Flow Pattern Maps in System Codes

(1) TRAC-BFI/MOD

· valid for both horizontal and vertical flow

· two distinct patterns

1) liquid continuous pattern at low □ : single liquid phase, bubbly, churn,

annular regime

2) vapor continuous pattern at high □ : dispersed droplet, single vapor

phase

- flow pattern determination logic

● bubbly/churn flow for  [eqn: alpha < { alpha }_{tran }]

● annular flow          [eqn: { alpha }_{tran } < alpha < { alpha }_{tran } +0.25]

● dispersed droplet flow  [eqn: alpha > { alpha }_{tran } +0.25]

where, by Ishii

[eqn: { alpha }_{tran } = (1+ 4 SQRT { { { rho }_{g } }over { {rho }_{ l} } } ) { 1} over { { C}_{0 } } -4 SQRT { { { rho }_{g } }over { {rho }_{ l} } }-0.15]

[eqn: { C}_{0 } = { C}_{ INF }-SQRT { { { rho }_{g } }over { {rho }_{ l} } }({ C}_{ INF }-1)]

[eqn: { C}_{INF } = 1+0.2 {( { { rho }_{l } } over { G} SQRT { g{D }_{H } } )}^{0.5}] in the shear model

[eqn: =1.393 - 0.0155 log { G {D }_{H } } over { { mu }_{l } }] in the heat transfer model

(2) RELAP5/MOD3

- 9 regimes

1) pre-CHF regimes

; bubby(BBY), slug(SLG), annular-

mist(ANM), mist(MPR)

2) post-CHF regimes

; inverted annulon (IAN), inverted-

slug(ISL), mist(MST), post-CHF

mist(MPO)

3) vertical stratified flow regime for sufficient low mixture velocity

- boundaries for vertical flow regime transition

· no bubble flow in tubes of small diameter

[eqn: { D}_{H }" " < " " 19 {[ { g( { rho }_{l } -{ rho }_{g })} over { sigma } ]}^{-1/2}]

· transition from BBY to SLG

[eqn: { rho }_{ AB}]		{	0.25	for G<2000 □/□·S
	=		0.25 + 0.001(G-2000)(0.25)	for 2000<G<3000
			0.5	for G>3000

· transition from SLG to ANM

[eqn: { alpha }_{AC }=min[ { alpha }`_{crit} ^{f } ,{ alpha }`_{crit} ^{e }]]    between 0.56 and 0.9

[eqn: { alpha }`_{crit} ^{f } = { 1} over {{u }_{g } }{[ {g {D }_{H }( { rho }_{l }- { rho }_{g } )} over {{ rho }_{g }^{2} } ]}^{1/2}]   for upflow

= 0.75       for downflow and counter-current flow

[eqn: { alpha }`_{crit} ^{e } = { 3.2} over {{u }_{g } }{[ {g sigma ( { rho }_{l }- { rho }_{g } )} over {{ rho }_{g }^{2} } ]}^{1/4}]

where [eqn: { alpha }`_{crit} ^{f }]  and [eqn: { alpha }`_{crit} ^{e }] are for small tube due to flow reversal and

large tube due to droplet entrainment, respectively

· transition to full mist flow

[eqn: 1- { alpha }_{AC } " " = "" { 10}^{ -4}]

· vertical stratification

1) the difference in □ of the volume above and below > 0.5

2) [eqn: G " "<= " " { } over {rho } { u}_{ TB } " "<= " "0.35 { } over {rho } {[ { gD( { rho }_{ l}-{ rho }_{ g}) } over {{ rho }_{ l} } ] }^{ 0.5}]

- horizontal flow regime

· similar to vertical flow pattern

except no post-CHF regimes

· BBL-to-SLG transition

[eqn: { alpha }_{AB} = 0.25] (constant)

· SLG-to-ANM transition

[eqn: { alpha }_{AB} = 0.85]

· horizontal stratification (Taitel and Dubler)

[eqn: { u}_{g }" " < " "{ 1} over {2 } { [ {( { rho }_{l} -{ rho }_{ g} )g alpha A } over { { rho }_{ g}D " "sin nu } ]}^{1/2 } (1-cos nu )]

[eqn: H= { D} over {2 }(1+cos nu )]      : water level

[eqn: pi alpha" " = " "nu " "-" "sin nu" " cos nu]

· high mixing flow map for such components as pumps

□ < 0.5	for BBL
□ > 0.95	for mist regime
0.5 < □ < 0.9	for transition regime

- 더 복잡하고 정확한  flow pattern 이나 transition criteria 를 사용할 수 있지만 이것들이 code 내 다른 inherent 가정 때문에 반드시 우수하지만은 않다

(예) numerical instability를 일으킬 수 있는 급작스러운 flow regime 변화를 피하기 위해서 □□를 0.1까지 cover 할 수 있는 transition region을 사용

∀ computational flexibility overshadows any accuracy from exact flow              regime maps.