Minimum Critical Power Ratio (nuclear engineering applications)

[pkress]

Homework Statement

Using the BWR data from Appendix IV of the textbook (NE, Knief), calculate the minimum critical power ratio for 100% power assuming the following axial linear power shape
a) The axial linear power shape can be expressed as

q’(z) = q’(ref)e^(-az/L)sin (pi(z)/L)

where a = 1.96. Determine q’(ref) such that q’(max) = 44 kW/m

b) The critical bundle power is 9319 kW

Relevant Equations

Minimum Critical Power Ratio = Critical Power/Operating Power
(unfortunately, the textbook is sparse in its relevant equations and examples)

Im having a really tough time with this problem, I am assuming that in order for q'(z) to be a maximum, e^(-az/L)sin (pi(z)/L) must be a maximum. I believe this occurs when the derivative with respect to with respect to z/L is zero, which gives me z = 0.322L, but I am not sure if this is correct or where to go from here. Any help would be greatly appreciated. A clearer version of the problem is attached( I am mainly referring to the second problem, but I am having some issues with the first as well so any help with that one is appreciated too.)

 

[Valkarie]

For Problem 2, you are correct that the maximum of q'(z) occurs when the derivative with respect to z/L is zero. This implies that z = 0.322L as you have stated. To find the maximum value of q'(z), substitute this value of z back into the expression for q'(z).For Problem 1, the maximum of q(z) occurs at the same point (z = 0.322L) since q(z) is the integral of q'(z). To find the maximum value of q(z), you need to evaluate the integral and substitute the value of z = 0.322L.