Figure Transition boiling curves

Transcription

1 Minimum Heat Fux 10.5 Transition Boiing and Minimum Heat Fux Transition Boiing Figure Transition boiing cures Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 1

2 Minimum Heat Fux Heat fux for transition boiing q = Fq (1 F) q + (10.132) F is the aerage proportion of the heating surface in contact with iquid T e (10.133) F = exp T e,max Heat fux during apor contact can be assumed to be equa to minimum heat fux q = q min (10.134) Heat fux time aeraged aue q q min / q max = (10.135) q 0.82 T / T max e e, cr Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 2

3 Minimum Heat Fux Figure Boiing cures of saturated FC 72 Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 3

4 Minimum Heat Fux Minimum Heat Fux The minimum heat fux point in the boiing cure is the boundary between the transition boiing regime and the fim boiing regime. The minimum heat fux, is reached when the heat fux is equa to the minimum apor formation rate that can sustain a stabe apor fim oer the heating surface. In controed-heat fux poo boiing, nuceate boiing is reestabished when the heat fux fas beow the minimum heat fux. Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 4

5 Minimum Heat Fux q = e n f min b b min (10.136) where e b represents the energy per apor bubbe, b is the number of apor bubbes reeased per unit area and per reease cyce, and f min is the minimum number of cyces per second needed to compensate for norma coapse rate. The energy per bubbe is assumed to be equa to the atent heat carried away by the bubbe with a radius equa to λ D / 4 and reeased at the node of the Tayor wae: e 4π λ D = 3 4 b 3 ρ h n (10.137) Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 5

6 Minimum Heat Fux The bubbe reease frequency, f min, is β n = (10.138) (10.139) where max is the frequency of the most-rapidy-growing disturbance obtained by an interfacia stabiity anaysis: 3 3 4( ρ ρ ) g β max = (10.140) 3 27( ρ + ρ ) σ The minimum heat fux can be obtained by substituting eqs. (10.137) (10.139) into eq. (10.136) and using eq. (10.128) to obtain λ D, i.e., 2 λ gσ ( ρ ρ ) q min = C ρ h 2 ( ρ ρ ) where C = C ( π /12)(4/3) is a new constant. f b = 2 D C β min 1 max 1 4 (10.141) Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 6

7 Minimum Heat Fux Benson (1961) recommended C=0.09 by fitting the experimenta data for poo boiing so that eq. (10.141) becomes gσ ( ρ ρ ) q min = 0.09ρ h 2 ( ρ + ρ ) 1 4 (10.142) Equation (10.142) is accurate within approximatey 50% for most fuids at moderate pressure and is ess accurate for higher pressure. Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 7

8 Minimum Heat Fux Exampe 10.4 Estimate the minimum heat fux for poo boiing of water at one atmosphere. When pressure increases, how wi the minimum heat fux change? Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 8

9 Minimum Heat Fux Soution: The properties of water at 1 atm can be found in Exampe The minimum heat fux for poo boiing of water can be obtained from eq. (10.142), i.e., gσ ( ρ ρ ) q min = 0.09ρ h 2 ( ρ + ρ ) ( ) 4 = = kw/m 2 ( ) Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 9

10 Minimum Heat Fux To estimate the effect of pressure on the minimum heat fux, it is necessary to simpify eq. (10.142). Considering the fact that, eq. (10.142) can be simpified as gσ q min = 0.09ρ h ρ Since the apor density, ρ, is a strong function of pressure, i.e., it increases significanty with increasing pressure, it is expected that the minimum heat fux q aso increases with increasing pressure. min 1 4 Transport Phenomena in Mutiphase Systems by A. Faghri & Y. Zhang 10