Relationships between the characteristics of CaCO3 fouling and the flow velocity in smooth tube

Accepted Manuscript Relationships between the characteristics of CaCO3 fouling and the flow velocity in smooth tube Liang-Chen Wang, Su-Fang Li, Liang-Bi Wang, Kai Cui, Qiao-Ling Zhang, Hong-Bin Liu, Gang Li PII: DOI: Reference:

S0894-1777(15)00344-1 http://dx.doi.org/10.1016/j.expthermflusci.2015.12.001 ETF 8644

To appear in:

Experimental Thermal and Fluid Science

Received Date: Revised Date: Accepted Date:

30 July 2015 17 November 2015 5 December 2015

Please cite this article as: L-C. Wang, S-F. Li, L-B. Wang, K. Cui, Q-L. Zhang, H-B. Liu, G. Li, Relationships between the characteristics of CaCO3 fouling and the flow velocity in smooth tube, Experimental Thermal and Fluid Science (2015), doi: http://dx.doi.org/10.1016/j.expthermflusci.2015.12.001

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Relationships between the characteristics of CaCO3 fouling and the flow velocity in smooth tube Liang-Chen Wang a, c, *, Su-Fang Li a, Liang-Bi Wang b, c, Kai Cui a, Qiao-Ling Zhang a, Hong-Bin Liu a, Gang Li a a

School of Chemical Engineering, Lanzhou Jiaotong University, 88 West Anning Rd., Lanzhou 730070, P. R. China

b

Department of Mechanical Engineering, Lanzhou Jiaotong University, 88 West Anning Rd., Lanzhou 730070, P. R. China c

Key Laboratory of Railway Vehicle Thermal Engineering (Lanzhou Jiaotong University), Ministry of Education of P. R. China, P. R. China Corresponding author: Liang-Chen Wang

* School of Chemical Engineering /Lanzhou Jiaotong University, fax: +86-931-4956556, 88 West Anning Rd., Lanzhou 730070, P. R. China Email: [email protected] Tel:+86-931-4956556 Fax:+86-931-4956556

Abstract The objective of this investigation is to study the effect of flow velocity on the calcium carbonate fouling in smooth tube. A number of experiments have been performed to determine the whole process of calcium carbonate deposition in a double pipe heat exchanger in a long term. Seven correlations of the fouling growth characteristics associated with Nusselt number ratio of the tube inner surface (Nu/Nu0), Reynolds number (Re) and dimensionless time (τ) have been established to describe four distinct time regions: a region where the thermal resistance is positive, a region where the fouling thermal resistance is negative, a region where the fouling resistance increases steady, and a region where the fouling thermal resistance remains constant. The index of n in dimensionless parameter τRen divided fouling process into four distinct time regions is related to the flow state in the tube: for laminar flow, n = -0.695; for transitional flow, n = -0.66; and for turbulence flow n = -1.1. The correlations between Nu/Nu0, Re and τ in the different regions are different. The 1

correlations are more consistent when flow states are laminar flow and transitional flow than when flow state is turbulent flow. The results indicate that fouling has two aspects regarding the effects on fluid flow as well as thermal performance of the heat exchanger in the induction period: an increased surface roughness, and followed by the decrease in metallic surface area of the test tube as fouling progresses. In laminar flow or transitional flow the fouling rate increases quickly with increasing velocity and the formation of the deposits may be controlled by the molecular transport. However, in turbulence flow the flow velocity has less effect on the fouling rate and the formation of the deposits may be controlled by the chemical reaction and the shear force enforced by fluid flow. Keywords: CaCO3 fouling, Reynolds number, Heat transfer, 316L stainless steel smooth pipe, Roughness delay period

Nomenclature A

heat transfer area [m2]

cp

specific heat of process solution [kJ/(kgK)]

d

diameter of the test tube [m]

K

overall heat transfer coefficient [W/(m2K)]

K′

overall heat transfer coefficient at start (time t = 0) [W/(m2K)]

L

length of the test tube [m]

Kso

the thermodynamic solubility product of calcium carbonate [(mol)2/L2]

G

Gibbs free energy [kJ]

h

heat transfer coefficient of the inside tube [W/(m2K)]

h′

heat transfer coefficient of the test tube for operating with distilled water [W/(m2K)]

Nu

Nusselt number [-]

Pr

Prandtl number [-]

Q

rate of heat transfer [W]

R

the gas constant [J/(molK)]

Re

Reynolds number [-] 2

Rf

fouling resistance [m2K/W]

S

the supersaturation ratio [-]

t

time [s]

T

temperature [K]

Th

temperature of the hot fluid [K]

Tc

temperature of the cold fluid [K]

ΔTm

log mean temperature difference [K]

t

the time to reach asymptote [h]

u

flow velocity [m/s]

V

volume flow rate [m3/s]

w

mean growth rate of fouling [kg/(hm2)]

Greeks δ

thickness of the viscous sub layer [mm]

λ

heat conductivity of fluid [W/(mK)]

λt

heat conductivity of the test tube [W/(mK)]

μ

average viscosity of fluid [Pas]

ρ

density [kg/m3]



shear stress [N/m2]



dimensionless time [-]

w

mass increment of fouling deposited in t and per unit area [kg/m2]

Subscript i

inside of the test tube

m

mean or average value

o

outside of the test tube

1. Introduction Fouling is the deposition of unwanted material on a heat transfer surface, which diminishes the heat transfer and deteriorates the performance of the process equipment and 3

even worse causes unscheduled equipment shutdown [1]. Fouling is generally classified in six categories: crystallization, particulate, reaction, corrosion, biological, and solidification, among which crystallization accounts for over 25% of fouling problems encountered [2]. Crystallization fouling on the heat transfer surface is usually caused by the crystallization of inverse solubility salts, which are highly temperature-dependent and require a degree of super-saturation before precipitation occurs. Crystallization fouling process is commonly divided into two periods, i.e. induction and fouling period [3-5]. In the induction period stable nuclei is formed and the crystal growth is taken place on the heat transfer surface. In the succeeding fouling period a compact fouling layer is built up slowly [6]. In water cooling systems, calcium carbonate is the predominant component of hard and tenacious fouling. Mechanism of crystallization fouling on the heat transfer surface is usually defined to two main steps: transport of ions from the bulk to the liquid-crystal interface and integration of ions into the crystal lattice at the surface. The mass transport step is attributed to the molecular transport of ions through the laminar boundary layer at the surface. The attachment step is described by the strongly temperature dependent surface integration of ions into the crystal lattice [7-9]. Depending on the operation conditions, crystallization fouling on the heat exchanger surface can be (i) transport controlled (mass transfer), (ii) reaction controlled (chemical kinetic), or a combination of both [10]. The characteristics of crystallization fouling on the heat exchanger surface have mainly been studied on the performance of tubular or micro-channel heat exchangers under crystallization fouling conditions [11]. The crystallization fouling condition includes hydrodynamic and thermal conditions of the system, but also relates to chemical kinetics,

4

thermodynamics and material properties [12]. The influence of flow velocity as the hydrodynamic condition has been studied intensively. Flow velocity has a clear effect on the fouling rate [13,14]. When the working medium flows, eddies and shear forces have directly affected on both of the deposition and removal rates of fouling on the heat transfer surface. On the other hand, the flow velocity has indirect effects on deposition strength, the mass transfer coefficient, and the stick ability. For a double pipe exchanger, Hasson et al. [15] have investigated the separating effects of flow velocity, scaling surface temperature, and water composition according to the rate model. Under conditions that the CaCO3 concentrations range from 110 to 575 mg/L, the surface temperature ranges from 67 to 85 ºC, Reynolds numbers changes from 13000 to 42000, and the corresponding flow velocity changes from 0.25 m/s to 0.82 m/s, they have found that CaCO3 deposition is mainly controlled by the forward transport rate of Ca2+ and HCO3- ion and the transport is increased by increasing velocity. When the CaCO3 concentration is about 250-1000 mg/L, Helalizadeh et al. [16] show that fouling of CaCO3 is controlled by the transport when the flow velocity changes from 0.4 m/s to 0.8 m/s, which corresponds Reynolds numbers from 20000 to 50000, but as the velocity increases from 0.8 m/s to 1 m/s or Reynolds number increases from 50000 to 65000, the surface integration controls the fouling process. When the CaCO3 concentration is about 350-750 mg/L, Najibi et al. [17] have studied the effects of flow velocity on the calcium carbonate fouling resistance for constant initial surface and bulk temperature, as Reynolds number changes from 27500 to 65000, which corresponds the flow velocity changes from 0.7 m/s to 1.6 m/s. They have obtained that molecular diffusion has a significant effect on the fouling rate at low flow velocity, as flow velocity increases, the boundary layer thickness

5

decreases, when Reynolds number is larger than 40000, the fouling rate is surface integration controlled. Pääkkönen et al. [7] have investigated the effects of the shear forced on the calcium carbonate fouling in a plate heat exchanger, the CaCO3 concentration is about 340 mg/L, Reynolds number changes from 5200 to 10400, which corresponds the flow velocity changes from 0.20 m/s to 0.40 m/s. The results show that the surface crystallization is found to be controlled by the strongly temperature dependent surface integration step, increasing flow velocity at the constant initial wall temperature decreases the fouling rate, which indicates that mass transfer does not determine the surface crystallization fouling processes, but the shear forces at the wall may prevent the crystals to attach to the surface when the flow velocity is high. However, in micro-channel heat exchangers the characteristics of crystallization fouling on surface is different from tubular heat exchangers. Moriz et al. [18] have investigated the impact of CaCO3 fouling on a micro-scale heat exchanger within flow rates from 10 to 40 mL/min, Reynolds number ranges from 66 to 264, and the CaCO3 concentration is about 500 mg/L. They demonstrate that the fouling resistance is small at higher flow rates (40 mL/min, Reynolds number is 264) and the crystallization fouling process is reaction controlled. Crystallization fouling is commonly preceded by an induction in which no significant change of thermal resistance is observed with increasing time, with exception of fouling under boiling conditions [19]. The influencing factors on the induction can be subdivided into two divisions [20]. One is process condition, such as salt concentration, super-saturation and pH value, flow velocity and regime, and additives. The other is interface condition, such as temperature, surface energy, roughness and topography, amount of nucleation spots, aging of

6

the fouling layer and the surface. In division of the process condition, the flow velocity is one factor that probably has the detrimental impact on the induction. Bansal et al. [21] has investigated the effect of the velocity on the CaSO4 roughness delay time in plate heat exchanger over the range of 0.2-1 m/s, the roughness delay time decreases with increasing the flow velocity from 0.2 to 0.55 m/s. When flow velocity is larger than 0.55 m/s, the thickness of the viscous sub layer as well as the wall temperature decreases, owing to the effect of turbulence, resulting in an increase in the induction time. Mwaba et al. [2] have studied the fouling of calcium sulfate on a flat plate, with increasing Reynolds number from 11000 to 34000, the induction time increases, the fouling rate decreases. Yang et al. [4] have investigated the CaCO3 fouling experiments in both cooling water and pool-boiling systems. The results show that the induction period increases with decreasing initial surface temperature and flow velocity. As the heat flux is fixed, the induction period increases with increasing flow velocity. As mentioned above, the flow velocity is an important factor for fouling types. Much more research needs to be carried out on the effect of velocity because its effect is much more complex than that of surface temperature [19]. Generally, it is accepted that a high velocity will damp fouling, but it is not certain exactly how velocity affects the fouling rate. The experiments to find a correlation between fouling rate and flow velocity are carried out in many references. Hasson et al. [15] has found that the scale-growth rate is the Reynolds number power 0.716 under the constant heat-flux conditions. Budair et al. [22] has developed a dimensionless fouling resistance model. The model is defined the fouling resistance (Rf) as a function of time, tube diameter, tube surface temperature and Reynolds number. Fahiminia et

7

al. [23] have derived a correlation between the induction period and super-saturation ratio at any given flow velocity and surface temperature based on classical nucleation theory. They find that for any given flow velocity and surface temperature, there is an Arrhenius relationship between the reciprocal of the induction period and the surface temperature. Mwaba et al. [2] has developed a semi-empirical correlation for crystallization fouling on heat exchange surfaces. The model is defined the fouling resistance (Rf) as a function of deposit strength, fluid shear stress, temperature, the time to reach asymptote and the induction time, solution properties and heat exchanger surface dimensions. Yang et al. [19] have developed a simple lumped parameter model based on fractional surface coverage θ to correlate experimental data in the induction period. They have integrated the fractional free surface (1θ), the fouling growth rate constant k1 and the removal rate constant k2 to obtain the relationship dθ/dt = k1θ (1- θ) - k2θ. The fouling layer grows on the covered surface and the fouling rate can be expressed as θRf', where Rf' can be any established fouling rate expression. Experimental data obtained during induction periods have been successfully correlated for systems including crude oil fouling, water scaling and whey protein fouling. However these models can not apply to the whole deposition process or all flow states. In summary, the above review shows that effects of the flow velocity on the fouling of CaCO3 on heat transfer surface are studied intensively. Many papers have focused on studying the effects of fouling on the heat transfer with higher velocity in many literatures, but the effects of low velocity on the heat transfer are reported fewer. Much reported data is obtained under accelerating fouling conditions, it is very necessary to adopt the actual working conditions to study the characteristics of CaCO3 crystallization fouling [24]. There are a few

8

reports which are focused on studying the characteristics of CaCO3 crystallization fouling in the induction period. The main reason for this can be attributed not only to the complexity of the fouling behavior in the induction period but also to the fact that no additional information can be gained when the induction period occurs in the experiments, since it appears as a steady state phenomenon, and no useful data can be collected. The flow velocity mostly is studied ranges from 0.2 m/s to 1.6 m/s, and flow state is turbulent flow. Some very important results are obtained. Unfortunately, these results still can not provide a more appropriate description of the effects of flow velocity on a fouling history (from the beginning of fouling to the dynamic steady state of fouling). This means that the deep mechanism of the velocity effects on the fouling of CaCO3 should be addressed additionally. Motivated by this, the present study not only tries to find the effects of flow velocity on the fouling characteristics of CaCO3, but also makes effort to cast the results into a correlation for deeper insights on the mechanism of the velocity effects on the fouling of CaCO3. In view of this, the paper mainly study the characteristics of CaCO3 crystallization fouling in double pipe heat exchanger of stainless steel smooth tube as the flow velocity ranges from 0.06 to 0.8 m/s (Reynolds number ranges from 618 to 9406) in a long run. In experimental processes, the inlet temperatures of the double pipe heat exchanger, the temperature differences between the outlet and the inlet of tube side, pH value and concentration of the test solution remain constant. Under different flow velocity the fouling resistance variation with time is recorded, the correlations of the fouling growth characteristics associated with Reynolds number and fouling time are established. 2. Experimental setup and procedure

9

2.1 Experimental setup Experiments are performed in a laboratory setup a double pipe heat exchanger. The schematic view of the experimental system is shown in Fig. 1. It contains four double pipe heat exchangers (with four same double pipe heat exchangers connected in parallel), a thermostatic water tank (30 L, 5000 W power), a water cooler, a cooling water tank with a agitator for containing the test solution, a circulating pump, a peristaltic pump, two tanks (2.5 L) with one for containing NaHCO3 solution and the other for Ca(NO3)2 solution, the rotameters and a computer controlled data acquisition system. A peristaltic pump with two heads can operate at 0.002-500 mL/min per head (≤ 50 W, 1-100 rpm motor). The test solution circulating pump can operate at 10 L/min with a maximum head of 8 m (45 W, 2800 rpm motor). The test tube is made by stainless steel (AISI 316L). The size of the test tube is ø8×1±0.05 mm and length of 1±0.001 m, the hydraulic diameter is 6 mm. The size of the shell of the double pipe exchanger is ø32×2.5±0.05 mm and length of 1.06±0.001m, the hydraulic diameter is 20.2 mm. To consider the effect of surface roughness on fouling formation, the inner wall of the test tube is polished. A digital profile meter is employed to record the surface roughness of the heating section. The surface roughness is between 0.03 and 0.04 mm which could be considered as a standard smooth surface roughness. Then the test tube is cleaned with acetate, followed with acetone, and finally with distilled water. The test solution is contained in the 304 stainless steel cylindrical tank, diameter of 330 mm and height of 800 mm, there are three baffles (are made by 304 stainless steel, length of 250 mm, width of 30 mm and thickness of 2 mm) are welded vertically on the inner wall of the tank,

10

the angle between two adjacent baffles is 120 degrees. The tank capacity at the top mark is 25 L. The stirrer of the tank is a propeller impeller with three agitator blades (are made by 304 stainless steel having a diameter of 120 mm). The speed of the stirrer is controlled by a variable speed drive. The inlet and outlet temperatures of all the fluids are measured by using calibrated K-type thermocouples (with their cold ends immersed in an ice bucket, and the maximum error is ±0.1 oC). The test solution and hot water flow are measured by the rotameters (the maximum error at the small flow rates is ±0.1 L/h, and ±0.5 L/h for the big flow rates). The concentration of the test solution is maintained the initial level by adjusting the speed of the peristaltic pump. A computer controlled data acquisition system is used to record a set of temperature data every 3 minutes.

Fig. 1 Experimental setup

2.2 Test solution 11

Calcium carbonate crystals exist in three forms: aragonite, calcite and vaterite. All three forms of this salt have an inverse solubility with temperature. CaCO3 crystallization fouling is diverse, complex and long-term in the actual work conditions. To simulate the conditions encountered in water cooling system, the sources of calcium ion and carbonate ion are calcium nitrate (Ca(NO3)2) and sodium bicarbonate (NaHCO3). The solutions are prepared using deionized water. The concentration of bulk solution is 375±38 mg/L (as CaCO3). The concentration of the test solution is measured by ethylene diamine tetra acetic acid (EDTA) titration. The temperature and pH of the test solution are monitored throughout the whole process. A crystallizing CaCO3 layer may deposit on the test tube from a supersaturated solution flowing through the test tube. The overall reaction involved in the wall crystallization process of CaCO3 is [15,25]

Ca2+ + 2HCO3-

CaCO3 (s) + CO2 + H2O

(1)

The mechanisms involved are an initial crystallization reaction: Ca2+ + CO32-

CaCO3 (s)

(2)

2.3 Experimental procedure The experiments are conducted in a controlled laboratory environment. In each run, the thermostatic water tank is first filled with deionized water and heated to 80 oC by electrical heating. When the desired temperature is obtained, hot water is pumped and then allocated to the shell of four double pipe heat exchangers simultaneously, and finally returned to the thermostatic water tank. Then, the known volume deionized water is filled in the cooling water tank. The distilled water instead of the test solution is circulated through the whole set-up until the temperature of the cooling water tank is about 47.5±0.5 oC, and the

12

temperature differences of the outlet and the inlet of four test tubes are controlled at about 10 o

C by adjusted the flow rate of hot water through the shell of four double pipe heat

exchangers. As the temperature and fluid flow in every measuring points keep stable, the heat transfer coefficient K′ (without fouling) is tested in 8 hours period run. Then, two concentrated salt solutions (Ca(NO3)2 and NaHCO3) are slowly added to the cooling water tank in which the deionized water is circulated. As the temperature and the calcium concentration of the test solution in the cooling water tank are stabilized at 47.5 oC and about 375 mg/L, respectively, the heat transfer coefficient K is tested every 3 minutes. In present case we have tried to investigate the effect of the velocity on the characteristics of the crystallization fouling at the initial stage, but the other parameters, such as the value of pH, the wall temperature, the supersaturation and the concentration of the solution are kept more close to the real operating conditions, which in many literatures are selected based on accelerating fouling test conditions, such as using high concentration of the solution. With these considerations, in present case the fouling experiments are done with twelve velocities only, they are 0.06, 0.10, 0.13, 0.16, 0.20 and 0.25 m/s for laminar flow and transitional flow conditions, and 0.30, 0.40, 0.50, 0.60, 0.70 and 0.80 m/s for turbulence flow conditions, the corresponding Reynolds numbers are 618, 1084, 1390, 1729, 2104, 2604, 3291, 4398, 5630, 6644, 7497 and 9406, respectively. The uncertainty in the measured velocity and Reynolds number is ±10%. The flow in the test section is in laminar, transition or near to fully turbulent flow regime with a developing thermal boundary layer. Heat fluxes of 3.9, 6.5, 8.4, 10.4, 13.0, 16.3, 19.5, 26.0, 32.5, 39.0, 45.5 and 52.0 kW/m2 are tested. In order to keep concentration of the test solution constant, a certain concentration of

13

Ca(NO3)2 and NaHCO3 solutions (the molar ratio = 1) are added continuously to the test solution by the peristaltic pump, respectively. Due to resistance caused by deposit formation, the test solution flow rate will be frequently adjusted to reach to the initial value during all the time of the experiments. 3. Data reduction 3.1 The thermal fouling resistance and the mean growth rate of fouling The global thermal fouling resistance Rf is calculated from

Rf 

1 1  K K'

(3)

where K′ and K are overall heat transfer coefficients at t = 0 and t > 0, respectively. K is determined by Q  VCp (Tco  Tci )

K

(4)

VCp (Tco  Tci )

(5)

ATm

where Tci and Tco are the inlet and outlet temperatures of the test solution, respectively, V is the volume flow rate of the test solution, Cp is the specific heat of the test solution, ρ is the density of the test solution, A is the heat transfer area, and ∆Tm is the log mean temperature difference of double pipe heat exchanger

tm 

(Thi  Tco )  (Tho  Tci ) (T h i  T c o ) ln     (Tho  Tci )

(6)

Where Thi and Th o are the inlet and outlet temperatures of the hot fluid, respectively. The mean growth rate of fouling on the surface of the test tube, w, is defined as w

1 w A t

(7)

where w is the mass increment of fouling deposited on the surface of the test tube within t, 14

t is the time to reach asymptote. Above mentioned data reduction process shows that the thermal fouling resistance is determined through measuring the flow rate, the inlet and outlet temperatures of the test solution and the hot water. The mean growth rate of fouling can be obtained by weighting method. 3.2 Shear stress on the inner wall surface and the thickness of the viscous sub layer Shear stress is caused by the flow of incompressible fluid on the wall of the average straight pipe is given by [26]



p di l 2

(8)

where p is pressure gradient of the tube, di is the inner diameter of the tube, l is the length of the tube, and in this paper l is 1 m. The thickness of the viscous sub layer is determined by [26] 0.5

       

(9)

where ν is kinematic viscosity of the test solution,ρis density of the test solution at the average temperature of the solution in the test tube. 3.3 Nusselt number on the inside tube surface When the crystallization fouling is formed on the surface of the test tube, Nui is given by Nui 

hi di

(10)



where hi is the heat transfer coefficient of the inside tube, λ is the heat conductivity of fluid, hi is determined from hi 

1

(11)

1 di do di  ln  K 2t di hodo

where do is the outer diameter of the tube, λt is the heat conductivity of the test tube, ho is the 15

heat transfer coefficient on the tube outside surface. It is calculated from ho 

di 1 di do 1 do ( '  ln  ' ) K 2 di hi

(12)

where K′is overall heat transfer coefficient of the test tube with distilled water, hi′ is the heat transfer coefficient of the inside tube under this condition hi' 

Nu'i  di

(13)

where Nui′ is Nusselt number of the inside tube with distilled water, it is calculated according to three cases: Under laminar flow conditions, Nui′ is calculated by d  Nu'i  1.86Re1/3 Pr1/3 ( i )1/3 ( i )0.14 L o

(14)

where Re is Reynolds number, Pr is Prandtl number, L is length of the test tube (L=1 m), μo is the viscosity of fluid at well temperature. Under transition flow conditions, Nui′ is determined from Nui'  0.023Re0.8 Pr0.4 (1 

6 105 ) Re1.8

(15)

Under turbulence flow conditions, Nui′ is calculated using Nu'i  0.023Re0.8 Pr0.4

(16)

3.4 The kinetic reaction for fouling formation of CaCO3 The driving force for the formation of a calcium carbonate is defined as the change in Gibbs free energy for going from the supersaturated solution to equilibrium [27]: G  RT ln S

(17)

where R is the gas constant, T is the absolute temperature, and S is the supersaturation ratio:

Ca CO  2 3

2+

S

(18)

Kso

16

Kso is the thermodynamic solubility product of calcium carbonate. 3.5 Uncertainty estimation Uncertainty analysis is crucial especially when the measured fouling resistances have small values. Detailed results are presented for a single representative case which is found to express typical fouling behavior in the experiments. In order to estimate the uncertainties of the experimental results, a method presented by Moffat R.J. [28] is used. The uncertainty of the heat transfer coefficient, the rate of heat transfer or fouling resistance can be traced to the errors in the measurements of volume flow rate, hydraulic diameter, and all the temperatures. For each of the flow rate, 1/K’ is a constant, so the uncertainty of Rf is only caused by the uncertainty of 1/K. The different of the outlet and inlet temperatures of the test solution is expressed as ΔTc. The operation conditions with their bias uncertainties at the 95% confidence level are presented for the example case in Table 1. 2

2

2 2 Tm   Tc    A  V    1   (1)   1  (1)   K Tm   Tc   A  V  

K

 Rf

2

(19)

2

2 2 Tc    A  V   Tm     (1)    1  (1)   1 Rf V   Tm   Tc   A   2  V   Tc   1   1  Q  V   Tc 

Q

(20)

2

(21)

Substituting the conditions listed in Table 1 into Eqs. (19), (20) and (21), respectively, and taking the partial derivatives, the example case is:

K

2

0.5   0.5   1.6 104   0.0006    1  (  1)   1   (  1)   11.2%  K 27.2   10.5   0.03768   0.0061  

 Rf

2

2

2

2

0.0006   0.5   0.5   1.6 104    (1)   1   (  1)   1  11.2% Rf 0.0061   27.2   10.5   0.03768   2

2

2

17

(22)

(23)

Q

2

2

 0.0006   0.5   1  1  11.1% Q  0.0061   27.2 

(24)

In this study, the flow rate is varied from 0.06 to 0.80 m/s, the uncertainties of the experimental results are mainly caused by random fluctuation in the flow rate and the temperature during the experiments, the less the flow rate is, the more the uncertainties. Therefore, the maximum uncertainty in the fouling resistance and the heat transfer coefficient measurements are determined to be within ±20%. The rate of heat transfer for the side of the test solution is determined to be within ±20%. Furthermore, to check the reproducibility of the experiments, some runs are repeated. Table 1 Conditions in the example case. Parameter Numeral value For u = 0.06 m/s V (m3/h) 0.0061 2 A (m ) 0.03768 o ΔTm ( C） 27.2 o ΔTc ( C） 10.5

Bias uncertainty ±0.0006 ±1.6×10-4 ±0.5 ±0.5

4. Results and discussion In this investigation, the experimental conditions of the test solution in the cooling water tank are strictly controlled with the range of following: pH = 7.55±0.005, c = 375±38 mg/L (Ca2+: 3.75×10-3 mol/L), T = 320.5±0.1K, S = 3.61, and G = 9.7 kJ. The operating conditions are exactly in the metastable zone of “CaCO3-CO2-H2O” system [29]. In this zone the test solution is supersaturated with respect to calcite and under saturated with respect to the monohydrated form. This means that the solution could be supersaturated with respect to anhydrous forms (vaterite, aragonite, and calcite) without any possibility of spontaneous nucleation. The metastability can be broken by fracture and removal of the crystals occurred in the fouling period. As fracture and removal of the crystals are migrated by the fluid to the

18

cooling water tank, spontaneous nucleation will take place, minute structures are formed at first from the collision of two molecules which are then collided with a third molecule and so on. Short chains or flat monolayer may be formed and eventually, the lattice structure is built up. This construction process takes place very rapidly, but it could not continue because the local super -saturation isn’t very high, so many of these sub-nuclei re-dissolve since they are very unstable. Many people [7,15-17] have reported the fouling characteristic of calcium carbon with the artificial water distribution same as this study, they have not considered individually the particles fouling. In this study, crystallization or particulates fouling have not considered individually. 4.1 The characteristics of CaCO3 fouling on tube inner surface under different velocity 4.1.1 The general characteristics It is well accepted that the characteristics of CaCO3 fouling on tube inner surface are indicated by Rf. Thus the experimental results of the characteristics of CaCO3 fouling on tube inside surface are shown in Fig. 2. Under different velocity, the results show nearly the same trends. Four distinct time regions are observed: a region where the fouling thermal resistance is positive (named the first region), a region where the fouling thermal resistance is negative (named the second region), a region where the fouling resistance increased steadily (named the third region) and a region where the fouling thermal resistance remains constant (named the fourth region). Each of these regions can be matched with different development phases in the crystallization fouling process: nucleation phase, growth phase and asymptotic/falling phase [2]. In general the process is also divided into the roughness delay time and fouling period [5]. The roughness delay time is classified into two periods: the initiation period and

19

the negative fouling resistance period. In the initiation period, the thermal fouling resistance increases with time at firstly, followed by decreasing with time, the total thermal resistance is greater than zero (see Fig. 2). In the negative thermal fouling resistance period, the trend of the thermal fouling resistance is just opposite with the initiation period. In the fouling period, the thermal fouling resistance increases quickly at first until the thermal fouling resistance reaching a certain value, after that the thermal fouling resistance increases asymptotically regarding time. In this study, according to the size of the Reynolds number, the fluid flow is divided into three intervals, such as laminar flow conditions, transitional flow conditions, and turbulence flow conditions. In each interval, the change of velocity is in the small-scale, and the change of the fouling resistance is in the same trends (see Fig. 2). As illustrated in Fig. 2, the evolution of fouling resistance with time at different velocity is different, and the change of fouling resistance reveals a significant tendency. Under laminar flow and transitional flow conditions, the maximum fouling resistance decreases with increasing velocity in the first region, but the minimum fouling resistance increases with the increase of velocity (except u = 0.06 m/s) in the second region, while the fouling resistance decreases with increasing velocity in the fourth region; however, under turbulence flow conditions, the maximum fouling resistance in the first region and the minimum fouling resistance in the second region vary in a small range with the increase of velocity, but the fouling resistance decreases slowly with increasing velocity in the fourth region. This could be explained by the change of flow characteristics near the wall surface of the test tube. Under the laminar flow and transitional flow conditions, the thickness of the viscous sub layer decreases with increasing velocity as

20

well as the number of fouling ions in the viscous sub layer, resulting the decrease in the fouling growth in the first and fourth regions; and at the same time, the reduction in the thickness of the viscous sub layer will cause the decrease in the roughness near the wall surface, which results the reduction in heat transfer caused by the additional disturbance, so the minimum fouling resistance increases with the increase of velocity in the second region; As velocity is more than 0.3 m/s, the flow is turbulence flow, with increasing velocity the removal rate increases significantly, the growth rate of fouling is no longer affected by the velocity. As showed in Fig. 2, the fouling resistance increases with time at the outset in the first region, however, this phenomenon can’t be observed clearly at some velocities (such as 0.5, 0.7 and 0.8 m/s), which is due to two reasons: one is the time period for the increase of fouling resistance at the outset is very short with respect to the total test run; the other is attributed to the reaction taken place on the wall of the test tube as Eq. (1), and the reaction rate increases with increasing velocity, which is ascribed to the reduction in the thickness of the viscous sub layer, so the fouling resistance increases rapidly at the outset in the first region until it reaches a maximum, the average wall temperature decreases quickly, and the fouling rate also reduces.

21

22

Fig. 2 Fouling resistance with time under different velocity: (a) u = 0.06 m/s, (b) u = 0.10 m/s, (c) u = 0.13 m/s, (d) u = 0.16 m/s, (e) u = 0.20 m/s, (f) u = 0.25 m/s, (g) u = 0.30 m/s, (h) u = 0.40 m/s, (i) u = 0.50 m/s, (j) u = 0.60 m/s, (k) u = 0.70 m/s, (l) u = 0.80 m/s.

4.1.2 The roughness delay time Typical fouling curves are illustrated in Fig. 3, in which the effect of the flow velocity is analyzed in the initiation period. Fouling is represented in terms of a reduction in the overall heat transfer coefficient with time, and K′ is increasing with increasing flow velocity. Under different flow velocity, the overall heat transfer coefficient exhibits nearly the same tendency, the overall heat transfer coefficient decreases from K′ to a minimum value, followed by an increase from the minimum value to K′, and the overall heat transfer coefficient is less than K′. However, it is generally believed that there is no fouling resistance in this period [10]. In many available references there is a contradictory phenomenon being detected in this period. Pääkkönen et al. [7] has investigated the effect of the flow velocity (see Fig. 8(a) in their paper) and the heat flux (see Fig. 8 (b) in their paper) on CaCO3 fouling. In these two figures 23

positive and negative fouling resistance are observed simultaneously in this period. Najibi et al. [17] has studied the typical variation of heat transfer coefficient with time (see Fig. 3 in their paper). The heat transfer coefficient versus time curve is characterized by a sharp decrease in heat transfer coefficient at the onset of the operating time. Florian et al. [30] have investigated roughness and constriction effects on heat transfer in crystallization fouling. They have found that the fouling resistance Rf shows a negative value over the whole time of the experiment apart from the very beginning (see Fig. 4 in their paper) in a double pipe heat exchanger. In spite of many observations and investigations of induction phenomena, this period in a fouling process has not been studied in a substantially quantitative manner. In the initiation period, the number of precipitating calcium carbonate crystals increases rapidly at the start of nucleation and at a later stage the particles stop increasing in number and subsequently grow. Nucleation takes place at localized sites, the nuclei is discrete, and the lateral growth of individual nucleation sites does not result in a complete coverage of heat transfer surface yet. And at the same time, the crystals form on the heat transfer surface, neither their number nor size reaches a critical value to affect the integral heat transfer [31]. As illustrated in Fig. 3, the shape of the heat transfer coefficient versus time curve is characterized by a decrease in heat transfer coefficient for a period of time, which indicates that the increase in number and size does not reach a critical value. The crystal growth is not large enough to lead to an increase in surface roughness and to an improvement of the local heat transfer coefficient due to additional turbulence. As time goes on, an increase in heat transfer coefficient is observed, which is due to increasing in both the number and size of crystal, and at the same time the metallic surface area of test tube decreases with increasing

24

crystal coverage. Therefore, for the test tube placed horizontally, there will be two effects occurred on heat transfer in this period. One is the decrease in metallic surface area of the test tube caused by stable nuclei formation and the crystal growth. Since the thermal conductivity of these crystalline deposits is very low, deposits of these crystals will reduce the overall heat transfer coefficient significantly [32]. The other is the increase in the additional disturbances caused by the crystal growth. The disturbances enhance the heat transfer and strengthen the deposition of fouling. Initially, with stable nuclei formation and the crystal growth, the effect of decrease in metallic surface area on heat transfer is greater than that of the additional disturbances, and heat transfer coefficient decreases steadily from K′ to a minimum value. With further increasing in number of stable nuclei and the crystal growth, the effect of additional disturbances on heat transfer is enhanced, so heat transfer coefficient increases steadily from the minimum value to K′. As heat transfer coefficient reaches K′, the effects of the decrease in metallic surface area on heat transfer is equal to the effects of additional disturbances.

25

26

Fig. 3 The overall heat transfer coefficient with time under different velocity during the initiation period: (a) u = 0.06 m/s, (b) u = 0.10 m/s, (c) u = 0.13 m/s, (d) u = 0.16 m/s, (e) u = 0.20 m/s, (f) u = 0.25 m/s, (g) u = 0.30 m/s, (h) u = 0.40 m/s, (i) u = 0.50 m/s, (j) u = 0.60 m/s, (k) u = 0.70 m/s, (l) u = 0.80 m/s.

In the negative fouling thermal resistance period as shown in Fig. 4, the initial deposit growth can cause the heat transfer coefficient to increase rather than decrease, and can result in a negative fouling resistance (see Fig. 2). The maximum heat transfer coefficient increases with increasing velocity, it is significant that the minimum fouling resistance increases with the increase of velocity (except u = 0.06 m/s) in this period (see Fig. 2). The duration of the negative thermal resistance increases with the increase of velocity, and followed by a decrease with increasing velocity, as velocity is about 0.5 m/s the duration of the negative thermal resistance reaches the maximum. Generally, many reporters have attributed this phenomenon to the change of the flow characteristics near the heat transfer surface, but the decrease in metallic surface area can′t be

27

ignored [19]. As mentioned above, the decrease in metallic surface area by deposition and the increase in additional disturbances simultaneously affect the heat transfer in this period. Due to increasing of the fouling deposition, metallic surface area of the test tube decreases with time, which causes the thermal fouling resistance increasing steadily with time. At the same time, with the crystal particle growth, a part of the crystal particle is large enough to penetrate the viscous sub-layer, which results in the additional disturbances, and the heat transfer is promoted. This is presented by a decrease in the thermal fouling resistance. However, both of the area decrease and the additional disturbances are increasing continuously regarding the increase of operating time. From the beginning of this period, the effect of the additional disturbances is larger than the effect of the decrease in metallic surface area. The increase in heat transfer coefficient might overcome the decrease of the heat transfer coefficient caused by the thermal resistance, so the net heat transfer coefficient increases with the time. Therefore, the negative thermal fouling resistance is observed, and the thermal fouling resistance decreases steadily from zero to a minimum value (negative value). When the effect of the decrease in metallic surface area is dominated, the metallic surface area decreases rapidly and the thermal fouling resistance increases steadily from the minimum value (negative value) to zero. As the thermal fouling resistance is zero, the effect of the decrease in metallic surface area on heat transfer is equal to that of the additional disturbances, and the metallic surface of test tube is already completely covered with a fouling layer.

28

29

Fig. 4 The overall heat transfer coefficient with time under different velocity during the negative fouling thermal resistance period: (a) u = 0.06 m/s, (b) u = 0.10 m/s, (c) u = 0.13 m/s, (d) u = 0.16 m/s, (e) u = 0.20 m/s, (f) u = 0.25 m/s, (g) u = 0.30 m/s, (h) u = 0.40 m/s, (i) u = 0.50 m/s, (j) u = 0.60 m/s, (k) u = 0.70 m/s, (l) u = 0.80 m/s.

4.1.3 The fouling period During the post-induction period, only secondary effects of the surface like the change in crystal habits or adhesion effects can influence the fouling resistance. With increasing of turbulence, fracture and removal of the crystals occur in the fouling period [7,30]. These particulate matters are attached to the crystals or trapped in the crystal matrix due to the adhesion strength, which causes an increase in the fouling rate. The precipitation of dissolved ions other than the particulate material may alter the surface energies and thus promote the particulate fouling [33]. At the same time, a steady increase in the removal rate would reduce the fouling rate. Namely, there is a competition between deposition and removal processes in this period. From the beginning of this period, the deposition rate enhanced by the adhesion of 30

particulate matters is larger than the removal rate, the fouling rate may increase quickly, as consequences, the thermal fouling resistance increases quickly, and this situation is keeping until the thermal fouling resistance reaches to a certain value of the fouling (see Fig. 2). Finally the removal rate and the deposition rate will be equal, so that an asymptote is observed. 4.2 Effect of flow velocity on fouling resistance in the fouling period The effect of the flow velocity on scale formation is related to flow regime. For every flow regime, the laminar flow or turbulent viscous sub layer has a strong effect on the fouling characteristics. The reduced velocity within the laminar flow or turbulent viscous sub-layer increases the residence time within these regions, enabling precipitation to take place and more particles to form [12]. In this investigation the diameter and the length of the test tube are same, so the thickness of the laminar sub-layer is mainly determined by flow velocity. Fig. 5 shows the viscous sub layer calculated by Eq. (9) and shear forces determined by Eq. (8) versus flow velocity. The thickness of the viscous sub-layer decreases with increasing velocity, specifically when velocity is increasing from 0.3 m/s to 0.4 m/s the decline is rapid, but when velocity is more than 0.4 m/s the effect of velocity on the thickness of the viscous sub layer reduces. Shear forces increases slowly with velocity from 0.06 m/s to 0.3 m/s, followed by a quick increase with increasing velocity.

31

0.5

Shear forces The thickness of the viscous sublayer

2.4

0.4

1.8

0.3

1.2

0.2

0.6

0.1

0.0

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

The thickness of the viscous sublayer, [mm]

Shear forces, [N/m2]

3.0

0.9

Velocity, [m/s]

Fig. 5 The effect of the flow velocity on the thickness of the viscous sub layer and shear forces

The effect of the flow velocity on fouling resistance in the fouling period can be detected from Fig. 6. In the region where the fouling resistance increases steady, the fouling resistance are determined by the flow characteristic in the test tube. As the flow velocity ranges from 0.06 to 0.25 m/s (Fig. 6(a)), the fouling resistance decrease rapidly, which is mainly caused by the decrease in the thickness of the viscous sub layer; but when the flow velocity is from 0.30 m/s to 0.80 m/s (Fig. 6(b)), the decrease in the fouling resistance is mainly caused by the increase in shear forces. In the region where the fouling thermal resistance remains constant, the fouling rate is nearly zero, and the absolute value of the fouling resistance decreases with increasing the flow velocity (Fig. 6), which is attributed to the increase in the removal rate caused by the higher shear forces [21,34]. Therefore it can be confirmed that a low or stagnant flow allows growth to more easily attaching to the surface, and stronger shear forces will not entirely prevent the deposits from forming, but will lead to thinner and firmer deposits.

32

Fig. 6 Effect of the flow velocity on the fouling rate in the fouling period: (a) under the laminar flow and transitional flow; (b) under the turbulence flow.

To determine the controlling mechanism of fouling, the effect of velocity on the fouling rate at beginning of fouling period is evaluated over the range of 0.06 to 0.8 m/s for constant super saturation of bulk solution and constant temperature difference of tube side. The effect of the flow velocity on the fouling rate at just beginning of the fouling period is illustrated in Fig. 7. When the velocity ranges from 0.06 to 0.20 m/s, the fouling rate increases quickly at first, and followed by a rapid decrease, the thickness of mass transfer boundary layer is still thick (see Fig. 5) and, therefore, molecular transport has a significant effect on the fouling rate. As flow velocity increases from 0.25 m/s to 0.8 m/s, the fouling rate decreases slowly with increasing the flow velocity. It is generally believed that if fouling is not influenced by diffusion mass transfer, the fouling rate should be independent of the flow velocity if the fouling surface temperature remains constant. That is to say the decrease of the fouling rate regard to the flow velocity may be the result of a lower deposition rate for the higher flow velocity, which demonstrates that the formation of the deposits could be controlled by chemical reaction at the heat transfer surface [17].

33

7.0E-6

Initial fouling rate, [m2K/W•h]

6.0E-6 5.0E-6 4.0E-6 3.0E-6 2.0E-6 1.0E-6 0.0 -1.0E-6 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Velocity, [m/s]

Fig. 7 The effect of the flow velocity on the fouling rate at just beginning of the fouling period

4.3 The effect of flow velocity on the roughness delay time The effect of flow velocity on the roughness delay time is illustrated in Fig. 8. The roughness delay time decreases as the flow velocity increases at firstly. When flow velocity is around 0.16 m/s, the roughness delay time has a minimum value. Then the roughness delay time increases as the flow velocity increases until the flow velocity is around 0.5 m/s. Further increasing the velocity the roughness delay time decreases.

Fig. 8 Effect of the flow velocity on the roughness delay time

The laminar sub-layer which forms next to the heat transfer surface has a strong effect on the fouling characteristics. The thickness of this layer is strongly affected by flow velocity. When the flow velocity regions from 0.06 m/s to 0.16 m/s, Reynolds number (Re = 618-1729) 34

is less than 2000 which means that the flow is laminar flow. In this flow state, an increase in the flow velocity will decrease the thickness of the viscous sub-layer and cause more fouling ions to diffuse to the heated surface, which increases the formation of CaCO3 fouling. At the same time, weaker shear force is acted on the tiny CaCO3 crystals attached to the wall surface. Therefore, the roughness delay time decreases with increasing the flow velocity. But when the flow velocity ranges from 0.20 m/s to 0.5 m/s and the corresponding Reynolds numbers from 2104 to 5630, the flow state transforms from the transitional flow to the turbulence flow, the thickness of the viscous sub-layer decreases with increasing flow velocity. At the same time the removal rate increases due to higher shear force. Therefore an increase in the flow velocity will lead to an increase in induction period [4]. However, as the flow velocity ranges from 0.5 to 0.8 m/s and the corresponding Reynolds numbers from 5630 to 9406, the flow state is complete turbulence flow, the thickness of the sub-layer decreases continuously, the advantage of the roughness is quickly overcome by the fouling resistance, which results in a shorter roughness delay time at the high flow velocities [21]. Flow velocity has a complicated role on fouling. The increase in velocity enhances mass transfer and promotes deposition, which is due to the increased turbulence and further ions transport [35]. Increased shear at the interphase reduces the probability of the adhesion of the depositing material reaching the solution fouling layer interphase. Therefore, the increase in the flow velocity may either increase the fouling rate (mass transfer controls) or decrease it if the interfacial shear has the greater effect (surface integration controls) [36]. 4.4 The effect of Reynolds number on the mean growth rate of fouling The deposition rate is found to be controlled by different mechanisms, depending on

35

flow velocity and surface temperature [17]. But in this investigation, the change of wall temperature for every test tube is nearly same, which ranges from 45 °C (inlet point) to 55 °C (outlet point), and super saturation of test solution remained almost constants. Therefore, the effect of the wall temperature on fouling is same for each test tube. The effect of Reynolds number on the mean growth rate of fouling is illustrated in Fig. 9. The results show that the mean growth rate of fouling increases with Reynolds number ranging from 618 to 2100. When Reynolds number is about 2100, the mean growth rate of fouling reaches a maximum value, followed by a decrease with increasing Reynolds number. This could be explained by the change of flow characteristics near the wall surface. Under the laminar flow conditions, the thickness of the viscous sub layer decreases with increasing Reynolds number, which results the increase in the mean growth rate of fouling. As Reynolds number is more than 3000, the flow is turbulence flow, with increasing Reynolds number the removal rate increases significantly, the mean growth rate of fouling is no longer affected the flow velocity.

Fig. 9 Effect of Reynolds number on the mean growth rate of fouling

4.5 SEM pictures of CaCO3 In order to further verify the accuracy of the experiment, the experiment conditions are

36

same as mentioned above, the flow velocity is 0.2 m/s with the test time of 300 h in the repeatability test. For morphological studies of CaCO3 crystals, test samples (5×5×1 mm) are cut from the test tube from both at two ends and at the middle. To characterize the deposits, samples are analyzed using a high resolution scanning electron microscope (SEM). Figs. 10(b)-(d) show SEM photographs of CaCO3 at the inlet end, the middle and the outlet end of the test tube along the direction of fluid flow, respectively. SEM analysis indicates that the deposits on the test tube found in this investigation consists of both rod-like aragonite and rhombohedral calcite crystals, which means that both crystals have precipitated simultaneously, and this may be related to the induction time discussed earlier, however the rhombohedral calcite crystals growth is quite predominant. SEM photographs also indicate that the deposit increases along the direction of fluid flow, which is due to the increase of wall temperature of the test tube along the direction of fluid flow [2]. The photographs also show that as wall temperature of the test tube increases, the crystals become bigger and calcite crystal changes from the single crystal to polymorph. For instance, the size of single calcite crystals is below 10 μm at the inlet end (in Fig. 10(b)); but at the middle (in Fig. 10(c)), polymorphs of calcite with the size about 30 μm emerges; while at the outlet end (in Fig. 10(d)), polymorphs of calcite with the size more than 50 μm are observed. Furthermore, in the initiation period, the nuclei is discrete, and the lateral growth of individual nucleation sites does not result in a complete coverage of heat transfer surface, this perfectly agrees with the results obtained by Florian et al. [17].

37

Fig. 10 SEM pictures of CaCO3: (a) the surface of the test tube, (b) the inlet end, (c) the middle, (b) the outlet end.

4.6 The correlation between Nu number and Reynolds number In this investigation, for every test tube the change of temperature is nearly same, so the effect of temperature is negligible, the deposition of fouling is mainly determined by velocity. Nu/Nu0 is defined to express the ratio of the intensity of convective heat with presence of

fouling to that with absence of fouling. The ratio is continuous variation in the four different fouling regions. Dimensionless time (τ) is defined as 

tu 36000di

(25)

where t was time, u was the mean flow velocity of test tube. The functional relationship between Nu/Nu0 with dimensionless time (τ) is showed in Figs. 11 and 12. When fluid flow is laminar flow, the following correlations are obtained (Fig. 11(a)).

38

 Re0.695  0 ~ 2 ( in the first region) Nu  0.503Re0.1  0.098 Re0.595  0.0572 2 Re1.29 Nu0

(26)

 Re0.695  2 ~18.6 ( in the regions from the second to the fourth) 0.695

 Re 2( Nu  0.4Re0.1  0.303Re0.1e Nu0

4.815 2 ) 4.253

(27)

When fluid flow is transitional flow, the following correlations are obtained (Fig. 11(b)).  Re0.66  0 ~ 3.6 ( in the first region) Nu  0.62Re0.06  0.056 Re0.6  0.0167 2 Re1.26 Nu0

(28)

 Re0.66  3.6 ~ 28.6 ( in the region from the second to the fourth) 0.66

 Re 8.654 2 2( ) Nu 6.741  0.588Re0.06  0.1349Re0.06e Nu0

(29)

Fig. 11 Nu/Nu0 as a function of dimensionless time: (a) laminar flow (Re < 2000); (b) transition flow (2000 ≤ Re < 3000).

This procedure is repeated for every test section curve and for all the experiments. It is worth noting that the values of R2 vary from 0.97 to 0.99. When fluid flow is turbulence flow, the following correlations are obtained (Fig. 12).  Re1.1  0 ~ 0.008 ( in the first region) Nu  0.383Re0.12 14.135 Re0.98 Nu0

(30)

 Re1.1  0.008 ~ 0.16 ( in the first region) Nu  0.256Re0.12  0.642 Re0.98 Nu0

(31)

 Re1.1  0.16 ~1.45 ( in the regions from the second to the fourth)

39

1.1

 Re 0.493 2 2( ) Nu 0.366  3.313Re0.12  0.317Re0.12e Nu0

(32)

1.0

u=0.3 m/s u=0.4 m/s u=0.5 m/s u=0.6 m/s u=0.7 m/s u=0.8 m/s

(Nu/Nu0) Re-0.12

0.8

0.6

0.4

0.2

0.0 0.0

0.4

0.8

 Re-1.1

1.2

1.6

2.0

Fig. 12 Nu/Nu0 as a function of dimensionless time under turbulence flow (Re ≥ 3000)

It should be mentioned that evaluating correlations adequacy is an important part of any correlations building problem. Compared Eqs.(26)-(32) with the semi-empirical correlation for crystallization fouling model [2]:

Rf 

A 1  exp B t -t0 

(33)

t0 =

tind +tasy 2

(34)

where A is a function of the surface temperature as B, the parameter t0 can be expressed in terms of the time to reach asymptote [2], tasy, and the induction time, tind. The semi-empirical correlation for crystallization fouling model can be transformed as: Nu  C  D exp B t -t0  Nu0

(35)

where C is a function of the surface temperature as D. It is clear that the form of Eq. (35) is different from Eqs. (26), (28), (30) and (31) in the first region, but the form of Eq. (35) is similar to Eqs. (27), (29) and (32) in regions from the second to the fourth, while the index of t in Eq. (35) is 1, the maximum index of  in Eqs. (27), (29) and (32) is 2. The correlation between Nu/Nu0 with dimensionless time (τ) reveals the characteristics of 40

heat transfer with the presence of CaCO3 fouling in different regions. As shown in Eqs. (26)-(32), the index of n in dimensionless parameter τRen is related to the flow state in the tube, for laminar flow, n = -0.695; for transitional flow, n = -0.66; and for turbulence flow n = -1.1. The value of index n reveals the effect of the flow state on the fouling resistance. Low Reynolds number (Re < 3000) flow has less effect on the fouling resistance than high Reynolds number (Re ≥ 3000) flow. Under low Reynolds number (Re < 3000), in the first region, there is a slightly difference in coefficient and the index for the variables τ and Re in Eqs. (26) and (28). In the regions from the second to the fourth, the same difference is observed in Eqs. (27) and (29). Therefore, it can be sure that the effects of τ and Re on the fouling resistance are consistent in laminar flow and transitional flow in the same region. Under high Reynolds number (Re ≥ 3000), in the first region, a slightly difference in coefficient for the variables τ and Re is observed in Eqs. (30) and (31); in the regions from the second to the fourth, Eq. (32) is entirely different from Eqs. (27) and (29). 5. Conclusions To provide a more appropriate description of the effects of flow velocity on a fouling history (from the beginning of fouling to the dynamic steady state fouling), the present study not only tries to find the effects of flow velocity on the fouling characteristics of CaCO3, but also makes effort to cast the results into a correlation for deeper insights on the mechanism of the velocity effect on the fouling of CaCO3. The main results can be summarized as followed. (a) Two distinct time regions are observed in the induction period: a region where the fouling thermal resistance is positive, and a region where the fouling thermal resistance is negative. Crystal formation and fouling built-up on the heat transfer surface give rise to two

41

effects in the induction period: an increased surface roughness followed by the decrease in metallic surface area of the test tube as fouling progress. As fouling reach to the fouling period, there is a competition between deposition and removal processes in this period. (b) When the flow velocity is less than 0.20 m/s, crystallization fouling is controlled by transport; while as the flow velocity is more than 0.20 m/s, the fouling process is reaction-controlled. (c) When the flow velocity ranges from 0.06 to 0.16 m/s, roughness delay time was decreasing with increasing flow velocity; while as u = 0.16-0.50 m/s, roughness delay time is increasing with increasing flow velocity; when u = 0.50-0.80 m/s roughness delay time is decreasing with the increase in flow velocity. (d) When Reynolds number is less than 2100, the mean growth rate of fouling is increasing with increasing Reynolds number; however, when Re > 2100 the mean growth rate of fouling is decreasing slowly with increasing Reynolds number. (e) The results have been cast into the correlations between Nu/Nu0 with dimensionless time (τ) and Re. The index of n in dimensionless parameter τRen is related to the flow state in the tube. The correlation between Nu/Nu0 with dimensionless time (τ) and Re is different in different fouling regions. Low Reynolds number (Re < 3000) flow has less effect on the fouling resistance than high Reynolds number (Re ≥ 3000) flow. (f) Under low Reynolds number (Re < 3000), the lower flow velocity is, the more negative in fouling thermal resistance in the negative fouling thermal resistance period, which is very important for the extension of the induction period to minimize the negative effects of fouling and maximize the endurance of the heat exchanger.

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Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 51166007).

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Highlights 

We study the effects of flow velocity on CaCO3 fouling in smooth tube.



Fouling growth characteristic relies on Nu/Nu0, Re and dimensionless time.



The index of n in dimensionless parameter τRen is related to the flow state in tube.

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Surface roughness and uncovered metallic surface area determine fouling regions.

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