Boiling viscous liquids in natural circulation vacuum evaporators

 

 

E. E. A. Rouillard

University of Durban-Westville

 

 

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ABSTRACT

Vacuum evaporative crystallizers are used by the South African sugar industry to produce more than 2 000 000 tons of sugar annually. The process fluid is very viscous and laminar conditions prevail in the apparatus. To date the equipment has been designed by rule of thumb. In order to develop a procedure for optimizing the design and operation of this equipment, research was undertaken to determine how the equations proposed for heat transfer and vapour hold-up, should be modified for boiling in laminar flow under vacuum.
It was found that the heat transfer coefficient can be estimated by the superposition method of Rohsenow and Griffith, but that different exponents and constants are required. A new equation is proposed for calculating the void fraction in the highly subcooled region, and the equation of Bowring for subcooling at the point of bubble departure must also be modified.

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Nomenclature

A flow area

B₀ constant (Equation 20)

Bl constant (Equation 10)

C₀ flow distribution parameter

C_p specific heat

C_sf constant in Rohsenow correlation

D tube diameter

f friction factor

G mass velocity

g acceleration due to gravity

h heat transfer

i_fg latent heat of vaporisation

K fluid consistency index

k thermal conductivity of liquid

m exponent in Rohsenow correlation

n flow behaviour index

Nu Nusselt number

Pr Prandtl number

Q volumetric rate of flow

Re Reynolds number

t(z) bulk liquid temperature at axial position z

u velocity of flow

V rising velocity of vapour

W mass rate of flow

X mass vapour quality

z axial coordinate

α void fraction

η empirical factor for bubble departure

ρ density

μviscosity

Φheat flux

Φ_cconvection heat flux

Φ_n nucleate boiling heat flux

σ surface tension

ΔP_F pressure difference due to friction

Δt_s superheat necessary to cause nucleation

Δt_sub subcooling at axial position

Δt_subd subcooling at point of bubble departure

 

Subscripts

b at bulk conditions

d at bubble departure

f liquid

fo total flow assumed liquid

g vapour

s at saturation

TP two phase

w at wall conditions

 

Introduction

In the sugar industry crystallization is carried out using natural circulation vacuum evaporative crystallizers known as vacuum pans. The fluid known as massecuite consists of a suspension of crystals in concentrated molasses. It is highly viscous, slightly non-Newtonian, exhibits pseudoplastic properties, and laminar conditions prevail in the apparatus.

Although research on the factors affecting the boiling characteristics of vacuum pans has been in progress for at least fifty years, improvements in the design of these crystallizers have been the result of trial and error, because no satisfactory method has yet been put forward for optimizing pan design and operation.

The equations proposed for forced convection boiling cannot be used, because they were established for turbulent flow under pressures higher than atmospheric. Boiling viscous fluid under vacuum has not been studied. Experiments were therefore designed to determine if the available equations could be adapted, and if not, what modifications would be required.

 

Theoretical background

The flow pattern and the liquid and tube surface temperature that occur over the length of a vertical evaporator tube are shown in Figure 1. The liquid that enters is sub-cooled, that is, its temperature is below the saturation temperature corresponding to the pressure at that point. In region AB heat transfer is entirely by single phase forced convection. As heat is transferred to the liquid the temperature adjacent to the heating surface increases until at point B the boiling temperature is exceeded, and vapour formation occurs, but the bulk of the liquid is still subcooled.

Between B and D the vapour bubbles grow because of the additional heat input, and as a result of decompression as the hydrostatic head decreases. At the same time heat penetrates towards the centre of the tube so that the liquid temperature increases. This is the region of sub-cooled boiling. Transition to saturated boiling occurs when the average combined enthalpy of liquid and vapour equals the saturation enthalpy of the liquid. This happens a short distance upstream of point D. At point D boiling extends across the entire sectional area of the tube, and from this point there is a gradual decrease of the fluid temperature because of the decompression effect. With viscous liquids, however, transition to saturated boiling does not take place, and subcooled boiling occurs up to the tube outlet.

A method proposed by Rohsenow and Griffith [11] to estimate the boiling heat transfer coefficient in both the subcooled and saturated regions consists in adding the single phase forced convection heat flux and the nucleate boiling heat flux

The single phase forced convection component is given by

where h_fo, the heat transfer coefficient for the total flow assumed liquid, is calculated using the Seider and Tate equation as modified by Charm and Merrill [3] for heat transfer to pseudoplastic fluids in straight tubes

The nucleate boiling heat flux has been correlated by Rohsenow [10] using the relation

where the value of the constant C_sf is determined experimentally, and that of the exponent m is given as O for water and 0.7 for other liquids. For pseudoplastic fluids this equation expressed in terms of the consistency and flow behaviour index is

Starting at point B when boiling begins three factors contribute to the pressure drop along the tube.

(1) The momentum effect which results from acceleration along the tube due to evaporation and expansion of the vapour phase.

(2) The gravitational effect which results from the change in elevation.

(3) The frictional effect due to the shear forces acting on the two phase fluid.

The acceleration and elevation losses can be calculated from a momentum equation if the mass vapour quality and the void fraction are known. The frictional component must however be determined empirically.

Griffith and Wallis [5] have proposed a method for estimating the friction loss of liquid-gas mixtures in the bubble flow regime. They related the friction loss to a modified Fanning equation

where f_f, the Fanning friction factor, is obtained from the conventional Reynolds number-Fanning friction factor plot using a velocity defined as

This method was modified by Oliver and Wright [9] for pseudoplastic non-Newtonian two phase systems. The liquid properties are considered to be dominant. The only parameter modified by the presence of gas is the liquid velocity which is obtained from the equation.

The liquid friction factor is calculated using the relation 16/eeneralized Reynolds number. The two phase generalized Reynolds number is calculated using this velocity and the equation of Metzner and Reed [7].

The amount of vapour present in the evaporator tubes must be established to permit calculation of the elevation and acceleration losses. In the case of natural circulation evaporative crystallizers, circulation results from the difference in hydrostatic head between the two phase mixture of massecuite and liquid in the tubes and single phase liquid in the downtake. Thus to calculate the circulation rate, the volumetric fraction occupied by vapour is necessary.

The change in void fraction that takes place in the evaporator tube is shown in Figure 1. At first the vapour formed consists of discrete bubbles attached to the tube su^rface, but at C they become detached to form bubbly flow. At point D boiling extends across the tube. Coalescence of the bubbles occurs fairly rapidly and transition to slug flow may take place.

The resulting void fraction is a function not only of the amount of vapour generated, but also of the rate at which it moves up the tube relative to the liquid velocity. The upward rate of flow of the vapour depends upon the vapour flow distribution that is, whether it is flowing close to the tube centerline or near the wall, and upon the bubble rise velocity.

In the highly subcooled region the bubbles grow and collapse but remain attached to the tube surface. A model has been proposed by Griffith et al [4] to estimate the void fraction in this region.

At low pressure this relationship becomes incorrect since the diameter of the bubbles is then a function of the pressure as well as of the hydrodynamic layer thickness. Under these conditions the voidage is overestimated.

At point C the vapour bubbles start to depart from the tube surface, and there is a rapid increase in the void fraction. Bowring [2] found that the subcooling at the point of bubble departure Δt_subd could be approximated by the relationship

Work by Levy [6] indicated that low pressures affect the value of the factor η. He also suggested an empirical model for the estimation of the void quality in region CD, the low subcooling region. He assumed that the true quality x' is related to thermodynamic quality x by the relationship

where x_d is the thermodynamic quality at the point of bubble departure given by

After the point of dubble departure the void fraction is obtained from the equation of Nicklin et al. [8] who showed that the rising velocity of the vapour is made up of two components: V, its rising velocity in still liquid, plus a contribution due to the non-uniform distribution of vapour in the moving liquid.

Rouhani and Axelsson [12] found that the non-uniform flow distribution parameter C_o has a value of 1,12. Zuber and Findlay [14] gave the following expression for the rising velocity in the bubbly flow regime.

 

Experimental apparatus

The experimental vacuum evaporative crystalliser is shown in Figure 2. It consisted of a single steam jacketed Schedule 40 mild steel tube 1,3 m long and with an internal diameter of 0,1m. These dimensions were representative of those used in some of the more recent vacuum pans. A previously calibrated positive displacement pump controlled the velocity of circulation in the tube. The condensed vapours were continously returned to the apparatus so as to keep the concentration constant.

 

 

Bleeding air continously through the pressure tappings prevented entry of the boiling fluid into the manometers and clogging of the pressure tappings by crystallization of sugar. The centerline temperatures were measured by means of a probe introduced axially through the top of the apparatus. The void fraction along the tube was determined by gamma ray absorption, the source and detector being mounted on a traversing mechanism.

Experiments were carried out using syrup, molasses and massecuite. With these fluids is was possible to study both subcooled and saturated boiling under laminar conditions. The range of the operating variables is given in Table 1.

 

Results

The temperature of the inner tube surface was calculated using equations for film type condensation, and neglecting the resistance of any scale or oily film that may have been present on the heat transfer surfaces. The rate of heat transfer was based on the amount of condensate collected in a given time. It was assumed that the steam was dry and saturated. The saturation temperature of the boiling fluid was obtained by a method suggested by Batterham and Norgate [1] for concentrated sugar solutions.

Data for the heat flux transferred by bubble nucleation was obtained by subtracting the single phase forced convection heat flux calculated using equation (3), from the total heat flux imposed during the experiment. The residual term was correlated as suggested by Rohsenow and Griffith [11]. A plot of the generalized Prandtl number [13]

which is shown in Figure 3 gave a value of 0,0673 for the constant C_sf and a value of 1,257 for exponent of the Prandtl number, so that m is equal to 0,257. It should be noted that the value of m recommended by Rohsenow and Griffith [11] is 0 for water and 0,7 for other liquids.

 

 

Figure 4 shows the typical void fraction profile measured by Gamma ray absorption. The low voidage associated with the highly subcooled region and the sudden increase that takes place at the point of bubble detachment can be seen. The flow distribution at the tube outlet was calculated using equation (14) in which

 

 

The evaporation rates measured were used to calculate the mass vapour quality, x, at the tube outlet, and thus obtain the volumetric flowrate of the liquid and vapour phases. The value of V, the rising velocity of vapour, was calculated from equation (15).

The average value of C_o was 1,13 for all the runs where saturated boiling took place. This is close to the figure of 1,12 that Rouhani and Axelsson [12] found applies to most conditions.

As noted previously, the model of Griffith et al. [4] for estimation of the void fraction in the highly subcooled region is not suitable, for it gives incorrect results at low pressures. It was postulated that the void volume per unit surface area, a, would be proportional to the ratio of the boiling heat transfer coefficient h_TP to the single phase heat transfer coefficient h_fo multiplied by a proportionality constant B_o, which would be a function of the pressure and of the hydrodynamic layer thickness which in turn, is related to the thickness of the termal boundary layer (k_f/h_fo

For a circular pipe the void volume per unit heated surface area can be related to the average local void fraction by the equation

which when substituted into equation (20) gives

The value of the constant B and of the exponents a and b was determined from a regression using data obtained from the void fraction profiles measured experimentally. The equation obtained was

with a correlation coefficient of 0,91. The correlation is shown in Figure 5.

 

 

The factor η in the equation of Bowring [2] for subcooling at the point of bubble departure was found to increase with decreasing pressure in the range between 9 and 25 kPa. This is shown graphically in Figure 6. A possible explanation is that, as the void fraction increases with decreasing pressures, the vapour bubbles project further away from the heat transfer surfaces and are swept away more readily by the frictional drag.

 

 

A regression of η versus Pr indicated that the Prandtl number also has a significant influence on the subcooling at the point of bubble departure, with departure taking place at a higher subcoolilng as the Prandtl number increases. Again, this must result from the more intense frictional drag acting on the bubbles, since variation in the value of the Prandtl number is caused mainly by the change in viscosity.

It was found that under the experimental conditions the factor η can be expressed by the equation

The correlation coefficient obtained was 0,85 and the results are shown in Figure 7.

 

 

Conclusions

This research has shown that most of the equations proposed for boiling in turbulent flow under pressure require modification for use in laminar flow under vacuum. The superposition method suggested by Rohsenow and Griffith [11] works well provided that the value of the Prandtl number is raised to the power of 1,257 instead of a value of 1 for water and 1,7 for other fluids as recommended. A new equation is proposed for the estimation of the void fraction in the highly subcooled region, since that of Griffith et al. [4] is not suitable for low pressures. The equation of Bowring [2] for subcooling at the point of bubble departure must also be modified since it was found that this parameter is a function of the pressure and of the Prandtl number.

 

References

1. Batterham, R. J., and Norgate, T. E., "Boiling point elevation and superheat in impure cane sugar solutions", International Sugar Journal, Vol. 77, 1975, pp. 359-364.         [ Links ]

2. Bowring, R. W., "Physical model based on bubble detachment and calculation of steam voidage in the subcooled region of a heated channel", OECD Halden Reactor Project Report HRP-10, 1962.

3. Charm, S. E., and Merrill, E. W., "Heat transfer coefficients in straight tubes for pseudoplastic food materials in streamline flow". Food Research, Vol. 24, 1959, pp. 319-331.         [ Links ]

4. Griffith, P., Clark, J. A., and Rohsenow, W. M., "Void volumes in subcooled boiling systems", Paper 58-HT-19, ASME-AIChE Heat Transfer Conference, Chicago, 1958.

5. Griffith, P., and Wallis, G. D., "Two phase slug flow", Journal of Heat Transfer, Transactions of the ASME, Vol. 83, 1961, pp. 307-320.         [ Links ]

6. Levy, S., "Forced convection subcooled boiling - Prediction of vapour volumetric fraction", International Journal of Heat and Mass Transfer, Vol. 10, 1967, pp. 951-965.         [ Links ]

7. Metzner, A. A., and Reed, J. C, "Flow of non-Newtonian fluids - Correlations of the laminar, transition and turbulent flow regions", AlChE Journal, Vol. 1, 1955, pp. 434-440.         [ Links ]

8. Nickiin, D. J., Wilkes, J. D., and Davidson, J. F., "Two phase flow in vertical tubes", Transactions of the Institution of Chemical Engineers, Vol. 40, 1962, pp. 61-68.         [ Links ]

9. Oliver, D. R. and Wright, S. J., "Pressure drop and heat transfer in gas-liquid slug flow in horizontal tubes", British Chemical Engineering, Vol. 9, 1964, No. 9, pp. 590-596.         [ Links ]

10. Rohsenow, W. M., "Heat transfer with evaporation", Heat Transfer Symposium, University of Michigan, Summer 1952, University of Michigan Press, 1953.

11. Rohsenow, W. M., and Griffith, P., "Correlations of maximum heat flux data for boiling of saturated liquids", AIChE-ASME Heat Transfer Symposium, Louisville, Kentucky, 1955.

12. Rouhani, S. Z., and Axelsson, E., "Calculation of void volume fraction in the subcooled and quality boiling regions, International Journal of Heat Transfer, Vol. 13, 1970, pp. 383-393.         [ Links ]

13. Skelland, A. H. P., "Non-Newtonian Flow and Heat Transfer", John Wiley and Sons, Inc., New York, 1967.

14. Zuber, N., and Findlay, J. A., "Average volumetric concentration in two phase flow systems", Journal of Heat Transfer, Transactions of the ASME, Vol. 87, 1965, pp. 453-468.         [ Links ]