Assignment:
Problem 1
Using the analytical equations for the temperature profile throughout the fuel, gap, cladding, and coolant, calculate the temperature profile for various fuel materials. Use the heat generation rate you calculated in problem 1 of HW 1. Use the thermal conductivities from the table on slide of lecture.
Assume the cladding is Zr, and use the properties from the table on slide of lecture. The gap is filled with 10% Xe. The fuel pellet has a radius of 5 mm, the cladding thickness is 0.65 mm, and the gap width is 30 microns. Assume the coolant temperature is equal to 600 K along the length of the cladding and has a thermal conductance of 2.5 W/(cm2K). Also, report if any of these fuels exceed their melting temperature.
The fuel materials are:
a) UO2
b) Metal fuel
c) UC
d) UN
e) U3Si2
Problem 2
Calculate the temperature profile in a UO2 fuel rod of radius 5 mm using a transient 1D solution with the Matlab pdepe function, as shown in class. The final neutron flux is 2.8e13 neutrons/(cm2 s), the enrichment is 4%, You can start from rod_temp_profile_1D.m available in modules, but you need to make three changes to the code.
First, rather than use a constant thermal conductivity, use the red part of the equation on slide of lecture.
Second, rather than setting the surface temperature, calculate the surface temperature using the coolant, cladding, and gap analytical equations on slide of lecture. Use all the values for the coolant, cladding, and gap from Problem 1.
Third, the neutron flux should start from zero and linearly increase to its final value after 1.0e4 seconds. Turn in the code you use for this problem.
a) Plot the temperature profile at four times on the same plot, t = 0.0, 0.1e4, 1.0e4, and 2.0e4 seconds.
b) Use your code to estimate at what time the temperature profile reaches steady state.
c) Plot the steady state solution found in part b) and the steady state solution from the analytical equation on the same plot. Are they similar or different? Explain why.
Problem 3
Calculate the transient temperature profile in a fuel rod of radius 5 mm and length 20 cm using a 2D solution with smeared pellets using the Matlab PDE toolbox, as shown in class. You can start from the rod_temp_profile_2D.m available in modules, but you need to make four changes to the code.
First, do not use axial symmetry and model the entire fuel rod (you'll need to change the top BC).
Second, change the thermal conductivity to change with temperature according to the red part of the equation on slide of lecture.
Third, have the value for Q vary axially according to the equation on slide of lecture. Have the centerline linear heat rate be 150 W/cm and use gamma = 1.3.
Fourth, rather than setting the surface temperature, calculate the surface temperature using the coolant, cladding, and gap analytical equations on slide of lecture (with all values from Problem 1 and an inlet temperature of 570 K).
In addition, have the coolant temperature vary axially according to the equation on slide of lecture. Use ll the values on slide of lecture, except for the half length of the fuel rod (which should be 5 cm). Turn in the code you use for this problem.
a) Plot the 2D temperature profile across the cross-section of the pellet at t = 3 s.
b) Plot the 2D temperature profile across the cross-section of the pellet at t = 30 s.
Problem 4
For each of the five fuel types analyzed in Problem 1, determine the maximum possible difference between the inlet and outlet coolant temperatures to maintain the fuel centerline temperature below 70% of melting. Use a coolant inlet temperature of 570 K and all the values from Problem 1. Use the melting temperatures shown in the lecture slides.