experimental study on forced convective boiling of ... - CiteSeerX

‫‪T. Khir, R. K. Rahim, N. Ghaffour and A. Ben Brahim‬‬

‫‪EXPERIMENTAL STUDY ON FORCED CONVECTIVE‬‬ ‫‪BOILING OF AMMONIA–WATER MIXTURES IN A‬‬ ‫‪VERTICAL SMOOTH TUBE‬‬ ‫* ‪Tahar Khir‬‬ ‫‪Mechanical Engineering Department‬‬ ‫‪Jeddah College of Technology, Jeddah, K. S. A.‬‬

‫‪Rahim K. Jassim‬‬ ‫‪Mechanical Engineering Department‬‬ ‫‪Jeddah College of Technology, Jeddah, K. S. A.‬‬

‫‪Noureddine Ghaffour‬‬ ‫)‪Middle East Desalination Research Center (MEDRC‬‬ ‫‪Muscat, OMAN‬‬

‫‪Ammar Ben Brahim‬‬ ‫‪Chemical Engineering Department.‬‬ ‫‪Gabes Engineering School, Gabes, TUNISIA‬‬

‫اﻟﺨـﻼﺻـــﺔ‪:‬‬ ‫ﻓﻲ إﻃـﺎر ﺑﺤﻮﺛﻨﺎ ﺣﻮل دورات اﻟﺘﺒﺮﻳﺪ اﻟﺸﻤﺴﻴﺔ ﺑﺎﻻﻣﺘﺼﺎص‪ ،‬وﺑﻐﻴﺔ ﺗﺤﻘﻴﻖ آﻔﺎءة أﻓﻀﻞ ﻟﻼﻗﻂ ﺷﻤﺴﻲ‬ ‫ﻣﺴﻄﺢ ذي أﻧﺎﺑﻴﺐ ﻣﺘﻮازﻳﺔ‪ ،‬ﺗﻢ إﻧﺠﺎز دراﺳﺔ ﺗﺠﺮﻳﺒﻴﺔ ﺣﻮل اﻧﺘﻘﺎل اﻟﺤﺮارة أﺛﻨﺎء ﻏﻠﻴﺎن ﻣﺤﺎﻟﻴﻞ ﻣﻦ اﻷﻣﻮﻧﻴﺎ‬ ‫واﻟﻤﺎء داﺧﻞ أﻧﺒﻮب ﻋﻤﻮدي ذي ﻗﻄﺮ داﺧﻠﻲ ﻳﺒﻠﻎ ‪ 6‬ﻣﻢ‪ .‬وﻗﺪ اﺳﺘﻌﻤﻞ أﻧﺒﻮب ﻣﺰدوج آﻤﻮﻟﺪ ﻟﻠﺒﺨﺎر‪ ،‬ﺣﻴﺚ ﺗﻢ‬ ‫ﺗﺴﺨﻴﻦ اﻟﻤﺤﻠﻮل اﻟﻤﻨﺴﺎب ﻋﺒﺮ اﻷﻧﺒﻮب اﻟﺪاﺧﻠﻲ ﺑﺎﺳﺘﺨﺪام اﻟﻤﺎء اﻟﺴﺎﺧﻦ‪ ،‬وﺗﻢ ﺗﺤﺪﻳﺪ ﻣﻌﺎﻣﻞ اﻧﺘﻘﺎل اﻟﺤﺮارة‬ ‫ﻋﻤﻠﻴًﺎ داﺧﻞ اﻷﻧﺒﻮب ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻤﺠﺎﻻت اﻟﺘﺎﻟﻴﺔ ﻟﻠﻤﺘﻐﻴﺮات اﻟﺘﺠﺮﻳﺒﻴﺔ‪ :‬اﻟﻔﻴﺾ اﻟﺤﺮاري ‪(kW/m2 18.521 -‬‬ ‫)‪ ،8.211‬وآﺜﺎﻓﺔ ﺳﺮﻳﺎن اﻟﻜﺘﻠﺔ )‪ ،(kg/m2.s 2688 - 707‬وﻣﻌﺪل ﺳﺮﻳﺎن اﻟﻜﺘﻠﺔ ﻟﻠﻤﺤﻠﻮل ‪(kg/s 0.076‬‬ ‫)‪ - 0.02‬وﻧﺴﺒﺔ اﻟﺘﺮآﻴﺰ )‪ .(% 61 - %55 - % 42‬وﺗ ّﻢ ﻣﻦ ﻧﺎﺣﻴﺔ أﺧﺮى اﻋﺘﻤﺎد ﺛﻼﺛﺔ ﻧﻤﺎذج ﻧﻈﺮﻳﺔ ﻟﺘﺤﺪﻳﺪ‬ ‫ﻣﻌﺎﻣﻞ اﻧﺘﻘﺎل اﻟﺤﺮارة‪ .‬وﻗﺪ أﺛﺒﺘﺖ اﻟﻨﺘﺎﺋﺞ اﻟﻌﻤﻠﻴﺔ ﺻﻼﺣﻴﺔ آﻞ ﻣﻦ ﻧﻤﻮذج ﻣﺸﺮي وﺑﻨﻴﺖ ‪ -‬ﺗﺸﺎن ﻟﺘﺤﺪﻳﺪ‬ ‫ﻣﻌﺎﻣﻞ اﻧﺘﻘﺎل اﻟﺤﺮارة أﺛﻨﺎء ﻏﻠﻴﺎن ﻣﺤﻠﻮل اﻷﻣﻮﻧﻴﺎ و اﻟﻤـﺎء‪ .‬وهﺬان اﻟﻨﻤﻮذﺟﺎن ﻳﻤﻜـﻨّـﺎن ﻣﻦ ﺗﺤﺪﻳﺪ ﻗﻴﻤﺔ‬ ‫ﻣﻌﺎﻣﻞ اﻧﺘﻘﺎل اﻟﺤﺮارة ﺑﺎﻧﺤﺮاف أﻗﺼﺎﻩ ‪ % ٢٠ ±‬ﻣﻘﺎرﻧﺔ ﺑﺎﻟﻨﺘﺎﺋﺞ اﻟﻌﻤﻠﻴﺔ‪.‬‬ ‫‪* Address for correspondence:‬‬ ‫‪Refrigeration and A/C Department‬‬ ‫‪Jeddah College of Technology‬‬ ‫‪P.O. Box 42204‬‬ ‫‪Jeddah 21541 Saudi Arabia‬‬ ‫‪E. mail: [email protected]‬‬

‫‪The Arabian Journal for Science and Engineering, Volume 30, Number 1B‬‬

‫‪47‬‬

‫‪April 2005‬‬

T. Khir, R. K. Rahim, N. Ghaffour and A. Ben Brahim

ABSTRACT As part of our work on the absorption solar refrigeration cycle and with the objective of optimizing the efficiency of flat plate solar collectors in the generation phase, an experimental study has been conducted on the forced convective boiling heat transfer of NH3–H2O mixtures flowing inside a 6 mm inner diameter vertical smooth tube. Using a water-heated double pipe type generator, the local heat transfer coefficients are measured inside the inner tube for a range of heat flux (8.211–18.521 kW/m2), mass flux (707–2688 kg/m2.s), mass flow rate (0.02 –0.076 kg/s), and ammonia mass concentration (42%, 55%, and 61%). Three theoretical models are used to predict the boiling heat transfer coefficients. Experimental data were compared with the available correlations. The obtained results confirm the good performance of Mishra et al. and Bennett and Chen’s models in predicting the convective boiling heat transfer coefficient of ammonia water mixtures. These models are able to predict the boiling heat transfer data within an accuracy of ± 20 %. Key Words: Two phase flow, mixtures, convective boiling, heat transfer, Ammonia-water

48

The Arabian Journal for Science and Engineering, Volume 30, Number 1B

April 2005


NOMENCLATURE A: tube area

m²

Bo: boiling number d: tube inside diameter

m

db: bubble diameter

m

Cp: specific heat of fluid

J.kg-1.K-1

F: convective boiling factor G: mass flux

kg.s-1.m-2

g: acceleration of gravity

m.s-2

H: enthalpy

J.kg-1

h: heat transfer coefficient

W.m-2.K-1

hm: mass transfer coefficient

m.s-1

Hlg: latent heat of vaporization

J.kg-1

m : mass flow rate

kg.s-1

P: pressure

Pa

Pr: Prandtl number pr: reduced pressure q: heat flux

W.m-2

Ra: surface roughness

10-6 m

Re: Reynolds number S: suppression of nucleate boiling factor Sc: Schmidt number T: temperature

°C, K

X: liquid mass fraction

kgAmL/kgmel

x: quality Y: vapor mass fraction

kgAmg/kgmel

z: total heated length of the tube

m

Z: distance along tube

m

Greek symbols δm: liquid mass diffusivity

m2.s-1

δth: thermal diffusivity

m2.s-1

∆: variation (according to variable) λ: thermal conductivity

W.m-1.K-1

χtt: Lockhart–Martinelli parameter µ: dynamic viscosity

kg.m-1.s-1

ρ: density

kg.m-3

η: thermal losses rate

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49


N.m-1

σ: surface tension Subscripts Am: ammonia

nb: nucleate boiling

av: average

npb: nucleate pool boiling

c: critical state

o: outer, outlet

cv: convective

sat: saturation condition

g: gas (vapor)

SC: subcooled

hw: heating water tp: two-phase

50

i, in: inner, inlet

W: water

l: liquid

w: wall

mix: mixture

z: at location z


April 2005


EXPERIMENTAL STUDY ON FORCED CONVECTIVE BOILING OF AMMONIA – WATER MIXTURES IN A VERTICAL SMOOTH TUBE 1. INTRODUCTION Ammonia and ammonia–water mixtures have been widely used in refrigeration and air conditioning cycles. However, the high pressure, the toxicity, and the aggressiveness of ammonia on copper alloys have reduced its use in thermal processes. Chlorofluorocarbon refrigerants (CFC) have taken the place of ammonia. However, given the problems of global warming and potential ozone depletion that the use of these fluids provokes, ammonia appears again, in our days, as one of the alternatives permitting better protection of the environment. Exhaustive research on forced convective boiling of ammonia–water mixtures inside tubes has not been conducted. As part of a research program conducted on absorption solar refrigeration cycles, an experimental study on forced convective boiling of ammonia–water mixtures inside a vertical tube has been performed. The experimental variable ranges have been defined according to the operating conditions of a flat plate solar collector used as generator, in order to analyze the heat transfer inside the tubes. In this paper, a review of previous works on convective boiling of binary mixtures is given, with mainly heat transfer correlations. The experimental device and the obtained results are presented. Finally a comparison between the experimental results and the predicted data is discussed. 2. PREVIOUS RESEARCH ON BINARY MIXTURES Several research works have investigated the forced convective boiling of refrigerant binary mixtures. The first studies in this field were conducted by Bennett–Chen [1] on aqueous ethylene/glycol solutions. A correlation has been developed to predict the heat transfer coefficient, where the effects of diffusive resistance on nucleate boiling and on two phase forced convection were taken into account separately. Mishra et al. [2] have performed an experimental study on forced convective boiling of the CFC refrigerant mixtures R22/R12 inside horizontal tubes. The experimental results showed a lower heat transfer coefficient for the binary mixture, with respect to the simple linear interpolation between the values corresponding to the two pure components. Hihara and Saito [3] have performed experiments on the CFC refrigerant mixtures R22/R114 in a horizontal tube. The experimental results have confirmed that heat transfer coefficients for mixtures are much lower than those for pure R22 and R114. A study on forced convective boiling inside horizontal tube was investigated experimentally by Murata et al. [4], using mixtures of the HCFC/HFC refrigerants R123/R134a. The heat transfer coefficient for the mixture was found to be lower than that for an equivalent pure refrigerant with the same physical properties. The reduction in heat transfer coefficient for mixtures is attributed to the mixture effect on nucleate boiling and to the heat transfer resistance in the vapor phase. An experimental study on binary mixtures of the CFC refrigerants R12/R114 in up-flow forced convective boiling has been conducted by Celata et al. [5]. The degradation of heat transfer coefficients with the mixture composition appears to be dependent on both saturation pressure and mass flux. The results obtained confirm the good performance of the Bennett–Chen correlation in predicting heat transfer coefficient in the case of refrigerant mixtures. 3. CORRELATIONS 3.1. Pure Fluids Two methods are used to express the heat transfer coefficient in forced convective boiling (htp). The first method is derived from the well-known Chen’s correlation. This method is used by Celata et al. [5] to predict the convective boiling heat transfer coefficients for R12/R114 binary mixtures. As reported by the authors, the convective boiling heat transfer coefficients can be expressed as the arithmetic summation of the two-phase convection contribution (hcv) and the nucleate boiling contribution (hnb). htp = hcv + hnb hcv = hl F (1 χtt

(1)

)

hnb = hnpb S ;

(2) (3)

hl is the single liquid phase heat transfer coefficient given by:

April 2005


51


hl = 0.023

λl di

0.4 Re0.8 ; l Prl

(4)

Rel is the Reynolds number in liquid phase expressed as: Rel = Gd i (1 − x ) µl ;

(5)

where d, G, x, and µ are the tube diameter, the mass flux, the quality and the dynamic viscosity respectively. The factor F represents the acceleration effect of liquid due to vapor shear stress. The pool boiling heat transfer coefficient (hnpb) is calculated for the same value of wall superheat as for forced convective boiling. The factor S represents the suppression of nucleate boiling due to liquid flow. The second method for the heat transfer calculation is based on the relationship: htp = hl f ( χtt , Bo )

(6)

where χtt and Bo are respectively, the Lockhart–Martinelli parameter and the boiling number expressed by:

(

1 χtt = ρl ρ g

where

0.1 ⎛

) ( µg

⎞

µl ) ⎜ ⎟ ⎝ 1− x ⎠

0.5

x

0.9

(7)

Bo = q (GH lg ) ,

ρ is the density and Hlg the latent heat of vaporization (Hlg = Hg – Hl). Several correlations have been proposed to calculate F, S, and hnpb. In the following we present the selected correlations used in this study. Chen [6] has proposed the following correlations: F = 1 for 1 χtt ≤ 0.1

F = 2.35 (1 χtt + 0.213)

and

(

)

S = 1 + 2.3510−6 Re1.17 tp

0.736

for 1 χtt > 0.1

−1

(8) (9)

⎛ λ 0.79Cp 0.45 ρ 0.49 hnb = 0.00122 ⎜ 0.5l 0.29 l 0.24l 0.24 ⎜ σ µl H lg ρ g ⎝

⎞ 0.24 0.75 ⎟ ∆T sat , ∆Psat ⎟ ⎠

(10)

where Retp is the two-phase Reynolds number expressed by: Retp = F 1.25 G (1 − x ) d i µl

(11)

σ is the surface tension , ∆T sat = Tw −T sat and ∆Psat = Psat (Tw ) − Psat (T sat )

Jung et al. [7] have proposed the following correlations to calculate, F, S and hnpb. F = 2.37 ( 0.29 + 1 χtt )

0.85

(12)

S = 4048 χtt1.22 Bo 1.13 for χtt < 1 and S = 2 − 0.1χtt−0.28 Bo −0.33 for 1 < χtt ≤ 5

hnpb

λ ⎛ qd b ⎞ = 207 l ⎜ ⎟ d b ⎝ λlT sat ⎠

0.745

⎛ ρg ⎜⎜ ⎝ ρl

⎞ ⎟⎟ ⎠

(13)

0.581

Prl0.533

(14)

where q is the heat flux and db the bubble diameter given by:

52


April 2005


⎡ 2σ d b = 0.146β ⎢ ⎢ g ρl − ρ g ⎣

(

)

⎤ ⎥ ⎥ ⎦

0.5

with the angle β = 35°

3.2. Mixtures Bennett and Chen [1] have proposed an extension of Equation (1) to binary mixtures. The hcv was calculated according to Equation (2) and using a factor Fmix taking into account the effective mass transfer on the thermal driving force. By the same method, the coefficient hnpb was calculated using an expression proposed by Forster and Zuber [8] for pool boiling taking into account the greater thermal gradient in the vapor generating zone near the wall due to the forced convection. A suppression factor Smix was defined as a function of the two-phase Reynolds number. This method is chosen to be applied in this study because it presents the advantage to be usable for binary mixtures of refrigerants without many restrictions. In the same way, this correlation includes physical properties of mixtures and some predictable quantities of state; the number of empirical parameters is limited with regard to other methods. As reported by Celata et al. [5], the final Bennett–Chen correlation in mixture case, is expressed as: htp = hcvmix + hnbmix

(15)

hcvmix = hl Fmix and hnbmix = hnpb S mix

where

Fmix = Ff (Prl ) ( ∆T ∆T sat

)nb

(16)

f (Prl ) = [ (Prl + 1) 2]

0.444

⎛ ∆T ⎞ dT sat (1 −Y )q ⎜ ⎟ = 1− ∆ ∆ ρ T H h T l sat dX lg m ⎝ sat ⎠nb

Pbulk

hm is the mass transfer coefficient given by: hm = 0.023

δm di

Retp0.8 Sc 0.4

(17)

where Sc is the Schmidt number expressed as: Sc = µ ( ρ L .δ m ) S mix =

S Cp l (Y − X ) dT sat 1− (δth δ m )0.5 H lg dX

(18)

δth and δm are the thermal and the mass diffusivity. Mishra et al. [2] have correlated their experimental data, obtained using R12/R22 mixtures, by: htp = hl E (1 χtt

)m Bo n

,

(19)

As reported by Celata et al. [5] the values of E, m, and n in Equation (19) are taken as follows: (a)

R 12 : 23 − 27% ⎫ ⎬ ⇒ E=5.64, m=0.23, n=0.05; R 22 : 77 − 73% ⎭

(b)

R 12 : 41 − 48% ⎫ ⎬ ⇒ E=21.75, m=0.29, n=0.23. R 22 : 59 − 52% ⎭

4. EXPERIMENTAL APPARATUS

The experimental loop is presented schematically in Figure 1. It mainly consists of a feed reservoir FR, of capacity of 50 liters, a boiler BL, a vapor generator G, a rectifier REC, an absorber ABS, and a chilling unit CHL.

April 2005


53


T

T

CD

E RSG

V

REC T

T HEX

PHS

P T

T

P T

E RSL

T

ABS

R

Heating water

P T Sg Tmix,o P

To vacuum pump

Vv

T

RT

F

CP

G

Service valve

CH L T

BL P Tmix,in

Sg

T

FR PP

PH

F

P

T

Vv TF P Pressure measure

T

Temperature measure

F: Filter - Sg: Sight glass - Vv: Valve Figure 1. Schematic of the experimental loop

An ammonia–water mixture, with defined initial concentration, is introduced in the reservoir FR. A piston pump with variable speed drive PP sends this mixture towards the adjustable power electrical pre-heater PH, permitting control of the value of the mixture inlet temperature. Afterwards, the mixture is sent towards the vapor generator G constituting of two stainless steel coaxial tubes (type 304) with a heated length of 1 m; the inside and outside diameters are 6 and 9 mm respectively. Ammonia–water mixture flows inside the inner tube and the heating water flows in the outer annulus. The inner and outer diameters of the external tube are 28 and 32 mm respectively. The heating water temperature is controlled by a thermostat connected to the electrical boiler BL. At the generator outlet, the mixture is introduced in the phase separator PHS. Then the generated vapor is cleansed in the rectifier REC. The pure vapor stemming from the rectifier is condensed in CD and after that stored in the reservoir SRG. The weak solution is cooled in the heat exchanger HEX and then stored in the reservoir SRL. The absorption phase is made later. Chilled water (CHL) is sent towards the condenser, the heat exchanger and the absorber by a centrifugal pump CP. All the elements in contact with the ammonia– water, mixture are made from stainless steel. For the purpose of reducing the thermal losses towards the surroundings, the generator elements are insolated by a wood–glass layer of 5 cm of thickness. The test channel is shown in Figure 2. The inlet and the outlet pressures are measured in (P) with two absolute pressure transducers type SEDEME and provided with integrated output regulators. The temperatures are measured with 0.5 mm K type insulated thermocouples.

54


April 2005


The temperature of the outside wall is measured at seven locations (T) along the tube length, with fifteen thermocouples oriented to measure the temperature at two sides of the tube perimeter as shown in Figure 2. Seven thermocouples are used to measure fluid bulk temperatures. The volumetric flow rates of the ammonia–water mixture and the poor solution are measured with the help of two turbine flow meters TF. Generated vapor flow rate is measured, at the condenser outlet, with the help of a volumetric technique provided by a precise stopwatch. Water volumetric flow rates in various circuits are measured by the rotameters RT. The errors on experimental parameters are indicated in Table 1. The ranges of experimental parameters are indicated in the Table 2.

21 Thermocouples

50

P

150

Water T A

150

T

A

150

A

1000

150

Ø6

Ø9

150

150

0,5

T

P

Gaskets

NH3- H20 Figure 2. Schematic of the generator tube

All measurements were recorded with a Hewlett–Packard data acquisition/control unit connected to a microcomputer, permitting storage of all of the sensor outputs after conversion to engineering units. Table 1 : Errors in experimental Parameters

Experimental parameters

April 2005

Errors

Temperature

0.1 °C

Pressure

0.2 %

Mixture volume flow rate

1.5 %

NH3 vapor volume flow rate

2

%

Water volume flow rate

3

%


55


Table 2 : Range of Experimental Parameters

Experimental parameters q kWm-2

Heat flux Mass flux

-2 -1

G kgm s 5

Pressure

P 10 Pa

Variation ranges

8.211 – 14.781 – 18.521 707 – 1590 – 2688 1.5 → 20

Boiling temperature T °C

70 → 90

Inlet temperature

Tin,mixt °C

40

Mixture flow rate

m kg/s

0.02 – 0.045 – 0.076

Mass fraction

XNH3 %

42 – 55 – 61

5. EXPERIMENTAL RESULTS 5.1. Evaluation of Thermal Losses

The thermal losses on the generator tube have been evaluated according to series measurements in single liquid phase. The thermal losses along the tube are defined as the relative error calculated considering, on the one hand, the heat flux q absorbed by the mixture inside the generator tube and, on the other hand, the heat flux qhw supplied by the heating water as follows:

η= q=

q hw − q q hw

(20)

m mix .Cp mix . (T omix −T inmix

q hw =

)

(21)

π .d i .Z m hw .Cp hw . (T inhw −T ohw

π .d i .Z

)

,

(22)

where: Tinmix, Tomix: The inlet and the outlet temperature of the mixture respectively, Tinhw, Tohw: The inlet and the outlet temperature of heating water respectively. For mixture flow rates varying from 0.02 to 0.06 kg/s and heating water flow rates varying from 0.027 to 0.08 kg/s, the thermal losses on the generator tube are lower than ±8 %. 5.2. Measurements on Ammonia–Water Mixtures

The decrease in the heating water temperature along the generator is less than 3 °C. In order to estimate the variation of the supplied heat flux, the generator length is divided into different sections. For each section (10 cm in length), a linear decrease of the heating water temperature is assumed. The difference between the heating water inlet and the outlet temperatures ∆Thw, for each section, is practically constant. The error in ∆Thw, engendered with this procedure, is about ± 4 %. For constant values of the specific heat and water flow rate through the annulus, the variation in the supplied heat flux along the generator is consequently less than ± 4 %. The average useful heat flux, absorbed by the mixture inside the generator tube, is given by: m mix − H inmix ⎤⎦ , ⎡H π d i Z ⎣ omix where Z is the total heated length of the generator tube (Z = 1 m). q av =

(23)

The local heat flux, absorbed by the mixture at each location z, is determined according to the enthalpy variation from the tube generator inlet to the level z, as follows:

56


April 2005


q=

m mix

πdi z

[H z

− H inmix

]

(23 ′ )

.

mix and the enthalpies, the heat flux accuracy was evaluated to Considering the errors on the mass flow rate m within ± 5 %. The boiling heat transfer coefficient htp is given by: htp =

q . (Tw − T z )

(24)

The inside wall temperature Tw, is calculated from the value of the external wall temperature using Fourier's law related to the radial thermal conduction. Tz is the local mixture temperature determined according to a polynomial interpolation of the temperature values measured in the longitudinal axis of the generator tube (Figure 2). Considering the uncertainties on q, Tw, and Tz, the accuracy of the heat transfer coefficient htp, was evaluated within ± 12 %. The sub-cooled liquid length is given by: z SC =

m mix Cp mix (T sat −T inmix (π d i q )

)

;

(25)

Tsat indicates here the mixture temperature at bubble line. Taking into account the uncertainties on the different variables in Equation (25), the error on zSC is estimated to be ± 7 %. Assuming the thermodynamic equilibrium, the quality at location z, xz is calculated as follows: xz =

Hz −Hl Hg −Hl

(26)

where Hz: the mixture enthalpy at location z, Hl: the saturation liquid mixture enthalpy, Hg: the saturation vapor mixture enthalpy. Three experience series are performed using three different values of heat and mass fluxes. In order to ensure an optimal generated vapor flow rate, the ammonia mass fraction is taken as 42, 55, and 61 %. According to the ammonia mass concentration, the boiling temperature varies between 70 and 86 °C. In order to avoid vaporization before the generator, the mixture inlet temperature that was taken is 40 °C. In Figure 3, the quality x is plotted as a function of the length along the tube, for various ammonia mass concentration, q, and G. The quality x increases linearly with z and its value depends on the ammonia mass concentration XNH3. For the all performed tests the quality is lower than 0.60. The heat transfer coefficient is plotted in Figure 4 as a function of the length along the tube for various ammonia mass fractions. The onset of sub-cooled boiling is marked by a fast increase of heat transfer coefficient htp. The length of the sub-cooled liquid region zSC is conversely proportional in the ammonia mass fraction. In the single phase liquid, the ammonia concentration does not have sensible influence on the heat transfer coefficient. In the two-phase region, the heat transfer coefficient increases slightly. The influence of the heat and mass fluxes on the heat transfer coefficient is shown in Figure 5; the values of htp are even greater when q and G are increased. 6. DATA ANALYSIS 6.1. Calculation Procedure

Three models are used to predict the convective boiling heat transfer coefficients. The first two models are both based on the Bennett–Chen’s method defined by Equation (15). Different correlations are used to calculate the nucleate pool boiling coefficient hnpb, the convective boiling factor F and the suppression factor S as follows:

April 2005


57


•

Bennett–Chen: F, S, and hnpb are calculated by equation (8), (9), and (10) respectively, (model I).

•

Jung et al.: F, S, and hnpb are calculated by equation (12), (13), and (14) respectively. This model is called Jung– Bennett–Chen (model II),

•

The third model is based on the Mishra et al. method [2]; two correlations are used according to the values of E, m and n in Equation (19) as follows: E = 5.64 ; m = 0.23 et n = 0.05. This model is called Mishra 1 (model III-1), E = 21.75 ; m = 0.29 et n = 0.23. This model is called Mishra 2 (model III-2).

0,6 .

qq = 8,211 - 14, 781 kW/m2 G = 707 - 1590 kg/m2.s

. 0,5

0,4 .

X XNH3 TTsat 55% 77 °C

x

. 0,3

○ 42%

86 °C

0,2 . 0,1 . 0 0

0,2 .

0,4 .

. 0,6 zz (m)

0,8 .

1

Figure 3. Variation of the quality (q) as a function of the tube length

25 2

q = 8,211 kW/m 2 G = 707 kg/m .s Tsat = 70 -- 86 °C

15

-2

-1

htp (kWm K )

20

10

XNH3 ○ 61 % ▲ 55 % 42 %

5

0 0

0,2

0,4

0,6 z (m)

0,8

1

Figure 4. Heat transfer coefficient as a function of the tube length

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The physical properties of ammonia–water mixtures are evaluated using correlations experimental validated in previous research works [9–13]. The heat transfer coefficient htp is obtained according to the following procedure: 1.

For a given q, G and initial ammonia concentration XNH3, determine Tsat and then calculate (25).

2.

From zSC and according to a chosen step (5 cm), calculate Tz according to a polynomial interpolation of the temperatures measured in tube axis.

3.

Calculate the local ammonia concentration in the liquid phase Xz and in the vapour phase Yz.

4.

Calculate the local enthalpy Hz and the saturation enthalpies Hl and Hg.

5.

Calculate the local quality xz from eq. (26).

6.

Calculate χtt from Equation (7).

7.

Calculate hl from Equation (4).

8.

Calculate F and S according to models I and II; then calculate Fmix and Smix from Equation (16) and (18) respectively.

9.

Calculate hnpb for the models I and II from Equation (10) and (14) respectively.

zSC from Equation

10. Calculate htp by Equation (15) for the models I, and II and Equation (19) for the models III-1 and III-2. Software elaborated in Turbo–Pascal language allows to perform the previously calculus into all the details. 6.2. Discussion

The evolution of the boiling heat transfer coefficient htp as a function of the quality x is shown in Figures 6a and 6b, for an ammonia mass fraction of 55 %. The model III-1 of Mishra et al. predicts the heat transfer coefficient htp with a precision of 12 %; contrary to the model III-2, which shows a wide undervaluation of htp as shown in Figure 6a. The models I and II present wide divergences from the experimental results especially for qualities x above 0.3.

Tsat = 77 °C X NH3= 55 %

htp (kWm-2K-1)

50

q = 18,521 kW/m G =2688 kg/m2.s

40

q =14,781 kW/m2 G = 1590 kg/m2.s

30 20 10

q = 8,211 kW/m2 G = 707 kg/m2.s

0 0

0,2

0,4

z (m)

0,6

0,8

1

Figure 5. Influence of the heat and mass fluxes on the heat transfer coefficients

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For increased values of q and G, the models I and II present more divergences in predicting the heat transfer coefficients as shown in figure 6b.

40 q = 8,211 kW/m G = 707 kg/m2.s Tsat = 77 °C XNH3 = 0.55

35

-1

htp (kWm K )

30

2

-2

25 20 15 10 □ Bennett-Chen (I)

5

Mishra 1 (III-1)

∆ Jung-Bennett-Chen (II) ● Experimental results

0 0

0,1

0,2

Mishra 2 (III-2)

0,3 x

0,4

0,5

0,6

Figure 6. (a) Boiling Heat transfer coefficients as a function of the quality

q = 18,521 kW/m2 G = 2688 kg/m2.s Tsat = 77 °C XNH3 = 0,55

htp (kWm-2K-1)

100 80 60 40 20

□ Bennett-Chen (I)

Mishra 1 (III-1)

∆ Jung-Bennett-Chen (II) ● Experimental results

0 0

0,1

0,2

Mishra 2 (III-2)

0,3 x

0,4

0,5

0,6

Figure 6. (b) Boiling Heat transfer coefficients as a function of the quality

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For vapor qualities above 0.25, a saturated nucleate boiling zone develops gradually along the generator tube [14,15]. In the same way, Bjorge et al. [16] have considered that the saturated flow boiling occurs for values above 0.05. In this zone the values of the heat transfer coefficients htp depend essentially on the dominant contribution of nucleate boiling, characterized by the coefficient hncmix in Equation (15). The contribution of the forced convective boiling, characterized by the coefficient hcvmix, is, consequently, less important. It seems that Chen [6] and Jung et al. [7] overpredict the coefficient hcvmix in their correlations. In fact the correlations related to the convective boiling factor calculation are modified for the purpose to decrease the contribution of the forced convective boiling. The convective boiling factor F depends on the inverse of the Lockhart–Martinelli parameter 1/χtt and, as a result, on the quality x. For the models I and II, the factor F is calculated from Equation. (8) and (12) respectively. These can be expressed as follows: F = r (1 χtt + s )

t

,

(27)

where r, s and t are parameters defined in Equations (8) and (12). The proposed modifications consist in correction of the exponent t (equation 27) in the aim to converge the huge differences between the theoretical and the experimental results related to the heat transfer coefficients. This correction has been defined according to the variation ranges of the heat and mass fluxes; the retained values of t are: Chen [6] t = 0.736 Jung et al. [7]

t = 0.85

This work

t = 0.45 for 8.5 ≤ q ≤ 15 kW/m2

and

800 ≤ G ≤ 1600 kg/m2.s

t = 0.3 for 15 < q ≤ 18.5 kW/m2

and

1600 < G ≤ 2688 kg/m2.s .

The obtained results after these modifications are shown in Figure 6c for the same experimental conditions already considered in Figure 6b. □ Bennett-Chen (I) Mishra 1 (III-1) ∆ Jung-Bennett-Chen (II) Mishra 2 (III-2) ● Experimental results

80

-2

-1

htp (kWm K )

100

60 40 20

q = 18,521 kW/m2 2

G = 2688 kg/m .s

Tsat = 77 °C XNH3 = 0.55

0 0

0,1

0,2

0,3

0,4

0,5

0,6

x Figure 6. (c) Boiling Heat transfer coefficients as a function of the quality

The modified models I and II present a good result in predicting the heat transfer coefficients. The maximum error, with regard to the experimental results, is less than ± 12 %. A comparison between the experimental and the predicted values of heat transfer coefficients is shown in Figures 7a and 7b. The data predicted from models I and II (without modification) present deviations of more than 40 % as shown in Figure 7a. After the convective boiling factor modification, the predicted heat transfer coefficients from models I and II agree with the experimental results with an accuracy of ±15 % as shown in Figure 7b. April 2005


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90

q : 8,211 - 18,521 kW/m2 G : 707 - 2688 kg/m2.s Tsat = 77 °C XNH3 = 0,55

-2

-1

htp,th (kWm .K )

80 70

+ 20 %

60 - 20 %

50 40 30 20 □ Bennett-Chen (I) ∆ Jung-Bennet-Chen (II) Mishra 1 (III-1)

10 0 0

10

20

30 40 50 60 70 -2 -1 htp,exp (kWm K )

80

90

Figure 7. (a) Comparison between the predicted and the experimental heat transfer coefficients

70 q : 8,211 -- 18,521 kW/m2 G : 707 -- 2688 kg/m2.s Tsat = 77 °C XNH3 = 0,55

50

+ 20 %

-2

-1

htp,th (kWm K )

60

- 20 %

40 30 20 10

□ Bennett-Chen (I with modification) ∆ Jung-Bennett-Chen (II with modification) Mishra 1 (III-1)

0 0

10

20

30 htp,exp

40 50 2 -1 (kWm K )

60

70

Figure 7. (b) Comparison between the predicted and the experimental heat transfer coefficients

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7. CONCLUSION

The heat and mass fluxes have a significant influence on the values of the forced convective boiling heat transfer coefficients of ammonia–water mixtures; contrary to the ammonia mass concentration, which has a less influence on the values of htp. The investigated variation ranges in this study concerning XNH3, q, and G, have confirmed the validity of the Mishra et al. model to predict the convective boiling heat transfer coefficients of ammonia-water mixtures. This model predicts htp within ±12 % of error. Bennett–Chen's model presents a large divergence in predicting the forced convective boiling heat transfer coefficients, especially for qualities above 0.25. In order to reduce this divergence, the correlations related to the convective boiling factor are modified. After modifications, the Bennett–Chen model predicts data with an accuracy of ± 20 % for more than 90 % of the considered data. In the same way, the adaptation of the Jung–Radermacher correlations to Bennett–Chen's method seems to give satisfactory results in predicting the forced convective boiling heat transfer coefficients of ammonia-water mixtures. The mean deviation, obtained according to this method, is lower than ± 18%. REFERENCES [1]

D. L. Bennett and J. C. Chen, “Forced Convective Boiling in Vertical Tubes for Saturated Pure Components and Binary Mixtures”, Applied International Chemical Journal, 26 (1980), pp. 454-461.

[2]

M. P. Mishra, H. K. Varma, and C. P. Sharma, “Heat Transfer Coefficients in Forced Convection Evaporation of Refrigerants Mixtures”, Letter of Heat and Mass Transfer, 8 (1981), pp. 127-136.

[3]

E. Hihara and T. Saito, “Forced Convective Boiling Heat Transfer of Binary Mixtures in Horizontal Tube”, Proceedings, 9th International Heat Transfer Conference, 2 (1990), pp. 123-128.

[4]

K. Mutara and K. Hashizume, “Forced Convective Boiling of Nonazeotropic Refrigerant Mixture Inside Tubes”, Journal of Heat Transfer, 115 (1993), pp. 680-689.

[5]

G. P. Celata, M. Cumo, and T. Setaro, “Forced Convective Boiling in Binary Mixtures”, International Journal of Heat and Mass Transfer, 36 (1993), pp. 3299-3309.

[6]

J. C. Chen, “Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow”, Industrial and Engineering Chemical Process Design and Development, 5 (1966), pp. 322-329.

[7]

D. S. Jung and R. Radermacher, “Prediction of Heat Transfer Coefficient of Various Refrigerants during Evaporation”, ASHRAE Transactions, 97 (1991), Pt. 2.

[8]

H. K. Forster and N. Zuber, “Dynamic of Vapour Bubbles and Boiling Heat Transfer”, American Institute of Chemical Engineers Journal, 1 (1955), pp. 531-535.

[9]

ASHRAE, Handbook of Fundamentals Atlanta, GA., American Society of Heating, Refrigerant and Air Conditioning Engineer, Inc., 1989.

[10] Y. S. Touloukian, P. E. Liley and S. C. Saxena, Thermophysical Properties of Matter, vol. 3, New York–Washington: IFI/Plenum, 1970. [11] R. C. Reid, J. M. Prausnitz and B. E. Poling, The Properties of Gases and Liquids, New York: McGraw-Hill, 1977. [12] R. H. Perry and D. Green, The Chemical Engineer’s Handbook Chapters 3.14 and 18.6. New York: Mc-Graw Hill, 1984. [13] P. C. Jain and G. K. Gabel, “Equilibrium Property Data Equations for Aqua Ammonia Mixtures”, Transactions, 77: (1979), pp. 149-151.

ASHRAE

[14] V. P. Carey, Liquid–Vapor Phase-Change Phenomena, London: Hemisphere Publishing Corp., 1992. [15] J. G. Collier, Convective Boiling and Condensation London; McGraw-Hill, 1981. [16] R. W. Bjorge, G. R. Hall, and W. M. Rohsenow, “Correlation of Forced Convective Boiling Heat Transfer Data”, International Journal of Heat and Mass Transfer, 25 (1982), pp. 753-757. Paper Received 30 June 2003; Revised 17 March 2004; Accepted 1 June 2004.

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