layer 18 centimeters (7.0 inches) deep. This la tter assumption 4-32 o
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.- .a - . ~ . - . . - . : ., , ,. - -- ,= ,
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reflects e lateral dispersion of melt in the fission gas plenum region located between the -.
. bottom of the core and the plugs..
Table 4.a3 sows the results of these calculations. Plugging is calculated to occur in 4.8 seconds or less based upon the asswnption of continuous crust growth. This result at -
first seems to contradict the heat sink analysis of Table 4.a4. The calculated behavior is that the oxidic melt is completely frozen as the result of heat transfer to the Zr plug that is only partially melted up to this time. Thus, the melt is first frozen before the plug has been m:lted completely. Subsequently, the continued exchange of energy may melt all of the zirconium in the absence of the additional heat sink of the grid straps. In any event, .i e
- the freezing of melt in the plug region will at least temporarily divert the melt sidewards.
Table 4.a5 Transient Freezing of Draining Oxidic Melt Upon ,
Outer Surface of Zirconium Alloy Plug Melt Oxide Freezing Time Fraction of Zirconium Melt Mass Porosity to Block Channel, Alloy Melted at - Penetrating Below s Blockage Time Plug Region,a Kg O
!: 0.0 4.8 0.90 1.6~
0.2 4.3 0.067 1.1 l
l
- Based upon a unit cell'having a side equal to the fuel rod pitch of 1.26 centimeter (0.4% inch).
g
! The transient freezing calculations assume that melt freezing ard penetration are limited by the continuous formation of a solid crust on the heat sink w alls. However, it is well known that such calculations significantly over predict the penetration of UO2 and mainly UO 2oxidic melts through rod structure, circular channels, as well as rectilinear -
gaps. This knowledge is based upon the results of experiments performed with reactor materials and analyses of the reactor material test results (Spencer et al.,1985; Spencer et .
l al.,1983; Spenter et al.,1979; Spencer et al.,1986; Schwarz et al,1989; Soussan et al.,1990; ,
Tattersall et al.,1989a; 1989b; Magallon et al.,1990). Thus, the melt penetration potentials indicated in Table 4.a5 as well as Table 4.a8 later on are almost surely overestimates. In 4-33
, - . - - -r .e+ . - - - , . - - - , . . - - ,. - ,;. , a , ..:. . .-- - ,; ,
reality, significantly lower masses would be expected to penetrate below the blockage (j location'during the process of blockage formation.
Before the frozen oxidic melt completely blocks the flow area, significant quantities of melt could drain through the zirconium plug region. In an as-assembled fresh assembly, the bottoms of the fuel rods are initially 2.0 centimeters (0.80 inch) above a 1.4 centimeter (0.55 inch) thick stainless steel debris filter plate. The debris filter contains numerous 0.48 centimeter (0.19 inch) diameter flow holes that normally admit flow to the coolant flow channels. The overlying assembly is supported by the twenty-four zirconium alloy control rod guide thimbles that are secured by screws to the debris filter. A zirconium alloy instrument guide thimble is also attached at the centrallocation of each debris filter.
The debris filter is welded to stainless steel legs that stand upon the 36 centimeter (14 inch) thick stainless steel core support plate. The flow holes correspond to about 35 percent of the plate cross-sectional area below a unit cell containing one fuel rod. A cold plate at the coolant saturation temperature thus provides a considerable heat sink to freeze melt that should enter any of the flow holes. Table 4.a6 compares the available plate heat sink with the enthalpy available in melt at the liquidus assumed to fill the flow holes.
Another perspective on the heat sink of the debris filter may be gained by calculating the equilibration tc mperature between the steel plate and melt filling the flow holes. Results are shown in Table 4.a7 where it is seen that the equilibration temperatures are well below l]
the stainless steel melting temperature. Transient freezing calculations of melt initially having 10 degrees Kelvin molten superheat flowing through a debris filter flow hole were carried out. In these calculations, the driving head for the melt was taken to be the 2.0 centimeters (0.80 inch) height between the debris filter and the zirconium alloy plug.
Results are presented in Table 4.a8. The hole is calculated to be blocked in only 2.9 seconds or less.
The mass calculated to penetrate below the hole at the time of hole blockage is rather low; 0.061 Kilogram per fuci rod in the case of nonporous melt.
However, the debris filter may also be heated by melt collecting atop the plate in the space between the plate upper surface and the bottom of the zirconium alloy plugs. This space may be as high as 2.0 centimeters (0.80 inch) cc,rresponding to the as-manufactured spacing. However, during operation, this distance may decrease by as much as 1.3 cen-timeter (0.5 inch) due to irradiation-induced growth.
C/ 4-34 I
I
) Table 4.a6 Heat Sink Potential of Stainless Steel Debris Filter Plate at
~-
Bottom of Fuel Assembly Blockage Porosity Stainless Steel Heat Sink Oxide Melt Enthalpy Between Melting Between Liquidus and Steel Temperature and 398K*, Melting Temperature,a KJ KJ-0.0 6.5 4.8 0.1 6.5 4.3 0.2 6.5 3.8 0.3 6.5 3.4 a Based upon a unit cell having a side equal to the fuel rod pitch.
Table 4.a7 Equilibration Temperature of Type 304 Staltdess Steel Debris Filter p Initially at 398 K with Oxide Melt Initially Having 10 K Molten Superheat G
Blockage Parority Equilibration Temperature K
0.0 1516-0.1 1440 0.2 1360 0.3 1270 Thermal equilibration of a heat generating melt layer 2.0 centimeters (0.80 inch) high with a preheated and heat generating blocked debris filter radiating downward to water will melt the complete debris filter steel thickness. Transient calculations predict melt-through times of 200 and 270 seconds for melt having porosities of 0.0 and 0.2. However, long before such times, heat transfer will melt through the control rod guide thimbles and the instrument thimble in the space between the debris filter and zirconium plugs.
For example, a 1.1 millimeter (0.045 inch) thick zirconium alloy wall is calculated to melt C/ 4-35
. - - - - . . -. - - - _ - ~ - . . . - - - . - . .
Table 4,r3 Transient Freezing of Draining Oxidic Melt inside -
~ /- Debris Filter Flow Hole ;
Melt Porosity Oxide Freezing Time to - Melt Macs Penetrcting Block Channel, - Below Debris Filter, a l
s Kg ,
L 0.0 2.9 0.061 O.2 2.8 0.047 a Based upon a unit cell having a side equal to the fuel rod pitch of 1.26 centimeter i (0.4% inch). .
through after only 1.4 and 2.0 seconds after contact with melt having a porosity of 0.0 and ,
0.2, respectively. ,
Without the support of the thimbles, the overlying portion of the blockage in the zirconium plug region could settle downward atop the debris filter and any oxide frozen L atop the debris filter while displacing melt in the space sidewards. Thus, the zirconium l plug region blockage may be relocated atop the debris filter blockage wlth a small amount of frozen oxide sandwiched in between. In this manner, a blockage would be formed atop the assembly inlet module legs atop the core support plate. ,
References
- 1. Magallon,D.,R.ZeyenandH. Hohmann (1990)"100Kg ScaleMoltenUO2 Out-of-Pile l
~ Interactions with I MFBR Structures: Plate Erosion and Fuel Freezing in Channels,"
International Conference on Fast Reactor Core and Fuel Structural Behavior, Inver-ness, June 4-6.
- 2. - Schwarz, M., P. Soussan, M.C. Stansfield and K. Miller (1989) " Interpretation of Out-of Pile Experiments on'the Propagation and Freezing of Molten Fuel," Liquid Metal -
Bolling Mbrking Group Proceedings-Volume II, Winfrith, September 27-29,1988,878, May.
- 3. Soussan, P.,- M. Schwarz, D. Moxon and B. Berthet (1990) " Propagation and Freez-ing of Molten Material Interpretation of Experimental Results," Proceedings of the 4 36
,+w-'* ~ - ~ ,r,, ,,-,
1990 International Fast Reactor Safety Meeting, Snowbird, August 12-16, Vol. II,223, American Nuclear Society.
- 4. Spencer, B.W., R.E. Henry, H.K. Fauske, G.T. Goldfuss and R.L. Roth (1970) " Sum-mary and Evaluation of Reactor Material Fuel Freezing Tests," Proceedings of the International Meeting on Fast Reactor Safety Technology, Seattle, August 19-23, Vol.
IV,1766, American Nuclear Society.
- 5. Spencer, B.W., D. Vetter, R. Wesel and J.J. Sienicki (1983) " GAP-4 Molten FuelIntersub-assembly Gap Drainage Experiment: Result and Analysis," Transactions of the Amer-ican Nuclear Society,1983 Winter Meeting, San Francisco, October 30-November 3, Vol.45,394.
- 6. Spencer, B.W., R.J. Wilson, D.L Vetter, E.G. Erickson and G. Dewey (1985) "Results of Recent Re:aor-Material Tests on Dispersal of Oxide Fuel from a Disrupted Core,"
Proceedings of the International Topical Meeting on Fast Reactor Safety, Knoxville, April 21-25, CONF-850410, Vol. 2,877, Oak Ridge National Laboratory.
- 7. Spencer, B.W., J.F. Marchaterre, R.P. Anderson, D.R. Armstrong, L Baker, D.H. Cho, J.D. Gabor, D.R. Pedersen, J.J. Slenicki and R.P. Stein (1986) " Status of Argonne Na-tional Laboratory Out-of-Pile Investigations of Severe Accident Phenomena for Liquid Metal Reactors," Status and Technology of Fast Reactor Safety, Guernsey, May 12-16,
' 1986, Vol.1,231, British Nuclear Energy Society.
- 8. Tattersall, R.B., R.J. Maddison and K. MilM (1989a) " Experiments at AEE Winfrith on the Penetration of Molten Fuel into Pin ' : :vs and Tubes," Liquid Metal Boiling Working Group Proceedings-Volume II, Wintriur,:5eptember 27-29,1988,535, May:
- 9. Tattersall, R.B., R.J. Maddison and K. Miller (1989b) " Experiments at AEE Winfrith on the Penetration of Molten Fuelinto Pin Arrays and Tubes," AEEW-R2480, March, Atomic Energy Establishment, Winfrith.
D 4-37
( /-
73 (( ADDENDUM TO CHAPTER 5))
I V; ADDITIONAL PREMIXING RESULTS The purpose of this addendum is to:
- 1. Show an expanded set of premixing results, including further variations of the breakup parameter (B), and longer premixing times;
- 2. Scope out the effect of higher ambient pressure (3 bar); and
- 3. Provide all premixing results in a new, more clear representation, so one can visually appreciate the explosive " quality" of the premixtures.
Starting with the last item, the idea is to provide snapshots in the ef - a plane, showing the composition of each computational cell by a point, the color of which is keyed to a colored length scale. Looking at a sequence of such snapshots one can visualize the extent of spatial volumes involving fuel and water together with the corresponding fuel length scales.
The following figures are such plots, each marked by the run identificat;on number and the time. The first 11 figures show in expanded form those portions of each run for which the premixture is most energetic (assuming it can be triggered). The relation of the i
O so-deducedenergeticqualityof thepremixtureswithquantitativeresultsobtainedthrough ESPROSE.m can be confirmed by comparison to the results shown in the addendum to Chapter 6, The rest of the figures in the present addendum show,in a smaller format, the complete premixing histories for three typical cases.
The runs made are summarized in Table 5.al, where the nomenclature utilized is the same as in the report. All runs were started from the beginning of the pour (this means that all runs reported previously were repeated with the latest version of PM-ALPHA.3D), with an appropriate inlet for the melt at the top of the computational domain. In the overlap region comparison with the old results was good. To save computation time the two RCI runs were made on a Cartesian (2D) grid, which is a good approximation given the width of the pour relative to the radius of curvature.
Especially interesting to see, in the long records, is how the f6 - o maps converge to a common " shape," with most points concentrated around the 6f ~ 0 and a ~ 90%
axes. Also, it is clear that the " sensitive" premixtures are small in size and of a short time duration. These trends confirm our previous conclusions, but are more clearly and comprehensively illustrated by the present method. Also, we can see that the 3 bar run shows nothing unusual compared to the other ones, n
5 13
t I
Table 5.a1 Summary of PM ALPHA.3D Premixing Runs
- C1' RC1 .C2 10- .C1-10 .
C2-10 20 C1-20 C1-20-2.5 cma C2-20 .
C1-20-3 bar6 30 C2-30 >
40 C2-40 nb Cl-nb Cl-nb-2 cma C2-nb
- The last entry indicates the grid size in centimeters.
6 Ambient pressure of 3 bar.. -
\
]
- L/ . 5-14
-y - - . g q s-- w 4 ,., .,g.-wF* *-'t - - - ' + k
q /N
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C1-10 Particle Diameter (cm) 0.50 1.00 1.50 2.00 0.5 t = 02 s t = 0.22 s t=024s t=026s 0.4 -
4 0.3 -
0.2 -
. . e 0.1 . . *-
0 ""* * * * *# * # * " "" * - ""#
0.5 t=028s t = 0.3 s t = 0.32 s t = 0.34 s -
0.4 -
0.3 -
. 1 0.2 . . .
0.1 .
0 0.5 1 0 0.5
. .. .c 1 0
. . . . _ . . .. L 0.5 1 0 0.5
. .d 1 a a a a i
,~
3*
I l I, ~,)
G w %/
C1-10 Particle Diameter (cm) 0.50 1.00 1.50 2.00 05 t = 0.36 s t = 0.38 s t = 0.4 s t = 0.42 s 0.4 -
0.3 -
4 8 =
U2 0.1 *
.a .* .,' , . -
o . . a. . . . * .3sre .
+ ..Id1 ., . .8 wn . . . . . -
0.5 ,
t = 0.44 s t = 0.46 s t = 0.48 s t = 0.5 s 0.4 .
0.3 -
er ,a 0.2 -
e 0.1
.< g. *. .
o . .. . . fE . . ,e' . . . . ,4 ._ s .,&
O 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 a a a a
,.~
_ ,x . ,e
-Y C1-20 Particle Diameter (cm) zw errussnE 0.50 1.00 1.50 2.00 0.5 t=02s t=022s t = 0.24 s t=026s 0.4 '
'O3 -
C 02 -
' O.1 . < . o.
, o n
0" " ""
- E "' **
- 0.5 t=028s t = 0.3 s t = 0.32 s t = 0.34 s 0.4 -
0.3 6 . 0 4 0.2 -
. .' =
0.1 ,
e . *e
- * * . 9 ?. 9% $ *a mamme
- a 9 ah __ -O W &*
O 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 a a a n
f C1-20 Partde Diameter (cm) m e n :+ a m 0.50 1.00 1.50 2.00 0.5 t = 0.36 s t = 0.38 s t = 0.4 s t = 0.42 s 0.4 0.3 -
6 0.2 -
0.1 a
.; .. .. t-o . - . ...=~ . . .. .,
. . a _ .. . .. wJ . . . . , . .a
- 0.5 -
t = 0.44 s t = 0.4G s t = 9.48 s t = 0.5 s 0.4 03 -
6 0.2 0.1 .
- w ^ * *
.e o -......... .'s % . .~ m - c.k . . . . , .,s.n s 4 n
. . . . m%, ;
0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 a a a a
n, ,. m ,-
C1-20 3 bar Parbcle Diameter (cm) i 0.50 1.00 1.50 2_00 0.5 ,
t = 02 s t = 0.22 s t=024s t=026s 0.4 -
0.3 -
o' 02 -
g < .
- 0.1 . = * . .
n 0" ** # ***
0.5 -
I t = 028 3 t = 0.3 s t = 0.32 s t = 0.34 s 0.4 -
0.3
- 5
. $
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. E 0.1 . . .
O
_ d* .* . . we. .. 2m e m .D*
0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 a a a a
O O O C1-20 3 bar Particle Diameter (cm) 0.50 1.00 1.50 2.00 0.5 t = 0.36 s t = 0.38 s t = 0.4 s t = 0.42 s 0.4 -
g a 0.3 -
S' g 1 O.2 0.1 .- * -
,.* ,e = ,
==
. ,. go
... .. L s1 . . . = . .. . , (s.1 _a. . .. . 1 < ,< a . .s . .a r. c ..e o
0.5 t = 0.44 s t = 0.46 s t = 0.48 s t = 0.5 s 0.4 0.3 -
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0.2
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fx m U (J J C1-nb wm 0.50 1.00 1.50 2.00 0.5 .!
t = 0.36 s t = 0.38 s t = 0.4 s . t = 0.42 s O.4 0.3 .
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O.3 -
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- *** * ** *** ' '# *** ** ' L***** -' *"
- O 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 u a a a
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RC1-20 Particle Diameter (cm) 0.50 1.00 1.50 2.00 0.5 t=02s t=022s t=024s t=026s 0.4 '
O.3 -
eews temme c>
. ye . .
02 a ** := 'l 0.1 , e ; 3 ll f 1; 4.
O b ' * * * **"* *
- 0.5 t=O28s t = 0.3 s t% 0.32 s t = 0.34 s ,p,=
0.4 ***
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s i,'i.: .
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J C2 Particle Dameter(cm) 0.50 1.00 1.50 2.00 0.5 t = 02 s t=022s t=024s t=026s 0.4 '
O.3 '
6 .
0.2 -
0.1 .. m. ",
= o g O "" C ** ## T*%
0.5 -
t=028s t=03s t=0228 1 = 0.34 s t
0.4 -
0.3 -
- {* l 4 #
02 0
=
h 0.1 . %- # ..
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0 05 1 0 05 1 0 03 1 0 05 1 a a a a
O O O i
t C2-10 Partde Diameter (cm) 0.50 1.00 1.50 2_00 0.5 t = 0.36 s t = 0.38 s t = 0.4 s t = 0.42 s 0.4
.. .., i 02
- d I 02 f. *
. , e - !
0.1 .' .
0 .. -
a;.4 - - . . . -.-a . ~ .
ax 0.5 m I t = 0.44 s . t = 0.46 s t = 0.48 s t = 0.5 s 0.4 0.3 -
= .J* .1 e 1 I *
- 02 -
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o, 0
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h 1 0 0.5 a
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C2-20 Partde Diameter (cm) 0.50 1.00 1.50 2.00 05 t = 02 s t=022s t=024s t=026s 0.4 -
03 6
0.2 **
- 0.1 .. == % o a ip ig 0 ** " " * * * "
0.5 t = 028 s t=03s t=032s t = 0.34 s ,
0.4 -
0.3 -
c .
. . . . e. " d.4 e
Jn 02 -
0.1 .
. . .a g 1 ., p *
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1
O O O C2-20 Partde Diameter (cm) 0.50 1.00 1.50 2 00 0.5 t = 0.36 s t = 0.38 s t = 0.4 s t = 0.42 s 3.4 -
0.3
- 02 $ k\
j $
=
0.1 *g 3 9 .
o . - - .a s Ak . . m., _ - - ' .. .n - .. d - a - -W t 4 i 0.5 e !
=
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0.4 -
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= =, =,
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= .
2 0.1
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Partcie Diameter (cm) 0.50 1.00 1.50 2.00 0.5 t=02s t=022s t=024s t = c_"5 :
0.4 -
03 6
02 -
= , *
. = .. . .
7
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,, =
0 " ** u~' '
O.5 l
t=028s t = 0.3 s t = 0.32 s t=034s 0.4 -
0.3
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=
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0.1 *
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0.5 r :. %
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h I
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NJ J cz-30 Particle Dameter (cm) 0.50 1.00 1.50 2.00 0.5 t=036s t=038s t = 0.4 s t = 0.42 s 0.4 0.3 -
I *
~
1 i '
i 02 . .
0.1 . .
te* .k
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w ***.Sa*r^ _-1 'u '* tn
- ' dis 3
0.5 - =
t = 0.44 s t = 0.46 s t = 0.48 s t = 0.5 s 0.4 .
0.3 -
J i i 0.2 -
- ** **=
- 0.1 .,. ,.= ,
O-
_. w L.* $E -
..=. .~M -
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1
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%d ] %d C2-40 Particle Diameter (cm) 0.50 1.00 1.50 2.00 0.5 t = 0.36 s t = 0.38 s t = 0.4 s
- t = 0.42 s 0.4 -
0.3 . .
C *\ en 4 9 02 -
0.1 . . . ,
. . . . f. .
. .. . s- .
v .
b
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- . l
. . i 0.3 .
- 4 4 4 8 >
02 -
e 0.1 . .* g - . 1- .$ .L 0
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a a a a '
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~s s (q_)
c24 Partde Dameter(cm) 0.50 1.00 1.50 2.00 0.5 t = 0.36 s t=038s t = 0.4 s , t = 0.42 s 0.4 0.3 ,
< . . , 4 , s, e -
0.2 , . ,
0.1 * * - * *
. , p g ,
, ,* * * " ""* = "#* , *
,, . .. % .. . .. "E ON d' * " " - ' ' * " ~"* '" * *^ *
- 0.5
. t = 0.44 s . t = 0.46 s t = 0.48 s t 0 0.5 s 0.4 -
==
0.3 -
j 6 4 4 9 %
0.2 -
4 a'
, a ..
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~
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0.5 x:u . . . .
.. . r2 ...
u x' . . z .e.n O 1 0 0.5 1 0 0.5 1 0 0.5 1 a a a a
O O O C2-10 Partcle Dameter (cm) 0.50 1.00 1.50 2.00 t=0s t = 0.02 s t = 0.04 s t = 0.06 s t = 0.08 s t = 0.1 s t = 0.12 s t = 0.14 s !
I e'
02 0 - -
t = 0.1G s t = 0.18 s t=02s t=022s t = 0.24 s t=O26s t=028s t = 0.3 s 02 *
=
- *= ** *.. *
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O' - " " * * * ^% ~~ --
00 t = 0.32 s t = 0.34 s t = 0.36 s t = 0.38 s , "t = 0.4 s t = 0.42 s t = 0.44 s 5 t = 0.46 s e ee, oy e, 0.2 I l h ! [ 3
^ ^
T' ~
^ ~ ^^
- ^^
0--
t = 0.48 s t = 0.5 s t = 0.52 s
- t = 0.54 s a t = 0.56 s t = 0.58 s t = 0.6 s t = 0.62 s 0.4 ,
~_
l { j " 4 02 ; ; e' f ="
) *
. % I h $ Ma n.k e, Y Q_____
0 0.5 10 0.5 10 0.5 10 0.5 10 0.5 10 0.5 10 0.5 10 0.5 1 a a a a a a a a !
n
-_-_. ___ _ ._m_ _m___m- _ - - __ -r .~t-
O O O C2-10
, Particle Diameter (cm)
- 0.50 1.00 1.50 2.00 t = 0.64 s t = 0.66 s t = 0.68 s t = 0.7 s t = 0.72 s t = 0.74 s . t = 0.76 s ' t = 0.78 s 0.4 *
= *
.
- c . . =. . .
02 -
< s s , .s 1
l O _- _ .
sb -_ . .. r ? -
L' --
1 $1 b] - -
Y ;
~
t = 0.8 s t = 0.82 s t = 0.84 s t = 0.86 s t = 0.88 s t = 0.9 s t = 0.92 s
- t = 0.94 s
'. , . +
> 0.4 *
- g ! I e * '
,)
4 02 ._ f .. .
j 0"-" $l""**bl t = 0.96 s t = 0.90 s a t=1s
~-
N" t = 1.02 s b " "' "
- l t = 1.04 s
.,5 $ i ' " A " A '
t = 1.06 s t = 1.08 s ,
t = 1.1 s 0.4 ,
02 * * *
- s a j g T 1 1
3 -
09 "
'P" "* M '
"" " - - N ' * "" -" <P- "- --- ~
<r--
t = 1.12 s t = 1.14 r t = 1.16 s t = 1.18 s t = 12 s *
} t=122s
.
- 4 t=124s t=126s e 0.4 . y e ;
. - I 0.2
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)
0..-. _
(*b . .. ,,. _ .
_,J ... .. J _ _ ... ,. ;
4 I
O C2-10 +
Particle Diametet(cm) i 0.50 1.00 1.50 2.00
- .y t = 1.34 s
- 8.
t = 1.28 s t = 1.3 s t = 1.32 s t = 1.36 s t = 1.38 s
- 0.4 t = 1.4 s .
t = 1.42 s
, ; e, ,
g .. *.- ,J ,*
- o' * * *
- 02
- 1 d L 1 / I.I.
- . = - - -
_ ,s - I O _-
t = 1.44 s J t = 1.46 s 0 05 10 05 10 05 10 05 10 05 10 0.5 1 0.4 *J a a a a a a e
t 0.2 Id &E j
04 w 05 J.l10 -a -
'A
! 0 0.5 1 '
a u
.i
\
1 l
l 4
O O O C2-20 Particse Diameter (cm) 030 1.00 1.50 2.00 g t-Os t = 0.02 s t = 0.04 s t = 0.06 s t = 0.08 s t = 0.1 s t = 0.12 s t = 0.14 s 02 0 -
~'
t = 0.16 s t = 0.18 s t = 02 s t=022s t=024s t=026s t=028s t=0 .3 s
- 02
- e 1
8
- Y;
.. +
.. 3. . . . .
. o or u
a L lL,
- n. w'. . :
Af 1, s i
t = 0.32 s t = 0.34 s t = 0.36 s t = 0.38 s t = 0.4 s t = 0.42 s t = 0.44 s t = 0.46 s
= * .
- *.1
- 0.2 1 1 f j i 0 -
^
T~ +- - -- -T -- ^~ ~
- +^ -
^- -
I t = 0.48 s t = 0.5 s t = 0.52 s t=054s t = 0.56 s 3 I t = 0.58 s a t = 0.6 s t = 0.62 s O.4 T.
T i
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0 05 10 0.5 10 0.5 10 0.5 10 0.5 10 0.5 10 0.5 10 0.5 1 a a a a a a a u
O O O C2-20 Partde Diameter (cm) i 0.50 1.00 1.50 2.00 t = 0.64 s t = 0.66 s . t = 0.68 s
- t = 0.7 s t = 0.72 s .. t = 0.74 s
- t = 0.76 s t = 0.78 s 0.4 . .-
O2 ,
, .4 . .* . .e ** ** *A f f 0
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^
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-- - 'r' '
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t = 0.8 s t = 0.82 s t = 0.84 s t = 0.86 s t = 0.88 s t = 0.9 s t = 0.92 s t = 0.94 s
" 9' o'O.2 k*
4 A
'i 4 9 @ % R
'h A
_ _s _a _8 3 -
- ' ' '"' ' J '
^ ^^ *II ~ - " " ^
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l t = 0.98 s t=1s t = 1.02 s t = 1.04 s t = 1.06 s t = 1.08 s t = 1.1 s .
t = 0.96 s e 0.4 *
- r t s . *, :<
.- **1 9 ,a . ='
g q q 02 % *1 1 ) ). .. *, *e<
- a e h % *A o<
_ . .h* , , =,
ed . . .-- ... ___
t = 1.12 s t = 1.14 s t = 1.16 s t = 1.18 s t = 1.2 s t=122s t=124s t=126s 9 -
0.4 1 ,
g o 1 4 . .* %
O2 *p
- s*
g- _
- O O O C2-20 Particle Diameter (cm) 0.50 1.00 1.50 2.00 0.4 t = 1.28 s ,
t = 1.3 s 3 t = 1.32 s ,
t = 1.34 s , t = 1.36 s .. t = 1.38 s j t = 1.4 s j t = 1.42 s 1 1
..d g y s Y
- O2 \*f 2 2
- a _ J .
._ _ _ . . _ _ _ )*. _ _
j
' ' ~ ** *'
t = 1.4' s t = 1.46 s t=1 .48 s j t = 1.5 s ' t = 1.52 s .i t = 1.54 s t = 1.56 s t = 1.58 s ,
- " 4
. 4 4
~
= 0.2
' 'E '$ *
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- ~
^d
^
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4< J ?. '~^ ^ "V ^- ^
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'j 0 05 10 05 10 05 10 05 10 0.5 10 05 10 0.5 1 0.4 t = 1.6 s ..l. a a a a a a a e t o~ e e 02 0 + ""
0 0.5 1 a
I i
i i
t t
O O O C2-nb Pa:ticle Demeter (cm) l O.50 1.00 1.50 2.00 t=0s t = 0.02 s t = 0.04 s t = 0.06 s t = 0.08 s t = 0.1 s t = 0.12 s t = 0.14 s g ;
02 !
O t = 0.16 s t = 0.18 s t=02s t=022s t=024s t=O26s t=028s t = 03 s 0.4 .
. o 02 (
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e O - '" " -"* D " "*
t=034% t=036s t = 0.3S s t = 0.4 s t = 0.42 s t = 0.44 s t = 0.46 s 0.4 t,= 032 s
- e. ,
c . y w 4 g J I .e, a 02 . . ,
A *.
L*.L*J a I. s * . .**S h 8 " e A . 3,j 01 A**
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i t = 0.6 s t-GA3s . t = 05 s , t = 0.52 s t = 0.54 s ,' t = 0.56 s ] t = 0.58 s j t = 0.62 s I i 0.4 *
,, , t ,
c 3 . .- .i .. . o 02 .
s t. . . . *
.. =
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n i m0.5J5' 10 8
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- i n % _ !. apfe l ' e = -
- v . .A ,
O 0.5 10 0.5 10 0.5 10 0.5 10 0.5 to 0.5 10 0.5 1 a a a a a a a a I
L i
i
?
J t i
i
i O O O :
c2-<e Parbcie Dameter (cm) 0.50 1.00 1.50 2.00 t = 0.64 r, 1 t = 0.66 s I t = 0.68 s , L t = 0.7 s .
t = 0.72 s
- t = 0.74 s t = 0.76 s t = 0.78 s OA .t .< .. . .. .
t 0.2 . I. .
.I.
- 8
. .#. .F.
s *(
OM J #- l b d* i b ^* # ' - - I' ** -1** l h* -
B= *- L 'S - -
t = 0.8 s ., t = 0.82 s % t = 0.84 s t = 0.86 s t = 0.88 s t t = 0.92 s t = 0.94 s
- . ; .. .. .. = .= -
h.,=0.9s
, 02 . . . . .. ..3 .,-
6 uu A
- n *. k . a *.
- 4 a:
t = 0.96 s t = 0.98 s t=1s t = 1.02 s t = 1.04 s A. kh .A ,
=
t = 1.08 s t = 1.1 s l t = 1.06 s l if 02 sq p<
s
, c ..he, a.. x % . . %, . . . _ u a.A - . . -
- ' ~
t = 1.12 s t = 1.14 s . t = 1.16 s . ' t = 1.18 s . t = 1.2 s t=122s # t-124s t=126s *
(
i 0.4 . .
i e
)j
_ s . .i .J *1 '
- ,4 0 *<
1 02
'11#1 p, g.
J '
.; I ..J .4
., e< >
d '* * -
** ' ** I "'* f ** ^* l' ****' "***# d ' " ***## E i '
i
! i i
1 !
1 i l
i ,
l
\ [
U c24 Partde Diameter (cm)
OJ50 1.00 1.50 2.00 0.4 t=128s 4 t = 1.3 s
- t = 1.32 s
- i t = 1.34 s * *d t = 1.36 s . t = 1.38 s .! t = 1.4 s
/. t = 1.42 s
. t 3 .:. .
. i
. .n 1 < <.
02 *g .
,, .a . i .a 9 .9 +1 i
.T . ' 4*
M# j 4 *.:4n A *2, ) .ti .
- g c'<
. 4 21 ui s .. . *.1 lit -V t.1 l n _
n n A. *e ,i i *. . %* r 0.4 1 = 1.44 s 1 ,
t = 1.46 s t = 1.48 s '.
t = 1.5 s
< t = 1.52 s
<- t = 1.54 s q
< ,l t = 1.56 s 8
f t = 1.58 s
[
a . , i i
! L 4 m. .Y IL 4 %. it 4ei
- ii das I t4k **i . 4 ' lM *
- ie-
,i
, 0 0.5 10 0.5 10 0.5 10 05 10 0.5 10 0.5 10 0.5 10 0.5 1 a a a a a a a a
)
I t
1 t
I 6 1
i
(( ADDENDUM TO CHAPTER 6)) :
ADDITIONAL EXPLOUION RESULTS
'The purpose of this addendum it to:
- 1. Extend previous ESPROSE.m runs to longer times;
- 2. More thoroug: ' explore the effect of trigger timing, and of the breakup parameter
(#) used in premaing;
- 3. Repeat selected cases with finer grids; and
- 4. Examine the effect of the entrainment factor in the microinteractions model.
The main results are summarized in Table 6.a1. The RC2 run in this table was u lggered with a doubled up (azimuthally) RC1 premixture. Also,it should be noted that while the RC1 premixing run was made on a Cartee.lan (2D) grid, both the RC1 and RC2 explosion runs were made in 3D (but with the same, small, grid size).
We see that a number of premixtures yield impulses in the 100 kPA s range but this occurs over short premixing intervals, while outside those intervals the impulses are in the 10s of kPa s. The 200 kPa s result in Table 6.1 corresponds to C2-20(0.30) that n
V yielded 120 kPa s. Repeated trials with neighboring triggers failed to reproduce the old result. This was peculiar to this case only, and we have to assume some sort of error, or singularity. Also, we find very good consistency with the finer grid runs. These results are confirmatory of those presented earlier, they elucidate more completely that it is unlikely that a more sensitive premixture has been missed, and support the previous conclusion that lower head failure is physically unreasonable. ,
The figures that follow show the detailed new results in the same format as before (like Figure 6.5) in the report. To give an improved perspective of the " spread" of the impulse, three area curves are presented. The solid line corresponds to the area subjected to pressure within 70% of the instantaneous peak value. The dot-dash line and dotted line show the areas with pressure greater than 700 and 350 bar, respectively. Occasionally the three lines are close enough to appear as a single solid line.
6 15
. ._ . ___ _ _ _ _ _ - _ . . - . - ~-
l I
l Table 6.a1 Summary of the ESPROSE.m 3D Explosion Runs
- C1 RC1 C2 RC2 10 50 (0.23) 100 (0.25) :
50 (0.24) !
17 (0.25) 90 (0.25)* '
80 (0.25)6 14 (0.30) 32 (0.30) j 14 (0.35) -13 (0.35) 20 100 (0.25) i 100 (0.30) 110 (0.30) 120 (0.30) 140 (0.30) 1 11 (0.35) 14 (0.35) 11 (0.40) 30 - 100 (0.25) 150 (0.30) g y
40 90 (0.25) 110 (0.30) nb 30 (0.25) 17 (0.35) 40 (0.25)
-45 (0.35) 52 (0.35) 17 (0.45) 25 (0.45) 26 (1.40) 20 '1,40)
(
The entries show the peak local impulse (kPa s) and the number in parenthesis is the trigger time, referred to be melt arriving at 1 m above the water. These times are offset by 0,18 s relative to the trigger time shown in Table 6,1 of the report. C1 and :
C2 denote the 200 and 400 kg/s cases, respectively, The nb case denotes "no breakup".
- Calculation carried out with entrainment factor twice the conservative value '
normally used. _
6 Calculation carried out with entrainment factor four times the conservative value :
. ' normally used,
, +
~ .. -. - _. .a - _ - - - . . - - . . . - . .. -:
t
?
t f
i f
t 1
i FIGURE 6.a1 i f
Pressures, impulses, and effective areas (see Chapter 6 of the report) ;
at the locations of peak loading in each run.- !
i l
b i
i f
1 I
4 4
4 9
d i
9 2
i-t 4
6-17 i
f f
,--~--.....--...--.,.--.,,,,,.-,,wn,--.-n-,,-.,,-.,--. , , . . =, - , , . ' , , . . .-av.m.,,,, ,ww..-
O 01-10(0.23) 2000 1500 '
1000 -
0 0 1 2 3 4 Time (ms)
C1-10(0.23) 60 g ,
7 40 -
3 -
O I"0 0 1 2 3 4 Time (ms)
C1-10(0.23) 0.01 i 0.006 -
0.006 - !
0.004 -
I, 0.002 -
I 0 1 2 3 4 Time (ms) a
I i
i i
i
?
t i
i C1-10(0.24) 2000 ,
f !
1800 -
f 1
1000 '
1 I
800 - :
^Y 0 !
0 1 2 3 4 :
Time (ms) l C1-10(0.24) e0 50 - <
40 -
30 -
f g i < !
+
10 - <
~
O 0 1 2 3 4 ;
Time (ms)
C1-10(0.24) 0.03 -
. t 0.025 -
T 0.0k -
- f. !,
E0 .015 .' i.
g ,1 0.01 *i l 0.005 -
I:
I :
0 0 1 2 3 4 Time (ms) s P
I
I l
O l C1-10(0.25) ~
280
' i 200 '
r 1 150 - < ;
50 '
0 -
0 1 2 3 4 i Time (ms) !
C1-10(0.25) ,
20 >
7 15 -
10 ' <
5 <
0 ,
0 1 2 3 4 t Time (ms)
C1-10(0.25) ,
0,04' < !
0.03 0.02 '
O.01 . .
s 0
0 1 2 3 4 Time (ms)
.t O
h r
i t
c C1-10(0.8) 120
[, t 100-f h N' 00' '
4 40 [
t
' i 20 1
0 'i 0 1 2 3 4 ;
Vme(ms) {
C1-10(0.8) i 15 7
10 -
- l. .
0 I 0 1 2 3 4 Time (ms) ;
C1-10(0.8) 0.01 ,
0.000 -
T_0.006
. 9 0.002 - -
0 0 1 2 3 4 Vme(ms) ,
1 f
s
& 9,- ... y-++. --y's3. , y e v- p e--r. w,-'v.,p. s,v,,y--.p ce r e e -ig-e ,-ve.-e,w---wrig v r. ..v ,w,-r. %-e.s ,-=,e.--
-e v e ....-v=.-e- .-n.,.-.w.. w-.ow-..-,- , - - >,wa-w,- 4-m+.
4 MI 4+L-e.. .'e+~Jd .4 J k=A aJ,.hwu, 4sha.4h4.-5.-h 4> 4 _ 3.; a ...wh__apa _4 bp.- ,.2...5A. Aah1gE.-%4.m 4_.4mu +w_,e.-m.. .4-,e.a.l..e. A-m i wam mmaa.m.,,-.s a w ma l
C1-10(0.36) l I ,
1 100 '
I i
0" 3 4 0 1 2 Time (ms) ci-10(0.35) .
15 !
7 g 10
- g. ,
0 1 2 3 4 Time (ms) c1-10(0.35) 0.01 0.000 '
{ 0.006 10 .
- 0,002 '
0 0 1 2 3 4' Time (ms)
O :
I
,m,. .,.._..,,...o
.,__,m.__...,.,_._,.._-,.,,-..m,, , . .- ,~._ _, , - .... y z,_.
A 24-a- - L34m e.--m--@ n- A. . , -- --4 e 4Q am st .u,a.nowa.a J. $ was2a 4a< is,. nK A h-&-= E-Mam- - +-A M4---e--am a. " AAS.a-m.-*
5 4
C1-20(0.3) 5000 1 3000 .
j_ 1000 -
0 1 2 3 4 Time (ms)
C1-20(0.3) 120 ,
100 -
7 i
O I .0 *
.0 .
0 0 1 2 3 4
- Time (ms)
C1-20(0.3) 1 0.0e .
'^
"~ 0.06 E i' O.04 -
,/gi ,
_ 0.02 8 Ii *i ,
e ', i 0 1 2 3 4 Time (ms) s
4
- _+sg., 4+d J.,___. 4,.,84.- % ,--+4w-,_#ha. Aw A M wa.. Msus diaig M ,_ a MJ.Whai.a ,h .*i m J.. m,a,4 ._sA sm.a._
a.p-g O
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g g . -
1
-1 00 .
j .0 . .
' 20 .
-J 0
0 1 .2 3 4 Time (ms) .
c1-20(0.35) 12 10 '
ilt O . I'6 2 :
0 0 1 2 3 4-Time (ms) c1-20(0.35) 0.01 0,008 -
- ^
g0.006
- f 0.004 0.002 -
0 0' 1 2 3 4 Time (ms) w - , e r.- ,,+--1, ,
r-- e -- .- + , s e
p 4 .e,.J - 4,, a a -- a - ans. ,id .#g,qA4 4uf,rd,JJ-J. ,a,.,,d.u- 4. 4. 6 A e e s A,5 3 .a .Ar.J=m 4m*c .mAe.a -, - imma a m -.-.mAwr-du**--m4-.m%w-i T
t O 4 C1-20(0.4) 120 100 -
f80 -
- g. .
l 40 20 -
0
.] s 0 1 2 3 4 Time (ms)
C1-20(0.4)
-12 ,
- 10 7
- g. 6
- o i4 2 0 1 2 3 4 Time (ms) ci-20(0.4) 0.01 0.006 -
{ 0.006 f 0.004 0.002 -
0 0 1 2 3 4 Time (ms) i .-
i-L LO rvey- g-w- +g- , - . + - * -- ,- -vy--w- s- n-w---
,,w --- a n. ~ + . . a - w _aam, a: a a. ~ .-- .s
,v: a 4
4 O
ci-rb(0.25) 200 150- <
l 100'
.0 0 1 2 3 4 ,
Time (ms) c1-nb(0.25) -
30 25 -
7-20 -
!O l '15 0
0 1 2 3 4 Time (ms) ci-n5(0.25) 0.01 0.008 -
0.006 -
f 0.004 0.002 -
0 0 1 2 3 4 Time (ms)
O
(
a i
+
' C1-nb(0.35) i 1800 4.
.f1000 i +
. 500 -
i a
if .
0
~
0- 1 2 3 4 Time (ms) s C1-nb(0.35) - _
4 50 n 40 -
9 e
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I h'10 -
l
(_
0
-0 1 2 3 4 i
Time (ms)
C1-nb(0.35) .
?: 0.os , . . .
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l .
! %, 0.02 -
i +
1 0,015 -
l :
0.01 -
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0
, 0 1 2 3 4 Time (ms) .
.), t
- l. -
(I .
t l
l~
,. w
a yc p* A .s a >4=6 a -<a, a-s.caxw-- r -.e nsa' 4s- p-1---rau a -~.-.e. .- :s u r a m a, - =~w s
I
-i O
C1-nb(0.45) 200 150 -
~ i 100 -
-i a
g , *
, 0- 1 2 3 4 Time (ms)
C1-nb(0.45) 20
/ '
2 15 1o .
i 3-5 -
0 1 2 3 4 Time (ms)
C1-nb(0.45) 0.01 0.008 -
0.006 -
f 0.004 O.002 -
0 1 2 3- 4 Time (ms)
F h-4 0
l -.
, q
sk.- .m ___ % ase.X.E -. e- I. m .m J...wa- m_h__mJ..r--,hm_~_a m._ _aw a.r e..,ma.me.amwa- , .am - _ .- p e.
O :
ci-nb(1.4) ;
500 400
. 1-200 -
100 -
0 0 1 2 3 4 Time (ms) c1-nb(1.4) -
30 25 -
7 '
i 15 -
10 -
5 -
0 0 1 2 3 4 Time (ms) c1-nb(1.4) 0.02 -
0.015 -
O.01
. 0.005 -
n 0 1 2 3 4 Time (ms) n.
.. f'
'\:
- n: -
m- -m-+
O RC1-20(0.8) .
2500
-- 2000 -
r 1500 -
1000 -
' 0 '
0- 1 2 3 4 Time (ms)
RC1-20(0.8) _
120 100 T -
80 -
O I '. 20 0
0 1 2 3 4 Time (ms)
RC1-20(0.3) 0.04 -
A h
I\
P= f,l !! i i.
0.01 l ij 0
}! 'i 0- 1 2 3 4 Time (ms) n O
.. - -w--,,.-.- ,,-vn - -, + = ,
A 3 n --n&,-- a a a-A.-a ss.La m ..e24, w s. - 4.0,d 4--
a e n.-w w - - ,-wvvw-- a-5 O
s RC1-nb(0.35)
'1000 800 -
600 -
j .
200 O
u 1 2 3 4 Time (ms)
RC1-nb(0.35) 20 2 15 -
i 10 -
cO I5 .
0 0 1 2 3 4 Time (ms)
RC1-n_b(0.35) 0.01 0.006 -
0.006 -
f 0.004 1
0.002 -
0 0 1 2 3 4 4
Time (ms)
- -u w -->-iw..sm a A. aa ha; 5ae eiwd463.,:,A 4, Wmnr pA..ah.e_ 4.a5... p 4 ks ,5A5, 4 .m J - .,4-. g4lp..E. nia ,.w. meg h m.eg.s -&iv.. :ena.m.i.mda. g b 4. 4ese&uj A p 4
O
~ C2-10(0.25)-
5000 P
j_ .
0 0-u 1 2- 3 4 Time (ms) ca-10(0.25) 100 -
9 80
_00 40 -
O -
0 1 2 3 4 Time (ms)
C2-10(0.25) 0,15 -
l 1
To.1 !1 1 il 4
- o.os -
!l -
i !.
0 A!
0 1 2 '3 4 3.:. Time (ms) ,
O 4
f gnyt ye r c -r- -cg <--m w e- - - - - ,e-e- -,,v--w-m, e ,,+ w a . - - - - , - e.-.a,--, c,= --
t O
C2-10(0.25)2X Entrainment 4000
- - 3000 -
1 j_- 1000 0
0 1 2 3 4-Time (ms)
C2-10(0.25) 2X Entrainment -
100 80 -
9 f 60
!O ja 20 0
0 1 2 3 4 Time (ms)
C2-10(0.25)2X Entrainment l
0,1 5 9
0.05 -
}.
0
' ~
O 1 2 3 4 Time (ms)
O 4
O C2-10(0.25)4X Entrainment 1500
, f,1000 .
500 .
0
. 0 1 2 3 4 Time (ms)
C2-10(0.25) 4X Entrainment 80 7 60 -
i 40 .
--( 20 0 1 2 3 4 Time (ms)
~
c?-10(0.25)4X Entrainment 0.12 -
0.1 .
T- O.06 -
Ef p.k.
0.06 -
'I j 0.04 -
0.02 -
i '.
O l' i 0 1 2 -3 4 Time (ms) 4 O
., . . _ ,4
. ~ . - = . - . . . . . . . . - . . .. . .- . _ - . . . . _ . . ~ . . . . - . - . . . . . . .-.
.,. l r
l l
C2-10(0.3) -
1000 800 -
h I
1 600 -
400 - I 200 0
0 1 2 3 4 Time (ms) ,
C2-10(0.3) 40
~
7 30 -
l 20 -
Jii 10 -
l
~
0 0 1 2 3 4
- . Time (ms)
C2-10(0.3) 0.03 -
0.025 -
$ 0.02 -
O.015 -
0.01 :
0.005 -
0 0 1 2 3 4 Time (ms) l l
,.D 9O c ff ,
2__ __w u 2 _4 ._m. _ . - - . ,
..._,.,,.__.a.
. , .,m__ m ..m... _.._,._.a_._% _ . .. .,, .. .,m,_ ...-. . _ . . ___ _ __ _
e 9
l
'O a
- C2-10(0.35) 120' 100 -
90 -
-l t 80 t
- j. .
. i m .
0 0 1 2 3 4 Time (ms) c2-io(0.35) 15 10 -
!o b ,
l 0
0 1 2 3 4 Time (ms) c2-1o(0.35) 0,01 0.008 -
f0.006 0.004 -
' O.002 -
0 0 1 2 3 4 Time (ms)
i 5
. I s .,
i: _
.C2-20(0.25) 2500 -l
~
2000 -
-i 1500 -
i 1000 -
/
500 -
0 0 1 2 3 4 Time (ms)
- C2-20(0.25) 100 -
- 80 -
e i
k;80 '
20 -
0 1 2 3 4 Time (ms)
C2-20(0.25) 0.4 .
.i"
~(' ,
E 0.2 -
0.1 : :
./1 i O
n\.
t 0 1 2 3 4 L-1 Time (ms) a 1 ~-
'i _.
d 4
y y- c w. g ,-p ut=>; e w - w. s. or y m.-r , - g- y , e .e=q g e.e e-~- %,e 7-,.m..- --w,, ,-w --p + , - , . e<ow-- w me -.,-w.----tw-,
, . . . . . . = - , . u - . . . ~ . -. _..a. .a.. - ~ . ., - - . . . . . -->.... .
e O
c2-20(0.8) e000 5000 -
'f4000
.000 .
2000 -
0 0 1 2 3 4 Time (ms) c2-20(0.3) 150 7
100 -
t g },0 .
0 0 1 2 3 4 Time (ms) c2-20(0.3) 0.0s -
p,
'S \\
~ 0.04 -
i I
0.02 -
{
l
.0 0 1 2 r 4 Time (me)
O
--,-,,--,---------,---,,--,-------,------w- - - ,-,m- w a .naa 2, s ,,ss,._n,,_un,-p_,g.say-,_se p_w,,._k, , _ _ - - ,4-ys x, , as .k.m-An.n.2354- J,- 4..,4.,,.,%s c2-20(0.35) 120 100 '
1+ 1
.0 -
T.
1 g , 1 0
-d' 0 1 2 3 4 ,
- Time (ms) c2-20 10.as) 15 7 l 10 - '
O I' ,
0 0 1 2 3 4 Time (ms) c2-20(0.35) 0.01 0.008 -
0.006 -
j 0.004 - -
. 0.002 -
0 0 1 2 3 4 Time (ms)
O
M a3 --W E m 4w-- w - - -
4 & 44 A di 6m<- ...Aw-4--62=4d =44w -*.MAA=- -ma--,~. p.m.A+>-h 8- e.w es "^=-J'AX= d-wm=-p WG w b
c2-30(0.25) 1000 i i
1 000 . .
1 .
f . 00 '
-i
~
0- .1 2. 3 4 Time (ms) c2-30(0.25) - !
120 100 -
7 80 00
! 40 -
20 -
- 0 1 2 3 4 Time (ms) e
+
C2-30(0.25) -
0.15 -
T. !!
~g 0.1 ,,! i
( , . . -
i 0.06 - ! i,
(
0 0- 1 2 3 4 Time (ms)
-g
- m. * --.e& _ S = 4.gr4.; _a 4_.444 .J.a. ..al.m 3..,.M 4>e hMd J # _J+. m,w __.4AJ#M.A, 5
i c2-30(0.3) '
5000 4000 -
1_ 1000 j 0
f -
0 1 2 3 4 Time (ms) c2-30(0.3) 200 i 100 -
O I*
0 1 0 1 2 3 4 N kN C2-30(0.3) 0.1 :
~~
0.06 -
1' g- 0.06 -
0.04 -
/i 0.02 -
Ii 5
0 0 1 2 3 4 i Time (ms)
O
I t
' 1x I.
i
- C2-40(0.25)- -
e00 500 t
t i
1200 - i 100 -
0
=0 1_ 2- 3 4.
Time (ms) .
C240.25) 100 ,
i gn ,
7 f80 -
g .0 20 -
i 0-0 1 2 3 4 Time (ms) 4 C2-40(0.25)
+
0.08 -
i 0 -
T .06 0.04 -
0.02 -
5 O
o 1 2 3 4 '
Time (ms) 4 4 4 +
4
. 1
A A adF-.+E.A
% --h.mlE. Aq= ...As. J J w., A - 4 .giw,,A-m.mA&w4 4'iwa-4g em _ a.a m.msa,,#,-um,_,waA.pa_ms aw4,, . a w_s.aa.a e
'. <4'*q'
- O C2-40(0.3) 2000 i
4
- 1. .
0 0 1 2 3 4 Time (ms)
C2-40(0.3) 120 100 -
7
.0 .
20 .
0 0 1 2 3 4
, Time (ms)
- C2-40(0.3) 0.06 -
0.05 -
j
$- 0.04 -
0.02 .
! i 1
1 0.01 1l I
g Il l 0 1 2 3 4 Time (ms)
,\
~
O
@ ( y w b ie- -
- - - - y v w:- g.- + - ?y- y w e w-
.x 4-Aa, , - , . 'H A__a s a S..+sa atm,,=,__,A, 2 _ssn.V. a 4 ,,k.,,g, w, m i, s _ a men,, .ms-v q L
O ,
c2-nb(0.25) 300 250-
. 200-1 150-100 50 0
0 1 _2 3 4 Time (ms) c2-nb(0.25) 50 40 -
9 f30 g20 10 -
0 0 1 2 3 4 -
Time (ms) c2-nb(0.25) 0.03 -
0.025 -
( 0.02 -
, 0.015 0.01 0.006 0
0- 1 _2 3 4 Time (ms)
U u
, -l-.
-,e g - , , - - , - m .<,w-
C-r a s _ip ;, a ,__ w 4,. 44 ,;_.a, ed._g ,4.44c._.s % J a. m + m - _.-a ...Js...ma.m,,a e e o-, 4 i
I O
C2-nb(0.35) 2000 I
~ 1500 -
1 1000 -
0 '
0 1 2 3 4 Time (ms) l c2-nb(0.35) 60 50 -
I a.
g 40 -
13 -
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(( ADDENDUM TO SECTION 2.1.2]) _
G DRIFT FLUX RELATIONS WITH PM. ALPHA.L ,
As with PM ALPHA, comparison with the drift flux model is performed to verify the capability of PM ALPHA.L in simulating correctly the momentum interaction in a i particle-fluid two-phase system.
The calculations were executed by specifying a finite mid-section of a long water column (54 cni long) a uniformly distributed particle cloud, The particle cloud is then
" fluidized" by providing a uniform inlet water flow from the bottom. The final " steady-state" particle volume fnetion and the corresponding dimensionless drift flux predicted by the calculation are then compared with the model.
Four cases are presented. In the first three cases, results are generated by an initially
- 18 cm long particle cloud.with a volume fre.ction of 15% and particle diameter of 0.5 cm. Three inlet velocities are used (20,30, and 40 cm/s) and they lead to three different equilibrium states (15-20,15 30,15 40) as shown in Figure 17. To test the effect of different initial pa rticle concentrations, an additional calculation is performed with an initial particle
, volume fraction of 2% and an inlet velocity of 40 cm/s (2-40). The four cases compare well with the drift flux correlation.
0.14 , , , , ,
0.12 #
15 -
0.1 - -
'5 0.08 -
(( 0,06 -
15 40 2-40 0.04 - -
"' ~ ~
. M.DW g i I f f I O 0.1 - 0.2 0.3 0.4 0.5 0.6 Particle Volume Fraction Figure 17. PM-ALPHA.L simulations compared to the drift flux curve.
O v 2.1.21 i
.~._- . .. .. ~ - . . . . - - . - - - . . . . . . - . . - - . - - - - - . . . - . . . . . -.. -- - - . -.
i (ADDENDUM TO SECTION 2.2.3)-
QUEOS TEST SIMULATIONS WITH PM-ALPHA.L' -
Herein we provide results of recalculation of sample QUEOS tests using PM-ALPHA.L.
Three cold tests (Q5, Q6, and Q8), and one hot test (Q10) are simulated. The Lagrangian particles are shown in projection, such as they appear in the photographs of the experi- l
- Inent.
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. (( ADDENDUM 1 TO APPENDIX B))
ON THE REGIMES OF PREMIXING by ;
Sergio Angelln!, Theo G. Theofanous and Walter W, Yuen Proceedings, OECD/CSNI Specialist Meeting on FCI !
J AERI-Tokai Reserch Establishment, Japan, May 19-21,1997 i O iJ s
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1 ADDENDUM 1 TO- APPENDIX B v
ON THE REGIMES OF PREMIXING
-Sergio ANGELINI, Theo G. THEOFANOUS and Walter W. YUEN Center for Risk Studies and Safety University of Califomia, Santa Barbara, Santa Barbara, CA 93106 USA Phone: (805) 893-4900; Fax: (805) 893-4927; e-mail: theo@theo.ucsb.edu Abstract: The conditions of the MAGICO-2000 experiment are extended to more broadly investigate the regimes of premixing, and the corresponding intemal structures of mixing zones. With the help of the data and numerical simulations using the computer code 1 PM-ALPHA, we can distinguish extremes of behavior dominated by inertia and thermal 4 ' effects-we name these the inertia and thermal regimes, respectively. This is an important distinction that should guide future experiments aimed at code verification in this area.
Interesting intermediate behaviors are also delineated and discussed.
Keywords: Premixing, Steam Explosions, Vold Fraction, Flash X-ray Radiography -
V 1. INTRODUCTION It is now well understood that large-scale steam explosions are highly dynamic events of propagative character. The media that support such propagations are called premixtures, and they are characterized by the volume fractions and length scales of their constituents-melt, liquid coolant, and vapor Premixing is called the process that leads to the formaticn of premixtures, and it is a highly transient, generally multidimensional process govemed by intense mult! phase interactions (although mild by comparison to the propagation itself). As a key step in developing the proper understanding and predic-tive capability, starting with the MAG'CO experiment (Angelini et al.,1992), premixing has been studied with the help of solid particle clouds. This focus on multifield aspects removes a key unknown, the melt length scale, and with well-defined initial and bound-ary conditions, allows unambiguous comparisons to predictive models. Perhaps more importantly this approach ellows for a systematic variation of the experimental condi-
. tion, so as to exercise the predictive tools, at the fundamental level, over wide ranges of conditions. This approach was continued with the MAGICO-2000 experiments, and more recently with the QUEOS and BILLEAU experiments in Germany and France, respectively.
-V B-37 m
The MIXA experiments, which opened the way, together with MAGICO, employed pre-g)
( broken up thermitic melts, and thus they weie also guided to a large extent by similar considerations (Fletcher and Denham,1993). How to build towards including breakup on this basis has been discussed and demonstrated in connection with specifying and using (for reactor assessment) the PM-ALPHA code (Theofanous et al.,1997a; Theofanous et al.,
1997b).
The present work is continuing the efforts on the multifield aspects. Our main pur-pose is to introduce the notion of " premixing regimes". Specifically, with the help of advanced MAGICO-2000 tests and PM-ALPHA calculations, we distinguish extremes of behavior dominated by inertia and thermal effects. We name these " inertial" and
" thermal premixing regimes," respectively, and expect them to provide an important additional anchor in planning future experiments and assessing completeness of code verification efforts.
- 2. PRELIMINARY CONSIDERATIONS As described previously (Angelini et al.,1995), PM-ALPHA calculations under cold MAGICO-2000 conditions revealed a plunger-like action-that is, deep cavities or " holes" in the liquid pool forming just behind the descending cloud and closing up a short time p later. The volume fraction of solids in the cloud, before entering the water, was ~10%
V and MAGICO 2000 experiments confirmed these predictions. This " plunger" effect is even more pronounced in the QUEOS experiments, where the mode of particle delivery produces very dense (" lumps") particle clouds with volume fractions of ~17%. Here, the length of the clouds is rather short (~30 cm), the water pools are saturated at the top and subcooled due to gravity head, and they are subcooled further due to self-pressurization, and the steaming appears as a short burst coincident w'ith the lifetime of the water " hole"
(~250 ms). Even with hot runs this is a heavily inertia dominated behavior, not really ger-mane to the premixing process. PM-ALPHA calculations indicate that to avoid theinertia regime, the particle volume fraction must be reduced to just a few percent. In MAGICO-2000, the pours are longer (150 cm), and by comparison to QUEOS rather dilute (~ 2%),
and this places them outside of the range of inertia dominated regimes. However, the corresponding pour duration is only ~0.33 s, and a purely thermally-dominated regime would have even lower particle volume fractions and, particularly, prolonged pour dura-tions. These considerations lead to a special adaptor in the MAGICO-2000 facility and the experiments reported here. In these experiments, we have achieved pours of ~0.5% par-ticle volume fraction, ~6.5 m length and ~1.5 s pouring time, for a thermally-dominated behavior.
q d B-38
- 3. EXPERIMENTAL APPAh ATUS AND MEASUREMENT TECHNIQUES V The MAGICO-2000 experiment has been described previously (Angelini et al.,1995).
Its central component is the graphite heating element, illustrated in Figure 1. It can deliver up to ~5 kg of ZrO particles at temperatures up to ~2000 *C. For the present experiment, this element was " fitted" with a special device, such as to deliver the cloud at a much
" diluted" condition-volume fract>on of 0.5%, pour length 6.5 m, pour duration 1.5 s. An overall view of the experimental ssand, including key dimensions, is shown in Figure 2.
In the present experiments, for the interaction tank we employ a two-dimensional slab geometry, as illustrated in Figure 3. The principal emphasis in measurements is placed in -
visualizing the internal structure of the whole premixing zone, and in obtaining respective composition maps. This is done by radiography, employing flash X rays, as explained h detail by Angelini and Theofanous (1997). With two film cassettes placed one on top of the other, we can map a 35 x 73 cm region, as illustrated in Figure 3. Particle volume fractions are obtained by counting. In all regions of the film not occupied by particles the steam volume fractions are obtained from the film density and appropriate calibrations.
The resolution is 200 dots per inch and the void fraction accuracy is estimated at 5%
(relative error).
I spacmg between holes: 8 mm O
2 5 cm diameter o
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200 mm i i r N/ l N ,
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203 mm \ l 196 mm Figure 1. The heating element in MAGICO-2000.
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In addition, we obtain photographic records with a 35 mm still camera and two video-cameras. During the pour the particle temperature is read using a two-color pyrometer.
- 4. EXPERIMENTAL RESULTS AND INTERPRETATIONS A total of eight experimental conditions were investigated, as summarized in Tables 1 and 2. The key point on these is that the ZrO2 Particulate volume fractions varied by about one order of magnitude. For the zero subcooling runs, saturation throughout was assured by boiling the wahr pool from below. In the following, code predictions will be shown alongside the presentation of experimental results. The code is the version documented by Theofanous et al.,1996, and the inputs for each run are according to the specifications given in Tables 1 and 2. Only the following additional clarifications are necessary:
- 1. The Cartesian geometry was modeled by matching exactly the dimensions of the tank.
- The pour area was modeled by matching its size in the direction of the tank width (the large dimension of the tank), and by spreading it over the entire depth of the 2D field (the small dimension of the tank). A 2x2cm (runs in Table 1) and 2.5x2.5cm (runs in Table 2) numerical grid was used.
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- 2. To determine more precisely the position of the fronts in the Eulerian calculation, we superposed Lagrangian tracer particles, made to move with the local (cell) velocity of the particulate fie.d.
Table 1. Conditions for the Cold MAGICO-2000 Runs in a 2D Slab Geometry Run Particle SizcTotal MassParticle VolurncImpact Velocity X-Ray Time Fraction
[mm) [kg) [%) [m/s] [s]
ZCN 2 5.5 ~6.5 ~5.2 12,0.25,0.3,0.35,0.4 ZCT 7 5.0 ~0.5 ~4.4 0.1,0.8
'/'s. . B-41
Table 2. Conditions for the Hot MAGICO 2000 Runs in a 2D Slab Geometry Run Particle Total Volume Impact Particle Water X-Ray Size M ass Fraction Velocity Temperature Subcooling Time
[mm) [kg) [%) [m/s) ['C] [*C] [s]
Z11 2 5.5 4.2 5.2 1550 0 0.3 Z12 2 5.7 4.2 - 5.2 1400 10 0.3 Zb13 7 4.8 5.5 5.2 1600 0 0.3 ZT14 7 5.1 0.5 4.4 1650 0 0.8 ZT15 7 4.4 0.5 4.4 1800 0 0.8 ZT16 7 2.6 0.5 4.4 2500 0 0.8 O .
The five radiographic images taken for the conditions of run ZCN (this means five repeated runs under identical conditions) are shown in Figures 5(a) through 5(e). The
- void fraction distributions deduced from the first three radiograplu are shown in Figures 6(a) through 6(c). We can clearly see the " hole" described above and its closing at ~0.35
- s. Notice the visualization detail as, for example, the " clean" shapes of the upper cavity boundary, the highly structured lower portion of the cavity, and the fine detail on the hydrodynamic jet and its disintegration into spray, following collapse. PM ALPHA pre-dictions are shown in superposition to these radiographic images in Figures 7(a) through 7(e). Note the " wing" pattern of th'e particle distribution and the accurate depiction of the key void characteristics in the calculation. Also interesting to note is the exact matching of closing and timing and even shape of the emerging jet. Some numerical diffusion is present, as seen for the particles, and a small amount of void (~10%) retained below the
, liquid surface after closing (Figure 7(c)).
The aim of ihe dilute pour runs was to avoid this inertia-dominated plunging regime, and this aim was achieved as illustrated with the results of runs ZCT in Figures 8(a) through 8(c). Note in these figures the unifonn particle cloud distribution in the air and O
b B-42
a e ~t he deceleration (increase in concentrktion) obtained 'in the water pool. We also see that a small amount of air, entrained with the particles, produces void fractions in the 10 to 20% _
range in the central portion of the mixing zone. Such small amounts of air are expected to '
be negligible under the strong steaming at hot run conditions.
The radiographs of the six hot runs conducted, under Table 2, am shown in Figure 9(a) through 9(f). It is clear from Figures 9(a) and 9(b) that the small particle runs produce
- highly voided regions (90 to 100%) even under 10'C subcooling, although in the latter case we see a more limited, in size, voided region. The void fraction maps for the other four, large particle, runs are shown in Figures 10(a) through 10(d). In the three dilute runs, the particle volume fractions in the mixing zone were found to be in the 0.6 to 1.1% range. It is
-interesting to note here the essential difference in regimes between Figures 9(c) and 9(d).
In Figures 10(a') and 10(b), we read corresponding void fractions in the 90 to 100% and 60 to 70% ranges. Also, it is interesting to note from Figures 10(b),10(c), and 10(d) that a ,
change in particle temperature from 1650 to 2000'C does not appear to have a significant effect on the resulting premixtures. Numericalinterpretations of these data are shown in Figures 11(a) through 11(f) We find all the essential qualitative and quantitative features to be in excellent agreement. These include the location of the particle lower fronts and upper boundaries, the void fraction levels and the locations of sharp gradients, and the voided region pinch-off in the subcooled run. The effect of the temperature and particle size seems to be captured very well also in the calculations.
The last three runs in this series are idealized representations of what we wish to call the " thermal regime" of premixing. As shown above, the behavior is not only quan-titatively but also qualitatively diPerent, and this difference becomes more vivid if the internal structures discussed above are viewed in the context of video records of the whole interaction vessel. Due to space and time limitations, this additional information will be presented in a future paper.
- 5. CONCLUSIONS The conditions of the MAGICO-2000 experiment were extended to more broadly investigate the regimes of premixing and the corresponding intemal structures of the mix-ing zones. With the help of the data and numerical simulations using the computer code PM-ALPHA, we could distinguish extremes of behavior dominated by inertial or thermal effects-we name these the inertial and thermal regimes of premixing, respectively. This is an important distinction that should guide future experiments aimed at code verification in this area.
n.
d . B-43 4
yS ACKNOWLEDGEMENTS ,
1*) 'Ihis work was supported under the ROAAM program carried out for the US DOE's Advanced Reactor Sevem Accident Program (ARSAP), under ANL subcontract No. 23572401 to UCSB.
REFERENCES
- 1. Angelini, S., E. Takara, W.W. Yuen and T.G. Theofanous, " Multiphase Transients in
' the Premixing of Steam Explosions," Proceedings NURETH 5, Salt Lake City, UT, September 2124,1992, Vol. II,471-478. [See also Nuclear Engineering & Design,146, 83-95,1994.]
- 2. Angelini, S., T.G. Theofanous and W.W. Yuen,"The mixing of hot particles clouds
. plunging into water", Proc. 7th International Meeting on Nuclear Reactor Thermo-hydraulic.4, NURETH 7, Saratoga Springs, NY September,1995;
- 3. Angelini, S. and T.G. Theofanous,"Vold fraction measurements by means of flash X-raycadiography", OECD/CSNI Specialists Meeting 01. Advanced Instrumentation and Measurement Techniques, Santa Barbara, CA, March 17-20,1997;
- 4. Fletcher, D.F. and M.K. Denham, " Validation of the CHYMES Mixing Model," Pro-7q U ceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994,89.
- 5. T.G. Theofanous, W.W. Yuen and S. Angelini," Premixing of Steam Explosions: PM-ALPHA Verification Studies," DOE /ID-10504, September 1996.
- 6. Theofe. nous, T.G., W.W. Yuen and S. Angelini, "The Verification Basis of the PM-ALPHA Code," OECD/CSNI Specialist Meeting on Fuel-Coolant Interactions, Jaeri, Tokal, Japan, May 19-21,1997a.
- 7. Theofanous, T.G., W.W. Yuen, S. Angelini, J.J. Sienicki, K. Freeman, X. Chen and T. Salmassi " Lower Head Integrity Under Steam Explosion Loads," OECD/CSNI Specialist Meeting on Fuel-Coolant Interactions, Jaeri, Tokai, Japan, May 19-21,1997b.
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1 S M-M
~~ ~ -:iQ :,D,N .y.+:. :M!'."y,-,
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~~ m'z., a s; .-. _ ,Qq,ifv,' JA *. i J
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)
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i
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V .. 3.- ._%Vf - l i i
,\x x
1 b.au _
--L-4 - _
m.. ,._ _ !
! s\
\'~'/ - Figures 7(c) and 7(d).
J %-m4 h..%e4*46thm.4--4..hm w . A #4 - e.e mam aa a. .a -"s.h
. hmma a h--w-- -- --m- -w---
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l l
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Figure 7(e).
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l l
- l l
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l ; ;y- A:.
1 l
. m,% n g",*[tg%}3f'j A, s n . ..
f 7{f%
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i, 4 *sN#@Y, ~..f $4' 7
$iyuhQ, NNh. -
1
}
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l I
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. ~ , o ,. _y \
l '*, % ,-. i i t. '
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. . p . . .e .* s. t * .y.
- o. .. .r ,. : . .*. ..
.g... , .
l l P
1 ,
l l
i I I l <
1 l
t l
4 k i
+ r. ,
Figure 8(a). Radiographs and deduced volume fraction distnbutions from runs ZCT:(a) image of a portion of the particle ck>ud in the air,(b) radiograph of the mixing region at 0.8 s following contact with water, and (c) quantified version of the radiograph, i
i l
i i
5
.. _> w P 3 r,
- l.
i
~, 1X - -
,,g , 1 xe
.. w gg ; j ja - tjid, , , ;- -,-A
. b - %,- ,ye .vo Id ;,g ,g;I ) C yk h
, N j !
.ap,; e; a. ,
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,,+
j r ; -:rg *kp$4a i -v 4, ,
., ,~ :. ,,n . ,
j
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, . - - >11.9,'$9@jf()sf;j;J
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d.: y, ,y
- k;,k ,'w i t , , .
"g 4 uf., -. *g w... *1 ,c 4t w
- 4j , - g"p[ f . 7,
- ~,',o.-,
c
'iw
. ', k t., . N_ . ., g gc , ,
s.m'p-% m 'i, i,i
'
- g> t,
?
Cl.
a
) wN' soo.+ e
-j i I l t
p i l
i e
6
(:
1 Figure 8(b).
i
.- . .....-__-...s
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i !
l !
]
) i l '
I '
i Vold Fraction i
(%)
100 .
,J '
Jc
,l 90
.. , i.
. ~' 's 80 t
.s .
s '
e,. ,
,* n 70 nu m
<, v. . t..--.c..
.L.- ,
60 gn
,1 <
9: , ,., vv ee . 9 ,
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'iv V.5 - D, it d[* '
7.Y * . Pj ,' . { r !: .
i
, 3, Ja c ,
. _ _ .S - # *. t- - 8. d.IT1D' ,,-.h I~ l 30 1
i i 20
- l. 10 i
1 0 F
h
..i
\
M. . .
I Figure 8(c).
i I
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l
~____ _ _ _ _ _ _ - - - _ _ _ _ _ - _ - . _ _ _ _ - . _ - - - _ _ _ _ . _ . . . . - - . , .
p I
t l'
l l
I i: ,
3 }" % %,M Y "3% rg 'V y (t{f"i A
~,,.9' V s:e
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f mgh, > s? yk.w. ' m. C yw j /
v ~- .n.
g
.s-
/n
~ ml g - L i
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l p ; *pg +.47 p.,97 s g4Ay ?;. , , .p.y. hg,Jfh ;s 44q d pj.4_? d pg afga. ,
my + gp > ,.s g; f *
- y j ; .v :e s e; ; ._ n ~ ,.
- N g/ 9
-e -
g %eg,
- e-
. o g
.. . F. ..G .* s,e l ' .y.
e
- o. ... r,. t .** . .g
- r .f .. . .
i I
i i
- l
.i 1
I I
I I
I i
d4 M
... -,t.
s .
.,,.i 4 .. -
Figure 8(a), Radiographs and deduced volume fraction distributions from runs ZCT:(a) image of a portion of the particle cloud in the air,(b) radiograph of the mixing region at 0.8 s following contact w ith water, and (c) quantified version of the radiograph.
i l
. _ .-.. - ,. - - - ---- - .- -- . - - - - . ~ . - . - - - . - - . - . . .
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)
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l l
i
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- 9.
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, s- -
e 4 .. 4. , t
, n ~ y v. . +- : :: n.t'"' ,
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, c .
g 1 ,..,
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A v l
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,. je vv;<$ peg, g- 3 ;
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. u,--3 p 4
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by,l$ h, ..n(%h?hq;y\f,,,_.,<,
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+
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4 i
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. :1 Figure 8(bK
. - . v. - - .w. _ - . . - - . . _ , . . . - . , . . , . . , . _ . . , . , _ - , - - _ ,_m,..mww.,,,,-,...,.w ..,e ,- . ..--,-,---,e-m ,..,-w,-,.
-*'6>AA44 -
.m A sp m m im.4dee.s.e.N A.wam-a- ---w4w-, ---a.
1
}
I 1
3 I
n
,1 i
1 Vold Fraction
(%)
~
, 100 ii.)i l .- -?J 90 "i
4
- I4 80 70 l
3 of:
?
eo i
&- ,L . o. 50
?
.. .. .a hoy..
,79; 40 i
m . ,..
w a... s.: .s.f. Q. .. ,.: rt.g w- ' -' .
a i
.n .
30 i I ! 20 i 10 1
1 0 I+
as .
Figure 8(c).
__ . . . .._.___ __.. .__ _ . . . _ . . . _y _____ _ _ . . _ _ . . - - _ . _ _ _ _ . . _ _ _ . . _ _ _ _ _ . _ . _ _
1 J
l 1
l e
i 9
1 ,
i b .
I 4
l y J
i j
1 s
a s -
s - t a
6 j
l l ,
4 i
1 r .
i 1
I
, l l
l I
, s., ;_-
1 of-;pM;c - A ,
i I
(kj5Vk ,g..,ygj;,jg{Jq jg;g[;
r t.p5%i: % k% s !?
& w f *"ys ;- x .% ;
Qg5p , . , n:?--
Wt ,
',y *}.?!'}' wnkhn
- -- h. ;- gi l
- }( ! { l Its 's O Q y e ip vv , s -J g;s .*n
.: s^M
[ s_y- 1
l 3 t : >, ; J_
- WN f4;f;, Vif>n ' , '_ff p;? ch .Y. s ...
e -
l?Nlk "~ '?OE~
Figure 9(a) The radiographs obtained in the runs of Table 2, lhe (a) through (O correspond to runs 1I through 16 in the table, t
f
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- l
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n I.k 4 ,. w . . . - , . _ . . . . . _ . . . , . . _ . . . . .
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=
l l l Figure 9(b).
1 1 -.
7._--_.
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l i
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y ./ 4 ) Y v
,/x* .e't w v/ w.j h..L s A' ',,
i
+- i
) -QW.9
,, 1
, , - ,. s ., i I
l r l i i l I l
., i 1
i M -
I Figure 9(c). ,
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1- _
i 1
l l
i l l.
4 -
~
l l
1 4-h, ., 1 op a 1 g ,, :. yp V A) t p[-
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w;i g .
4 p -.-o pq 3-o scy ; , ,
f & ,[' .t
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t ., , > '(, , - ; L, y,
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- m ..nz s. n- x _.a , . ,;....
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v%.' % dt- , ;' % ? % ,
g .d.a
- %. ', 'i. 'cs3 t. ,.
3
,'i',.,* .% .E
- b<
t 2
- l Figure 9(d).
t
- - , . . - . . . . . . _ , - - . . . - . - , - - , - - , . - , - - - - - _ _ , . . - - . . . . . . - , , . _ - . . . - _ . - - . . . - , _ - - . . _ . - _ - - - - - - - - ~ - - - .
. - - _ _ - - - _ _ _ . _ - _ ~
4 h
1 I
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1
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8 n.
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. >. , ;, l% Qf9 - m{l.f 7
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t 3 ,3 ( .w ' -
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4T l . - -)j n d.h.f. - '
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\
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~,
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Figure 9(e).
t I
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . . _ _ _ _ _ _ . . _ . _ _ _ _ _ _ _ . _ _ . . , . . _ . , . .. .._,,_..,_,_.m,..._.-__...,.__.
- - - - - - - - - - - - ----------,-.am,-
,. . - . ,. , ,,,,m, mm .-gw_.__.---m----- -- - - .y , ,--,,,%---
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l
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y 7, *:
l
'R %;b*g . '; ) ~, , ,
. + ;W + , ~ , j , :
, t;<.s ,. 9;; "
' ?e I
I Figure 9(0 !
_ .. . , _ . _ . . _ _ . , , _ . . - , _ . _ _ _ _ , - . . - . _ . _ - . . _ , . _ _ _ , . . _ . - - , , , , , , , - - . . _ ._.,, ._--,,-._. ,m--.
lO v,
) h.:
i i t) l ')
lt' k $ Vold E Fraction i
(%)
! 100 90 l 80 7
!O 4
F 60 4
5 mu 50 I,
f,.-3 q,#
[' . :.
- 1. 10 u,,t q '
l vUM .stg y&
ic f' v y . W
. c. ' ,p,c x-'
i
{a.4 0 i
s, .pt .a A,
'. ,' < .1 -3 A=
, y . ), s. ^
.Jy ,f ,
4 +. s . ) , .I ) [
l 1 ~ :
. 3 \ i< b 1E d
.. i I
Figure 10(a). Quantified images of the radiographs in Figure o The (a) through (d) correspond to the (c) through O (f) in Figure 9. Figure 10(at) represents the upper film shown in Figure 10(a). but scanned so as to emphasize the region of very high void fractions.
4-- Ah-h* Jam- --->4me n e m e mlin E -amM4 a .m
-am--w sr_mm- - - -- - -
i 4
- o !
3 l
i l '
Void Fraction i l
[%)
I
'3 ll {
v O ( : 98 95
,l
! 1t I x, -
,g. + "-'
70 2,,_ y. --
gg
, 6 l I
.~ ,, .
.1 ) .h . 3
) 1
! p #
- l ..
$, q,, , _
M .. .
h Figure 10(at) l
---_ _ _ _ . - - . - - - - - . _ _ - - - - , - - -.---,_n-- ..--n--, -c.,- , - - . -~_ne----. .ve ,v-w~ -
I E.)
t.;
i 4
l l ..
- j, -
~g Void L. ,.
Fraction ,
l' . [%) ;
l i e 100
- # ' f-90
- 2
- . .s ,
~
80 :
g" .
70 g:. ,
y ,
- y. 60 mw w w. ~
nya en OU l ,,
w..
93l wa 40 i ew/9 "
1%vv 30 v5 1 -. j;ns b4 w' J ...3 9W.
+,$ .ths e+
20 '
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w 10 i < m :jg
. . b-~ ~
,~H5 w - 0 W7 t . . '.W <w , . 7 'k i [
& Y f
i W
eq i
i t . . . _ . - - -
j
?
Figure 10(b).
i I
i
- - - . . . , _ - - , _ . . - ~ - ~ . . . - - - - - , . - , . , __
1 i
4 I
i
, -- r. .
l . .
s@
1': Vold
' .dl Fraction r.yf
[%)
a, . <.
- 4.o. 100
- Wjf,7,2 l
l.\/- ...
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90 4.,, . i 'n ,..g . 80 ee .
' 'gh s y, ,,, .g s
g
'P8 $
- t. ;; c + v :;;.q u. y t
, 60
- , 4R L . in" W ' _
w, n9m 50
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n.
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e.g.19.p J.s, .
. _ 4,
. e,e e et.- .
l
.4 - .x u .. .f t,.
Figure 10(c). '
t
+
l---._ _.-- _ -,. - _ __.--- _ _ ,--. ..- .- w - ---,---,...n,,-- --,.,,-,,,,,---,,-n.,, _ , , , - . . . , _ . , , , - . , _ . - , , , , - - - _ -
l l
- w n.. . s j s.
i, ,
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! u l Void l l l Fraction 1 * '
l
, ! [%) i j ;. e. J I
- I
~
100 l <g 90
- 1 1
(.,.. 80
+ .
70
.: 60
= ' M 50 fm
' ~ -
m :n di{gt 40 wy: f,:n:.:
go .
34
. -W;r;tl6 i [df 3.:;rbj .. A.;98:. g . 20
! M t .J . -
$hf{$ - kh ,
b0 r
, vyi. i f: p 1 m
_;-(~lf .
& 0 '
d
,! ?]4" ; m@ 16 t ;. @} > .
,,.y-
- g. . $ - yjh '
- <y ,
l 4
i ;- ; ;
I Figure 10(d).
4 I
O l
l l '
J 1 ,
... s, .
1.0 !
] ,.
l
- q l
b2 9.8 4 .
- s . l i
I.,. 0.0
$ he '$ ,
' ~
g g j 0.2
! < O.0 ,
i vold l l fraction l
i ~
( v'
'f i
1 Figure ll(a). PM ALPHA predictions of void fraction and particle volume fraction distributions at the time and O conditions corresponding to radiographs of Figure 9. Predicted particle volume fraction contour lines are from 0.5% to 4% in 0.5 % interval.
i l
l l w~'
I l
I i
~
1 i, s., ,
1 l
1.0
. , e' l " h. . . . g "*"""" IN O.8 li ,
i :., .
~ll s '
s ' l
~ -
s ..
0.2 0.0
~
VOld fraction l ~
s l
i j
I i
i i
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j ,
i Figure ll(b). I'redicted particle volume fraction contour lines are from 1% to 6% in 0.5% interval.
l I i i l l
l-
j
'l i
)
1 t
J l
s j
l i 1
A i
1 .,, , 1 1
,> , . . +,
?,:
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x 1.0 ,
l .g '
. , g, --
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2 9r -,9 70.8
<, p k:'
i ha .. ;s' . [k 9 ifh,. , af,c 3 0.6
, , 1 l
?:; n;: :-lpjf t
, ~ . _ .- , 0.4 N
' O.2 R .
0.0 void fraction l
l l
i Figure i1(c). Predicted particle volume fraction contour lines are from 0.5% to 3% ir. 0.5% interval.
l l
i
~J .},r ' h d' y N_, ,
- ' h' h& ., ..fI $_J.
- s '-1\>*hk?h'
+~ . . . u : nn ,> s ~ ny. i
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^
r _ ,* .g.,:%.; < ,??kj- n
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s 0.6 dA w.,
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- ';M 0.2 y
0.0 a.
Y s vold 9 fraction
+
I
(
Figure 11(d). The measured (from the radingraphs) particle volume fraction distributions were in the 0.6 to 1.1%
range. Predicted particle volume fraction contour lines are from 0.6% 'o 1.8% in 0.2% interval.
7
l d
i
- )
]
t 9
4 s
n,n ; .:ve, *
- n
'gllGi I j. 0.6 c
%w;y.dy, ,;~
o pjA y.<, :
0.4
- g
- '
- ;(gj r.c. 0.2 y
0.0 4
4 void fraction t
i 1
Figure ll(e). The measured (from the radiographs) particle volume fracion distributions were in the 0.6 to 1.1%
range. Predicted particle volume fraction contour lines are from 0.6% to 2% in 0.2% interval.
I t
l 1
t
i l
l l
r l l
l l
J f
i i
i - .. .
Mfb ,
.n, , v, ,. ,suu.w
- e. , *
+ . , .
S bn..
s 7 ,.-
(
., 4.?
T- x.',;;; ;.e,, ';c. ._ +x' ' 1.0
- 2 'e
'.- y ; ;s.
pf '.
- }
re--_' h,4r>*
, q.,
A; g y p, 'K . .,
- g J.- i,O.8
,.3
~
, m u ..v tp f@
0.6 i
t9a umy yy -;
if:9
,c e-0.4 0.2 ff 0.0 void
- fraction l
d b Y l
4 4
3 l
1 I i Figure 11(0. The measured (from the radiographs) particle volume fraction distributions were in the 0.6 to 1.1%
i range. Predicted particle vo'ume fraction contour lines are from 0.6% to 2% in 0.2% interval.
4 ,
b
i i
-(( ADDENDUM 2 TO APPENDIX B))
.rQ b MAGICO SIMULATION WITH PM-ALPHA.L Here we provide results of recalculations of the MAGICO run ZCN (see Table 1 of Addendum 1 for run identification) using PM ALPHA.L. The timing of these plots corresponds to those of Figures 5b through 5e in Addendum 1. Figure 5a is not included because upon further evaluation this particular run was judged to have a less than perfectly reproduced pour.
4 tg B-77
i
. ~ ~ - - - . .... _ _ _ _ _ _ , . , . , _ _ _ _ , _ _ _ , __,_
\ !,
t ;
i 1'
> I i 1 r
-. 3 .
.I
.::,. it , , . .
~;p /, ..:,;
r .n ~ . . .
l
.t w I p .* i .% -
. s.. .
p- . .
c*
f (a..l*
- f. :
. . HY.' '
': ? me . 33..
.:. l
..,.,. n . .. .
i :
I I
}
j 0.25s 0.35s i
l-.-.----.. . - - - - - -. - - . - . - _ . . - - . - . . . . . _ -
..--...,.~.-.-.-..7- . . - . . . . . - . .
I 1 V
i
}
unus ty m m ac>g
(' . ,,
.L_- - ~
g 443f"g
) ;i R.jt ._.
30.53~ %% ~ gy R. 7;f "
g ,c ;[ .
,,. , y
.u. . y , ,,, 3
.4'
, 3 ;b .) *.'. - ! :- i .
- y M/ ' -
N, . . ,,L,*.,
,.,s. ' ,g.. ( / , ,-
i
-3:~~. $.'; , ,
'.; y t . . N_-- _,. es t
. ,. -x 1-, .p, .
. . . 4. P .',5 .
, =
..s iy g.. s .. .
I i
!s l 0.3s 0.4s 4
. - . - - - ~ . . - - - - - . . _. . ._ - , ._ _ _ , . . .___,_.
p) -
(w PM. ALPHA.L Simulation of run ZCN.
,. ~ . ..
, (( ADDENDUM TO SECTION 3.1.2))
FURTHER COMPARISONS BETWEEN THE 2D AND 3D CODES The previous comparison is updated ir Figures 3 and'4, obtained with the latest version of the two codes, and improved graphics, 2- , , , , , , ,
PM. ALPHA.2D PM.ALPHAJD 1.5 - -
n j -
+
v /
2 1 8
E-0.5 - -
l 0
O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time (s)
Figure 3. Comparison between the PM-ALPHA and PM ALPHA-3D predictions of the pressure in a premixing transient.
Figure 4. The structure of the premixing zone as computed by PM-ALPHA and PM-ATHA-3D.
(see next few pages) t' 31.2-1 m + - - - * -
s-r
I r l 4
r 4 -
1 1
j-i j
! l 1
l O.16 PM-ALPHA 2D PM-ALPHA 3D l
p n -, , .. .. . n- q yvv- ~~ "v- ~ x m - w ,m; '
$ q 3 (/
O.12 ..
b '
l- g-[ < ii '
g g,
- ,j y; 0.6 l 0.08 l
0.06 0.4 l
.i I
0.04 0.2 0.02 0.0 Fuel. Time = 0 s Time = 0 s Void Volume Fraction Fraction i
O r
.---.w-- - , < - . . , - , --.-,a,- -.-,---n -~--.,-.-,--,.-,-.----e - - , , - - - - , - - , - , . , - . - . . - . , . . , - - - - - , , - , - =
h i
i 1
i
+
a 0.16 PM-ALPHA 2D PM-ALPHA 3D
+=r y 4 cpy,% " * - > b r+-- *
,? t; +^ * "* " "'--N - { + t b . ,4 .
.g-q% 1,c p 3 9*]
l ['
- i.
- i, 0,0 0.12 -- l
",.4
- Ji
~~
. W -
)
- 0.06 0.4 ;
e F
i ,
0.04 0.2 l
0.02 0.0
- Fuel Dme=0.1a Eme=0.1s Void Volume - Fraction 1
Fraction I
l f
i i
e i
l r
f e ,
_ _ _ _ . . _ _ . _ . _ _ _ _ _ _ _ _ _ _ _ - . _ __ - _ _ . _ _ _ _ . . _ . . _ . _~.
4 i
I iO J
l 1-1 e
l '
{
i 0.16 PM-ALPHA 2D PM-ALPHA 30 l .s 4
^;
a .
l puem . -
y , , .m , ~1,-w p- .<
m.- -
- . ~ , , ,
i s su , ,,.
0.8 O.12 ., ,
- 3. .
x _
t 0.08 .
0.0 i
0.06 0.4
( .
l ..
0.04 - . 0.2 0.02 0.0 Fuel Time = 0.2 s Time = 0.2 s Void i Volume Fraction Fraction O
. - . , . . . . _ - - . . . _ . - - , - . - - ~ . . - . . - - - . . . . . - . . _ - . - - . . , ~ . . . ,
i-l l
I i
1 l
l 4
i i
1 l
1 0.16 PM-ALPHA 2D PM-ALPHA 3D j q
,,,~- .-
e .-s- r -m,. .n y,-- v: e -- e -. c ~. . -r ~ :, +
L'.
- 2 ._
j ,.t
- - ; 0.8 0.12 ; s = f;-
- i
+
l . , .,
, . . _ m.... - .
r v
0.6
, 0.08 .
0.06 0.4 b
0.04 0.2 ll 4
l h,
v 0.02 - 0.0 Fuel fime = 0.3 s Time = 0.3 s Vold i Volume Fraction
! Fraction i
4 1
i d
i h
i 4
O 0.16 py. ALPHA 2D PM-ALPHA 3D C h
.yy - . , , - , . , ~ - , , - - _ s- . .-. n e - .
0.12 0.8 V;
v:-/ j, .:g} , . -:j 0.08 0.8 0.00 0.4 0.04 0.2 0.02 0.0 Fuel Time = 0.4 s Time = 0.4 s yojo Volume Fraction Fraction O
i
e O
PART III. ADDENDA TO DOE /ID-10503 0
6 O
. (( ADDENDUM TO SECTION 2.1.2))
2D WAVE DYNAMICS WITH COARSE NODALIZATION The purpose of this addendum is to show wave dynamics comparisons at rele-vant length (meters) and time scales (milliseconds). The quality of agreement between ESPROSE.m and the analytical solutions shown in Figures 22-24 is very similar to that presented previously.
O M
' . l'
.2.1.21
l l
i O
ESPROSE.m Analytical Sol.
g i = 0.2 ms a t = 0.2 ms 200 200 e
100 100 0 0 LO I. <
g i = 0.4 ms g i = 0.4 ms' N
, 200 200 e
100 100 c
0 0 4
Figure 22, Comparison between ESPROSE.m and the analytical solution of a the two-dimensional pressure distribution in an infinite pool with source type A. (The mass source parameters are A i= 1.e7, n = 1, and R = 14.14 cm, EEPROSE.m data are generated with Ar = Az =10 cm and At = 1.e-5 s).
1 t__.__..__.__ _ . _ _ . _ _ _ _ __ _
4 4
t I O'
u ESPROSE.m Analytical Sol.
l 300 t = 0.6 ms 300 t = 0.6 ms 200 200 100 100 0 0 l
1 O
300 t = 0.8 ms 300, t = 0.8 ms 200 200, e
100 100 n.
0- 0 Figure 22. (Continued)
O
i l
O l
t-ESPROSE.m Analytical Sct t = 1 ms 300 t = 1 ms 300 l
200 200 100 100 0 0 0
t = 1.2 ms 300 t = 1.2 ms 000 1 200 200 e
1co f100 n.
0 0 l
1 i
' Figure 22. (Continued)
LO l
l l
l
. . ~ . - - - . - _ - . . . . . . . . . . - . . . - - - - - - - - - . _ _ _ . - . _ - - _ - - _ _
O 1
l ESPROSE.m Analytical Sol.
g i = 1.4 ms go t = 1.4 ms I
i 200 200 ;
100 100 E
i 0 0 O !
l l
l I I
g, t = 1.6 ms g i = 1.6 ms a M l t 100 100 n.
0 0 i
l Figure 22. (Continued)
- O
O ESPROSE.m Analytical Sol.
0 0 O
g t = 2 ms 300 t = 2 ms 200 2m ls. 4*
O O Figure 22. (Continued) s.
O
,y . - - . - . . - . - . . , , , - . , . - wn. , x x- n..~, , ..~.-mn....~~.... ,. , - a m
- ~i 1
7
.]
3 i %. g
-i IV. ..
.[
t
! ~N *I . . .. se =
. t = = .m l. ... ,
, e * . t o.J ee g 4 ... . g .... .
J ... .
j ... .
. .. t .. 4.. ... . . . . . . ... . . . - . .. t .. t.. ... ... ... ... ...
stems put
. e. . en 8 8.. **
I m .
-I m .
_... . j - ... . ,
p _ _
= .)
,e.., .e n -
I ... .
Im . ',
f ... . <
i.. .
s s
j Figure 23. Comparison between ESPROSE.m and the analytical solution for the base pressure distribution (z = 0) for the run as specified in Figure 22.
i:
V Y
s t, y
.y-
,w, a .. ,, uce- , , y, y_ , ,+u+ - , -, p ,- ,p- -
- 9
fN-g
'A
)
i ....
I t I ... . ', I ... .
4 9
g.. g
,' t.. -
g
~, %,
l .. . ... .
. .. ....g.. ... . . . . . . . . . . . . . .. l .. t.. . . . ... ... ...
seen. ens
..'*~ ....
l .
I ... . ', I ... . ',
1 ... .% s ... .
s
~~ - s ... . ~- ,
i.
.A -
.q) - -
Figure 23. (Continued)
,-\
is 4
+
_s .
I )
- h/
- e.sene. . ....
. . .w < ... . .
'a-I _ ... -
3 ... .
l .. . j ... .
. .. t.. t.. . . . ... ... . . . ... . ...t.. t .. .........s.. ... ...
.M . tuot g -. . ...
- 8'**-
.j , gg, .
I ... .
I m .
l : ... -
l ... .
.. .. ..., ... ... . . . ... ... ... . 8. t .. t.. ... ... ... ... ...
BM .M
_f \
4 1 g I ... .
.I ...
' l . . ..' . j ... .
.M .M Figure 24. Co'nparison between ESPROSE.m and the analytical solutiori for the centerline pressure distribution (r = 0) for the run as specified in Figure 22.
ja:7
_ - I. _-
,E. -
.j 1
a-
. * ~:.
... . ; i, ,- , ... . i, .....
). ... .
I ... . ,-
1
= g t.. g
- g
' l .. . 1.. .
. ..t., t., ... ...-3., . e.. . .. i .. t .. ... g., as, a., 4..
.M 8M-8.. , 3.. ,
m . g-- ,
I c ... ',
. - \,
i , I.
.] ... .
N %
j- ... .
's %
~. - ~.
. . - M O
Figure 24. (Continued)
. a m
=-
w-x., .--
w s
. . _ -__m_-___._.t._-_ _--
(( ADDENDUM TO APPENDIX C)}
NEW SIGMA-2000 RESULTS WITH STEEL MELT Experimental Simulation of Microinteractions in Large Scale Explosions by Xiaoming Chen, Rui Luo, Walter W. Yuen and Theo G. Theofanous Proceedings, OECD/CSNI Specialist Meeting on FCI J AERI Tokai Research Establishment, Japan, May 19-21,1997 k
~ '
[]
c-29
q ADDENDUM TO APPENDIX C g
EXPERIMENTAL SIMULATION OF MICROINTERACTIONS IN LARGE SCALE EXPLOSIONS Xiaoming Chen, Itul Luo, Walter W. Yuen and Theo G. Theofanous Center for Risk Studies and Safety University of California, Santa Barbara Santa Barbara, CA 93106 USA Phone: (805) 893-4900; Fax: (805) 893-4927; e-mail: theo@theo.ucsb.edu Abstract: This paper presents data and analysis of recent experiments conducted in the SIGMA-2000 fteility to simulate microinteractions in large scale explosions. Specifically, the fragmentation behavior of a high temperature molten steel drop under high pres-sure (beyond critical) conditions are investigated. The current data demonstrate, for the first time, the effect of high pressure in suppressing the thcrmal effect of fragmentation under supercritical conditions. The results support the microinteractions idea, and the ESPROSE.m prediction of fragmentation rate.
Keywords: Fragmentation, Molten Drops, Microinteractions
- 1. INTRODUCTION Over the last few years, a systematic research program has been conducted at the Center of Risk Studies and Safety (CRSS) at the University of California at Santa Barbara (UCSB) to understand the fragmentation kinetics of molten drops under a sustained high pressure environment expected in a large scale explosion (Patel and Theofanous,1981; Yuen et al.,199e; Chen et al.,1995) . Utilizing the SIGMA facilities (both the original SIGMA and the current SIGMA 2000), fragmentation behavior of gallium and mercury drop (under isothermal condition) and high temperature molten tin drops (between 670 and 1800 *C) at various shock pressures (between 68 and 200 bar) were observed. These experiments led to the microinteractions concept and the development of a computer code ESPROSE.m (Yuen and Theofanous,1995). The computer code was successful in interpreting the steam explosion data generated at the KROTOS facility (Theofanous, et.al.1995).
While the existing tin data were useful in illustrating the relative importance be-tween thermal and hydrodynamic effects on fragmentation in a sustained high pressure C-31 g
q environment, they are still short of the range of pressures and temperatures of interest U (supercritical pressure and fuel temperature in excess of 2000 *C). An important ob,'ective of the current research program is thus to expand the data base to higher pressures and temperatures so that the physics of molten drop fragmentation and microinteractions can be further understood. The data can also be used to further develop the constitutive laws for microinteractions. Steel is selected for the present experiment because while it has about the same density as tin, it has a much higher thermal energy content (twice the heat capacity and four times the latent heat). Steel is thus a good material to examine the importance of thermal effects. To gain a perspective of the present experiment in relation to previous one, a summary of the thermal properties of steel, tin and gallium is presented in Table 1.
Table 1. Physical Properties of Steel, Tin and Gallium Melting point Surface tension Specific heat Latent heat Density Material (*C) (g/cm ) (mN/m) O/g.k) O/g)
Steel 1450 6.87 1550 0.449 247 (1700 C) n Tin 232 6.10 500 0.220 60.7 V (1700 C)
Gallium 29.8 6.07 660 0.371 29.7
- 2. EXPERIMENT A schematic of the SIGMA-2000 facility is shown in Figure 1. A detailed description of the facility and the experimental procedure were given in previous publications and will not be repeated here. In the present set of experiments, a one-gram molten steel drop is released in subcooled water (20 C). Six experiments, conducted at two shock pressures (68 bar and 265 bar), are presented. Two of the six experiments are conducted with a 6 %
void fraction section both ahead of and behind the drop (by distributing plastic air bubbles in the water, the detail of this procedure is described in Chen (1996)) as shown in Figure 2.
The collapsing of the void by the shock wave creates a high coolant velocity at the point of fud-coolant interaction thus allowing to obtain considerably higher velocity for the same pressure behind the shock. Three drop temperatures (1550,1620 and 1650 *C) are used to determine the effect of melt superheat. Since the melting temperature of steel is high (1450*C), the current data illustrate both the effect of high temperature and low superheat O C-32
O Driver Section clief Valve Pressure Blasting Cap Gage Diaphragm N
\ Check Valve Gas 3 +-- Nitrogen Booster Gas Solenoid Valve
+- Argon P.T.1 [ 'j Gas Photo i ,
Thermocouple Cell 'jll g.+ + .f
.,... Laser' r.e .
[ ,,' y Beam Q,
/ .: . -
- .- .mmmmm Computer
(
W an / P.T.2 :::
Melt Induction Power t Windows .
Generator Supply
.. Debris Powerof T,le i '.,: .* .'- Catcher Blasting Cap l
, , - Water l
l.
l l
l
- Figure 1. Schematic of SIGMA-2000 (not to scale).
I C-33
g -
l
- 0:
- a. .- Dmp
- ?'
, $I* Window 2::
- 2:
Water s
{ Water / Bubble F 7 r"- 7 Single Phase Two-phase Figure 2. Schematic of the void fraction distribution for the single-phase and two-phase runs (the figure is in scale in the vertical direction only).
(100,170 and 200*C, respectively). This is in contrast to the previous high temperature tin data which were obtained with a superheat of over 1000 *C (Chen, et.al.1995) . The initial conditions for the tests are summarized in Table 2. Each run is labelled with an identification code. S-4-16.5 and S-4-16.5(0.06), for example, stand for runs with a shock pressure of 265 bar (4000 psi), steel temperature of 1650 C, fully liquid and two-phase coolant ahead of the drop respectively. The two similar tests S-4-16.5a and S-4-16.5b were conducted to demonstrate the repeatability of the experiment.
The amplitude of the shock wave is measured by the pressure transducer of location I'T2. Data from test S-4-16.5a are shown in Figure 3a and the expanded early transient is shown in Figure 3b. The transient data show that the pressure rose quickly to about 250 bar and remains relatively constant until the wave was reflected back from the bottom of the shock tube. There is a period of about 2 ms in which the pressure around the molten drop C-34
4 Table 2. Test Conditions of the Six Runs-
. Run~ ID e ? P(bar)/T('C); Void Fraction- Bo X-ray Time _(ms)
S-1-16.2 ,
68/1620. _ 0 34
. S-4-15.5 : 265/1550- 0 300 0.32 S-4-16.5a ' 265/1650 0 300
- S-4-16.5b - 265/1650- 0 300 S-4-15.5(0.06). 265/1550 0.% 1500 0.12 S-4-16.5(0.06) 265/1650 0.% 1500- 0.22 remained constant. The corresponding pressure data for a two-phase run (S-4-16.5(0.%))
'are shown in Figures 4a and 4b The shock pressure is oscillatory (due to collapsing of the void) and has a lower average pressure of ~ 200 bar. The time period of constant pressure is reduced to about 1.5 ms due to mflection from the two-phase liquid interface below' the observation widow. 1
(~ The molten steel dmp was released at 5.cm above the observation window prior
- to the arrival of the shock. As described previously, the timing of the drop release and the initiation of the shock was synchronized such that the interaction between the shock and_ the drop cecurred at the observation window. The fragmentation and subsequent entrainment were then recorded by a high speed movie camera at 50,000_ frames per ,
second. To gain a better perspective of the initial conditio,n of the molten drop, a drop test with the same drop temperature and water temperature was conducted inside the shock tube without the shock. The image of the drop and the surrounding vapor film was recorded by a video camera and is shown in Figure 5. The color image clearly shows that the ellipsoidal red-hot drop was surrounded by a large vapor bubble as it fell through the subcooled water. Since flash.X-ray is used to capture the fragmentation behavior during the fuel coolant interaction, an X-ray image of this unbroken molten drop, together with -
. a contour map of the 2-D projected mass distribution, are also shown in Figure 5. The drop falling speed, . measured from the video tape, was estimated to be about 0.7 m/s at -
the observation window. For the shock amplitude of 68 and 265 bar, the induced water Lvelocities were 4.5 and 15 m/s respectively. For the two-phase run at 265 bar, the water
-. velocity is about 38 m/s. The corresponding Bond numbers for all experiments are also shown in Table 2.'
p-V' C-35
._.__,.___.-_m_m_____..m-. - . -
. . . - . . . _ _ . . . _ _ _ . ~ . _ _ _ . . . _ _ . _ _ . _ . . _ . _ _ . _ . - _ . _ _ . . _ _ _ _ _ . _ _ _ . . -
600 ..... ... . ,,,....i....;...., .....,
E i !
500 . .
- ReflectedWave p :
i
~
C 400 d
~
\4 :
2 g 300 ) -
200 h -
1 incident shock Wave :
~
100 -
y/ -
0 i
1 0 1 2 3 4 5 6 7 -
T!me (ms)
Figure 3a. Pressure transient as recorded by PT 2 in run S-416.5a. ,
O 350 , ,,.,,,,,,,,,,,,,,q 300 - -
- A .
?
4 8 80 I
~ l
% ~:-
~
200 j' ~
E 150 - [I g : :
A 100 h j
- 1 :
50 ) {
0 ' - '
O 0.5 1 1,5 Time (ms)
Figure 3b, Expanded pressure transient during the first two milliseconds of interactions <
in run S-416.5a.
M(3 . C 36
i s
(f 700_,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
600 h y
, 500 F i u _ .
3 400
~
2 l .
E 300 F i s :
lw 200 ?
I h -
A 100 - ' 2 ,
O M
~
100 '''''''''''''''''''''''' ~
1 0 1 2 3 4 5 6 Time (ms)
Figure 4a. Pressure transient as recorded by PT 2 la run S-4-16.5(0.06).
500 ,,,,,,,,,,,,,,,,,,,,,
400 - -
rce
_ ) :
6 300 ,- L
,1 2 -
~
f d R 200 0
- i l l
} j-
{h -
w _
I .
D* ~
}
100 -
0 2
_,i,, ,i, ,,i,, ,,,,,, -
0 0.5 1 1.5 2 Time (ms)
("')
V inFigure 4b. 0.06),
run S-416.o Exp(anded pressure transient during the first two milliseconds of C-37 e ,.r--
l i
! l i
lO
)
i i
l
\
\
\
M. . ,
I i ;
i I
s
' l
'l 0.6 -
I l
> %. l 0.5$[*[! -
O
%) .' .
X:.~:
0.4 ~. ^
0.3
~
l
\
0.0 -
l i
e l l
Figure 5. The visible image, X-ray image and mass distribu'.ilon contours of a molten steel O drop (1650 "C) in 20 'C water from a drop test run. l C-3S
p The high speed movie images for all six experiments are presented in Figures 6a V' through 6f. In run S-4-16.5a (Figure 6c), for example, the first image shows a free falling molten steel drop surrounded by a bubble before the arrival of shock wave. The white spot at the center of the image was caused by the flashlight as it was projected in the normal direction to the vapor bubble surface and passed straight through. The shrinking of the bubble which is apparent in the second frame indicates the arrival of the shock wave.
The bubble was completely collapsed 40 s after the passage of the shock wave, and left a tiny non-condensible gat. bubble on top. At 80 ps (frame 5), the initial ellipsold drop cxpanded both in and transverse to the flow direction and formed a much bigger mass cloud. As time passed, this cloud continued to asymmetrically expand. Crests appeared at the upper right comer of the cloud at 0.22 ms. After 0.3 ms, the cloud elongated faster than it expanded in the horizontal direction and eventually formed a mushroom shape cloud. The cap of the cloud had a wavy surface and continued to expand in all directions, while the diameter of the stem became smaller as it moved with water. At 1.32 ms, the lower part of the cloud moved out of the window. Except for the difference in timing and the detail of the " cloud" generated by the interaction, all experiments follow the same qualitative behavior. A direct comparison between runs with different steel temperatures fm (for example, S-4-15.5 and S-416.5) shows that even with a temperature difference of only
()100 *C, the volume of the " cloud" is larger for the high temperature case. The remarkable similarity between Figures 6c and 6d confirms the repeatability of the experiment.
To gain a perspective directly on the fragmentation kinetics, flash X-ray images at selected time of the interaction are generated for three runs. The timing of these X-rays is .
shown in Table 2. Since water and steam are essentially transparent to the X-ray (relative to the high absorptivity of steel), these images give quantitative information about the fragmented steel. These images and the deduced mass fraction contours, together with the corresponding movie image are shown in Figures 7a through 7c. In contrast to the original symmetrical and smooth drop images as shown in Figure 5, the region of high mass concentration is highly distorted and " flattened" due to its interaction with the shock.
An interesting feature of the fragmentation, relative to the volume of the " cloud" deduced from the movie image, can be observed from the high temperature two-phase run, S 16.5(0.05), as shown in Figure 7c. The region of high mass concentration (the d rop) is much smaller than the observed " cloud". The debris seem to be concentrated along narrow strips cppearing to shed off the edge of the parent drop in a manner reminiscent of the previous mercury runs.
73 C-39
i i
l a
1 l S e
l i
a
'h'Y' E 8 a t
+
1 l,
'r '
=,.n ..- , , , - - , . . ,. , a-
<i ,
l Free Falling Shock Ardynl 0.04 0.08 0.12 0.16 (t = 0.0 me) i .
l /
<... ,.. .n, . . , . . . . .. es + n i 0.24 0.32 0.40 0.56 0.72 0.88 t
l l
l l
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l C-45
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l C-46
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4 C-47
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- drop at 0.22 ms after shock arrival for Run S-4-16 KO.06).
C-48 :
i l
L_________________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ . _ _ . _ _. . . _ . . , _ . _ _ _ . . . , _ _ _ . . . .
g 3. DATA ANALYSIS
) Debris are collected from each experiment and analyzed. Data for the four high pressure tests are shown in Figure 8. The cetresponding size distributions and the size distribution of debris colle ted for the low pressure run are shown in Figures 9. For the two single phase runs "0% (in mass) had sizes greater than 1 mm (in fact, for S-4 16.5a, this mass was a b!;; porous particle with diameter of about 1.5 cm),20% belonged to a group of millimeter size debris, fine debris with diameter less than 300 pm was 3.5%, and the remaining 6.5% of the mass was lost during retrieving and handling which was believed to be the fine debris. The two phase runs, on the other hand, had relatively uniform debris size distributions. Significant fractions of the debris (~ 30% and 50%) had particle sizes of less than 0.1 mm. These results give clear evidence of a stronger fuel coolant interaction for the two phase runs. Some typical SEM pictures of the debris are presented in Figures 10a to 10d. In each figure, SEM pictures of a typical"large" particle and "small" particle are shown to illustrate the debrics morphology and its dependence on the test parameters.
While all debris show a highly convoluted and porous structure with drawn, sharp edges, a comparison between Figures 10a and 10b shows that debris from the high temperature run (S-416.5a) has a " finer" structure. This can be attributed to the faster freezing in the low temperature run (S-415.5) which preserves more the " larger" debris strtucture.
A comparison between Figures 10b and 10c shows the effect of the high liquid velocity associated with the two phase run. The stronger fuel coolant interaction leads to a much more convoluted and porous structure than the single phase case.
The debris collected from the low pressure test (S-1 16) shows a striking dissimilarity frem that of the high pressure tests. Approximately 70% of the mass was retrieved and as shown la Figure 9, all debris have size less than 1.0 mm with 12% less than 300 pm.
The SEM images in Figure 10d show millimeter-size debris consisted of highly porous particles and flakes.
To separate debris mass from the drop mass in the X-ray images, we first use a pro-cedure developed in a previous work (Chen et.al.,1995) which identifies a " boundary" between the still coherent drop mass and the surrounding debris by a sudden drop-off in the mass thickness. For the two-phase runs, this leads to a " cutoff" thickness of 0.2 mtn for the drop. The accuracy of this " cutoff" thickness is consistent with the mass distribution curves generated from the contour plots shown in Figure 11. The mass thickness of 0.2 mm corresponds approximately to a point of inflection which implies a change in the mass concentration. Based on this " cutoff" thickness, the debris mass fraction for the two phase runs are determined to be 22 % (for S-4 15.5(0.06)) and 48 % (for S-4 16.5(0.06)). The same p
V C-49
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Figure 8. Photographs of debris collected for four runs conducted at 265 bar. i C-50 ,
i k
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0.9 0.3 0.1 0 Debris Sire (mm)
Figure 9. Size distribution of debris for the different runs.
procedure, however, yields inconsistent cutoff mass thickness for the sirgle phase run.
The determination of debris mass for S-415.5 is therefore not presented in view of this O uncertainty.
V To understand the implication of the two-phase fragmentation data on the microint-eration model, we ran the ESPROSE.m code to simulate the two phase run using the same fragmentation constant (of = 0) and entrainment factor (f, = 7) determined from the fragmentation data of mercury, gallium and tin (Chen et.al.,1995). A thermal exhance-ment factor ( m) of 3 is required to match the fragmentation data. The transient debris mass fraction predicted by ESPROSE.m, together with the two data points, is shown in Figures 12,
- 4. CONCLUSION This paper presents data and analysis which confirm results fror. sur previous in-vestigation that at supercritical condition, the thermal effect on fragmentation is highly suppressed. A hydrodynamic-based fragmentation modelis sufficient to characterize the fragmentation behavior. The microinteractions idea is qualitatively confirmed, but more data and analysis are needed to make the next quantitative step.
C) C-51
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Figure 10a. SEM photographs for run S-4-15.5. The top photograph is for a "large" particle and the bottom photograph is for a "small" particle.
C 52 i.
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Figure 10b. SEM photographs for run S-416.5a. The top photograph is for a "large" l' article and the bottom photograph is for a "small" particle. :
C-53 i
b b
v
_m-ewwyren
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__ L Figure 10c SEM photographs for run S-4-16.5(0.06). The top photograph is for a "large" particle and the bottom photograph is for a "small" particle.
C-54
=v s -
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9 .
. y .
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Figure 10d. SEM photographs for run S-1 16.2. The top photograph is for a "large" particle and the bottom photograph is for a "small" particle.
e C-55
. . - -.. . . - . - . ... .. . - .. ~..- _-._ . ....- - . -.. .. . . ..-.~.... -.-.... . . - . -
l i
h S.4 15.5 (0.06) 1 i i- i i . l v
g i i 0.5 - 1 j
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Th kkmess (c m) !
i e
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1 S.4 16.5 (0.06)
I 0,g- 1 -
1 i
g* 0.e- 3 -
~g i X
I 0.4 - -
I i
0.2 - I -
t ,
I i n i i i i
- 0 0.1 0.2 0.3 0.4 0.6 0.6 0.7
- Thkkness (cm)
Figure 11.- Mass distribution curves and the identification of the " cutoff" mass thickness for the two-phase X ray data.
\ C-56 ta
.f
. ( , i, , e - , , ,.-.+r-.'..,,I,,4
.,-~m-, .l..v--- .u_,, ,.*- ,4 . ., ..--_.! , -
1.0 , i i i d ESPROSE.m '
O.8 -
o Data j 0.6 - .
z' O.4 - S 4 16.5 (0.00) ;
0.2 -
S-4 15.5 (0.06) 0.0 ' ' ' '
O.0 0.1 0.2 0.3 0.4 0.5 Tune (ms)
Figure 12. The ESPROSE.m interpretation for the two-phase runs using an enhancement factor m = 3.
- 5. ACKNOWLF.DGMENTS This work was supported by DOE's ARSAP program at UCSB,with Mr. Steven Sorrell (DOE Idaho Operation's Office) as the program manager. We are grateful for the support and the " environment" allowed for us to carry out our research.
- 6. REFERENCES
- 1. Chen, X., W.W. Yuen and T.G. Theofanous, "On the Constitutive Description of the Microinteractions Concept in Steam Explosions," NURETH 7, Saratoga Springs, NY, September 10-15,1995, NUREG/CP-0142, Vol.1,1586-1606.
- 2. Chen, X., " Fragmentation Kinetics and Microinteractions in Simulated Large Scale Thermal Detonation", Ph.D Thesis, University of Califomia, Santa Barbara,1996.
- 3. Patel, P. D. and Theofanous, T. G. (1981), " Hydrodynamic Fragmentation of Drops,"
Journal of Fluid Mechanics, Vol. 103,1981, pp. 207-223.
- 4. Theofanous, T. G., W. W. Yuen, S. Angelini, and X. Chen, "The Study of Steam Explo-sion in Nuclear System," DOE /ID-10489, January,1995.
O) q c.s,
rw S. Yuen, W. W., X. Chen and T. G. Theofanous (1994), "On the Fundamental Microinter-b actions that Support the Propagation of Steam Explosion," Nuclear Engineering and Design,146 (1994), pp.133146.
- 6. Yuen, W. W. and T. G. Theofanous (1995) "ESPROSE.m: A' Computer Code for Ad-dressing the Escalation / Propagation of Steam Explosions," DOE /ID 10501, April 1995.
I n
v Ch 4,_) C-58