The Zero Power Physics Reactor (ZPPR) operated from April 18, 1969, until 1990. ZPPR operated at low power for testing nuclear reactor designs. This paper examines the temperature of Pu content ZPPR fuel while it is in storage. Heat is generated in the fuel due to Pu and Am decay and is a concern for possible cladding damage. Damage to the cladding could lead to fuel hydriding and oxidizing. A series of computer simulations were made to determine the range of temperatures potentially occuring in the ZPPR fuel. The maximum calculated fuel temperature is 292°C (558°F). Conservative assumptions in the model intentionally overestimate temperatures. The stored fuel temperatures are dependent on the distribution of fuel in the surrounding storage compartments, the heat generation rate of the fuel, and the orientation of fuel. Direct fuel temperatures could not be measured but storage bin doors, storage sleeve doors, and storage canister temperatures were measured. Comparison of these three temperatures to the calculations indicates that the temperatures calculated with conservative assumptions are, as expected, higher than the actual temperatures. The maximum calculated fuel temperature with the most conservative assumptions is significantly below the fuel failure criterion of 600°C (1,112°F).
ZPPR (Zero Power Physics Reactor) was the largest of the split-table fast reactor critical facilities. ZPPR was operated as a criticality facility from April 18, 1969, until being decommissioned in 1990. It was used to obtain a large amount of very detailed data on a variety of full-sized reactor configurations including large, commercial-sized fast reactors with powers of up to 1200 MW (electric). The purpose was to construct assemblies that closely resembled various fast reactor designs and then use the experimental results to validate and refine the data and methods used to design large fast reactors. There were 21 major assemblies, most of which had several major variants (e.g., beginning of cycle, middle of cycle, end of cycle, various control rod positions, etc.). The experiment campaigns included several large plutonium reactors, engineering mockups for both major design concepts for the clinch river breeder reactor designs, larger fast reactor designs as part of the JUPITER collaboration with Japan, the SP-100 space reactor, and assemblies supporting the integral fast reactor design [
The ZPPR critical assembly is put together from rectangular building blocks of fuel, coolant, and structural materials inserted into drawers. Figure
Experimenter loading fuel in the ZPPR.
The fuel, shown schematically in Figure
Schematic diagram of the ZPPR fuel elements.
The fuel elements are stored in aluminum clamshells as shown in Figure
Open clamshell with some fuel elements.
When loaded in one direction, a clamshell can hold up to 12 eight-inch-long fuel plates, and in the other way it can hold up to 16 six-inch-long fuel plates. The posts in the clamshells used to store plates are set up to contain sufficient spacing for 1/4-inch plates. The plates shown in Figure
Clamshells are stored in 4 inch-high by 8 inch-wide steel sleeves embedded in concrete as illustrated in Figure
Clamshell with 12 eight-inch fuel elements perpendicular to front of storage bin.
A picture of the storage bins is shown in Figure
Concrete storage bins with three-inch deep security doors.
Each storage sleeve (cavity) is closed by small individual steel doors on each end. Large steel security doors on each end provide a single closure that covers all the individual openings at once (see Figure
The bin is all concrete. Figure
The combination of the 27-inch deep and 72-inch high concrete bins covered by security doors abutted to security bins on each side makes for highly insulated fuel elements and potentially high temperature fuel elements heated by the decay heat from the plutonium in the fuel.
Dimensions of a clamshell are shown in Figure
Planar view of lower section of empty clamshell.
The base heat transfer model considers a single clamshell inserted in a closed fuel storage cavity with the cavity and bin doors closed. In order to make the calculation tractable, the heat transfer region analyzed is segregated from the rest of the storage bins by considering that adiabatic planes exist at the back of the clamshell (i.e., half way through the storage bin) and in the concrete 4 inches above, below, and from the sides of the cavity steel liner. This is a good assumption in those bins where all the fuel and the clamshell loadings are identical in each cavity. Since a majority of the clamshells do not contain heat generating elements, for example, the uranium fuel (which generates minimal heat) and nonfuel metal elements, the temperatures calculated will be necessarily higher than actual experience. That is, these nonheat or lower heat generating elements will act as heat sinks to the high Pu heat generating elements. As long as the fuel temperatures calculated with this model are acceptable, it is not necessary to go to a more detailed heat transfer model based on actual fuel distributions. The effect of these heat sinks was estimated in two computer runs. This effect is estimated simply by assuming the adjacent cavities have no heat generating clamshells.
Reasonable results were achieved when all the major heat transfer paths were finally represented. Leaving out any major heat transfer path resulted in bin and cavity doors and clamshell temperatures which are much higher than expected. Such unreasonably high temperatures imply that the fuel element temperatures would also be unreasonably high. So the current model is the simplest model which yields close to what the authors consider realistic temperatures, although they are still high. The comparison of calculated and measured bin door, cavity door and clamshell temperatures have shown that the fuel temperatures calculated with this model are conservatively high.
The largest heat generation rates occur in the high concentration of Pu fuel elements designated as PUMH (plutonium, uranium, molybdenum) in Klann, 2001. The maximum heat generated is in clamshells which are full of this PUMH fuel. In order to be full, all the fuel elements in the clamshell must contain either sixteen 6-inch-long elements (placed parallel to the bin door) or twelve 8-inch-long elements (placed perpendicular to the bin door). Both configurations yield the same total fuel length (
There are four types of fuel elements that can fill a clamshell. The highest heat generation rate is in the PUMH fuel which has a heat generation rate of 2.13 W/kg for a total heat load in a full clamshell of 23.1 W. The remaining three types have heat generation rates of about 0.98 W/kg and a total heat generation of about 10.5 W for a full clamshell. The expected temperatures for both the PUMH fuel and the lower heat generating fuel are estimated in this paper. It would take an extremely long time for a clamshell full of fuel elements placed in a cavity to heat up the concrete of the storage bins to come to equilibrium. On the order of weeks, since the fuel has been sitting in the bins for a much longer time than that, steady-state equilibrium temperatures are expected and are of most interest.
The fuel compositions are based on the 2001 report [
The base model analyses a storage bin full of clamshells which are all the same and completely full of 6-inch fuel elements (of the composition identified in Klann et al. [
Clamshells will only fit lengthwise into the storage sleeve. The end closest to the bin door is termed the front end and the other the back end. The analysis assumes a clamshell loaded with 6-inch fuel elements placed parallel to the bin front and with the back end of the clamshell insulated. The back end insulation occurs because of symmetry; that is, the storage cavities contain two clamshells back to back loaded with the same loading pattern and amount of fuel. This symmetry requires that the highest temperature is the last fuel element in the clamshell. As an approximation, the back of the last fuel element is considered insulated no matter how many fuel elements are in the clamshell. This approximation is tested in parametric studies.
The heat transfer is represented in two dimensions, one vertical, the other along the horizontal depth of the cavity. The heat transfer out the vertical sides of the storage cavities is estimated by increasing the thermal conductivity of the steel sleeve and the concrete. Although this distorts transient calculations a bit, steady-state temperatures are only dependent on the thermal conductivities and not the densities or specific heats. Also, the identical storage cavities above and below indicate there would be adiabatic surfaces above and below each cavity, which are estimated to be midway between the clamshell cavities. The vertical distance between the storage cavities is 8 inches. The adiabatic top boundary is estimated to be 4 inches above the top of the cavity, and the adiabatic bottom boundary is estimated to be 4 inches below the bottom of the cavity. With all the other surfaces insulated, the bin door boundary is the only one through which the heat generated by the fuel is transferred to the storage room. This boundary is the outside of the bin storage door. The properties of the material used are listed below. The January 1, 1977, fuel composition was approximately 34.9% Pu and 65.1% U with a small amount of Am and Mo. The Pu and U percentages are used to estimate the properties of the fuel. The decay of Pu-241 to Am-241 is not taken into account in the material thermal properties.
The heat transfer through the cavity door and bin facial concrete contains many difficult paths to analyze. The bin door covers a two horizontal by six vertical matrix of cavity doors and encloses a 3-inch deep air space between bin concrete face and inside bin door. This air space is not air tight so some air can come in the bottom of the space and flow out the top due to buoyancy. It is at a lower temperature at the bottom and heats up as it rises. This effect is not explicitly considered but is small in comparison to the uncertainty of estimating the Nusselt number between the storage sleeve doors and bin door. The bin door frame is attached to the concrete bin face in a nonsymmetric manner and is only approximately represented. This geometry introduces the most uncertainty of all the other factors in the fuel temperature estimation. Elements of the geometry are introduced in the model in ways meant to overestimate the fuel temperature. The discussion of uncertainties in this representation and the comparison of measured temperature uncertainties are included in latter sections.
The thermal properties used in the analysis are included in Table
Thermophysical properties used in analyses.
Material number | Specific heat | Thermal conductivity | Density | Material |
---|---|---|---|---|
J/kg °C | W/m °K | gm/cc | ||
1 | 910 | 237 | 2.7 | Aluminum |
2 | 1008 | 0.02 | 0.001 | Air Nu = 1 |
3 | 123.49 | 20.25476 | 19.3443 | 0.349 Pu, 0.651 U fuel |
4 | 460 | 43 * 1.66 | 7.85 |
|
5 | 890 | 1.1 * 3.0 | 2.1 |
|
6 | 1008 | 0.02 * 11.8 | 0.001 | Air Nu = 11.8 |
7 | 460 | 43 * 2.33 | 7.85 |
|
8 | 880 | 1.1 * 3.66 | 2.1 |
|
9 | 1008 | 0.02 * 4 | 0.001 | Air Nu = 4 |
130 | 6.74 | 19.8 | Pu | |
120 | 27.5 | 19.1 | U |
Note that the thermal conductivity of air for
Detailed composition and heat generation rates for each isotope in the PUMH fuel are included in Table
Fuel properties used in the analysis for PUMH fuel.
gms | W/kg | W | Element Wt | Wt fraction | Fuel dimensions | |||
---|---|---|---|---|---|---|---|---|
Pu238 | 0.2676 | 567 | 0.151729 | Plate Thk = | 0.2025 | in | ||
Pu239 | 209.1584 | 1.93 | 0.403676 | Height = | 1.93 | in | ||
Pu240 | 80.4538 | 7.1 | 0.571222 | Length = | 7.802 | in | ||
Pu241 | 10.3554 | 3.39 | 0.035105 | Vol. of plate | 3.049217 | in3 | ||
Pu242 | 4.3821 | 0.12 | 0.000526 | 304.6173 | 0.337627 | Vol. of plate | 49.96771 | cm3 |
Am241 | 6.6815 | 114 | 0.761691 | 6.6815 | 0.007406 | Mass | 902.2299 | gm |
U235 | 1.1998 | 0.0142 |
|
Area | 97.14729 | cm2 | ||
U238 | 567.174 | 0.0001 |
|
568.3738 | 0.629966 | Clad thick | 0.015 | in |
Mo | 22.5573 | Tot. Watts = | 1.924022 | 22.5573 | 0.025002 | Weld thick | 0.02 | in |
Total Wt (gm) | 902.2299 | Tot. W/kg = | 2.132519 | Pu239/241 | Pu/(Pu + U) | Weld area | 0.0853 | in2 |
Dens. gm/cc | 18.05626 | W for 12 | 23.08827 | 219.5138 | 0.348935 |
Weight data from Table
The properties of the 8-inch-long fuel plates (PUMH) above were used in the following analysis but modified for the shorter 6-inch plates. The extensive properties are proportional to length; the intensive are the same as the 8-inch fuel.
The input material description for the 6-inch plates is included in Figure
Material input.
The input from outside the bin door to the sleeve door in Figure
This concrete contacts the steel frame of the bin door. Figure
Heat flow path from storage sleeve through concrete to the bin door.
The metal frame which supports the bin doors contacts the concrete over a 1-inch width. Even though the conduction path is less than 1-inch-thick steel, the conductivity of steel is so high that this conduction path will conduct all the heat from the wider contact area, so it is more important to represent the contact area between the metal and concrete than the heat transfer thickness. The contact area in the model is located 3 inches from the storage sleeve on both the upper and lower ends of the model, but the actual geometry is much more complicated.
Each of the subregions shown in Figure
Increments used in each region and dimensions.
The coefficient representing heat transfer from the storage bin surface to the storage room is taken as 100 W/m2 °K. The storage room temperature is usually kept at 35°C (95°F) by a thermostat controlled cooling system.
As mentioned previously, each storage cavity is insulated from the others except for problems in which the neighboring empty cavities are included in the analysis. Also, the back of the last fuel element in this model is specified as insulated. It is more accurate to represent the additional air space behind this fuel element and the end of the clamshell and then insulate the back of the clamshell. The former geometry has been used in most of the analyses. A case with the more accurate geometry has been run and shows that slightly higher temperatures (5°C [9°F] max) are obtained without the more accurate geometry so use of the simpler geometry predicts a slightly higher temperature.
This section presents results obtained with the best estimate input model (as judged by the authors). The largest conservative factor in this model is the surface contact resistances. Conservative and best estimate values of the resistances are presented in this section. One nonconservative value for the decay heat is used here. This nonconservatism is investigated in the parametric study in Section
There is a desire to produce conservatively high temperatures in these studies. If the results show that the fuel is not damaged with the conservative results, then it can be concluded that no damage to the fuel will occur at the lower storage temperature. This objective is met by assuming high heat transfer resistances for surfaces in contact with each other. There is also a desire to produce close to realistic results. This objective can be approached with more realistic assumptions for these resistances. Three cases are investigated in this section. The first case (base Case A) uses high heat transfer resistances. Case B uses intermediate resistances and Case C uses low resistances.
The steady-state center line fuel best estimates temperatures for a clamshell full of 6-inch high heat generation PUMH fuel for a total heat generation in the clamshell of 23 W and a specific heat generation rate of 2.13 W/kg is shown in Figures
Temperatures at specific locations of high heat generation PUMH fuel.
The temperature distribution on a horizontal plane through the center of the fuel is shown in Figure
Temperature on plane through center of fuel high heat generation PUMH fuel.
The vertical and horizontal temperature fields are shown in Figure
Entire temperature field high heat generation PUMH fuel.
Figure
Uniformity of the temperature of the clamshell.
This model has been used in three places: the placement of the clamshell on the inside of the sleeve and the placement of the fuel on the surface of the clamshell. In addition, the bottom portion of the sleeve has been assumed to be separated from the concrete and to have this 0.1-inch air space. More realistic values for each of these locations are considered in this section.
The results for Case B are shown in Table
Comparisons of results of the various heat transfer resistances (°C).
Storage room | Outer door | Inner door | Clamshell | Fuel 1 | Fuel 4 | Fuel 10 | Fuel 16 | |
---|---|---|---|---|---|---|---|---|
Distance from front of bin door (cm) | 0 | 0.25 | 8.51 | 10.10 | 11.25 | 14.81 | 21.88 | 28.74 |
Conservatively |
35.0 | 38.7 | 74.8 | 106.6 | 140.3 | 174.6 | 183.5 | 185.8 |
High |
35.0 | 38.7 | 68.6 | 77.1 | 114.1 | 150.8 | 160.3 | 163.2 |
Same as above and Med |
35.0 | 38.7 | 68.1 | 75.9 | 96.7 | 111.6 | 114.8 | 116.2 |
The following model is used to estimate the effective interface heat transfer coefficient between the fuel and clamshell. The two surfaces of the metals have a roughness so contact each other only on the crests of these bumps and only when the crests are in the same place. That is, many of the crests are unable to touch because one metal has a crest at the location that the other has a valley. The heat transfer through the metal areas that contact each other where
Eliminating the intermediate temperature
The heat transfer through the air portion,
Case C results in Table
An important item to notice from comparing the base Cases A and B is that temperature measurements of the outer bin door, the inner sleeve door, and the clamshell would show a measurable difference between the high and low heat transfer resistance for the clamshell to sleeve and sleeve to concrete cases interfaces.
It was hoped that these measurements could be used to infer the conservatism in the fuel temperature measurement; however, this is not the case but it can possibly bracket the fuel temperature. It is observed that, in Table
Another important assumption introduced into the model is the amplification of the conductivity in the concrete and steel to take into account the third dimension of heat transfer. The conductivity factor has been reduced to 1 for the concrete and steel (materials 4, 5, 7, and 8) to determine its effect for Case A and Case C. The comparisons are shown in Table
Effect of setting thermal conductivity amplification factors to one (°C).
Storage room | Outer door | Inner door | Clamshell | Fuel 1 | Fuel 4 | Fuel 10 | Fuel 16 | |
---|---|---|---|---|---|---|---|---|
Distance from front (cm) | 0 | 0.25 | 8.51 | 10.10 | 11.25 | 14.81 | 21.88 | 28.74 |
Case A | 35 | 39 | 75 | 107 | 140 | 175 | 183 | 186 |
Case A1 | 35 | 40 | 94 | 127 | 158 | 191 | 200 | 202 |
|
||||||||
Case C | 35 | 39 | 68 | 76 | 97 | 112 | 115 | 116 |
Case C1 | 35 | 40 | 90 | 103 | 123 | 138 | 142 | 143 |
Parametric studies were conducted using a preliminary model for the base case. The preliminary base case yields slightly higher temperatures than the best model but the effect of the parameter changes should be similar. The first eleven cases analyzed six-inch fuel elements parallel to the storage sleeve door. The high heat transfer resistances of the first best estimate case have been used in these studies. The cases analyzed are high heat generation fuel, PUMH (base case), higher fuel emissivity, lower heat generation fuel, high power, no heat generation in neighboring cavities, and PUMH fuel, low power, no heat generation in neighboring storage cavities, no thermal radiation, rubber pad inserted on bottom of clamshell, only six fuel elements, cell cooling being turned off, higher power due to decay of Pu-241 to Am-241, higher power plus cell cooling being turned off, 8-inch fuel elements perpendicular to cavity door.
A summary of the parametric study is presented in Table
Summary of calculated fuel temperature results.
Temperatures, °C | ||||||||
---|---|---|---|---|---|---|---|---|
Case | Number of fuel plates | Problem description | Max fuel | Front clam | Cavity door | Bin door | Compare to | Max fuel Temp. diff. from base |
Fuel placed parallel to front of storage bins—6-inch elements | ||||||||
A | 16 | Base, eps = 0.3 | 186 | 107 | 75 | 39 | Best Est. | Base case |
|
||||||||
1 | 16 | Base, eps = 0.3 | 219.3 | 146.9 | 87 | 39.6 | Base for | Parameter study |
2 | 16 | Increase eps = 0.8 | 191.6 | 147.7 | 87.4 | 39.6 | Case |
Minus 29 |
3 | 16 | Low power | 137.4 | 96.2 | 61.6 | 37.2 | Case |
Minus 83 |
4 | 16 | No heat next cavity, high power | 200.2 | 123.4 | 67 | 37.6 | Case |
Minus 20 |
5 | 16 | No heat next cavity, low power | 124.3 | 81.7 | 50.7 | 36.2 | Case |
Minus 13 |
6 | 16 | Rub mat and Al plate | 224.1 | 147.2 | 87.5 | 39.7 | Case |
Plus 4 |
7 | 16 | No thermal radiation | 530 | 392 | 185.8 | 39.5 | Case |
Plus 310 |
8 | 6 | Only 6 fuel elements | 182.8 | 110.1 | 58.4 | 36.8 | Case |
|
9 | 16 | Cell cooling off | 235.3 | 166.3 | 111.6 | 70.2 | Case |
Plus 15 |
10 | 16 | Hi power 35 W | 280.4 | 186.8 | 109.2 | 42.1 | Case |
Plus 60 |
11 | 16 | Hi power 35 W and cell cooling off | 292 | 202 | 130.5 | 72.6 | Case |
Plus 72 |
|
||||||||
Fuel placed perpendicular to front of storage bins—8-inch elements | ||||||||
12 | 12 | 8-inch fuel | 210 | 146.9 | 87 | 39.6 | Case |
Minus 10 |
The maximum fuel temperature for the high power preliminary base case (Case 1) with the PUMH fuel and fuel emissivity of 0.3 is 220°C (428°F). The cavity door temperature is 87°C (189°F), and the clamshell temperature is 147°C. Case 1 also shows that clamshell temperature is almost uniform which allows the problem to be split into two: the determination of the clamshell temperature based upon the total heat generation and the determination of the fuel temperature knowing the clamshell temperature. This is discussed more later in this section.
Using a higher fuel emissivity of 0.8 (Case 2) yields a lower temperature of 192°C (378°F), but the lower emissivity of 0.3 for the shiny cladding is considered to be more realistic.
The temperatures are much lower for the lower power clamshells with Pu containing fuel with a power density of 0.99 W/kg as shown in Case 3. These results may be more representative of most of the fuel than the high power in Case 1. The fuel temperatures are less than 140°C (284°F).
The temperatures would be lower if the neighboring cavities had lower power generation. This is checked out in Case 4 where Case 1 was rerun with zero power in the adjacent cavities.
The low power case, Case 3, was rerun with no heat generation in neighboring cavities as Case 5.
Some clamshells contain a 1/16-inch rubber pad to prevent damage to the fuel. The insulating effect of this pad is estimated in Case 6. The properties used were for Rubber Silicone with
Case 7 shows that including thermal radiation in the model is very important. The fuel temperature is much higher at 530°C (986°F) when thermal radiation is neglected. Thus, thermal radiation is extremely important in estimating these temperatures. It carries much more heat across the air spaces than the conduction and convection of air.
Case 8 shows that reducing the number of elements to six decreases the temperature of all the six fuel elements. The reason for this is that these fuel elements are no longer receiving heat from the elements seven to sixteen.
Case 9 considers the case where the storage room cooling is off. Experience has shown that the room temperature increases to a maximum of 150°F (65.5°C). Because thermal radiation is not linear, the maximum fuel temperature increases by only 15°C (27°F) even though the ambient temperature increases by 30.5°C (55°F). The transient behavior of this case is discussed later on.
Case 10 analyzes a clamshell where a significant amount of Pu-241 has decayed to Am-241. Calculations indicate that enough Pu-241 has decayed to Am-241; that is, the decay heat for a full clamshell in 2012 is almost 34 W. So a clamshell with 35 W heat generation was analyzed for Case 10. The maximum fuel temperature has increased to 280°C (536°F), an increase of 60°C (108°F) over the base of 220°C (428°F). This is still much lower than the 600°C (1,112°F) failure limit of the fuel. Both the cavity door and the clamshell temperatures have increased considerably.
Case 11 is Case 10 redone assuming the loss of cell cooling. The combination of the maximum heat generation and loss of cooling yields the maximum fuel temperature possible in storage. This temperature is 292°C (558°F). This is an increase of 12°C (22°F) over Case 10.
Case 12 estimates the temperature of the 8-inch fuel elements. Due to the high conductivity of the clamshell, the clamshell temperature only depends upon the total heat generated in the clamshell (as long as it is somewhat evenly distributed). This is verified by observing that the clamshell temperatures are the same for Cases 1, 2, and 6. They have the same heat generation, so the clamshell temperatures are the same even though the fuel temperatures are different. Since a clamshell fully loaded with twelve 8-inch fuel elements has the same total heat generation as the fully loaded clamshell with 6-inch fuel elements, the temperature of the 8-inch fuel elements was determined with a model that included only the clamshell and the fuel. The clamshell temperature was specified to be the same as in Case 1. Case 12 shows that fuel elements placed perpendicular to the bin door produce maximum fuel temperature of 210°C (410°F) which is 10°C (18°F) lower than that in the base case (Case 1).
More detail is presented in the following for Case 1, Case 8, and Case 9.
As mentioned previously, the high thermal conductivity of the aluminum clamshell causes the clamshell to be at a near uniform temperature and indicates the possibility that adding additional convection and radiation heat paths between the last fuel plate and the end of the clamshell would reduce the fuel temperature. The more accurate detail was added to the model, and the modified results are shown in Figure
Temperature through center of fuel with end added to clamshell.
There is still somewhat of an asymmetry because the clamshell temperature does increase 4°C across the clamshell in the horizontal direction. To check on what the temperature would be if it were symmetric, a subset of this problem modeling just the clamshell assuming it was at a uniform temperature of 147 (297°F). The results are shown in Figure
Temperature through center of fuel with a specified clamshell temperature.
This also means that the temperature of the clamshell depends upon the heat generation and not on the temperature distribution of the fuel in the clamshell. Thus, the heat transfer problems can be separated into two analyses. A heat transfer analysis outside the clamshell with a specified heat generation within the clamshell would determine the clamshell temperature. This temperature could then be used to determine the temperature distribution in the fuel inside the clamshell. This fact was needed to determine the temperature of the eight-inch fuel elements placed perpendicular to the door in Case 12. That is, since a two-dimensional code is being used, the fuel placed perpendicular to the bin door would require a three-dimensional analysis. Since the two problems can be separated, a two-dimensional analysis, one in the vertical direction and another parallel to the bin door, was sufficient to determine these fuel temperatures. If the problems could not be separated, then a three-dimensional analysis would be required to represent the nonheat generating space between the fuel elements.
The temperatures with only six fuel elements in the front part of the clamshell are described in this section, and the results are presented in Figure
Centerline profile with only six fuel elements (ZPPR 2d 18 12 TRkRad1.xlsm).
The steady state obtained with the storage room cooling fails or is turned off as shown in Figure
Storage room cooling fails off.
The geometry that has been modeled is shown in Figures
The conduction equation for the temperature
The boundary condition on the outside bin door (specified to be the left boundary) is given as
The solution method uses an explicit numerical transient solution for all interior nodes. The boundary nodes are solved for after the interior nodes and since the interior temperatures are known, the only unknowns in the boundary equations are the boundary temperatures which are solved for explicitly.
The Nusselt number is to be used as a multiplier to indicate how much the effective conductivity of air is increased due to natural circulation. When
In this section, literature values for heat transfer in spaces similar to those encountered in the ZPPR storage were evaluated. This evaluation shows that the Nusselt number in the air space between the bin and cavity doors is large (
Experiments and analysis are used to determine the enhancement of the heat transfer coefficient,
Thus Nu can replace
The bin door geometry in ZPPR is most like parallel plates closed at the top and bottom, but some air can escape through the upper doorjamb since it is not sealed at the top. The bottom is open so since the air between the door and the bin front is hotter than the surroundings, colder room air would come in the bottom to replace air lost out of the top.
Several investigators present data for heat transfer across an air space in the range of interest [
The heat transfer between the fuel plates is estimated by a rectangular enclosure using a width of the distance between elements (0.25 inches) and the height of the element (2 inches). The Grashof number based on this distance is small enough that
The space between the cavity door and the clamshell with a
The vertical distance from the top of the fuel to the ceiling of the clamshell is 0.25 inches. Using Yin’s correlation with
For the space above the clamshell, Grashof number is calculated with
Jacob and Hawkins [
For the bin door temperature of
The thermal radiation model assumes that the radiation occurs between surfaces that are close together and parallel to each other. This implies that the radiation occurs mainly between surfaces that are parallel and opposite to each other so that the view factor between these surfaces is equal to one and equal to zero for other surfaces. Although this is an approximation, energy is still conserved [
The model used for determining radiation between two parallel surfaces is shown in Figure
Geometry for the radiation model.
At interface
The higher temperature solid,
The radiation term is rearranged as
In the finite difference solution, the
The thermal conductivities in the steel regions and the concrete regions are modified to take into account some three-dimension heat losses. Increasing the thermal conductivity is equivalent to increasing the area of heat transfer. Although the transient behavior is affected by increasing the thermal conductivity, the steady state depends only on the thermal conductivity and not on the density or specific heat. The main interest here is the steady state, and the only transient of interest is the loss of storage cell cooling.
The length of the fuel element is 6.0 inches. The outside width of the fuel cavity liner is 8 inches. There is approximately 4 inches of concrete above, below, and to the sides of the 4-inch× 8-inch fuel storage cavity which results in a rectangle of 16 inches wide and 12 inches high. Using the midpoint of the 2-inch fuel to separate the higher from the lower portion of the area gives a distance of 7 inches to the top of the rectangle and 5 inches to the bottom. The upper concrete area for the 3D model heat loss is the
The ratio for the upper concrete is
The ratio for the lower concrete is
The ratio for the upper steel is
The ratio for the lower steel is
Since the thermal conductivity of the steel is so high, the corrections to the steel do not make much difference in the answer.
Temperature measurements were made of the outside bin door, the storage sleeve door, and the clamshell in the ZPPR fuel storage cell in three locations. By comparing these measurements to the calculated temperatures, an estimate of the conservatism in the calculations of fuel element temperatures can be made. The fuel temperatures cannot be measured directly due to contamination and fuel preservation concerns which make it impractical to insert thermocouples into the clamshells while they are in storage. In order to measure the temperature of the fuel, it is necessary to open the bin doors, then open the cavity doors, then remove the clamshell, and bring it into the examination room. Then the bolts closing the clamshell can be removed and the clamshell is opened to expose the fuel, and then an optical pyrometer could be used to measure the fuel temperature. Significant heat loss would occur during this process in this new environment which would lower the maximum temperature of the fuel. The measured temperature would not represent the maximum temperature of the fuel in storage.
The conservatism in the model is contained mainly with the heat transfer through the air spaces where Nusselt numbers must be estimated and are used to represent the increase in conductive heat transfer due to free convection and the contact heat transfer resistances. The thermophysical properties of the solids are believed to be fairly accurate, although the emissivity of the surfaces is also an estimate based on experience. The emissivity of the fuel cladding is estimated on the low side as another conservative factor.
The measurements were made with an optical pyrometer. Measurements were made of the outside bin door, the inside cavity door, and the clamshell temperature. It is recognized that the cavity door temperature will decrease slowly after the bin door is opened, and the clamshell temperature will decrease slowly when the cavity door is open. Therefore, the cavity door temperature was measured quickly after the bin door was opened. Then the cavity door was opened, and the clamshell temperature was measured quickly.
Measurements were made at three different storage locations. Location 1 contains sixteen 5-inch Vendor 75 plates, and the other two locations have fifteen 6-inch Vendor 75 plates. The decay heats used in the computer base case computer run were based on sixteen 6-inch fuel elements with a total heat generation of 23.08 W calculated using the 1977 composition. The heat generation calculated for fuel where the Pu-241 has all decayed to Am-241 is 36.8 W. Comparisons here were made to the calculated base case of 16 fuel elements with 23.08 W. (Fifteen 6-inch fuel plates generate 21.6 W at the 1977 assumed fuel concentrations.) There is uncertainty about the heat generation in this fuel. It could be lower or higher than assumed in the model. The measurements were taken in a row of storage bins which were not backed against a symmetric set of bins but were backed against a concrete wall so that there was heat loss out the back of the bin rather than an adiabatic condition as assumed in the model. The particular bin was located between two other bins. The storage tubes were part of the middle four in the vertical alignment of six tubes so there were tubes above and below the measured tubes. The storage tubes on the sides and top/bottom contained clamshell with similar fuel to the ones measured so that the reflective heat transfer boundary conditions for the sides and top/bottom assumed in the model were reasonably represented. The loss of the adiabatic condition on the back of the storage bin might be represented by the difference shown in Table
The measurements made at the latter two locations are the closest to the base Case A modeled in the calculations. These are shown in Table
Measured and calculated temperatures at 3 locations.
Distance from bin door front | Location 2 | Location 3 | Estimated error | Case A | Case B | Case C | |
---|---|---|---|---|---|---|---|
Units | cm | Temperature °C | |||||
Bin door | 0 | 46.9 | 45.8 | 1.1 | 38.7 | 38.7 | 38.7 |
Cavity door | 9 | 63.3 | 58.3 | 5.0 | 74.8 | 68.6 | 68.1 |
Clamshell | 10 | 73.3 | 70.0 | 5.0 | 106.6 | 77.1 | 75.9 |
Note that the differences between the temperatures of locations 2 and 3 are used as an estimate of the error (listed in Table
Figure
Comparison of measured temperatures to best model results.
Figure
As a side note, the calculated bin door temperature is lower than the measurement indicating the estimated heat transfer coefficient to the storage room is too high. If this was decreased to obtain agreement, the other temperatures would increase.
There are two differences between the model and the clamshells measured which should be mentioned but do not change the above conclusions. The first is that the base case clamshell has one more fuel element than the clamshells at locations two and three since it has sixteen 6-inch fuel elements instead of 15. Modelling only 15 fuel elements instead of 16 would only lower the temperatures a small amount. The second is that the Pu-241 should have mostly decayed to Am-241 during the years of storage. This would increase the heat generation rate to 35 W rather than the 23 W assumed. The parameter study indicates the fuel temperature would be 60°C higher with the higher heat generation (or 72°C higher for the loss of cooling case). These temperatures are still far below the threshold of fuel damage.
Although there is uncertainty as to the heat generation rate in the measurements and uncertainty about how well the model matches the physical geometry, it is still evident that the calculations with high interface heat transfer resistances are higher than measurements in the locations measured. Although it has not been possible to measure the fuel temperatures in the clamshells, with the conservative assumptions being made, the authors expect that conservatively calculated fuel temperatures are significantly higher than actual temperatures. The maximum calculated fuel temperature with the most conservative assumptions (292°C, (558°F)) is significantly below the no-fuel failure criterion of 600°C (1,112°F). The main conclusion of this paper is that no damage has occurred due to the highly insulated characteristics of the ZPPR fuel storage facility. This conclusion is consistent with the measured data of the bin doors, the cavity doors, and the clamshell.
Due to the uncertainty in the temperature measurements locations, the heat generation rate, and the physical geometry of the cells measured, the following considerations are warranted. (1) The potential for high fuel element temperatures exists. These can occur in fully loaded clamshells. High fuel temperature can lead to problems. (2) The bin door enclosure represents a three-inch deep air resistance to heat transfer from the storage bin. (3) Measurement of the cavity door temperature as soon as the bin door was opened and then measurement of the clamshell temperature as soon as the cavity door was opened have been made. These measurements have been used to calibrate the model temperatures of the fuel in the clamshell. (4) In order to verify the conclusion that no cladding damage has occurred from the high storage temperatures, some of the fuel should be inspected. The stored fuel where the storage temperatures are predicted to be the highest and have been stored at that temperature for a long time should be the ones checked for damage. If the fuel remains at high temperatures for a long time, it is possible that some cladding degradation would take place. Although the environment of the cell is probably low humidity, stress corrosion cracking is a possibility in the cladding.
These calculated results have been calibrated by measurement of the bin door, cavity door, and clamshell temperatures. The temperature measurements made show the analytical results are higher than the measurements and would be still higher if the higher heat generation corresponding to Pu-241 has decaying to Am-241 is used.
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The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the US Department of Energy, Office of Nuclear Energy, under DOE Idaho Operations Office Contract DE-AC07-05ID14517. Accordingly, the US Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for US Government purposes.