13_ConvectionCoolant_web

13_ConvectionCoolant_web - ENU 4134 – Convection to...

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Unformatted text preview: ENU 4134 – Convection to Coolant – Part I D. Schubring Fall 2011 Learning Objectives I 3-e Apply knowledge of single-phase and two-phase convective heat transfer to convection from fuel rods to coolants, including adjustments to correlations regarded in assembly geometry I 4-a Use equations from nuclear heat transfer (as simple functions of axial coordinate z ) to perform simple, analytical single-channel analysis (SCA) I 4-b Derive finite volume method for use in steady-state SCA I 4-c Implement finite volume method in scripting or compiled language to solve a wide range of LWR SCA problems (Pr. 2) I 4-d Use general SCA code to efficiently perform design/safety analyses for LWR (Pr. 2) I 4-e Integrate knowledge from course to evaluate safety- and design-significance of results from SCA code (Pr. 2) + all cross-cutting technical objectives (#5) General Equation for T co- T m Convective heat transfer is typically understood through the heat transfer coefficient: q 00 co = htc ( T co- T m ) (1) T co- T m = q 00 co htc = q 2 π R co htc (2) Computation of htc can be non-trivial, particularly for the 2-phase case, but this equation is general for any htc . Solution of the nuclear TH (single-channel analysis) problem is greatly aided by the fact that q is usually given. Must consider adjustments to htc due to rod bundle geometry. Example Problem I P = 14.608 MPa I Geometry: P = 12 mm, D =10 mm, R fo = 4.6 mm, R ci = 4.7 mm I htc g = 5000 W m- 2 K- 1 I Equation for htc (heat transfer coefficient) (Weisman 1 φ , Schrock and Grossman 2 φ ) I k c = 20 W m- 1 K- 1 and k f = 3 W m- 1 K- 1 I q = 25 kW/m I ˙ m = 0 . 15 kg/s (per channel) I T 1 = 320 ◦ C , T 2 = T sat = 340 x 2 = 0 . 2 Equations for Solution T co- T m = q 2 π R co htc (3) T ci- T co = q 2 π k c ln R co R ci (4) T fo- T ci = q 2 π R g htc g = q π ( R ci + R fo ) htc g (5) T max- T fo = q 4 π k f (6) This is the end of material in the scope of Exam 2 Single Channel Analysis I Single-phase coolant, constant properties & heat transfer coefficient (analytical solutions) I Single-phase coolant, variable properties & heat transfer coefficient (numerical solution) I Two-phase coolant I Miscellanea I Engineering judgment and single-channel analysis 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 ) (7) T ci ( z )- T co ( z ) = q ( z ) 2 π k c ( z ) ln R co R ci (8) T fo ( z )- T ci ( z ) = q ( z ) π ( R ci + R fo ) htc g ( z ) (9) ffT max ( z )- T fo ( z ) = q ( z ) 4 π k f ( z ) (10) 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 (11) dT m dz = q ( z ) c p ( z ) ˙ m (12) T m ( z ) = T m , in + Z z- L / 2 q ( z ) c p ( z ) ˙ m dz (13) Axial Dependence (3)...
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This note was uploaded on 10/22/2011 for the course ENU 4134 taught by Professor Schubring during the Fall '11 term at University of Florida.

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13_ConvectionCoolant_web - ENU 4134 – Convection to...

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