Author: Cliff B. Davis Evaluation of Fluid Conduction and Mixing Within a Subassembly of the...
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Author: Cliff B. Davis Evaluation of Fluid Conduction and Mixing Within a Subassembly of the Actinide Burner Test Reactor
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Transcript of Author: Cliff B. Davis Evaluation of Fluid Conduction and Mixing Within a Subassembly of the...
Author: Cliff B. Davis
Evaluation of Fluid Conduction and Mixing Within a Subassembly of the Actinide Burner Test Reactor
2/15
Introduction
• RELAP5-3D is being considered as the thermal-hydraulic system code to support the sodium-cooled Actinide Burner Test Reactor (ABTR)
• An evaluation* was performed to determine if existing code models could be used to represent important features of the ABTR
– Fluid heat conduction (axial and radial)
– Radial subchannel mixing
* This work was presented at NURETH-12
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Read first bullet as is:2nd bullet: Because RELAP5 was developed to support the analysis of LWRs, an evaluation was performed to determine if there were phenomena that were important in the ABTR that were not important in LWRs and hence not might be modeled in RELAP5. Two such phenomena were identified: fluid heat conduction (both axial and radial) and radial subchannel mixing. RELAP5 neglects both heat transport mechanisms because the first is unimporant in LWRs and RELAP5 is not a subchannel code. However, heat conduction in the fluid has the potential to be much more important in the ABTR because the thermal conductivity of sodium is about 100 times that of water. The ABTR has wire-wrapped rod bundles that promotes subchannel mixing. Therefore, an evlaulation was performed to determine the relative importance of these phenomena and if existing code models could be used to model them.FYI: Other unmodeled phenomena have the potential to be important for the ABTR, but this paper only talks about these heat transport mechanisms.
3/15
The EBR-II XX09 subassembly was used as a surrogate for the ABTR
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A conceptual design for the ABTR is available now, but was not available when this work started. The results shown subsequently (obtained with the XX09 subassemly) should be qualitatively similar to those expected for the ABTR. The XX09 subassembly was selected as a surrogate because the geometry was readily available.The left figure shows an axial view; cold sodium flows from the bottom, into the core region, and gas plenum region, and then out the top. The gas plenum region of the fuel rod is relatively long compared to LWRs to accomodate the relatively large amount of fission gas release in fast reactors.The right figure shows a cross-sectional view of the fuel region. The bundle contained 61 wire-wrapped rods, of which 59 were heated; the outer "annulus" (the thimble flow region) provides space for control rod insertion. The four hexagonal solid lines in the bundle define the radial nodalization in the 2D model shown later.
4/15
Two RELAP5 models were used
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Outlet
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1D 2D
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Two models werre used in this evaluation. The 1D model was used to study axial conduction. The 2D model was used to study radial conduction and mixing. Each model represented the major axial regions of the bundle, including the inlet, active core, gas plenum, outlet, and thimble regions. The 1D model used a single channel to represent the core and gas plenum regions. The 2D model represented these regions with 5 radial rings.Boundary conditions of flow and fluid temperature were applied at the bottom of the models. Pressure was applied at the top of the models.
5/15
The control system was used to simulate fluid heat conduction and mixing• The control system provides a generalized
capability to evaluate algebraic and differential equations using standard mathematical operations and functions that can interact with the code’s hydrodynamic calculations
• The control system was used to calculate the heat transfer associated with heat conduction and radial mixing
• The calculated amount of heat was then added to or subtracted from the various control volumes in the model
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Because RELAP5 does not have built in models to represent heat conduction and mixing in the fluid, the RELAP5 control system was used to represent these phenomena. Then read bullets 1 through 3FYI (in case a question is asked): The control systems were rather large. For axial conduction the control variables were regular enough that they could be copied and modified by hand. For radial conduction and mixing, I eventually wrote a little Fortran program to generate the input. This simplified the process of making sure that I entered the data correctly.
6/15
Fluid heat conduction and mixing were represented as
)T(TDq 1mmm1,mm1,m D = f ( k, geometry)
Heat conduction:
*ε
Radial mixing:
= effective transverse mass flux / axial mass flux
geometry) *,( fm where)T(TCmq TjipTij
023.0*013.0 for the XX09 subassembly
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Fluid heat conduction was represented with the first equation:q represents the heat transfer between two control volumes; D is a function of thermal conductivity and geometry; T is a volume fluid temperature. Radial mixing was represented with the second equation:mdot is transverse mass flow rate (i.e. in the radial direction) that is a function of e, the effective eddy diffusivity and the geometry; cp is specific heat capacity. e is relatively big for the XX09 subassembly because the rods are wrapped with a helical wire that promoted mixing between adjacent subchannels.Details of the equations and/or underlying correlations are presented in the paper.FYI: The equations are entered as equation objects; the projecting PC used requires Equation Editor to display properly.
7/15
The 1D model was used to determine the effects of axial conduction for a wide range of steady-state conditions
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The 1D model was used to determine the effects of axial conduction in the fluid for a wide range of steady state conditions. This is a figure of normalized value (flow or power) vs. time. Conditions varied from 100% (the design condition) to 0.01% (which corresponds to the design flow and power multiplied by 0.0001) so that the same steady outlet temperature would be achieved in each case. The range examined here greatly exceeds that expected during most transients, where minimum values on the order of 1% generally occur. The lower values were intentionally chosen to try to find a place where axial conduction in the fluid was important.
8/15
Axial conduction affected the temperature profile at very low flows
Without axial conduction With axial conduction in the fluid
• Results were consistent with theory
• The effects of axial conduction in the heat structures were smaller than those in the fluid
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The steady state results showed that axial conduction in the fluid affected the temperatures only at very low flows.The left figure is a plot of fluid temperature versus distance for the case without axial conduction. A value of 0.0 m represents the inlet. The dashed vertical lines define the major axial regions (inlet, core, and gas plenum). Five different cases are shown, corresponding to 100% to 0.01% cases shown on the previous figure. As expected, the exit temperature was nearly the same for all the cases because the power-to-flow ratio was the same for all the calculations. The axial temperature profiles are also nearly identical.The right figure is the same except that results were obtained with the axial conduction model turned on. The effects of axial conduction were almost imperceptible until the normalized power and flow were decreased to 0.01%. In this case, axial conduction preheated the fluid entering the core. These results are consistent with theory; a non-dimensional energy equation indicates that axial conduction is important only at very low Peclet numbers which corresponds to very low flow rates. Other calculations showed that the effects of axial conduction in the heat structures were smaller than those of axial conduction in the fluid, which are generally small.
9/15
The 1D model was used to simulate a loss-of-flow transient
• Transient was for a loop-type reactor and simulated a loss of primary pumps, scram, and a pony motor trip near 330 s
• Inlet flow was assumed to completely stagnate for 40 s to maximize the effects of axial conduction
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The 1D model was also used to simulate a loss of flow transient. The loss of flow transient was selected because it is an important transient from a safety perspective for sodium cooled reactors. The figure shows the boundary conditions of normalized flow and power as a function of time.Then read the two bullets to the right.FYI: The other type of sodium reactor design is a pool reactor; the loop reactor is more prone to flow stagnation. Boundary conditions are based on a reported calculation from ANL.
10/15
The effects of axial conduction during the transient were small
• The results of axial conduction were exaggerated by the assumption of complete flow stagnation and the lack of natural circulation in the 1D model
Maximum clad temperature Fluid temperature profile
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The effects of axial condution were small during the transient. The left figure shows that axial conduction decreased the PCT by about 16 K. The effect on the fluid temperature profile at 430 s, which was near the time of the peak temperature profile, was also small as shown in the right figure.The effects of axial conduction were exaggerated by the assumption of complete flow stagnation and the lack of natural circulation in the 1D model. As will be shown later, internal natural circulation is an important cooling mechanism at low flows.
11/15
The radial variation in temperature was large at high flow rates
Fluid temperatures at the top of the core
• Results are from the 2D model without radial heat transport
• The outer ring is cooler because the subassembly wall is unheated
• Buoyancy effects flattened the temperature profile at low flows
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The steady-state calculations described previously in the evaluation of axial conduction were repeated with the 2D model. The figure shows radial fluid temperature profiles at the top of the core. Results are from the 2D model without radial heat transport. The radial variation in temperature was large for the 100% and 10% cases. The outer ring is much cooler than the inner rings because the subassembly wall is unheated. Thus, the power-to-flow ratio in the outer ring is much lower than in the inner rings. The radial temperature profiles were nearly flat when the normalized power and flow were 1% or less of the design values. For these cases, buoyancy enhanced the flow through the inerior rings and reduced the flow in the outermost ring.
12/15
Radial heat transport flattened the temperature profiles at high flows but did not significantly affect the temperature profiles at low flows
100% power and flow
• The effect of radial mixing was larger than conduction for 100% flow, but was smaller for <10% flow
• The 1D model significantly underpredicts the maximum fluid temperature at high flows
1% power and flow
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Radial heat transport flattened the temperature profiles at high flows (see the left figure) but did not have much affect on the temperature profile at low flows (see the right figure). Results are shown for the 2D case without radial heat transport, 2D with radial conduction only, 2D with radial mixing, and the 1D model.For the 100% case, all 2D models predicted about the same peak temperature value (i.e. at a radius of 0.0 m). Radial mixing had a larger effect on the profile than radial conduction at 100%. Although not shown here, the effect of radial conduction was larger than radial mixing for the 10% case. The 1D model significantly underpredicts the maximum fluid temperature at high flows.
13/15
The 2D nodalization and radial fluid conduction affected transient results
• The 2D models predicted significant internal recirculation which lowered the peak cladding temperature
• Radial heat conduction reduced the flow at the top of the core
• The effects of radial mixing were small because of the low axial flow rates during the transient
Maximum cladding temperature Fluid velocity at the top of the core
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The loss of flow transient described previously was also simulated with the 2D model. The 2D nodalization and radial fluid conduction signifcantly affected the transient results. The left figure shows the effect of the various models on the maximum cladding temperature. The 2D models predicted significnat internal recirculation which lowered the peak cladding temperature. The fact that the 2D results with radial conduction was higher than the 2D results without radial conduction was a surprise. One would generally expect conduction to reduce differences between the inner and outer channels and thus reduce peak clad temperature. However, the radial conduction affected the 2D flow pattern during natural circulation as shown in the right figure. Natural circulation was the dominant heat transport mechanism and radial conduction reduced the flow, which resulted in increased cladding temperature. The effects of radial mixing were small because the amount of mixing is proportional to the axial flow rate, which was relatively small during the transient.
14/15
Conclusions
• The effects of axial conduction in the fluid are not important for most ABTR applications
• Subchannel effects are important in the calculation of cladding temperature
– The 1D model underpredicted the maximum temperature during normal operation and overpredicted the maximum value during the loss-of-flow transient
• The effects of radial conduction in the fluid are important in the calculation of cladding temperature
• The effects of radial mixing in the fluid are important at high flow rates
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The effects of axial conduction in the fluid are not important for most ABTR applications. Even so, the calculated effects shown here were probably overstated because the analyses were performed with the 1D model, which neglects the inernal flows caused by buoyancy effects. The effects of natural circulation are expected to overwhelm the effects of axial conduction at very low flow rates.The remaining bullets can be read as is.
15/15
Conclusions (cont’d)
• The control system model can adequately simulate the effects of heat conduction in the fluid and radial mixing between subchannels
– The use of the control system places a burden on the user in terms of the amount of work required to represent the phenomena
– Internal code models would be much easier to use
– Because of the finite number of control variables available, the approach can only be used at about 430 junctions
– Internal code models that calculate the effects of heat conduction and mixing in the fluid should be added to RELAP5-3D to support analyses of the ABTR
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Bullets can be read as is.
