NUCLEAR SYSTEMS I (2 nd Printing): THERMAL HYDRAULIC FUNDAMENTALS ERRATA

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Jessica Harmon
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1 NUCLEAR SYSTEMS I ( nd Printing): THERMAL HYDRAULIC FUNDAMENTALS Neil E. Todres nd Mujid S. Kzimi ERRATA /10/04 48 (Eq. 3-0)... = q S n... = q n S n 69 (Fig. 3-11, Cption)... for irrdition time of seconds [8]. 119 (Eq. 4-19) v r v r ++ v r v r v r + v r... for the essentilly infinite irrdition time of seconds [8]. 137 (Fig. 5-) Sensors r 4 nd r 6 indicte vpor. Sensors r 3 nd r 5 indicte liquid only. This contrdicts Fig. 5-. Qlz 140 (Eq. 5-43) { jl}= = K A 145 (Lst Line) (shown in Figure 5-4 in the xil direction: 146 (Eq. 5-64)... ρg cos θda Replce the outputs for sensors r 4 nd r 6 with those of r 3 nd r 5. Qlg { jl}= =K A (shown in Figure 5-4 in the xil direction):... ρg cos θda z A z 150 (Lst Line) (5-86) (5-86) 151 (Line 4) chnge of phse to liquid into vpor: chnge of phse of liquid into vpor: 166 (Tle 5-3, Momentum eqution, where) 166 (Tle 5-3, Energy eqution, Phse) Gm p p + α 1 α ρ = { vvvz }+ l v l z m q wk α wk P w { ( )} G m ρm A z { } + = { ρvvvzα}+ ρ l v l z( 1 α) q wk α wk P w 169 (Pro. 5-3) {j v } = 3.5 m/s {j v } = 3.31 m/s 191 (Eq. 6-4, middle term) (Fig. 9B) (Fig. 6-9B) 36 (Pro. 6-6) 1. A perfect gs of C p = A perfect gs of γ = (Line 7) For m wpd : For m wp : 4 (Line ) Het trnsfer from mss wpr... only to mss wpd: 30 (Fig. 8-, y-lel) k p dt T 100 C Delete ( true sttement, ut not relevnt since mss wp is considered s the susystem) T 100 C k ρ dt

2 319 (Fig. 8-13, Eq. 8-68) β α - 1 β α (Line 3)... = q res 4π ρ s ρ = q res 4π ρ s ρ (Line 10) R v = 0.311; R = 0.343; R 1 = 0.56R fo R v = 0.311R = 0.343R 1 = 0.56R fo 350 (Line 14) The vlues of C D re typiclly 0.3 to 0.7 depending on the nozzle geometry. The vlues of C D re typiclly 0.7 to 0.95 depending on the nozzle geometry [13]. 358 (Tle 9-1) 0.5 (1 - β ) 0.5 (1 - β) n n=1 pproximte for Re > 10 4 n=0.75 more exct 376 (Eq. 4-19) r r r v = v + v v r = v r + v r 376 (Eq. 9-59) [ ρv r ]= 0 [ ρv r ]= 0 r ρ rr r v r r r ρ v rr rr r ρvv p ρv v ρg 376 (Eq. 9-60) + [ ]= + [ τ ]+ + [ ρvv]= p+ [ τ ρvv ]+ ρg 378 (Eq. 9-74) + τ ρ R = R w / + τ R = w ρ R / ν ν 38 (Line 6) (discussed in sections II.D.3 nd VII). (discussed in sections II.D. nd 386 (Fig. 9-4) ordinte is: (f Re ) T ordinte is: (f Re n ) T 387 (Line 14) regimens regimes 393 (Eq. 9-98) 8 E θ = j i θ i i =0 E j θ = 8 i =0 i j θ i 398 (Tle 9-5) ρ form = + K c ρ V ρ form = + K c ρ V 407 (Line 3)... geshwin digkeitsverteilung geschwindigkeitsverteilung (Pro. 9-4, Dt) Pressure drop cross ssemlies Pressure drop cross ech ssem 409 (Fig. 9-40) p A 40 cm Fuel Bundle Orificing Block p A 360 cm 400 cm 40 cm Fuel Bundle Orificing Block Assemly Assemly 1 Assemly (within Zone ) Assemly 1 (within Zone 1)

3 3 46 (Line 0)... concept of equivlent heted dimeter where: 4 flow re 46 (Eq ) D H heted perimeter = 4A f P h 46 (Lines -3) In mny cses... dimeters. Tle concept of equivlent hydrulic dimeter where: 4 flow re D e wetted perimeter = 4A f P w Delete [In mny cses... dimeters. ] Tle (Tle 10-4) (Lines 1-13) for the Reynolds numer nd D H, where: D H = 4A f for the Nusselt P h numer reltion for the Reynolds numer. 449 (Line )... predicted y Eq predicted y Eq (Line 3)... Eqution Eq (Ref. ) Kys, W.M. Convective Het nd Mss Trnsfer, New York: McGrw- Hill, [ ( ) ] g ρ 469 (Eqs & 11-16) K l ρv σ 1 jvρl Kys, W.M. nd Crwford, M.E. Convective Het nd Mss Trnsfer, nd Ed., New York: McGrw-Hill, [ ( ) ] 1/ 4 1/ 4 g ρ / K l ρv σ 1/ { jv} ρl 475 (Fig ) TRANSITION (TCT) TRANSITION TO CHURN- TURBULENT

4 4 484 (Fig ) As drwn, vlues in the figure re not consistent nd need to e mde so with those in the tle on the sme pge. Void Frction, {α} Homogeneous for G 1, G nd G3 Drift Flux G 1 M-N for G 1, G nd G3 Drift Flux G Drift Flux G (Line 10) To evlute the friction multiplier φ lo in the HEM model, (Fig. 11-1, cption) ( φ lo ) ( φ lo ) 506 (Line 11) α in = 1... α x - x ρ in = 1 g 1 + ρ 1 - x g x Qulity, x To evlute the friction multiplier φ lo given y Eq ,... ρ g ρ f (Ref. 33) RELAP-5 MOD1 Code Mnul, EGG-70, Rnsom, V.H., el l., RELAP5/MOD1 Code Mnul, Vols 1 &, NUREG/CR- 186, EGG-070, Mrch (Line 19) Prolem 11-3 Regime mp for horizontl flow (section II) Prolem 11-3 Regime mp for verticl flow (section II) 519 (Line 1)... for horizontl stem genertor.... for the secondry side of verticl stem genertor. 58 (Lst Line)... flow pttern leds to forced convection het trnsfer mechnism (Fig. 1-4) Forced convection het trnsfer through liquid film 530 (Line 10) Finlly, s the thermodynmic qulity reches unity, (Fig. 1-9, Eq. 1-8) T = T f + σt fv fg h fg 1 r * 54 (Line 7) q FX F ( ) tt 09. = k Re Pr ( T T ) c l l l w st... flow pttern leds to convection het trnsfer mechnism... Convection het trnsfer through liquid film In the post-dryout region, even efore the thermodynmic equilirium qulity pproches unity,... T f = T st + σt stv fg h fg 1 r * q FX F k D ( ) tt l 09. = Re Pr ( T T ) 559 (Eq. 1-6) {( p) + ( p)[exp ( p) x e ] etc. {( p) + ( p)exp [( p) x e ]} etc. c l l w st

5 5 560 (Line 1) Becuse F 1,... reduces the criticl het flux. 560 (Line ) The prmeter C decreses... for the het flux shpe. In rector chnnel the minimum DNB rtio occurs downstrem of the pek het flux. Hence, the F-fctor t the minimum DNBR loction is generlly greter thn unity; the xil non-uniformity in the het flux reduces the CHF. The prmeter C decreses with incresing qulity; t high qulity C will e smll nd the effect of the het flux shpe will e less pronounced. 560 (Eq. 1-67) D h x e G D x e G (4 Brnett correltion)... sme sic form s McBeth s correltion. The rms error sme sic form s McBeth s correltion. The correltion is cple of predicting oth DNB nd dryout CHF conditions. The rms error (Eq. 1-74) Ah fg B h f - h i C L 566 (Eq. 1-74) A = 30.7 D h 0.68 G exp D eg... A B h f - h i C L A = 05 D h 0.68 G exp D eg 566 (Eq. 1-74c) B = D h G B = D h 1.61 G (Eq. 1-74d) C = 849 D e G 0.1 C = 744 D h G (Ref. 17) Collier, J.G. Convective Boiling nd Condenstion (nd ed.). New York: McGrw-Hill, (Pro. 1-) Assume tht the mximum cvity rdius is very lrge. Collier, J.G. nd Thome, J.R. Convective Boiling nd Condenstion (3rd ed.), New York: Oxford, Assume tht the mximum cvity rdius is very lrge. You my use the Rosenhow correltion for nuclete pool oiling [5]: q s = µ l h fg g ρ l - ρ v σ 574 (Line 7) k = 0.68 W/m C k = 0.68 W/m C 1/ c p,l T w - T st C s,f h fg Pr l s where s = 1 for wter nd C s,f = , n empiricl constnt for wter nd mechniclly polished steel surfces. 577 (Eq. 5-14) p = p v α + p 1 (1 - α) ρ = ρ v α + ρ 1 (1 - α) ρ 578 (Eq. 13-7) Term: V m V m m Term: V m ρ m V m

6 6 586 (Line 13) First y comining Eqs nd 13- we find tht the fuel centerline temperture, T C L corresponding to T mx in Eq ) nd T m is given y: 598 (Eq ) q q x = x in + + sin πz mh fg mh fg L First y comining Eqs nd we find tht the fuel centerline temperture, T C L (corresponding to T mx in Eq ) is given y: x = x in + q q + sin πz mh fg mh fg L 615 (Pro. 13-1) 1. Q «= 5760 MW. Q «= 3960 MW 3. Q «= 5390 MW 1. Q «= 5731 MW. Q «= 3954 MW 3. Q «= 5456 MW 617 (Pro. 13-4) p fric = 14.4 kp p fric = 0.6 kp 649 (Tle D-3) J 1 (.3) = J 1 (.3) = (Tle D-3) x =.5 J o (x) = x =.5 J o (x) = (Fig. F-) H O Sturted Vpor nd H O Liquid re interchnged The higher line for H O Sturted Vpor should e thicker to indicte it is relly H O Liquid; nd the lower line indicting H O Liquid should e thinner since it is relly H O Sturted Vpor

( ) Same as above but m = f x = f x - symmetric to y-axis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists.

( ) Same as above but m = f x = f x - symmetric to y-axis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists. AP Clculus Finl Review Sheet solutions When you see the words This is wht you think of doing Find the zeros Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor Find