number A of potential accidents in pressurized water reactors can lead to over power transients where the reactor power exceeds normal operating levels. One concern in setting the high power reactor trip is that the maximum fuel temperature not exceed the fuel melt temperature. A PWR is to be designed to operate at 3411 Mwt. For the given data, determine the number of fuel rods necessary to prevent fuel melt at the reactor trip set point. Derive the equations necessary to compute the temperature drop across the rod. You may assume uniform volumetric heat generation rate and the fuel and cladding are in contact at the clad inner radius such that the temperature drop across the gap can be given in terms of a gap conductance HG. Problem Data Fuel Melt Temperature Reactor Trip Set Point Fraction of heat produced in fuel Rod Diameter Clad Thickness Gap Conductance Coolant Temperature Convective Heat Transfer Coefficient Clad Thermal Conductivity Power Peaking Factor Rod Height SOLUTION 4980 3718 97.4 0.374 0.0225 1000 590 8500 9.6 2.43 12 F Mwt % inches inches Btu/Hr-ft2-F F Btu/Hr-Ft2-F Btu/Hr-Ft-F ft
The general solution for the temperature drop across the fuel region of a solid cylindrical fuel rod with temperature dependent conductivity thermal is
r
for
T ( R)
k (T )dT
0
T (0)
k (T )dT +
0
R 0
1 q(r )r dr dr = 0 r 0
q(r ) = q
Note:
r
q(r )r dr = =
0
qrdr
0
r
qr 2 2
q = q( Ro )2Ro =
q(r)2rdr = qR
R 0
2
Fuel Rod 09
R 0
1 r
r
q(r )r dr = =
0
R
0
qr dr 2
qR 2 4 q = 4
Therefore
In addition we have
T ( R)
k (T )dT
0
T ( 0)
k (T )dT +
0
q =0 4
(a)
1 R 1 1 T ( R ) T = q( R ) R + ln o + R hR H G Ri k c i c o
or
T ( R ) T = q 2 1 1 R 1 + ln o + R hR H G Ri k c i c o
(b)
For a given fuel centerline temperature, Equations (a) and (b) contain the unknowns T ( R ) and q which may be solved for iteratively. Solving Equation (a) for q
T ( 0) (q)1 = k (T )dT 0
k (T )dT 4 = 9684.8 0
T ( R)
k (T )dT 4 0
T ( R)
(c)
and Equation (b) for q 1 1 R 1 (q) 2 = 2 [T ( R) T ] + ln o + R hR H G Ri kc i c o
1
= [T ( R) 590] 66.948
(d)
We therefore have two equations in the two unknowns, q and T ( R ) . The solution is iterative and gives
q = 63,078.9 Btu hr ft = qmax T ( R) = 1532.2 F
which gives for the number of fuel rods
n=
& f QFq
qmax H
=
(0.974)(3718 103 )(3413)(2.43) = 39,678 (63,078.9)(12)
Fuel Rod 09