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Thermal analysis of an in-reactor LMFBR irradiation creep experiment
Nuclear Engineeringand Design 53 (1979) 1-10 © North-Holiand Publishing Company
THERMAL ANALYSIS OF AN IN-REACTOR LMFBR IRRADIATION CREEP EXPERIMENT * Earl E. FELDMAN Argonne National Laboratory, Argonne, IL 60439, USA Received 28 July 1978
Thermal analyses of an in-reactor liquid metal fast breeder reactor (LMFBR) irradiation creep experiment and the test probe experiment which preceded it have been performed with the aid of a finite-difference heat transfer computer code. The calculated axial temperature distribution for the probe experiment is compared with the measured distribution. Although there is a 15% overprediction, the relative axial temperature distributions agree rather well. The thermal response of both experiments to a loss-of-flowtransient is also analyzed.
1. Introduction The Cladding and Duct Materials Development Program Experiment S-3 [1 ] is a multiaxial in-reactor creep experiment which was developed to test reactor structural materials in the thermal and irradiation environment of an LMFBR. One of the unique requirements of the experiment is that all of the creep specimens are to have the same 510°C irradition temperature. The specimens are incorporated into creep capsules which are used to provide the desired multiaxial stress states. The creep capsules are placed in a specimen container [2] which fits into an experimental subassembly of the Experimental Breeder Reactor II (EBR-II). This subassembly is located within the outermost ring of the reactor core subassemblies, where it is referred to as experiment X314-A. The predecessor to this experiment, experiment X314 [3], occupied the same reactor core position and was similar to the creep experiment X314-A. In the earlier experiment, pieces of stainless steel were used in place of the creep capsules in order to test the design of the specimen container - particularly to measure its internal temperatures - without jeopardizing the creep capsules. In both experiments passive temperature monitors [4] were distributed throughout the interior of the specimen container. From these monitors, a post-
experiment value of the maximum temperature experienced by each monitor is obtained. Measured results for the probe experiment are available, but measurements from the creep experiment cannot be obtained until after it is removed from the reactor.
2. Description of the experiments Fig. 1 shows the radial location of the specimen container within the experimental subassembly. The inert gas layer in the subassembly thermally isolates the innermost hex can and the specimen container from the outer two hex cans and the bypass flow. Fig. 2 represents a diametral cross section through the innermost hex can of the subassembly and the specimen container. The specimen container is essentially a round closed tube totally contained within a second round closed tube. Each specimen is placed in one of five 7.6 cm high cups which are placed on top of one another to form five tiers. The gas space above and below the inner tube minimizes axial heat transfer to the outer tube. When the subassembly is placed in the reactor, sodium flows through the lower drain tube and fills all available space inside the inner specimen container tube. Although the flow which follows the drain path during irradiation is very small, it does influence the temperature distribution within the specimen container. The main sodium coolant flow
2
E.E. Feldman / Thermal analysis of LMFBR creep experiment
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Fig. 1. Experimental subassembly cross section.
between the innermost hex can and the outer surface of the specimen container carriers away most of the heat produced within the specimen container. This
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heat reaches the main coolant flow by passing through the inert gas gap of the double-walled specimen container. The temperature differential across this gap is on the order to 100°C. The following tend to make the specimen container interior temperature distribution nonuniform: (1) the nonuniform axial distribution of reactor power, fig. 3, with its peak near the reactor midplane, (2) the flow entering the interior of the specimen container through the lower drain tube, and (3) the axial temperature rise along the path of the main coolant flow. Because a uniform aixal temperature distribution is desired, the design attempted to minimize these effects. In order to increase the heating near core top and bottom, more steel was placed in the top and bottom tiers than in the middle three, with the greatest loading being in the bottom tier. A multistage orifice was placed in the lower drain tube in order to minimize flow there. The tube at the top of the specimen container, however, was not orificed so that any pressurized gas which might leak from a
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Fig. 3. Relative axial power deposition for the S-3 experiments.
E.E. FeMman / Thermal analysis of LMFBR creep experiment
metric model, as shown in fig. 4, was used in the analysis o f b o t h experiments. The total mass o f steel o f each tier is represented b y two concentric annular rings o f rectangular cross section. While the combined mass o f the two rings is exactly that o f the tier, the mass o f the outer ring only approximates that o f the lateral wall o f the cup. As indicated b y the figure, the total volume represented b y the model is divided into 22 axial levels, each o f which is subdivided into 16 annular rings to form a total of 352 subvolumes or nodes. All o f the solid boundaries o f the model are assumed to be insulated with the only heat crossing the perimeter o f the model being carried b y the two sodium flows. Table 1
defective creep capsule could more easily be vented. The main coolant flowrate was designed sufficiently large to limit the axial temperature rise in this coolant to about 20°C.
3. Analysis
3.1. Description o f the model Except for the contents of the tier cups, the specimen container is essentially axisymmetric. The sodium matrix within each tier cup tends to eliminate temperature gradients there. Therefore, an axisym-
Table 1 Summary of the data used in the analyses
Total steel mass of tier cup and contents (g) 1 2 3 4 5 Total volume of gas in tier cup (cm 3) 1 2 3 4 5 Peak power a) (W/g) Stainless steel Sodium
Creep experiment X314-A
Probe experiment X314
347.6 256.6 232.4 242.0 275.0
312.1 248.2 225.9 234.9 285.0
3.32 10.12 10.12 7.48 10.12
0. 0. 0. 0. 0.
3.11 3.86
2.99 3.70
Coolant flowrate (cma/s) Main Drain path
332. 2.52
332. 2.52
Coolant inlet temperature of fig. 4 model (*C) Main Drain path
374. 443.
374. 377.
Helium-argon gas gap Thickness at room temperature (cm) Differential thermal expansion (cm) Thickness at irradiation temperature (cm) Mole fraction of argon Thermal conductivity at 449°C b) (mW/cm2 C)
3
0.0287 0.0051 0.0236 0.1965 1.850
a) See fig. 3 for axial distr~ution. b) In the analyses, thermal conductivity is represented as a function of temperature.
0.0297 0.0038 0.0259 0. 2.651
4
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provides values for the principal parameters used in the analyses of both experiments. The axial distribution of power deposition in both the stainless steel and the sodium are assumed to be the same. Fig. 3 provides this distribution for both experiments. The fundamental principle of conservation of energy is applied to each node and the resultant set of simultaneous equations is solved for the steady state temperature of each node. This procedure was implemented via the THTB computer code [5], which is a FORTRAN-IV code designed for general transient three-dimensional heat transfer analysis. 3. 2. Principal gas gap
Most of the difference between the temperature at the subassembly inlet and that inside the specimen container occurs across the inert gas gap of the container. Therefore, careful attention had to be given to the size, gas composition, and thermal conductivity of this gap. Both of the two concentric specimen container tubes have a 0.0762 cm thick wall and gain some of their rigidity and relative alignment from their end constraints. In addition, the gap between the tubes is maintained by eight circumferential rows
of six equally spaced dimples at 5.08 cm axial intervals in the outer tube. Before the specimen containers were completely assembled, several measurements of the gap size were made along the perimeter at the ends of the inner tubes. In the analyses, the gap size of each container is taken to be the average of all of its gap measurements. The differential thermal expansion between inner and outer tubes, which occurs when the container is heated to irradiation temperatures, was also included in the analyses. Because the thermal conductivity of helium is about eight times that of argon, the use of helium in place of argon allows the gap size to be proportionately larger and causes the manufacturing tolerance of the gas gap to be much less significant. However, in order to allow for some temperature adjustment, the specimen container was designed so that the desired 510°C irradiation temperature is achieved by using helium mixed with a small amount of argon. In the probe experiment, pure helium was employed and the measured temperature distribution was used in the determination of the mole fraction of argon to be used in the gas mixture of the creep capsule experiment. In the analyses, the thermal conductivity of the gas [6] is represented as a function of temperature. Radiant heat transfer across the gas gap between the two specimen container walls was also included in the subassembly model. An emissivity of 0.3 was assumed for both surfaces. The effect of radiant heat transfer was tested by reanalyzing the creep experiment with this mode of heat transfer eliminated from the model. The temperatures inside the inner specimen contain tube rose by only about 2°C, demonstrating that only a very small amount of heat is transferred by radiation. 3.3. Effect o f the gas within the X314-A creep capsules
Some of the creep capsules of the second experiment contain pressurized helium gas which is used to help achieve the desired stress state in the test specimen portion of the capsule. The test specimen in all of these creep capsules is a small hollow cylinder, whose outer lateral surface forms part of the outer perimeter of the capsule. Because the test specimen is in direct contact with the sodium matrix inside the specimen container, the gas inside the capsule has a
E.E. FeMman / Thermal analysis of LMFBR creep experiment
minimal effect on the test specimen temperature. The gas, however, can significantly affect the temperature of some of the internal mechanism used to achieve the desired stress state. Therefore, the capsules for which this could cause a problem were analyzed with the aid of the THTB computer code. Internal temperatures as high as IO0°C above the capsule surroundings were calculated. Helium gas was chosen for capsule pressurization in preference to argon because if argon had been used, this temperature difference would have been about three and a half times as large. While heat is easily conducted through the sodium matrix and around the small gas pockets in the capsules, the space occupied by the gas would otherwise be occupied by heat generating material. Therefore, this gas is taken into account in the model of the creep experiment. The cylinder indicated by the dashed line in fig. 4, which applies only to the creep experiment, represents the total volume of helium gas in all of the capsules. Because the gas displaces only enough sodium to reduce the specimen container temperature only about 3°C, the tier by tier distribution of gas is only approximately represented in the model. 3.4. Flowrates and inlet temperatures
For both experiments the main and drain path flowrates were determined experimentally to be 332. and 2.52 cma/s, respectively. Because the six equally spaced 0.318 cm diameter drain holes along the bottom of the lateral wall of each tier cup are too small to allow a significant ingress of sodium, most of the flow through the drain path is along the exterior of the cups. In the model, the sodium inside the tier cups is assumed to be stagnant, and all of the drain path flow is assumed to be in the annular space between the specimen container and walls of the tier cups. While the sodium enters the subassembly at 371 °C, heat generated in the lower portion of the subassembly heats the sodium before it reaches the portion of the subassembly represented by the analytical model of fig. 4. An annular gas gap limits the heat flow from the lower susceptor to lower drain tube (see fig. 2). In both experiments, heat generated mostly by the lower susceptor and the innermost hex can heat the main coolant flow about 3°C, to 374°C.
5
In the probe experiment X314 the heat generated in the lower drain tube heats the flow inside it about 6°C, to 377°C. In the creep experiment X314-A with its larger lower end cap, as explained below, the drain path flow inlet temperature is raised to about 443°C. In the early phases of the design of the probe experiment, it was thought that because proper oriricing could make the drain path flowrate extremely small, it was not thermally significant. While the hardware for the probe experiment was being manufactured, the significance of this flow was realized and a multistage orifice was added to the lower drain tube. The drain path flow was subsequently included in the analytical model, which demonstrated that, even with the new orifice, the lowest tier was adversely effected by an ingress of relatively cold sodium. 3.5. Creep experiment lower end cap
In the creep experiment X314-A, the adverse thermal effect of the drain path flow was reduced through the use of a more massive lower end cap, as indicated in fig. 2. The added mass generates heat which warms the drain path flow before it reaches the first tier. The new lower end cap fills most of the space between the bottom tier and the lower susceptor and leaves an insulating gas layer of slightly more than 0.15 cm thick along the bottom and lateral surfaces of the lower end cap. The heat generated in the portion of the drain tube which passes through the lower susceptor heat the drain path flow about 3°C, to 374°C. If all of the 0.275 kW, which is generated by the added lower end cap mass and the portion of the drain tube which passes through it, were added to the drain path flow, the temperature of this flow would be increased by another 101°C, to 475°C. Because the insulating gas layer at the bottom and lateral area of the end cap is not completely effective, a significant amount of the end cap heat is lost and a temperature substantially less than 475°C is obtained. The 130 node axisymmetric model of fig. 5 was used to analyze the lower end cap. Because the top 0.318 cm of the lower end cap is already included in the specimen container model of fig. 4, only the bottom 2.87 cm is represented in rig. 5. The lateral boundary of the model corresponds to the inside surface of the outer specimen container tube, and the
E.E. Feldman / Thermal analysis of LMFBR creep experiment /-ADDED MASS OF X314-A END CAP
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lower boundary corresponds to the top of the lower susceptor. Both of these boundaries are assumed to be 374°C. The upper boundary corresponds to part of the lower boundary of the specimen container model of fig. 4. Because the thermal condition at this upper boundary is not precisely known, several boundary conditions were considered, as shown in the first column of table 2. In all of these cases, the upper boundary was assumed to be either of uniform temperature or insulated. A thermal solution for each of the seven cases was obtained using the THTB computer code. From these solutions, the heat lost by conduction through the surrounding gas layer was calculated. This lost heat was increased by 10% to account for heat lost by radiation through the gas layer. The remaining fraction of the total 0.275 kW is
shown in the second column of the table. The third column shows what temperature the 374°C lower end cap inlet flow temperature would be raised to if it received all of this remaning heat. Hence, the temperatures in the third column correspond to the X314-A drain path inlet temperature for the specimen container model of fig. 4. As the table shows, this specimen container drain path inlet temperature is rather insensitive to the upper boundary condition of the end cap. The specimen container analysis was performed with both a 441°C drain path inlet temperature and a 446°C temperature. The higher temperature caused the bottom quarter of the first tier to be about 3°C hotter and the top quarter of the tier to be about 0.6°C hotter than did the colder temperature. Both solutions indicated that the top of the lower end cap has temperatures ranging between about 468 and 496°C. Therefore, a drain path inlet temperature of 443°C was used in the analytical model of fig. 4. The analysis indicates that the temperature gradients within the lower end cap, fig. 5, are not severe. The maximum internal steel temperature for the 482°C upper boundary case, for example, was only 502°C. 3. 6. Loss-of-flow transient An important consideration in the design of any experiment is its performance during a reactor loss-offlow transient. In this regard, the probe and creep experiments are well designed because most of their
1.0
Table 2
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Fraction of total heat going to specimen container
Specimen container drain path inlet temperature for fig. 4 model (o C)
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E.E. Feldman 'Thermal analysis of LMFBR creep experiment 1.0
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steady state temperature rise is due to the temperature rise across their principal gas gaps. Near the start of a loss-of-flow transient the reactor is scrammed and a sharp drop in subassembly power substantially reduces the gas gap temperature rise. This drop in temperature more than offsets the transient increase in main coolant temperatures caused by the reduction in flowrate. The anticipated type of loss-of-flow transient, specified in the EBR-II project experimenter's guide, was analyzed. The power history, fig. 6, used is for structural experiments and the flow coastdown, fig. 7, corresponds to a loss of primary pumping power while the primary system auxiliary pump continues to operate. Because the power history specified in the guide includes only the first 100 s of the transient, it was conservatively assumed that the power remains constant after this time interval. The computerized models used in the steady state analyses were also used in the transient. The small steady state coolant temperature rises between the subassembly inlet and the bottom of the fig. 4 specimen container model, which exist in both coolant flows of the probe experiment and in the main coolant flow of the creep experiment, were assumed not to vary during the transient. In the creep experiment, the 3°C coolant temperature rise between the subassembly inlet and the bottom of the lower
7
end cap was also assumed to remain constant. A transient analysis, however, was performed with the aid of the computerized model of the lower end cap, fig. 5, to obtain the transient coolant temperature near the top of the creep experiment lower end cap. Two cases were considered and the analysis of both was simplified by ignoring the relatively small amount of radiant heat transfer from the lower end cap. In the first case, the upper boundary was assumed to be at a constant uniform temperature of 482°C. In the second case, which produced the higher transient exit coolant temperature, the upper boundary was assumed to be insulated. For both cases, the maximum stainless steel temperature declined throughout the transient, while the coolant exit temperature rose for about 35 s to its maximum, which was 493°C for the second case, before declining. The transient exit coolant temperature of the second case was taken to be the transient drain path inlet coolant temperature for the model of fig. 4. Because the passive temperature monitors used in both experiments record only maximum temperatures, steady state specimen temperatures must not be exceeded during the transient. The transient analysis shows that the top four tiers and most of the bottom tier of both experiments meet this requirement. In both experiments, however, the temperature of the drain path flow below the first tier rose significantly above its steady state value. Fortunately, this is a very localized effect which, as analytical estimates indicate, may raise the specimen temperatures near the bottom of the first tier by no more than about 1°C above their steady state values.
4. Results Steady state radial temperature distributions produced with the analytical models of the experiments are shown in fig. 8. The axial location of these temperatures is near the center of the middle tier cup and is indicated by the horizontal row of dots in fig. 4. This location was chosen because it is near the peak of the axial power distribution, fig. 3, where the largest radial temperature gradients exist. In the region between the main coolant flow and the lateral walls of the tier cups, the geometry of the analytical model closely resembles the experiment. Within the
8
E.E. Feldman / Thermal analysis o f LMFBR creep experiment
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Fig. 8. Radial temperature distributions near the midplane of the analytical models.
Fig. 9. Axial distribution of the specimen temperatures for the probe experiment X314.
tier cups, however, a three-dimensional matrix of sodium containing pockets of stainless steel, some of which contain pockets of gas, was approximated by an axisymmetric two-dimensional annular model. Therefore, care is required in interpreting the results obtained for the interior of the tier cups. The model indicates a maximum temperature difference of about 20°C from the lateral cup wall to the sodium near the centerline of the cup. The actual difference is expected to be about half of this calculated value because the sodium matrix connects all regions of the cup interior while the model has an annular wall of stainless steel. All of the test specimens of the creep capsules are in direct contact with the sodium matrix and all of the temperature monitors measure sodium temperatures. Therefore, the purpose of the analyses is to predict sodium temperatures inside the tier cups. The temperatures of the first column of sodium nodes outside the rings representing the specimens, as indicated by the vertical column of dots in fig. 4, were chosen to represent the axial distribution of specimen temperatures. For the middle cup these temperatures are about 3°C above the corresponding lateral cup wall temperatures.
Fig. 9 provides the axial distribution of specimen temperatures in the probe experiment X314. The upper solid line is based on the analytical model of fig. 4 and the data provided in the third column of table 1, while the circles represent the measured data.
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Fig. 10. Calculated axial distribution of the specimen temperatures for the creep experiment X314-A.
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The relative minima in the analytic curves occur at the axial locations where there is a sodium gap between the stainless steel specimen ring of the model of one tier and that of the next. While the distribution of material in the experiment is expected to create local peaks and valleys, they need not correspond to those in the analytical curves. Fig. 10 provides the analytical prediction of axial specimen temperature distribution for the creep experiment X314-A, which is currently in the reactor. Based on the reactor inlet temperature of 371°C and the steady state exit temperatures of the two coolants, 7.84 kW are produced in the probe experiment and 8.32 kW are produced in the creep experiment. Figs. 11 and 12 provide the transient thermal performance of the two experiment during the anticipated type of loss-of-flow accident described in the previous section. During the transient, the dropping flowrate causes the main coolant temperatures to initially rise to a maximum where the falling subassembly power forces the coolant temperatures to decline. The behavior of the specimen container temperatures is easily explained. The sudden drop in power precipitated by the reactor scram causes a sharp initial drop
Fig. 12. Thermal performance of the creep experiment X314-A during a loss-of-flow transient.
in the maximum temperature inside the specimen container. The rising main coolant temperatures temporarily reverse this trend. Then the temperatures inside the specimen container resume their decline.
5. Discussion and conclusions
The temperature rise distribution is defined to be the temperature distribution reduced by the 371 °C subassembly inlet temperature. The adjusted calculated temperature distribution of fig. 9 is obtained by dividing the temperature rise distribution calculated for the probe experiment X314 by 1.15 and increasing the results by 371 °C. The extremely good agreement between the adjusted calculated curve and the measured curve is a clear indication that all of the principal phenomena which can influence the relative axial temperature distribution of the experiment have been
10
E.E. Feldman / Thermal analysis of LMFBR creep experiment
properly represented in the analytical model. This was not true of some of the preliminary analyses of the specimen container, for example, where the mission of the drain path flow caused the temperature distribution of the bottom tier to be almost a mirror image of that of the top tier. The predictive capability of the present analytical model has made it possible to analytically evaluate and optimize various aspects of the design of the experiments, such as the distribution of specimens, the drain path orifice, the lower end cap of the specimen container, and the principal gas gap size and composition. As fig. 9 indicates, the calculated temperature rise is 15% too high. The temperatures within the specimen container are very sensitive to the subassembly power level, the gas gap size and uniformity, and the thermal conductivity of helium. The uncertainty associated with these quantities can account for much, if not all, or the 15% discrepancy. In conclusion, an analytical model has been developed for the thermal analysis of the creep experiment. The predictive capability of the model has been
tested and confirmed in the steady state analysis of the probe experiment X314. Analytical results indicate that reasonable specimen irradiation temperatures are expected for the creep experiment X314-A. Analysis of both experiments has also demonstrated that the anticipated type of loss-of-flow transient can cause no significant adverse effects.
References [1 ] J.E. Flinn et al., Argonne National Laboratory, unpublished information, November 1977. [2] O.S. Seim, J.C. Wendte and E.E. Feldman, Trans. Am. Nucl. Soc. 28 (1978) 193. [3] J.E. Flinn et al., Argonne National Laboratory, unpublished information, July 1977. [4] W.E. Ruther and Sherman Greenberg, Argonne National Laboratory Report ANL-8042 (1973) p. 22. [5 ] G.L. Stephens and D.J. Campbell, General Electric Report R60FPD647 (1961). [6] J.R. Moszynski and Ankur Purohit, Argonne National Laboratory Report, in press.
THERMAL ANALYSIS OF AN IN-REACTOR LMFBR IRRADIATION CREEP EXPERIMENT * Earl E. FELDMAN Argonne National Laboratory, Argonne, IL 60439, USA Received 28 July 1978
Thermal analyses of an in-reactor liquid metal fast breeder reactor (LMFBR) irradiation creep experiment and the test probe experiment which preceded it have been performed with the aid of a finite-difference heat transfer computer code. The calculated axial temperature distribution for the probe experiment is compared with the measured distribution. Although there is a 15% overprediction, the relative axial temperature distributions agree rather well. The thermal response of both experiments to a loss-of-flowtransient is also analyzed.
1. Introduction The Cladding and Duct Materials Development Program Experiment S-3 [1 ] is a multiaxial in-reactor creep experiment which was developed to test reactor structural materials in the thermal and irradiation environment of an LMFBR. One of the unique requirements of the experiment is that all of the creep specimens are to have the same 510°C irradition temperature. The specimens are incorporated into creep capsules which are used to provide the desired multiaxial stress states. The creep capsules are placed in a specimen container [2] which fits into an experimental subassembly of the Experimental Breeder Reactor II (EBR-II). This subassembly is located within the outermost ring of the reactor core subassemblies, where it is referred to as experiment X314-A. The predecessor to this experiment, experiment X314 [3], occupied the same reactor core position and was similar to the creep experiment X314-A. In the earlier experiment, pieces of stainless steel were used in place of the creep capsules in order to test the design of the specimen container - particularly to measure its internal temperatures - without jeopardizing the creep capsules. In both experiments passive temperature monitors [4] were distributed throughout the interior of the specimen container. From these monitors, a post-
experiment value of the maximum temperature experienced by each monitor is obtained. Measured results for the probe experiment are available, but measurements from the creep experiment cannot be obtained until after it is removed from the reactor.
2. Description of the experiments Fig. 1 shows the radial location of the specimen container within the experimental subassembly. The inert gas layer in the subassembly thermally isolates the innermost hex can and the specimen container from the outer two hex cans and the bypass flow. Fig. 2 represents a diametral cross section through the innermost hex can of the subassembly and the specimen container. The specimen container is essentially a round closed tube totally contained within a second round closed tube. Each specimen is placed in one of five 7.6 cm high cups which are placed on top of one another to form five tiers. The gas space above and below the inner tube minimizes axial heat transfer to the outer tube. When the subassembly is placed in the reactor, sodium flows through the lower drain tube and fills all available space inside the inner specimen container tube. Although the flow which follows the drain path during irradiation is very small, it does influence the temperature distribution within the specimen container. The main sodium coolant flow
2
E.E. Feldman / Thermal analysis of LMFBR creep experiment
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Fig. 1. Experimental subassembly cross section.
between the innermost hex can and the outer surface of the specimen container carriers away most of the heat produced within the specimen container. This
r
heat reaches the main coolant flow by passing through the inert gas gap of the double-walled specimen container. The temperature differential across this gap is on the order to 100°C. The following tend to make the specimen container interior temperature distribution nonuniform: (1) the nonuniform axial distribution of reactor power, fig. 3, with its peak near the reactor midplane, (2) the flow entering the interior of the specimen container through the lower drain tube, and (3) the axial temperature rise along the path of the main coolant flow. Because a uniform aixal temperature distribution is desired, the design attempted to minimize these effects. In order to increase the heating near core top and bottom, more steel was placed in the top and bottom tiers than in the middle three, with the greatest loading being in the bottom tier. A multistage orifice was placed in the lower drain tube in order to minimize flow there. The tube at the top of the specimen container, however, was not orificed so that any pressurized gas which might leak from a
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Fig. 3. Relative axial power deposition for the S-3 experiments.
E.E. FeMman / Thermal analysis of LMFBR creep experiment
metric model, as shown in fig. 4, was used in the analysis o f b o t h experiments. The total mass o f steel o f each tier is represented b y two concentric annular rings o f rectangular cross section. While the combined mass o f the two rings is exactly that o f the tier, the mass o f the outer ring only approximates that o f the lateral wall o f the cup. As indicated b y the figure, the total volume represented b y the model is divided into 22 axial levels, each o f which is subdivided into 16 annular rings to form a total of 352 subvolumes or nodes. All o f the solid boundaries o f the model are assumed to be insulated with the only heat crossing the perimeter o f the model being carried b y the two sodium flows. Table 1
defective creep capsule could more easily be vented. The main coolant flowrate was designed sufficiently large to limit the axial temperature rise in this coolant to about 20°C.
3. Analysis
3.1. Description o f the model Except for the contents of the tier cups, the specimen container is essentially axisymmetric. The sodium matrix within each tier cup tends to eliminate temperature gradients there. Therefore, an axisym-
Table 1 Summary of the data used in the analyses
Total steel mass of tier cup and contents (g) 1 2 3 4 5 Total volume of gas in tier cup (cm 3) 1 2 3 4 5 Peak power a) (W/g) Stainless steel Sodium
Creep experiment X314-A
Probe experiment X314
347.6 256.6 232.4 242.0 275.0
312.1 248.2 225.9 234.9 285.0
3.32 10.12 10.12 7.48 10.12
0. 0. 0. 0. 0.
3.11 3.86
2.99 3.70
Coolant flowrate (cma/s) Main Drain path
332. 2.52
332. 2.52
Coolant inlet temperature of fig. 4 model (*C) Main Drain path
374. 443.
374. 377.
Helium-argon gas gap Thickness at room temperature (cm) Differential thermal expansion (cm) Thickness at irradiation temperature (cm) Mole fraction of argon Thermal conductivity at 449°C b) (mW/cm2 C)
3
0.0287 0.0051 0.0236 0.1965 1.850
a) See fig. 3 for axial distr~ution. b) In the analyses, thermal conductivity is represented as a function of temperature.
0.0297 0.0038 0.0259 0. 2.651
4
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provides values for the principal parameters used in the analyses of both experiments. The axial distribution of power deposition in both the stainless steel and the sodium are assumed to be the same. Fig. 3 provides this distribution for both experiments. The fundamental principle of conservation of energy is applied to each node and the resultant set of simultaneous equations is solved for the steady state temperature of each node. This procedure was implemented via the THTB computer code [5], which is a FORTRAN-IV code designed for general transient three-dimensional heat transfer analysis. 3. 2. Principal gas gap
Most of the difference between the temperature at the subassembly inlet and that inside the specimen container occurs across the inert gas gap of the container. Therefore, careful attention had to be given to the size, gas composition, and thermal conductivity of this gap. Both of the two concentric specimen container tubes have a 0.0762 cm thick wall and gain some of their rigidity and relative alignment from their end constraints. In addition, the gap between the tubes is maintained by eight circumferential rows
of six equally spaced dimples at 5.08 cm axial intervals in the outer tube. Before the specimen containers were completely assembled, several measurements of the gap size were made along the perimeter at the ends of the inner tubes. In the analyses, the gap size of each container is taken to be the average of all of its gap measurements. The differential thermal expansion between inner and outer tubes, which occurs when the container is heated to irradiation temperatures, was also included in the analyses. Because the thermal conductivity of helium is about eight times that of argon, the use of helium in place of argon allows the gap size to be proportionately larger and causes the manufacturing tolerance of the gas gap to be much less significant. However, in order to allow for some temperature adjustment, the specimen container was designed so that the desired 510°C irradiation temperature is achieved by using helium mixed with a small amount of argon. In the probe experiment, pure helium was employed and the measured temperature distribution was used in the determination of the mole fraction of argon to be used in the gas mixture of the creep capsule experiment. In the analyses, the thermal conductivity of the gas [6] is represented as a function of temperature. Radiant heat transfer across the gas gap between the two specimen container walls was also included in the subassembly model. An emissivity of 0.3 was assumed for both surfaces. The effect of radiant heat transfer was tested by reanalyzing the creep experiment with this mode of heat transfer eliminated from the model. The temperatures inside the inner specimen contain tube rose by only about 2°C, demonstrating that only a very small amount of heat is transferred by radiation. 3.3. Effect o f the gas within the X314-A creep capsules
Some of the creep capsules of the second experiment contain pressurized helium gas which is used to help achieve the desired stress state in the test specimen portion of the capsule. The test specimen in all of these creep capsules is a small hollow cylinder, whose outer lateral surface forms part of the outer perimeter of the capsule. Because the test specimen is in direct contact with the sodium matrix inside the specimen container, the gas inside the capsule has a
E.E. FeMman / Thermal analysis of LMFBR creep experiment
minimal effect on the test specimen temperature. The gas, however, can significantly affect the temperature of some of the internal mechanism used to achieve the desired stress state. Therefore, the capsules for which this could cause a problem were analyzed with the aid of the THTB computer code. Internal temperatures as high as IO0°C above the capsule surroundings were calculated. Helium gas was chosen for capsule pressurization in preference to argon because if argon had been used, this temperature difference would have been about three and a half times as large. While heat is easily conducted through the sodium matrix and around the small gas pockets in the capsules, the space occupied by the gas would otherwise be occupied by heat generating material. Therefore, this gas is taken into account in the model of the creep experiment. The cylinder indicated by the dashed line in fig. 4, which applies only to the creep experiment, represents the total volume of helium gas in all of the capsules. Because the gas displaces only enough sodium to reduce the specimen container temperature only about 3°C, the tier by tier distribution of gas is only approximately represented in the model. 3.4. Flowrates and inlet temperatures
For both experiments the main and drain path flowrates were determined experimentally to be 332. and 2.52 cma/s, respectively. Because the six equally spaced 0.318 cm diameter drain holes along the bottom of the lateral wall of each tier cup are too small to allow a significant ingress of sodium, most of the flow through the drain path is along the exterior of the cups. In the model, the sodium inside the tier cups is assumed to be stagnant, and all of the drain path flow is assumed to be in the annular space between the specimen container and walls of the tier cups. While the sodium enters the subassembly at 371 °C, heat generated in the lower portion of the subassembly heats the sodium before it reaches the portion of the subassembly represented by the analytical model of fig. 4. An annular gas gap limits the heat flow from the lower susceptor to lower drain tube (see fig. 2). In both experiments, heat generated mostly by the lower susceptor and the innermost hex can heat the main coolant flow about 3°C, to 374°C.
5
In the probe experiment X314 the heat generated in the lower drain tube heats the flow inside it about 6°C, to 377°C. In the creep experiment X314-A with its larger lower end cap, as explained below, the drain path flow inlet temperature is raised to about 443°C. In the early phases of the design of the probe experiment, it was thought that because proper oriricing could make the drain path flowrate extremely small, it was not thermally significant. While the hardware for the probe experiment was being manufactured, the significance of this flow was realized and a multistage orifice was added to the lower drain tube. The drain path flow was subsequently included in the analytical model, which demonstrated that, even with the new orifice, the lowest tier was adversely effected by an ingress of relatively cold sodium. 3.5. Creep experiment lower end cap
In the creep experiment X314-A, the adverse thermal effect of the drain path flow was reduced through the use of a more massive lower end cap, as indicated in fig. 2. The added mass generates heat which warms the drain path flow before it reaches the first tier. The new lower end cap fills most of the space between the bottom tier and the lower susceptor and leaves an insulating gas layer of slightly more than 0.15 cm thick along the bottom and lateral surfaces of the lower end cap. The heat generated in the portion of the drain tube which passes through the lower susceptor heat the drain path flow about 3°C, to 374°C. If all of the 0.275 kW, which is generated by the added lower end cap mass and the portion of the drain tube which passes through it, were added to the drain path flow, the temperature of this flow would be increased by another 101°C, to 475°C. Because the insulating gas layer at the bottom and lateral area of the end cap is not completely effective, a significant amount of the end cap heat is lost and a temperature substantially less than 475°C is obtained. The 130 node axisymmetric model of fig. 5 was used to analyze the lower end cap. Because the top 0.318 cm of the lower end cap is already included in the specimen container model of fig. 4, only the bottom 2.87 cm is represented in rig. 5. The lateral boundary of the model corresponds to the inside surface of the outer specimen container tube, and the
E.E. Feldman / Thermal analysis of LMFBR creep experiment /-ADDED MASS OF X314-A END CAP
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Fig. 5. Analytical model for the mass added to the X314-A lower end cap.
lower boundary corresponds to the top of the lower susceptor. Both of these boundaries are assumed to be 374°C. The upper boundary corresponds to part of the lower boundary of the specimen container model of fig. 4. Because the thermal condition at this upper boundary is not precisely known, several boundary conditions were considered, as shown in the first column of table 2. In all of these cases, the upper boundary was assumed to be either of uniform temperature or insulated. A thermal solution for each of the seven cases was obtained using the THTB computer code. From these solutions, the heat lost by conduction through the surrounding gas layer was calculated. This lost heat was increased by 10% to account for heat lost by radiation through the gas layer. The remaining fraction of the total 0.275 kW is
shown in the second column of the table. The third column shows what temperature the 374°C lower end cap inlet flow temperature would be raised to if it received all of this remaning heat. Hence, the temperatures in the third column correspond to the X314-A drain path inlet temperature for the specimen container model of fig. 4. As the table shows, this specimen container drain path inlet temperature is rather insensitive to the upper boundary condition of the end cap. The specimen container analysis was performed with both a 441°C drain path inlet temperature and a 446°C temperature. The higher temperature caused the bottom quarter of the first tier to be about 3°C hotter and the top quarter of the tier to be about 0.6°C hotter than did the colder temperature. Both solutions indicated that the top of the lower end cap has temperatures ranging between about 468 and 496°C. Therefore, a drain path inlet temperature of 443°C was used in the analytical model of fig. 4. The analysis indicates that the temperature gradients within the lower end cap, fig. 5, are not severe. The maximum internal steel temperature for the 482°C upper boundary case, for example, was only 502°C. 3. 6. Loss-of-flow transient An important consideration in the design of any experiment is its performance during a reactor loss-offlow transient. In this regard, the probe and creep experiments are well designed because most of their
1.0
Table 2
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Creep experiment lower end cap results Upper boundary condition
Fraction of total heat going to specimen container
Specimen container drain path inlet temperature for fig. 4 model (o C)
0.737 0.721 0.704 0.689 0.672 0.656 0.671
448 446 444 443 442 440 441
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E.E. Feldman 'Thermal analysis of LMFBR creep experiment 1.0
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steady state temperature rise is due to the temperature rise across their principal gas gaps. Near the start of a loss-of-flow transient the reactor is scrammed and a sharp drop in subassembly power substantially reduces the gas gap temperature rise. This drop in temperature more than offsets the transient increase in main coolant temperatures caused by the reduction in flowrate. The anticipated type of loss-of-flow transient, specified in the EBR-II project experimenter's guide, was analyzed. The power history, fig. 6, used is for structural experiments and the flow coastdown, fig. 7, corresponds to a loss of primary pumping power while the primary system auxiliary pump continues to operate. Because the power history specified in the guide includes only the first 100 s of the transient, it was conservatively assumed that the power remains constant after this time interval. The computerized models used in the steady state analyses were also used in the transient. The small steady state coolant temperature rises between the subassembly inlet and the bottom of the fig. 4 specimen container model, which exist in both coolant flows of the probe experiment and in the main coolant flow of the creep experiment, were assumed not to vary during the transient. In the creep experiment, the 3°C coolant temperature rise between the subassembly inlet and the bottom of the lower
7
end cap was also assumed to remain constant. A transient analysis, however, was performed with the aid of the computerized model of the lower end cap, fig. 5, to obtain the transient coolant temperature near the top of the creep experiment lower end cap. Two cases were considered and the analysis of both was simplified by ignoring the relatively small amount of radiant heat transfer from the lower end cap. In the first case, the upper boundary was assumed to be at a constant uniform temperature of 482°C. In the second case, which produced the higher transient exit coolant temperature, the upper boundary was assumed to be insulated. For both cases, the maximum stainless steel temperature declined throughout the transient, while the coolant exit temperature rose for about 35 s to its maximum, which was 493°C for the second case, before declining. The transient exit coolant temperature of the second case was taken to be the transient drain path inlet coolant temperature for the model of fig. 4. Because the passive temperature monitors used in both experiments record only maximum temperatures, steady state specimen temperatures must not be exceeded during the transient. The transient analysis shows that the top four tiers and most of the bottom tier of both experiments meet this requirement. In both experiments, however, the temperature of the drain path flow below the first tier rose significantly above its steady state value. Fortunately, this is a very localized effect which, as analytical estimates indicate, may raise the specimen temperatures near the bottom of the first tier by no more than about 1°C above their steady state values.
4. Results Steady state radial temperature distributions produced with the analytical models of the experiments are shown in fig. 8. The axial location of these temperatures is near the center of the middle tier cup and is indicated by the horizontal row of dots in fig. 4. This location was chosen because it is near the peak of the axial power distribution, fig. 3, where the largest radial temperature gradients exist. In the region between the main coolant flow and the lateral walls of the tier cups, the geometry of the analytical model closely resembles the experiment. Within the
8
E.E. Feldman / Thermal analysis o f LMFBR creep experiment
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Fig. 8. Radial temperature distributions near the midplane of the analytical models.
Fig. 9. Axial distribution of the specimen temperatures for the probe experiment X314.
tier cups, however, a three-dimensional matrix of sodium containing pockets of stainless steel, some of which contain pockets of gas, was approximated by an axisymmetric two-dimensional annular model. Therefore, care is required in interpreting the results obtained for the interior of the tier cups. The model indicates a maximum temperature difference of about 20°C from the lateral cup wall to the sodium near the centerline of the cup. The actual difference is expected to be about half of this calculated value because the sodium matrix connects all regions of the cup interior while the model has an annular wall of stainless steel. All of the test specimens of the creep capsules are in direct contact with the sodium matrix and all of the temperature monitors measure sodium temperatures. Therefore, the purpose of the analyses is to predict sodium temperatures inside the tier cups. The temperatures of the first column of sodium nodes outside the rings representing the specimens, as indicated by the vertical column of dots in fig. 4, were chosen to represent the axial distribution of specimen temperatures. For the middle cup these temperatures are about 3°C above the corresponding lateral cup wall temperatures.
Fig. 9 provides the axial distribution of specimen temperatures in the probe experiment X314. The upper solid line is based on the analytical model of fig. 4 and the data provided in the third column of table 1, while the circles represent the measured data.
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Fig. 10. Calculated axial distribution of the specimen temperatures for the creep experiment X314-A.
E.E. FeMman / Thermal analysis o f LMFBR creep experiment zooo [
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The relative minima in the analytic curves occur at the axial locations where there is a sodium gap between the stainless steel specimen ring of the model of one tier and that of the next. While the distribution of material in the experiment is expected to create local peaks and valleys, they need not correspond to those in the analytical curves. Fig. 10 provides the analytical prediction of axial specimen temperature distribution for the creep experiment X314-A, which is currently in the reactor. Based on the reactor inlet temperature of 371°C and the steady state exit temperatures of the two coolants, 7.84 kW are produced in the probe experiment and 8.32 kW are produced in the creep experiment. Figs. 11 and 12 provide the transient thermal performance of the two experiment during the anticipated type of loss-of-flow accident described in the previous section. During the transient, the dropping flowrate causes the main coolant temperatures to initially rise to a maximum where the falling subassembly power forces the coolant temperatures to decline. The behavior of the specimen container temperatures is easily explained. The sudden drop in power precipitated by the reactor scram causes a sharp initial drop
Fig. 12. Thermal performance of the creep experiment X314-A during a loss-of-flow transient.
in the maximum temperature inside the specimen container. The rising main coolant temperatures temporarily reverse this trend. Then the temperatures inside the specimen container resume their decline.
5. Discussion and conclusions
The temperature rise distribution is defined to be the temperature distribution reduced by the 371 °C subassembly inlet temperature. The adjusted calculated temperature distribution of fig. 9 is obtained by dividing the temperature rise distribution calculated for the probe experiment X314 by 1.15 and increasing the results by 371 °C. The extremely good agreement between the adjusted calculated curve and the measured curve is a clear indication that all of the principal phenomena which can influence the relative axial temperature distribution of the experiment have been
10
E.E. Feldman / Thermal analysis of LMFBR creep experiment
properly represented in the analytical model. This was not true of some of the preliminary analyses of the specimen container, for example, where the mission of the drain path flow caused the temperature distribution of the bottom tier to be almost a mirror image of that of the top tier. The predictive capability of the present analytical model has made it possible to analytically evaluate and optimize various aspects of the design of the experiments, such as the distribution of specimens, the drain path orifice, the lower end cap of the specimen container, and the principal gas gap size and composition. As fig. 9 indicates, the calculated temperature rise is 15% too high. The temperatures within the specimen container are very sensitive to the subassembly power level, the gas gap size and uniformity, and the thermal conductivity of helium. The uncertainty associated with these quantities can account for much, if not all, or the 15% discrepancy. In conclusion, an analytical model has been developed for the thermal analysis of the creep experiment. The predictive capability of the model has been
tested and confirmed in the steady state analysis of the probe experiment X314. Analytical results indicate that reasonable specimen irradiation temperatures are expected for the creep experiment X314-A. Analysis of both experiments has also demonstrated that the anticipated type of loss-of-flow transient can cause no significant adverse effects.
References [1 ] J.E. Flinn et al., Argonne National Laboratory, unpublished information, November 1977. [2] O.S. Seim, J.C. Wendte and E.E. Feldman, Trans. Am. Nucl. Soc. 28 (1978) 193. [3] J.E. Flinn et al., Argonne National Laboratory, unpublished information, July 1977. [4] W.E. Ruther and Sherman Greenberg, Argonne National Laboratory Report ANL-8042 (1973) p. 22. [5 ] G.L. Stephens and D.J. Campbell, General Electric Report R60FPD647 (1961). [6] J.R. Moszynski and Ankur Purohit, Argonne National Laboratory Report, in press.