Minimum Critical Power Ratio

[daveb]

From Todreas & Kazimi, Nuclear Systems I, Problem 2-3

Homework Statement

Calculate the minimum critical power ratio for a typical 1000 MWe BWR operating at 100% power using the data in Tables 1 – 2, 1 – 3, and 2 – 3. Assume that:

a) The axial linear power shape can be expressed as

q’(z) = q’(ref)e^(-az/L)sin (az/L)

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

b) The critical bundle power is 9319 kW

Homework Equations

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

The Attempt at a Solution

From the referenced table, the efficiency of a BWR is 32.9%, so the operating power is 3039 MWth.

For q’(z) to be a maximum, e^(-a/L)sin (az/L) must be maximum. This maximum occurs when the derivative with respect to z/L is zero (or at the ends). Solving this, I find z = L*tan^(-1)(pi/a)/pi = 0.322L, and q'(ref) = 4685 kW/m. From here I have no clue what to do (especially with the given critical bundle power).

 

[anorlunda]

See: https://www.nuclear-power.com/nucle...and-condensation/dryout-critical-power-ratio/

The CPR is that power in the assembly calculated by applying the appropriate correlation(s) to cause some point in the assembly to experience boiling transition, divided by the actual assembly operating power.

So, can you use the data given to determine where some point in the assembly will experience the boiling transition?