Influence of sintering on deposit formation during pool boiling of calcium sulphate solutions

Experimental Thermal and Fluid Science 34 (2010) 1439–1447

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Influence of sintering on deposit formation during pool boiling of calcium sulphate solutions M. Esawy a, M.S. Abd-Elhady b, M.R. Malayeri a,*, H. Müller-Steinhagen a,c,1 a

Institute for Thermodynamics and Thermal Engineering, University of Stuttgart, Pfaffenwaldring 6, D-70550 Stuttgart, Germany Department of Mechanical Engineering, Beni-Suief University, Beni-Suief, Egypt c Institute for Technical Thermodynamics, German Aerospace Centre, Pfaffenwaldring 38-40, D-70569 Stuttgart, Germany b

a r t i c l e

i n f o

Article history: Received 20 April 2010 Received in revised form 6 July 2010 Accepted 8 July 2010

Keywords: Crystallisation fouling Boiling Sintering Asymptotic behaviour Thermal desalination

a b s t r a c t The objective of this work is to determine the influence of sintering effects on crystalline deposits formed during pool boiling of CaSO4 solutions. Fouling experiments have been performed with plain tubes where the surface temperature of the heating element was varied to investigate its effect on boiling and crystallisation. Samples of the deposit layers were removed at the end of each fouling run for subsequent analysis using the scanning electron microscope. It was found that sintering of the fouling layer occurs if the temperature of the fouling layer is above a minimum sintering temperature, and that the fouling resistance reaches an asymptotic value if sintering takes place. Operating heat exchangers under pool boiling at a temperature above the minimum sintering temperature of the fouling layer accelerates the asymptotic behaviour and leads to a thinner and more compact deposit, compared to non-sintering conditions where the fouling layer thickness and thermal resistance continuously increase. Crystallisation fouling during pool boiling mainly occurs at sites where the steam bubbles grow, i.e. large pores in the deposit known as steam chimneys. However, as sintering takes place, the size and the number of pores are reduced, leading to reduced number and size of bubbles, and consequently to a declining fouling rate. For pool boiling heat transfer, the sintering-related change in fouling layer from a porous structure to a fully sintered structure is the main cause for the asymptotic behaviour. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction Scale formation or crystallisation fouling is defined as the precipitation of materials originally dissolved in process fluids on heat transfer surfaces, to form an additional resistance to heat transfer. While scale formation during convective heat transfer has most commonly been investigated (e.g. Bott [1]) some researchers have also attempted to understand and control fouling during pool boiling [2–4]. Theoretical considerations about the mechanisms of crystallisation fouling during pool boiling can be found in the review paper by Jamialahmadi and Müller-Steinhagen [5]. Scale deposits during boiling are formed from salts whose solubility decreases with increasing temperature [6], i.e. which have an inverse solubility [7]. Typical representatives of this group are calcium carbonate and calcium sulphate in water. Fouling due to calcium carbonate can be controlled by varying the acidity of the

* Corresponding author. Tel.: +49 711 68567656; fax: +49 711 68563505. E-mail addresses: [email protected] (M. Esawy), mohamedabd_elhady@ hotmail.com (M.S. Abd-Elhady), [email protected] (M.R. Malayeri), [email protected] (H. Müller-Steinhagen). 1 Tel.: +49 711 6862358; fax: +49 711 6862712. 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.07.007

water [8], while calcium sulphate precipitation is not significantly affected by the pH of the water. Kircher et al. [9] investigated the initial stages of calcium sulphate scale formation in seawater desalination at 100–150 °C. It was found that crystallites of calcium sulphate hemihydrate [10] first formed in the solution and then became attached to, and subsequently grew on the heated metal surfaces. The precipitation of scale poses serious problems during the evaporative purification of water. Jamialahmadi et al. [11] reported that boiling phenomena further enhance the problem of fouling in thermal seawater desalination units. Jamialahmadi and Müller-Steinhagen [8] studied calcium sulphate deposition on heat transfer surfaces during pool boiling. Calcium sulphate was dissolved in water and the influence of the concentration of calcium sulphate and the temperature of the heating surface on the fouling process was examined. The bulk temperature of the water was the saturation temperature with respect to the given pressure and CaSO4 concentration, and was always higher than 100 °C. In all the experiments an asymptotic fouling layer was reached. It was found that the density and thermal conductivity of the fouling layer increased with increasing temperature of the heating element. This was explained by the observation that, as time goes on, crystals became thicker and grew together.

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Nomenclature Ao Do Dth I k L q_ Ra Rf t To Ti

base area of heater (m2) base diameter of heater (m) diameter at the position of the thermocouples (m) heater current (A) thermal conductivity (W/mK) length of heating zone (m) heat flux (W/m2) arithmetic mean roughness (lm) fouling resistance (m2 K/W) time (s) outer surface temperature of the fouling layer (K) inner surface temperature of the fouling layer (K)

However, there are substantiated reasons to believe that sintering of the deposit may have taken place, as well. In general terms, sintering leads to the reduction of the void volume and the reinforcement of the contact bridges between the crystals or particles of the fouling layer [12]. It is, therefore, responsible for the decrease in porosity of the fouling layer as has been measured by Skrifvars et al. [13,14]. The reduction in porosity due to sintering also results in increased thermal conductivity as was observed by Rezaei et al. [15] for coal ashes and synthetic ash samples. Sintering of fouling layers occurs if the temperature of the layer exceeds the minimum sintering temperature [16], which is a property of the deposit material. The minimum sintering temperature is usually far below the melting point of the fouling layer material [17,18]. Malayeri et al. [19] performed similar experiments to [8] but for a tube bundle. It was found [8,19] that fouling layers at higher surface temperatures were denser, harder, more compact and more adherent than those formed at lower surface temperatures. Abd-Elhady et al. [20] studied the influence of the gas-side temperature on particulate fouling of a gas-cooler in a biomass gasifier. They observed that the particulate fouling rate in the gas cooler decreases with gas-side temperature, and that the fouling layer structure was powdery at the low temperature section, i.e. the economizer, and sintered at the high temperature section, i.e. the superheater. The observation of AbdElhady et al. [20] was concurring with the observations of van Beek et al. [21] for the structure of particulate fouling layers in waste incinerators. It can be concluded from the above literature survey that the fouling layer structure during boiling is highly sensitive with respect to the temperature of the heat transfer surface, which determines whether sintering will take place or not. The influence of sintering on crystallisation fouling during pool boiling is examined in the present investigation. Fouling experiments have been performed in which CaSO4 was used as foulant. Plain tubes are used as the heat transfer surfaces, i.e. the heating elements, and the temperature of the heating element is varied to investigate the effect of sintering on crystallisation fouling. The fouling resistance is measured continuously during the whole fouling experiment. Samples of the produced fouling layers are taken at the end of each experiment for analysis using the scanning electron microscope.

Tb Ts V

bulk temperature (K) surface temperature of heater (K) heater voltage (V)

Greek symbol a heat transfer coefficient (W/m2 K) Abbreviations FL fouling layer MST minimum sintering temperature SEM scanning electron microscope

main components of the setup are boiling vessel (1), loop for steam condensation and return to the vessel, preheater (4), power control units (5), and data acquisition system to record and analyze the input and output data. The boiling vessel is a cylindrical stainless steel tank with a 304 mm inner diameter and a capacity of 30 L. Two glass view ports are provided at each end of the vessel for visual observation. The vessel is heated externally by a resistance band heater (2). A closed flow loop including condenser (3) and preheater (4) is used to condense and preheat the evaporated liquid before returning it as saturated liquid to the vessel. An electrically heated rod of HTRI design is used for the experiments and is presented in Fig. 2. The heater is made of stainless steel with a smooth surface with a measured mean roughness of 0.6 lm using the Stylus instrument (perthometer M4Pi, Mahr, Götingen, Germany) and a maximum power of 500 kW/m2. Four E-type thermocouples are embedded into the heater to measure the wall temperature. One of these thermocouples is used to trip the power supply if the internal temperature of the heater exceeds a set limit. The condenser (3) is a three-stage single tube heat exchanger; the number of stages in operation can be adjusted according to the required heat flow rate. Centrally provided chilled water is used as coolant and controlled by a rotameter in conjunction with a manual flow control valve. A safety relief valve is fitted at the top of the flow circuit to relieve the pressure in case of a failure in cooling or power control. A set of power control units (5) is utilized to adjust the input power to the heater, consisting of variable transformers with an electronic temperature controller. Boiling vessel, condenser, preheater, and all pipes are insulated to minimize heat losses from the rig. For initial degassing of the test liquid, the pressure is reduced by a vacuum pump connected to a cold location of the condenser. To protect the vacuum pump from condensate, a steam trap is installed before the pump. An OMEGA PXM209 absolute pressure transducer is connected to the vessel (1) to measure the internal pressure. Three K-type thermocouples with the thickness of 3.5 mm are inserted inside the boiling vessel to measure the bulk temperature and the condensate return temperature. Output from one of these thermocouples is used to trip the variac power unit if the bulk temperature exceeds a set limit. An Agilent 34970A data acquisition system, with 34901A armature multiplexer was used for all temperature, pressure, voltage, and current measurements. A compatible PC was used to control the data acquisition unit and record all data via PCI–GPIB interface.

2. Experimental setup and experimental procedure 2.2. Preparation of CaSO4 solution 2.1. Pool boiling experimental setup A schematic diagram of the pool boiling test rig is shown in Fig. 1. The heat transfer coefficient at various heat fluxes and CaSO4 concentrations can be measured at atmospheric pressure. The

Saturated calcium sulphate test solution is prepared by directly dissolving calcium sulphate hemi-hydrate (CaSO41/2H2O) in distilled water. The weight W of the required calcium sulphate hemi-hydrate was calculated using the following equation:

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(7) (7)

(8) (2)

(3)

(6) (1)

(5) (4)

(1) Boiling vessel (5) Power control units

(2) Band heater (3) Condenser (6) HTRI heater rod (7) Data acquisition

(4) Preheater (8) Vacuum pump

Fig. 1. Schematic diagram of the pool boiling test rig.

216 mm

400 mm 99.1 mm A

10.67 mm Resistance heater

82.6 mm

A

Section A-A E-type Thermocouple Heater element

Power cable Fig. 2. Design of HTRI heater rod.

WðCaSO4  1=2H2 OÞ ¼ C b CaSO4  WðH2 OÞ     MWCaSO4  1=2H2 O 100   MWCaSO4 purity

ð1Þ

where Cb is the required bulk concentration, and MW is the molecular weight. The purity of the used calcium sulphate hemi-hydrate was found in several titration trials to be 90%. As calcium sulphate is difficult to dissolve in water, an ultrasonic device is initially used for 1 h, followed by stirring at 1400 rpm for 24 h. Afterwards the calcium sulphate solution was left for one more day to allow any remaining particles to settle. The test solution used for the present investigations had a CaSO4 concentration of 1.6 g/L, i.e. was saturated for the given bulk conditions. 2.3. Experimental procedure and data reduction Consistency of the experimental procedure is of prime importance due to the dominant influence of initial conditions on the subsequent deposition process. The heater rod is first carefully cleaned with distilled water and finally with acetone, to remove

any dirt from the surface. In addition, the heater had to be polished with sand paper to have similar mean roughness of 0.6 lm for all fouling runs. This procedure ensures that surface texture and roughness are comparable at the start of each fouling run. The boiling vessel is cleaned thoroughly from any remaining deposits from the previous fouling run. Afterwards the heater rod will be mounted and fixed horizontally into the vessel. Before filling the vessel with solution, it should be evacuated for about 1 h to check the system integrity and to remove air from the system. Prepared calcium sulphate solution will then be charged into the vessel using a 0.25 in. flexible sample line, until it is filled to a level approximately 3 cm below the top. The vessel is then left to continue degassing until the vacuum remains constant. Preheating of the solution to the saturation temperature is accomplished by switching on the vessel’s band heater. The vacuum pump is used at regular intervals during preheating to remove residual gases, since any dissolved gases present in the solution may affect the boiling heat transfer. Simultaneously the cooling water flow to the condenser is turned on at early stages to create a natural siphon and to provide degassing of the unheated section of the test

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rig. The data acquisition system is switched on to assess the stability of the operating conditions. After approximately 3 h of preheating the system becomes stable at saturation conditions. To ensure the consistency of the results, a comparison is made between the saturation temperature for the measured pressure and the liquid temperature measured by the thermocouples. Once steady-state conditions are confirmed, the power to the test section will be turned on by adjusting the power supply to the desired heat flux. The data acquisition system then records all inputs every 30 s and stores them as a Microsoft Excel spreadsheet. For determination of heat transfer coefficients, experimental data such as bulk temperature, heat flux, and average wall temperature of the tube are required. The bulk temperature is obtained by averaging the two bulk thermocouple readings. The heat flux is calculated using: :

q¼

VI Ao

ð2Þ

where V and I are the measured heater voltage and current, respectively, and Ao is the outside surface area of the heater which can be calculated as:

Ao ¼ pDo L

ð3Þ

where Do and L are the heater outside diameter and heated length, respectively. The correctness of measured heat fluxes and resultant heat transfer coefficients were examined when they were compared with well-established Gorenflo’s correlation for similar operating conditions for distilled water which resulted in good agreement between the experimental and the predicted results. There are also four embedded thermocouples, but one of them is used to trip the heater power if the surface temperature exceeds a certain limit. The surface temperature of the heater Ts is hence determined from three thermocouples located inside the heater wall and by assuming one-dimensional heat conduction through the wall as follows:

Ts ¼

3 1X T s;i 3 i¼1

ð4Þ

in which:

T s;i ¼ T th;i 

  Do q_ Do ln 2k Dth

ð5Þ

Here, k is the heater thermal conductivity which is temperaturedependent and Dth is the diameter at the position of the thermocouples. The average heat transfer coefficient (a) can then be determined as:

a¼

q_ ðT s  T b Þ

ð6Þ

Finally the fouling resistance Rf due to deposition of calcium sulphate is calculated as a function of time as:

Rf ¼

  1

a

t



  1

a

ð7Þ 0

or

Rf ¼

    Ts  Tb Ts  Tb  q_ q_ t 0

ð8Þ

where subscripts t and 0 denote conditions at any time and at the beginning of the experiment when the heater is considered to be clean. 2.4. Experimental error and uncertainty analyses Experimental errors of heat transfer coefficients and resultant fouling resistances are due to associated errors of heat fluxes, surface and bulk temperatures. A bias error of approximately ±2% is

due to current and voltage for the measurement of heat flux. The systematic errors of both the bulk and surface temperatures are approximately ±0.4 K. Uncertainty with 95% confidence is calculated for both heat transfer coefficient and fouling resistance at the beginning and end of a fouling test of 1.6 g/L CaSO4 and 185 kW/m2. For heat transfer coefficient, it changed from 6.7% to 2.9% while for fouling resistance from 24% to 4.8%, respectively. Eqs. (6) and (8) also underline that the largest experimental uncertainty for both heat transfer coefficient and fouling resistance occurs for the smallest temperature difference, i.e. at the start of the experiment. 3. Experimental results 3.1. Constant heat flux experiments The variation of fouling resistance (Rf) as a function of time for a heat flux of 185 kW/m2 (which corresponds to an initial surface temperature of 130 °C) and a concentration of 1.6 g/L is shown in Fig. 3. It can be seen that the fouling process consists of several consecutive stages, which can be defined via the fouling rate. As shown in detail in the additional graph on the left of Fig. 3a, the fouling resistance at the very beginning of the fouling process, i.e. during the first few hours of operation, increases rapidly until it reaches a peak. It then drops towards a minimum after which it increases again, linearly. This fouling behaviour at the beginning of operation during nucleate boiling has been observed by several researchers, e.g. Palen and Westwater [3] and Jamialahmadi et al. [5,11,22]. During the following first stage of fouling, dRf /dt = constant, i.e. the deposition rate is constant and the fouling resistance increases linearly with time. In the second stage, the fouling rate decreases with time until it approaches zero in the last stage of fouling where a constant or asymptotic fouling resistance is reached. Ignoring the initial deposition behaviour, regions 1–3 in Fig. 3a represent the dominant consecutive stages of fouling, i.e. constant and decreasing fouling rates as well as the asymptotic behaviour. Abd-Elhady [23] showed that the main reason behind the change in the fouling rate during particulate fouling in biomass gasifiers is due to the change in the fouling layer structure, which occurs by sintering. Sintering changes the fouling layer structure from powdery and porous to a robust and non-porous structure and it occurs if the temperature of the fouling layer is above the minimum sintering temperature (MST). The MST ranges from 2/3 to 4/5 of the melting point of the concerned material [24]. Since the melting point of calcium sulphate hemi-hydrate (CaSO41/2H2O) is about 163 °C [25,26], it may be concluded that the MST for CaSO41/2H2O ranges from 109 °C to 130 °C depending on the purity of the material. The surface temperatures of the inner and outer surfaces of the fouling layer is presented in Fig. 3b. The inner surface of the fouling layer is the surface attached to the heater and the outer surface is the surface at the solution side, as shown in Fig. 4. The temperature of the inner surface of the fouling layer (Ti) is equal to the surface temperature of the heater, which is measured with the three thermocouples installed along the circumference of the heating element, and the average of these readings is taken. The outer surface temperature of the fouling layer (To) can be approximated from the measured Ti and the fouling layer thermal resistance Rf by

_ f T o ¼ T i  qR

ð9Þ

where q_ is the heat flux. It can be seen that the temperature of the outer surface of the fouling layer is between 110 °C and 117 °C which is at the border to sintering. However, the temperature of the inner surface of the

M. Esawy et al. / Experimental Thermal and Fluid Science 34 (2010) 1439–1447

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Fig. 3. Fouling resistance (a) and inner and outer surface temperatures of the fouling layer (b) as a function of time. The Sections 1–3 are the three stages of fouling, i.e. constant fouling rate, decreasing fouling rate and asymptotic behaviour. The heat flux is 185 kW/m2 and the calcium sulphate concentration of the solution is 1.6 g/L.

Solution side

Outer surface of FL, i.e. top of FL Inner surface of FL, i.e. bottom of FL

Heating element

Fouling layer (FL) Fig. 4. Fouling layer (FL) position with respect to heating element and solution.

fouling layer is always higher than 130 °C (185 kW/m2) which indicates that sintering at the inner surface will take place during the whole fouling process. A sample of the fouling layer was removed

at the end of the experiment, and the inner and outer surfaces of the fouling layer, i.e. top and bottom of the fouling layer, were observed under the SEM, as can be seen in Fig. 5. It can be seen that the top and more noticeably the bottom of the fouling layer are non-porous indicating that the crystalline deposits have become connected to a sintered fouling layer over the course of the experiment since the temperature on both sides was above the MST. In the top layer, individual clusters can still be identified, which are in a less homogeneous state, whereas the bottom of the sample has sintered into a completely flat layer. This experiment has been repeated and four fouling samples were taken and analysed which all showed similar behaviour. The surface roughness of the fouling layer has been measured using the Perthmeter M4Pi (Mahr GmbH, Germany), and it was found that the arithmetical mean roughness (Ra) of the top of the fouling layer is equal to 2.2 lm while for the bottom of the layer a value of 0.71 lm was measured. It can be inferred from the surface roughness measurements and the SEM

Fig. 5. SEM image of the inner surface (a) and the outer surface (b) of fouling layer (heat flux 185 kW/m2 and concentration 1.6 g/L). The fouling layer examined is the layer at the asymptotic stage of fouling.

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images that the layer structure near the surface of the heater is smoother than the layer structure on the fluid side. This is attributed to the higher temperature at the inner surface of the fouling layer compared to outer surface, which leads to a higher sintering rate at the inner surface than at the outer surface, and hence a more compact and smoother surface. Bubble nucleation and detachment occur at the outer surface of the fouling layer, i.e. the surface in contact with the solution, assisting the shear-related removal of some crystals from the outer surface of the fouling layer, and consequently leading to a rough surface. The above experiment was repeated to investigate the change in the fouling layer structure during the different stages of fouling. The first experiment was stopped after 10 h of operation, i.e. during the constant fouling rate stage; and the second experiment was stopped after 30 h of operation, i.e. during the decreasing fouling rate stage. A further sample was taken at the end of each experiment and inspected using SEM. The fouling layers after 10 h and 30 h of operation are shown in Figs. 6 and 7, respectively. It can be clearly seen that the structure of the fouling layer near the heated surface is highly sintered and non-porous. At the solution side, the fouling layer has a needle-like shape in Fig. 6 and is rough and porous in Fig. 7. The outer surface of the fouling layer after 30 h of operation is less porous and more compact than in the case

Solution – side (Outer surface of FL)

of 10 h, also the needle-like shape after 10 h of operation is sharper than after 30 h of operation. Jamialahmadi and Müller-Steinhagen [5] and Malayeri et al. [19] showed that as the deposition process continues, the deposited layer increases in compactness and density as well as becoming more adherent to the heating element surface (see Table 1). This has been explained by the fact hat the crystals have become thicker and grown together. However, as the crystals grow in size and numbers, the sintering will ultimately the mechanism to achieve a homogeneous and compact fouling layer. The porosities of fouling layer have also been calculated for

Table 1 Thermal conductivity (wet), density (dry) and porosity of deposit layer from a CaSO4 solution with a concentration of 1.2 g/L [5]. Heat flux (W/m2)

Thermal conductivity (W/m K)

Density (kg/m3)

Porosity (-)

9631 19,261 28,892 77,045 249,964 301,204

0.75 0.85 1.09 2.1 2.09 2.2

1270 1870 2120 2420 2429 2445

0.671 0.626 0.517 0.059 0.063 0.014

Heater– side (Inner surface of FL)

Fig. 6. Cross-section of the fouling layer (FL) deposited on the heating element after 10 h of experiment. The examined fouling layer is obtained during the first stage of fouling, i.e. constant fouling rate (the heat flux is 185 kW/m2 and the calcium sulphate concentration of the solution is 1.6 g/L).

Fig. 7. SEM image of the inner surface (a) and the outer surface (b) of the fouling layer after 30 h of operation. The examined fouling layer is obtained during the second stage of fouling, i.e. the decreasing fouling rate (the heat flux is 185 kW/m2 and the calcium sulphate concentration of the solution is 1.6 g/L).

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Fig. 8. Fouling resistance (a) and inner surface temperature of the layer (b) as a function of time. The concentration of the solution is 1.6 g/L.

different heat fluxes from thermal conductivities which are given in Table 1. The values of the calculated porosity are reasonable as by increasing heat flux the porosity decreases, consequently the thermal conductivity increases. It can hence be concluded from the performed SEM analysis that sintering of the fouling layer is an on-going process which starts at the inner side of the fouling layer, near the heated surface where the temperature of the layer is higher than the MST, and spreads across the layer. Sintering is a time and temperature dependent process. In the above experiment the heat flux was kept constant and the operating time was varied, such that the longer the experiment continued the more sintering was obtained. 3.2. Variable heat flux and constant operating time experiments

MST of the fouling layer which has is somewhere between 110 °C and 130 °C. However, the inner temperature of the fouling layer for the 40 kW/m2 experiment was always below 120 °C, which is likely to be lower than the MST. This implies that the fouling layer during nucleate boiling reaches an asymptote if sintering takes place, or continues and grows as long as no sintering occurs. The fouling rate during the initial stage of fouling in case of a heat flux of 300 kW/m2 is 5  109 m2 K/J, as can be extracted from Fig. 8a. This is twice the fouling rate for 185 kW/m2 which is about 2.5  109 m2 K/J, and 13 times higher than the fouling rate for 40 kW/m2 which is about 3.8  1010 m2 K/J. In addition it has been observed that the fouling resistance reached an asymptotic value after 20 h of operation for 300 kW/m2, while it took 60 h of operation for 185 kW/m2. This underlines the fact that the higher

Asymptotic Rf [m2K/W]

The above experiment is repeated but at different heat fluxes of 300 kW/m2 and 40 kW/m2, i.e. at different temperatures of the heating element, to investigate the influence of the temperature of the heat transfer surface on the fouling process. The fouling resistance is presented in Fig. 8a as a function of time and heat flux, together with the corresponding inner surface temperatures of the fouling layer in Fig. 8b. Firstly, it can be seen that fouling resistance for 40 kW/m2 is much lower than the other two heat fluxes. This is because for lower heat fluxes which correspond to lower surface temperatures, fewer bubbles are generated on the surface. Thus less fouling is expected, i.e. lower fouling resistance. Secondly, asymptotic values were reached for heat fluxes of 300 kW/m2 and 185 kW/m2, while a linear increase in the fouling resistance occurred for 40 kW/m2. This can be attributed to the operating conditions, i.e. the surface temperature of the fouling layer. The inner temperature of the fouling layer varied from 130 °C to 211 °C for the heat flux of 300 kW/m2 and from 130 °C to 180 °C for 185 kW/m2. All these temperatures are certainly higher than the 3.0x10-4 2.5x10-4 2.0x10-4 1.5x10-4 1.0x10-4 0

50

100

150

200

250

300

Heat flux [kW/m2] Fig. 9. Asymptotic fouling resistance versus heat flux for a concentration of 1.6 g/L and the surface roughness of 0.4 lm (adopted from Jamialahmadi and MüllerSteinhagen [8]).

Fig. 10. Hypothetical boiling mechanism from porous deposit according to Macbeth [31] during the first stage of fouling (a) where sintering has not started, and at the last stage of fouling (b) where sintering has become effective and reduced the porosity of the fouling layer.

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the surface temperature is above the MST, the faster the sintering process becomes, as has been stated by Ristic [12]. The asymptotic fouling resistance in case of a heat flux of 300 kW/m2 is 3  104 m2 K/W, which is lower than the asymptotic value for 185 m2 K/W which is 3.21  104 m2 K/W. It can be concluded that increasing the surface temperature or in other words the heat flux results in decreasing the asymptotic fouling resistance. This conclusion is consistent with the work of Jamialahmadi and Müller-Steinhagen [8], who investigated the influence of heat flux on calcium sulphate scaling during pool boiling. Values of the asymptotic fouling resistances as a function of heat flux are evaluated from the results presented in [8] and are plotted in Fig. 9. It can be clearly seen that as the heat flux (and hence the surface temperature of the heating element) increases, the asymptotic fouling resistance decreases.

4. Discussion Crystallisation fouling comprises of nucleation and crystal growth, as concluded by Mullin [27]. Nucleation is the process

where minute crystalline nuclei are formed, while crystal growth is the ordered growth of these nuclei into larger well-formed crystals, as defined by Bott [1]. Crystal growth can only occur after nuclei are formed [1], and the attainment of supersaturation is essential for crystallisation to occur. Bubbles of steam that are generated on the heated surface during pool boiling lead to a triple interface between the solid heat transfer surface, the liquid solution and the steam [28]. The microlayer beneath the bubble evaporates according to Mikic and Rohsenow [29]. Najibi et al. [30] showed that microlayer evaporation at the base of the bubble increases the local concentration of calcium sulphate in the liquid beneath the bubble significantly and hence the possibility of precipitation. After the release of the bubble, liquid will flow towards the surface to replace the volume originally occupied by the bubble. The sequence is repeated and thus a deposit layer gradually builds up on the heat transfer surface. This deposit layer is initially porous and results in boiling characteristics that are quite different from those of the originally clean surface. Porous deposits contain pores with different shapes and sizes connected together. Macbeth [31] observed steam issuing from

Fig. 11. Bubble size (a) at the beginning of the experiment, (b) during the first stage of fouling and (c) at the asymptotic stage. The heat flux is 300 kW/m2 and the calcium sulphate concentration 1.6 g/L.

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the pores in the deposit which he termed ‘‘steam chimneys”. The liquid containing the foulant imbues the small pores in the fouling layer in the direction of the heat transfer surface due to capillary forces [31]. These small pores are connected to larger pores, which are the steam chimneys, as shown in Fig. 10a. The steam flows in the steam chimneys if the capillary pressure is sufficient to overcome the frictional pressure drop in the chimneys, and that can happen if the diameter of the chimney is larger than that of the wetted pores. As the steam bubbles depart from the steam chimney, they leave behind deposits which formed at the base of the bubbles due to microlayer evaporation and the associated increase in the local calcium sulphate concentration. Steam bubbles generated at the beginning of the experiment, during the first and during the last stage of fouling are shown in Fig. 11. The steam bubbles at the beginning, i.e. before any deposit is formed, are small and limited in number (see Fig. 11a). Then, during the first stage of fouling where the deposit is highly porous, they become large and numerous as shown in Fig. 11b. Subsequently, their number and size decreases again reaching a minimum at the third stage of fouling, i.e. the asymptotic stage (see Fig. 11c). These observations agree with those of Jamialahmadi and Müller-Steinhagen [8], who found that the initial presence of deposit sharply increased the number of active sites compared to the beginning of the experiment and that the number of active nucleation sites then decreased with time [8]. They have also measured quantitatively the bubble diameter and shape for a heat flux of 19 kW/m2 and 1.6 g/L concentration of CaSO4 in different time steps which concur with observations of the present study [8]. The steam chimneys have a comparably large diameter at the beginning as depicted in Fig. 10a, which lead to the production of large steam bubbles. However, as sintering takes place the porosity of the fouling layer decreases, thus reducing the size of the pores and hence the diameter of the departing bubbles. This can be seen in Figs. 6 and 7, and is schematically represented in Fig. 10b. The steam chimneys are blocked when the fouling layer is strongly sintered, i.e. the porosity of the fouling layer reaches zero as in the case shown in Fig. 5. The resulting drop in the number of active nucleation sites consequently decreases the deposition rate until the asymptotic region is reached. It can also be concluded that sintering would also facilitate the aging process of deposit layer when it becomes more dense and solid thus harder to remove. 5. Conclusions Sintering of fouling deposits occurs if the local temperature is above the minimum sintering temperature (MST). Operating heat exchangers with pool boiling at a temperature above the minimum sintering temperature of the fouling layer accelerates the asymptotic behaviour and leads to thinner and more homogeneous fouling layers compared to non-sintering conditions, where the fouling layer thickness and the thermal resistance continuously increase. This trend increases with increasing heat flux and hence surface temperature. Crystallisation fouling during pool boiling occurs at nucleation sites where the steam bubbles exist. As the steam bubbles depart from the nucleation sites, precipitation of new deposits occurs at the base of the bubble due to microlayer evaporation, which leads to an increase in the local concentration of calcium sulphate. As crystals grow in size and numbers, they connect and form porous structure with steam chimneys. However, once the surface temperature exceeds the minimum sintering temperature, the porosity of the fouling layer decreases leading to decreasing bubble number and size, and consequently declining fouling rate. The channels of the steam chimneys are completely blocked when

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