HW3Prob5 - A PWR has dimensions and operating conditions...

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Single Phase 22 1 A PWR has dimensions and operating conditions given below. Core Height 144 inches Core Mass Flux 2.62 x 10 6 lbm/hr-ft 2 Number of Fuel Rods 56,876 Rod Diameter 0.374 inches Rod Pitch 0.496 inches Core Inlet Loss Coefficient 1.5 Core Exit Loss Coefficient 1.5 Grid Loss Coefficient 0.5 Number of Grids 8 Pressure 2250 psia Core Inlet Temperature 560 F Maximum Channel Heat Flux 265,700 Btu/hr-ft 2 Extrapolation Distance 0.866 ft You may assume an axial heat flux profile of the form ′′ = ′′ + q z q z H e ( ) sin ( ) 0 π λ Determine the acceleration, friction, forms, elevation and total pressure loss. Compare to that which would be obtained from a simple Bernoulli’s Equation approach where the density is approximated by the average channel density 2 / ) ( inlet exit ρ ρ + and the density is evaluated at the average coolant temperature. Assume the same treatment holds for viscosity also. Solution Integrate the conservative form of the steady-state Momentum Equation over the channel length ( ) 1 1 g A z vvA P z P A g g c x x w w x c ρ τ ρ θ = − sin (1) or 1 2 2 2 2 2 g z G P z f D G g K z z G g g g c e c j j c j c ρ ρ δ ρ ρ θ ⎟ = − + ( ) sin (2) where we have assumed a uniform flow area and a vertical flow channel. For convenience the momentum equation has been written in terms of the mass flux. 1 2 2 2 1 2 1 2 2 1 2 2 1 2 1 2 g z G dz P z dz f D G g dz K z z G g dz g g dz c e c j j c j c ρ ρ δ ρ ρ = − + ( ) (3) ( ) ( ) 1 2 2 2 1 2 1 2 2 2 2 1 1 H H g g g G K g G D L f P P g G c c j j j j i c i i e i i c i = ρ ρ ρ ρ ρ (4) Rearranging gives for the core pressure drop
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