Determination of the void fraction and drift velocity in a twophase flow with a boiling solar collector

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

DETERMINATION OF THE VOID FRACTION AND DRIFT VELOCITY IN A

TWO-PHASE FLOW WITH A BOILING SOLAR COLLECTOR

†

M. E. VIEIRA , P. O. O. DUARTE and H. L. B. BUARQUE

Applied Solar Energy Laboratory, Federal University of Ceara, Campus do Pici, 60455-760, Fortaleza, Brazil

Received 26 August 1998; revised version accepted 15 May 2000

Communicated by BRIAN NORTON

Abstract—This paper presents an approach to determine the void fraction and the drift velocity in a two-phase

flow with a boiling solar collector using easily obtained experimental data. The solar collector operates in a thermal siphon circuit, where the working fluid absorbs solar radiation mostly while boiling. The vapor bubbles release their latent heat in a condenser, while heating up a flow of water–glycol. Two numerical procedures are developed to calculate the void fraction because its experimental values cannot be easily measured. The use of a flow meter causes an additional pressure drop in the thermal siphon circuit and, consequently, changes the circulated mass flow rate. The first numerical procedure is based on a force balance in the thermal siphon loop and is used to estimate the total mass flow rate and the void fraction in the circuit. The second uses a drift flux correlation to estimate the void fraction and the drift velocity. Both procedures use the experimental values for the vapor mass flow rate, which is determined by an energy balance in the condenser. The volumetric flow rate of the water–glycol mixture and its temperature difference across the condenser are experimentally measured. The pipe length of the two-phase flow in the solar collector is experimentally determined using 44 thermocouples attached to the back of flow channels in the absorber plate. The results show that the two numerical models compare well and that either one can be used to estimate the void fraction in the two-phase flow solar circuit.  2000 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION 1988, 1989; Kaushika et al., 1982; Abramzon et

al., 1983; Neeper, 1985; Vieira, 1992) can be

Solar collectors operating in single-phase thermal

found in the literature about the operation of siphon loops, using either water mixtures or oils

boiling collectors in thermal siphon loops, in-as the working fluid, have found various

applica-formation about the void fraction at the collector tions in water heating, water desalination, and

exit, either experimental or numerical, was not solar cookers (Schwarzer and Krings, 1996;

found. Most models treat the boiling collector as a Hafner, 1993). These systems present the

advan-unit where the total mass in the collector starts tages of self-pumping and self-controlling, and the

boiling, that is, either sub-cooled or saturated low costs associated with maintenance and

opera-liquid enters the absorber plate, and either satu-tion. As disadvantages, a lower natural convection

rated or superheated vapor exits. This is not a heat-transfer coefficient in the flow channels is

correct assumption since only a small part of the found in comparison with the forced convection

mass flow rate boils and there is usually a two-coefficient. Boiling collectors in closed thermal

phase flow at the collector exit. This conclusion siphon loops present the advantages of

single-was shown by Price (1984), who developed two phase natural convection systems and, when well

models for use with TRNSYS (1983), considering designed, can operate at a lower absorber plate

the collector and condenser together as a single temperature due to the higher boiling heat-transfer

component. In the first model, it was assumed that coefficient. As disadvantages, these systems

re-saturated liquid entered the collector, re-saturated quire higher installation costs and tighter

con-vapor exited, and that there were no pressure struction, since most systems operate at low

losses in the connecting lines. In the second pressure.

model, these assumptions were removed. Using Even though various articles (Soin et al., 1979;

the homogeneous two-phase flow model and Al-Tamimi and Clark, 1983; El-Assy and Clark,

assuming that the mass flow rate of the working

† fluid through the collector was the same as

Author to whom correspondence should be addressed. Tel.:

through the condenser, a mass balance calculation

155-85-288-9599; fax: 155-85-288-9636; e-mail:

eugenia@ufc.br showed that the initial liquid length fraction in the

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316 M. E. Vieira et al.

system should have been 0.05. For best per- second uses a drift flux correlation to estimate the void fraction and the drift velocity. Both pro-formance, this liquid length varies from 0.7 to 1.0

cedures use the experimental values for the vapor (Soin et al., 1979) and, therefore, the vapor

mass flow rate, which is determined by an energy quality, defined as the rate of the vapor mass rate

balance in the condenser. to the total mass rate, at the collector exit is much

less than 1.0.

The two-phase flow with a boiling circuit can

2. METHODOLOGY

be described using Fig. 1. In operation, liquid

This section is divided in two parts. The first refrigerant is fed from an accumulator tank to the

shows the development of the force balance collector by gravity. As it flows upwards through

model used to calculate the total mass rate and the the absorber plate channels, it is sensibly heated

void fraction through the system (Vieira et al., until boiling starts and vapor bubbles are formed.

1997). The experimentally measured vapor mass These bubbles rise, dragging liquid and initiating

rate and the pipe length of the two-phase flow in a two-phase flow. When the two-phase flow leaves

the collector are used in the calculation, and it is the collector, it moves through a standard T-type

considered that the two phases flow as the same connection where the liquid separates from the

velocity. The second part presents the drift flux vapor and returns to the collector inlet. The vapor

correlation (Chexal et al., 1991), which requires moves upward to the condenser, where it releases

knowledge of the vapor mass rate and the total its latent energy by heating a water–glycol flow

mass rate through the system. This correlation that circulates through this heat exchanger. Solar

emphasizes the relative motion of the two phases systems available in the market have the

con-instead of the separate flux of the liquid and vapor denser located right above the solar collector. This

phases individually. The relative motion is de-design was not used in the present work for two

termined by a few key parameters related to the reasons: first, some piping space was needed for

flux of each phase. instrumentation (pressure and temperature

sen-sors), and second, the results found can also be

2.1. Force balance model used when the condenser is installed inside the

To calculate the total mass rate and the void storage tank, avoiding the use of a water pump.

fraction, it is considered that the total frictional This paper presents an approach to estimate the

pressure drop equals the pressure gain due to the void fraction and the total mass flow rate in the

difference in gravity in the single phase and the two-phase flow thermal siphon system using

two-phase vertical parts of the system, easily obtained experimental data. Two numerical

procedures are developed to calculate the void g f

DPT1 DPT50 (1)

fraction because its experimental values cannot be easily measured. The use of a flow meter causes

Two models for the two-phase flow frictional an additional pressure drop in the thermal siphon

pressure drop (Owens, 1961; Marchaterre, 1961), circuit and, consequently, changes the circulated

based on the pressure drop for single-phase flow, mass flow rate. The first numerical procedure is

are used. To experimentally determine the pipe based on a force balance in the thermal siphon

lengths of liquid and two-phase flow, 44 ther-loop and is used to estimate the total mass flow

mocouples are mounted along the flow channels rate and the void fraction in the circuit. The

on the backside of the absorber plate. Fig. 2 shows the average wall temperature values at specific positions along the collector pipes. It is observed that from the inlet to about 1 / 3 of the flow channel, the working fluid is heated until boiling starts. In the boiling length, the tempera-ture remains approximately constant.

Using the pressure drop model presented by Marchaterre (1961) and Eq. (1), an expression for the total mass flow rate is expressed as,

s s 4 s

~

m_T5a. (r 2 r_l _v)?L_i?g?sinu ? p ?D ?r_l

s 21 s 2

Fig. 1. Schematic view of the thermal siphon circuit. The full _?₍₁₂₈_?_ml₎ hLspf1(12a)?(rl)

line represents the working fluid loop and the dotted line the

s s 22 21

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Fig. 2. Temperature along the flow channel on the back of the absorber plate.

~

where mT is the total mass flow, a, the void ties. A generic transient two-phase flow problem

fraction, u, is the angle of inclination, D, the can be presented either by the two-phase separate equivalent diameter of the tube, L , the length ofi model or by the drift flux model, depending upon tube in the two-phase flow, Lspf, the length of tube the degree of dynamic junction between the two in the single-phase flow (liquid), L , the lengthtpf phases. In the separate two-phase flow model,

of tube in the two-phase flow (liquid and vapor), each phase is considered separately and the

s s

rl, the saturated liquid density, rv, the saturated problem is formulated in terms of two groups of

s

vapor density, andml, the saturated liquid viscosi- conservation equations of mass, momentum, and

ty. energy for each phase. The use of two momentum

Eq. (2) has two unknowns, the total mass flow equations introduces considerable difficulties due and the void fraction. Using the definition of the to the mathematical complication and uncertain-void fraction and considering that the two phases ties in the specifications of the interaction terms flow at the same velocity, the total mass flow rate between the two phases. In the drift flux model,

is expressed as, one kinematics equation is used to specify the

relative motion between the phases. In other

s s 21

~ ~

mT5[11(12a) .rl. (arv) ] mv (3) words, the problem is simplified to five field

equations: two conservation of mass, two of ~

where m is the vapor mass flow rate.v

energy, and one momentum equation for the Solving Eqs. (2) and (3) simultaneously, an

mixture. The model that is used mostly employs expression that allows the calculation of the void

one conservation of energy equation. fraction can be written as,

In the drift flux model presented by Chexal et

s s 21 s _al_{. (1991), the void fraction is estimated by a few}

~

a 5[11(12a)r ?_l (a r_v) ]?m_v?128?m_l

key parameters, such as the superficial velocities

4 s s s 21

?[p ?D ?r ?l g?sinu ?(r 2 rl v)?L ]i _{of the liquid and vapor, bubble concentration}

s 2 s _{parameter, and the slip velocity. The void fraction}

?hL_spf1(12a)?(r_l) ?L_tpf?[(12a)?r_l

is expressed as,

s 22

1a rv] j (4)

21

a 5Jg?[(Jg1J )f 1V ]g j (5)

2.2. Drift flux model

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318 M. E. Vieira et al.

The superficial velocity for the vapor, Jg, and gained by the water–glycol flow in the condenser the superficial velocity for the liquid, J , aref to the working fluid’s latent heat.

defined as, A 1.22-m long sight glass is installed to

indicate the liquid level in the collector when

21

Jg5Wg?(r ?g A) (6) charging the system. The solar collector tilt angle

is 458 and the diameter of the copper piping is

21 _{12.7 mm. The working fluid circuit (solar}

collec-Jf5Wf?(r ?f A) (7)

tor, copper piping, and condenser) is evacuated and then completely filled with liquid refrigerant where W and W are the liquid and vapor massf g

to a liquid level of 1. Ambient data are also flow rates, rf and rg are the liquid and vapor

obtained from the meteorological station. The densities, and A is the total flow area.

instruments are scanned every 20 s and are The bubble concentration parameter, C , for ao

averaged at each minute. two-phase flow mixture flowing through an

in-clined pipe, by angle u, is estimated using the

parameters for the vertical and horizontal direc- _{4. RESULTS}

tion, Cov and C .oh

Fig. 3 shows the values for the void fraction

Co5F Cr ov1s12F Crd oh (8) calculated using the two procedures. The void

fraction values are plotted throughout the day

where F is a flux orientation parameter.r (morning and afternoon hours). When the solar

The drift velocity, V , for a parallel up-flowg j radiation intensity is low, these values are also

parallel and inclination angle 08,u ,908 is de- _{low, since less vapor bubbles are formed. At}

fined as, _{higher solar radiation intensity values, the void}

fraction and the bubble concentration parameter Vg j5F Vr g jv1(12Fr) Vg jh (9) _{are higher. It is seen that the void fraction values}

calculated using the drift flux model are lower where Vg jv and Vg jh are the drift velocities for a _{than those of the force balance model because the} horizontal and vertical flow, respectively.

liquid phase does not flow at the same velocity as the vapor phase, as assumed in the latest model. However, the difference remains approximately

3. EXPERIMENTAL

constant throughout the day.

Fig. 4 shows the drift velocity, V , throughout

Experimental measurements are performed to g j

the day. At low solar radiation intensity, the vapor determine the incident solar radiation on

horizon-bubbles flow at a higher velocity than the liquid tal and tilted planes, the temperature of the

phase. A smaller number of bubbles implies that absorber plate and of the outside walls of the

there is less surface area between the two phases copper piping, the working fluid pressure and

and, consequently, less drag. At high solar radia-temperature at the collector inlet, and the pressure

tion intensity values, there is more surface area at the outlet. Incident radiation measurements are

between the two phases, which flow at closer made with two precision pyranometers,

tempera-velocity values. ture transducers (60.58C or 4.0%, whichever was

greater) are copper–constantan, special limit type-T thermocouples, and pressure values are mea-sured with a diaphragm transducer. The pipe length of the two-phase flow in the solar collector is experimentally determined using 44 thermocou-ples attached to the back of flow channels in the absorber plate.

On the storage-tank side, the volumetric flow rate through the condenser and the temperature difference between the inlet and outlet are mea-sured. A five-junction thermopile (61% of the reading10.058C) is used to measure this tempera-ture difference across the condenser, and a tur-bine-type meter measures the volumetric flow of

the water–glycol solution. The vapor mass rate is Fig. 3. Void fraction (drift flux and force balance models) versus solar radiation intensity throughout the day.

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¨

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¨

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En-˜