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Unformatted text preview: ENU 4134 – Convection to Coolant and Full SingleChannel Analysis – Part 2 D. Schubring November 12, 2010 Learning Objectives I (4a) Use equations from nuclear heat transfer (as simple functions of axial coordinate z ) to perform simple, analytical singlechannel analysis (SCA) I (4b) Derive finite volume method for use in steadystate SCA I (4c) Implement finite volume method in scripting or compiled language to solve a wide range of LWR SCA problems (Pr. 2) I (4d) Use general SCA code to efficiently perform design/safety analyses for LWR (Pr. 2) I (4e) Integrate knowledge from course to evaluate safety and designsignificance of results from SCA code (Pr. 2) Single Channel Analysis I Singlephase coolant, constant properties & heat transfer coefficient (analytical solutions) I Singlephase coolant, variable properties & heat transfer coefficient (numerical solution) I Twophase coolant I Miscellanea I Engineering judgment and singlechannel analysis + all crosscutting technical objectives (#5) Axial Dependence There are simple(ish) equations for the unknown temperatures. However, many of the variables are actually functions of z (if not also local T ’s). T co ( z ) T m ( z ) = q ( z ) 2 π R co htc ( z ) (1) T ci ( z ) T co ( z ) = q ( z ) 2 π k c ( z ) ln R co R ci (2) T fo ( z ) T ci ( z ) = q ( z ) π ( R ci + R fo ) htc g ( z ) (3) ffT max ( z ) T fo ( z ) = q ( z ) 4 π k f ( z ) (4) Axial Dependence (2) Typically only T m ( L / 2) & P ( L / 2) – coolant bulk temperature, pressure at inlet – are known. T m ( z ) must be determined from an energy balance. Neglecting boiling for the moment: q ( z ) dz = c p ( z ) ˙ mdT m (5) dT m dz = q ( z ) c p ( z ) ˙ m (6) T m ( z ) = T m , in + Z z L / 2 q ( z ) c p ( z ) ˙ m dz (7) Axial Dependence (3) So the equations, given T m , in as a starting condition: T m ( z ) = T m , in + Z z L / 2 q ( z ) c p ( z ) ˙ m dz (8) T co ( z ) T m ( z ) = q ( z ) 2 π R co htc ( z ) (9) T ci ( z ) T co ( z ) = q ( z ) 2 π k c ( z ) ln R co R ci (10) T fo ( z ) T ci ( z ) = q ( z ) π ( R ci + R fo ) htc g ( z ) (11) T max ( z ) T fo ( z ) = q ( z ) 4 π k f ( z ) (12) As is often the case in TH, analytical solutions are only available for carefully selected cases. SinglePhase Coolant, Constant Properties and htc ’s I Singlephase coolant I Determined via energy balance, i.e. , Δ h = q total / ˙ m < Δ h sub I Potentially must consider subcooled boiling I Constant properties I Always an approximation. Consider Δ T × d ( prop ) / dT . I Constant htc ’s I Single phase htc (P/D, properties, D h , ˙ m ) I Gap conductance – always an approximation This is a “classroom example” – this wouldn’t be used in an actual industry code, but produces useful results for study. SinglePhase Coolant, Constant Properties and htc ’s (2) Under these assumptions, our equations reduce to: T m ( z ) = T m , in + 1 c p ˙ m Z z L / 2 q ( z ) dz (13) T co ( z ) T m ( z ) = q ( z ) 2 π R...
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This note was uploaded on 07/18/2011 for the course ENU 4133 taught by Professor Schubring during the Spring '11 term at University of Florida.
 Spring '11
 Schubring

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