ML20236T080
| ML20236T080 | |
| Person / Time | |
|---|---|
| Site: | University of Michigan |
| Issue date: | 07/23/1998 |
| From: | Hartman M MICHIGAN, UNIV. OF, ANN ARBOR, MI |
| To: | |
| Shared Package | |
| ML20236T076 | List: |
| References | |
| NUDOCS 9807270420 | |
| Download: ML20236T080 (11) | |
Text
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l I
Development of a Model Characterizing IIeat Transfer in the MTR Fueled !
Ford Nuclear Reactor l
l Michael Hartman l Michigan Memorial Phoenix Project University of Michigan Ann Arbor, MI 48109 23 July 1998 ,
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l 9807270420 990723 I" PDR ADOCK 05000002 S PDR.
i I. Introduction We present the derivation of an improved heat transfer model for the Ford Nuclear
. Reactor (FNR) core. The effa t to develop the more accurate model has come about out of a desire to have a better physical appreciation for the temperature of reactor coolant as it traverses the fueled region of the reactor and also to gain the ability of predicting the clad temperature throughout the fueled region. Using the improved model,it is possible to study in greater detail the operating envelope of the reactor and some abnormal conditions ofinterest such as obstruction of coolant channel passages.
II. Coolant and Clad Temperature Distributions II.A. Core Power Distribution The generation of heat in the FNR reactor core is primarily dependent upon the interaction of thermal neutrons and fissile materials in the core. The FNR uses MTR type 2
UAL, elements with a "U enrichment of 19.5 wt. %. The fuel is assumed to be evenly distributed in the fuel meat, thus the heat generation is then dependent solely upon the distribution of the neutron flux. Using a self-powered Rhodium detector, a flux mapping of the FNR core was performed. The flux maps are fitted to a product of three one-dimensional flux distributions, summarized in Table I, such that the three-dimensional flux distribution 0(x,y,z)is given by:
(1) O(x,y,:) = RX(x)Y(y)2(:).
Table I. Summary Of Curve Fitting To Detector Flux Mapping Coordinate Axis Core Direction Analytical Flux Description :
!- North-South r a g' x X(x) = cos (27 + 18; East-West r Y(y) = cos 4.'
). ( 33>
I Axial fd z Z(:) = cos 36;
(
Note: Coordinates are in units of [ inch), with the origin based at the core center.
The coolant in the MTR fuel element flows downward so the axial flux distribution is of the greatest interest in making a model that represents heat transfer in the coolant channel. The North-South and East-West analytic flux descriptions will play a role later l when it is desired to choose an x-y peaking factor to model a specific region of the core, but for now let us concentrate on the axial flux description.
2 As stated previously, we assume that the power production in the fueled region is proportional to thermal neutron flux, and consider the axial distribution q(z) of power produced per unit length of fuel plate located at position (x,y).:
(2) q(:) = yocos C , B=36, -H/2 5 z $_H/2.
sB>
where H is the active core height. Given the core power output P,,, and the number N of fuel plates, we obtain the parameter q, in Eq. (2) by integrating the linear heat generation rate q(z) over H and equating it to the total power produced in the plate:
w2 , m,2 <g (3) q(2)d: = q,, cos -
d: = p";" F,,,,,,,,,,
4/2 Ar2 ' B/ .\
where F,3,,,,, is the power produced in a plate at position (x,y) normalized by the average plate power. Equation (3) yields:
(4) q ,, _= F,m,,, .
2BNsin< 2B)
II.B. Axir.1 Coolant and Clad Temperature Distributions At this point, we are now ready to look at the problem of determining the temperature profile axially along the fuel plate. Consider the differential control volume of a coolant
. channel described in Figure 1. The control volume assumes that the heat produced in a given fuel plate is evenly removed by the coolant channel on either side of the plate. A i simple energy balance for the channel with mass flow rate W and coolant enthalpy rise dh
! over channel length dz yields:
(5) Wdh = q(:)d: = WC,,dT,,
where dh is written equivalently in terms of heat capacity C, and coolant temperature rise i- dT,.
Wh n
Flow of - Side Plate Side Plate q(zy2 Coolant __+ 4- .f dz q(zy2 :
u v l
- W(h + dh)
Figure 1. Coolant Channel Differential Control Volume.
3 Integrating Eq. (5) and using the inlet temperature T,,, at the top of the channel, we obtain an expression for the coolant temperature T,(z):
' *~
q,, B nH' '
(6) , -H/2 < z < H/2.
[(:) = E,, + IVnC,, _ sin r2B) + sin =Bi _
We can determine the clad temperature Tr for the fuel plate of width w by utilizing Newton's law of cooling:
q(:)
(7) = hw T -E f
where h is the heat transfer coefficient for the coolant channel. Rearranging Eq. (7) and solving for Tr yields:
(8) T,( ) = E(:) + q(:)
2hw.
if we now substitute Eq. (6) for T,(z) into Eq. (8) we obtain:
(9) q,, B ~ . ' ;rH' ' I y
cos f
c'
_sm 2B)+ sin =B + 2hw> _
T (:) = T,, + IVnC,,
f
\ s \ B) where q,is defined in Eq. (4).
By setting the derivative of Eq. (9) to zero, we can determine where the hot spot for the cladding is located on the fuel plate:
- y,, z' g,,x .
'='
i (10) l 0 = IVC,, coB) - 2hwB sm B) \
1 Solving Eq. (10) for z results in the location of the hot spot z s B '2hwB (l1) :<,,,,,= -arctan .
From Eq. (l1) it can be seen that increasing the coolant flow rate W results in shifting z.,a towards the core midplane. while decreasing the flow rate in the channel has the opposite effect.
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)
y
~
4 II.C. Temperature Distribution in the Hot Channel Thus far we have concentrated on developing the theory behind the improved model and now we are prepared to apply the model to some specific problems relating to heat transfer in the FNR reactor core.
First. let us use the model to illustrate the temperature profiles in the hot channel of the core used for the FNR Safety Analysis Report (Ref.1). Using the parameter values listed in Table 11, we plot Eqs. (6) and (9) for the average and hot channels in Figure 2, j Table II. Parameter Values Used in FNR Safety Analysis Report Parameter Parameter Value 1 Reactor Power. P,,,, 4.68 MW Number of heat producing fuel plates. N 414 Hot channel x-y peaking factor, F,m,,, 1.55 j 1
Core coolant mass flowrate, W 900 gpm Coolant specific heat capacity, C, 1.00 Btu /(ibm *F)
Coolant inlet temperature, T. I16"F 1
Core height. H 24 inches j 1
Heat transfer coefficient, h, 1071 Btu /(hr ft2 .p) l Fuel plate width 2.52 inches and compare with the saturation temperature T,, of the coolant. The number of fuel plates, N = 414, and the hot channel factor. F,w,,i = 1.55, are for a small core with 25 fuel elements. Typical FNR core loadings involve 42-45 elements in recent years. While the rated flowrate for the FNR core is 1000 gpm, we conservatively use a reduced flowrate '
W = 900 gpm in our analysis.
i L
l f
5 240.00 iij
,_ t , j,,, ,
- . - -[
- Te Hot channel
/ A - Tg Hot channel
- Tg 200.00 \, .. Tc Avg channel E "*
, , . . ==
- ==. ,, .. TfAvg channel g 180.00 .,
^ ,,
i 8,160.00 x '
( T E
y ' ...'
- - N '
,,, N .*.,
140.00 % ..,,
120.00 ,
h '*== ,
Flow I i 100.00 12 10 8 6 4 2 0 -2 -4 -6 10 ~ -12 Position From Reactor Core Midplane [in] ,
l Figure 2. Axial Temperature Profiles for the FNR Core. .
From Figum 2, we see that the coolant temperature increases monotonically along the length of the channel. The clad temperature has a peak where the worst case conditions between heat flux and heat transfer occur. It is important to note that the peak clad, i temperature is not located at the core midplane, but instead it is found somewhere below .
~ ~
the midplane. In fact, ifwe employ Eq. (11) we find that the peak in Troccurs at
{
appmximately 4 inches below the core midplane. 'Also note that the peak clad i temperature is well below the saturation line at all points along the hot channel, reaching a maximum temperature of approximately 232 'F. The approximate model used in the FNR SAR predicts that T, will reach the coolant saturation temperature of 235 'F for the parameters listed in Table II. The difference between the two models comes about because the SAR model assumes that the worst heat transfer conditions occur at the -
location of the peak heat generation, the core midplane.
III. Blocked Channel Flow Analysis A second useful application of the axial temperature model of Eq. (6) is in the analysis of j blocked flow in the coolant channels. Blocked flow is of significant concem because it l can lead to a localized degradation in heat transfer, which has the potential of violating safety limits for the reactor core. Before we can analyze the blocked flow condition, we must expand and adapt the model developed in Sect. II.B. Let us start by picturing the blocked flow problem that is illustrated in Figure 3.
l l
u------------_-_----
6 Insulation 4 y g ne}
Side plate a f fuel Plate Side plate
'"" ^ti a 4 5 $ $ $ $ Mt E ;""*A T G E M __ _
Blocked Flow
- Region M Active Flow Region :
Figure 3. Illustration of the Blocked Flow Problem To perform a simple analysis of blocked flow we introduce several assumptions and approximations:
( a ) The flow perturbation exists the entire length of the coolant channel. This is a conservative assumption. The flow will actually mix and become uniform across the coolant channel at some distance downstream of the blockage.
( b ) For the purpose of calculating clad temperature Tr in the active region, the entire heat generation in the plate is introduced into the actively cooled portion of the coolant channel. This occurs via convection for the portion of the fuel plate that is in the actively cooled region. It should be noted that this is a conservative approximation since in reality there will be heat transfer to the adjoining fuel assemblies through the side plates and also into ,
the stagnant water that blankets the blocked region. I
( c ) Once the clad temperature in the active region is determined, a simple 1-D slab type heat conduction analysis is performed for the fuel plate in the blocked region to determine the peak clad temperature in the blocked region. For the purpose of this heat conduction analysis, the normal volumetric heat generation rate that would be present without the blockage is retained in calculating the peak clad temperature. The temperature of the fuel plate at the point of contact with the side plate and that of the boundary between the blocked and active flow regions are set equal to the clad temperature that is determined for the active region. These boundary conditions are conservative since the heat flux in the active region has been artificially increased to transfer the entire heat generated in the plate into the actively cooled region. Also the boundary on the left side plate of Figure 3 is in contact with water and fuel assemblies unaffected by the flow blockage, so in reality it is expected that this boundary temperature will be far less than the clad temperature predicted for the active region.
7 Now that the assumptions for the model are in place let us adapt the equations developed in Sect. II.B and also derive the 1-D heat conduction model necessary to determine peak clad temperature in the blocked region. First consider Eq. (6), for coolant temperature in the unobstructed coolant channel. We have modeled the blocked flow problem as consisting of an active and blocked portion throughout the entire length of the channel, yet we have acknowledged in our assumptions that somewhere downstream of the blockage the flow will indeed become uniform across the coolant channel. In the region where the flow is again mixed, the mass flow rate in the active channel will be reduced by some factor R:
w (12) R= l2w , l I
where w,is the width of the blockage. Equation (6)is thus changed to reflect the J
reduction in mass flow rate in the blocked channel: l (13) y,, B
' sin f
rH' 'r' ' .
T(:) = T,,, + {lVnC,)R .
< 2Bs + sin B) _
Now we must consider Eq. (9), which determines the clad temperature in an unblocked channel. For the obstructed channel, the heat nux in the active coolant channel must be increased by a factor 1 to account for the additional heat load that we require the active region to dissipate:
l i
w l (14) l= .
w-w, in addition, the convective heat transfer coefficient has to reflect the reduction in the mass velocity. Thus, with the introduction of heat transfer coefficient h, for the blocked channel, Eq. (9) is modified to:
'=' ' + q,,1 c'
~
q,, B .
'xH' .
f (15)
T,(:) = T,' + (IVnC,)R _sm2B) +sm Bs . 2h,wcos\ B)
Equations (13) and (15) now provide us with the tools to analyze the conditions in the actively cooled portion of the blocked channel, but we still need to find the clad temperature in the blocked region since this will be the highest temperature and therefore l the temperature of concern. To find the clad temperature T(x) in the blocked region we use 1-D heat conduction with a uniform volumetric heat generation rate Q for the fuel width w,in the blocked region:
d'T(x)
(16) k , =-G,0$x$w, n dr
{
l
E .. .
8 l -
where k is the thermal conductivity of the fuel plate.
With the boundary condition T(0) = T(w,) = Tr., where Tr is the temperature of the clad in the actively cooled region from Eq. (15), we obtain from Eq. (16):
~- G(x' - w,x)~
(17) T(x) = + T, .
Because the boundary conditions for the right and left sides of the plate are the same and we have assumed a uniform volumetric heat generation, the temperature profile of Eq.
(17) has symmetry about the point x=w/2. That is to say that the peak temperature in the blocked region occurs at the point halfway across the width of the blockage:
' w, ' Qw,'
(18) T"*' = T <2> - 8k + T' .
Figure 4 is a qualitative description of the expected cladding temperature profile for the blocked channel analysis.
T(x)n l 1
l l
Tr
,s Blocked Active Distance Along Region " Region Fuel Plate, x 0 w, w Figure 4. Temperature Distribution for a Fuel Plate in a Partially Blocked Channel 1 i
Using equation (13), (15), and (18), we may now perform analysis for the blocked channel flow condition. Table III gives a summary of some cases ofinterest. I l l l
\
e 9
Table Ill Blocked Channel Analysis For Various Cases l
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l Parameter j Case Number . . .
l Core Size 25 25 43 43
- Reactor Power, 2.00 2.00 2.00 2.00
! Po , [MW]
Core Coolant 900 900 900 1150 Flowrate, W
[gpm]
Ileat transfer 800 700 600 675 coefficient, h, 2
l [ Btu /(ft hr F)]
l Inlet 116 116 116 103 Temperature.
T,,[F]
l Core Location L37 L37 L37 L65
% of Channel 10 26 34 43 i Blockage (w,M) l Peak Clad '80 235 235 235 i Temperature, T,,,,[F]
Margin to 55 0 0 0 boiling [F]
For case 1, we see that a 10% blo:kage of the hottest channel (L37) for a compact FNR i core considered in the SAR, results in an increase in the maximum fuel clad temperature !
T,,,, but there is still a large margin to boiling. In case 2, if we further increase the !
extent of the blockage, the temperature of the clad does not reach the saturation l
temperature for water at the depth of the core until 26% of the flow channel is blocked.
Cases 2 and 3 in Table Ill are identical with the exception of core size. We see that as we increase the size of the core we reduce the fuel plate surface heat flux, and therefore the larger core (Case 3) can support a blockage that is 30% larger than for the smaller core (Case 2) prior to the clad temperature reaching the boiling point of water in the core.
I Case 4 illustrates the effect of modeling an element on the periphery of the core. The l
lower flux in location L65 leads to a lower x-y peaking factor, F % ,a of Eq. (3), which in turn means that a greater portion of the channel can be blocked before the fuel clad temperature reaches the saturation temperature of water.
IV. Summary We have developd an axial thermal-hydraulic model that is capable of providing temperature profiles aio g the axial length of any fuel element for both the coolant and
I 10 j
1 fuel cladding. The model is used to show the characteristic trends of the coolant and fuel I clad temperatures along the channel. The model coupled with a 1-D heat conduction !
analysis for the fuel plate, is used to represent blocked coolant channel flow. Using the I blocked coolant channel model we are able to predict that the fuel clad reaches the saturation temperature of water in the core at a fuel channel blockage of 29% in a compact 25-element core considered in the FNR SAR. Further, we have shown that by adjusting the parameters in the model we may analyze core flow blockage in any element in the core as in Case 4 of Table III. Refining of the model is stili ongoing and further effort is being dedicated to improve the blocked channel analysis through the use of a 2-D heat conduction model for the blocked region.
V. References
- 1. " Ford Nuclear Reactor Safety Analysis Report", Rev. 3. US NRC Docket 50-2, (1994).
- 2. J.J. Duderstadt and L.J. Hamilton, Nuclear Reactor Analysis Wiley (1976).
- 3. F.P. Incropera and D.P. De Witt. Introduction to Heat Transfer,2"d ed., Wiley (1990).
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