Minimum Critical Power Ratio (MCPR) for a BWR

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SUMMARY

The discussion focuses on calculating the Minimum Critical Power Ratio (MCPR) for a typical 1000 MWe Boiling Water Reactor (BWR) operating at full power. The axial linear power shape is defined by the equation q’(z) = q’(ref)e^(-az/L)sin(az/L), with a specified value of a = 1.96. The critical bundle power is given as 9319 kW, and the calculated reference power density q’(ref) is determined to be 4685 kW/m. The MCPR is derived using the formula Minimum Critical Power Ratio = Critical Power/Operating Power.

PREREQUISITES
  • Understanding of nuclear reactor physics, specifically BWR operations.
  • Familiarity with the concept of critical power ratio in nuclear engineering.
  • Knowledge of axial linear power distribution in reactor cores.
  • Proficiency in calculus, particularly in finding maxima and derivatives.
NEXT STEPS
  • Research the implications of Minimum Critical Power Ratio in reactor safety analysis.
  • Study the effects of axial power distribution on reactor performance.
  • Learn about the calculation methods for critical power in BWRs.
  • Explore advanced topics in nuclear reactor thermal-hydraulics.
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Nuclear engineering students, reactor design engineers, and professionals involved in the safety analysis and operation of Boiling Water Reactors.

antony1103
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From Todreas & Kazimi, Nuclear Systems I, Problem 2-3


1. 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


2. Homework Equations

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


3. The Attempt at a Solution

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).
 
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I was on the right track and got the answer after a little frustration. Thanks anyway though! I'll have to remember this site when I am having trouble in my NUC E/M E classes this year.
 
did you ever figure out what to do with the critical bundle power... i know this is an old thread. sorry
 

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