- Email: [email protected]
CaSO4 fouling characteristics on the rectangular channel with half-cylinder vortex generators
Accepted Manuscript Research Paper CaSO4 fouling characteristics on the rectangular channel with half-cylinder vortex generators Zhimin Han, Zhiming Xu, Jingtao Wang PII: DOI: Reference:
S1359-4311(17)33043-0 http://dx.doi.org/10.1016/j.applthermaleng.2017.09.051 ATE 11108
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
4 May 2017 3 September 2017 11 September 2017
Please cite this article as: Z. Han, Z. Xu, J. Wang, CaSO4 fouling characteristics on the rectangular channel with half-cylinder vortex generators, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/ j.applthermaleng.2017.09.051
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
CaSO4 fouling characteristics on the rectangular channel with halfcylinder vortex generators Zhimin Han, Zhiming Xu*, Jingtao Wang
College of Energy and Power Engineering, Northeast Electric Power University, Jilin, Jilin Province, China * （ Corresponding Author: [email protected]）
ABSTRACT In order to study the fouling characteristics on the rectangular channel with half-cylinder vortex generators, the deposition process of CaSO4 fouling were studied by numerical simulation method. The fouling characteristics under different operation conditions and structures such as the concentration of CaSO4, the wall temperature, the inlet velocity, the length, the radius and the spacing of the half-cylinder vortex generators were investigated. The results show that the asymptotic value of fouling resistance increases with the increase of the surface temperature and the concentration, and decreases with the increase of the inlet velocity. The value of fouling resistance first decreases and then increases with the increase of the length. The value of fouling resistance reaches the minimum when the length was 4/8H. The value of fouling resistance increases with the increase of the spacing. The value of fouling resistance reaches the maximum when the spacing was more than 55mm, and the fouling characteristics tends to be similar as the situation without the vortex generators. The value of fouling resistance decreases with the increase of the radius.
KEYWORDS: Vortex generator, Fouling resistance, Numerical simulation, CaSO4 fouling
1. Introduction Fouling, was the accumulation of solid matter on a heat transfer surface, which reduces the heat transfer rate and increases the pressure drop of equipment, such as evaporators, heat exchangers, crystallizers, membranes etc.. It can cause a decline in operating efficiency of heat exchangers, power plants and other chemical industries [1]. In heat exchangers, the fouling was usually caused by supersaturation of the fluid due to a change in temperature [2]. The principal mode of calcium sulfate deposition was referred to as crystallization fouling. The normal
Nomenclatures A the length of the vortex generator (m) B width of the rectangular channel (m) cF concentration of salt solution (kg/m3) cS saturation concentration (kg/m3)
Cin
inlet concentration (kg/m3) 2
D dh dp
E, F G H, L
diffusion coefficient (m /s) hydraulic diameter (m) mean crystal diameter (m) inlet, outlet extending zone (m) spacing between two vortex generators (m) height, length of the rectangular channel (m)
P/K kt kR
cohesion coefficient ( kg·m/s2) mass transfer coefficient (m/s) rate of reaction (m4·kg/s)
Re Sh Sc Tf
Reynolds number Sherwood number Schmidt number temperature of fouling layer surface (K)
Tw
temperature of heat transfer surface (K)
∆T temperature gradient (K) ∆t computing time step (s) source term Sφ u,v,w velocity component (m2/s) xf thickness of crystal layer (m) Greek Symbols ρ density of salt solution (kg/m3) ρf density of fouling layer (kg/m3 ) λf thermal conductivity of fouling layer (W/(m· K)) ᵟ linear expansion coefficient generalized variable φ diffusion coefficient Γφ ƞ dynamic viscosity (kg/m·s)
total mass (kg/m2) m d deposition mass rate (kg/m2·s) removal mass rate (kg/m2·s) m r R radius (m) Rf fouling resistance (m2· K/W) solubility salts scales on cold surfaces, while the inverse solubility salts causes the scaling on heated surfaces. The
m
calcium sulfate was belongs to inverse solubility salts. The fouling model of heat transfer surfaces was established often based on the approach of Kern and Seaton [3] in which the difference between the mass deposition rate and the mass removal rate was the overall mass deposited on the surface. Hasson [4] as the founder of crystallization fouling research, proposed a classical ion diffusion model in study of CaCO3 fouling problems. Afterward, many scholars have done a lot of research on this basis [5-8]. In order to account the temporal and spatial variations in the fluid properties of complex heat exchangers, the Computational Fluid Dynamics (CFD) can be used [9-12]. Brahim et al. [9] in a preliminary simulation the case of the crystallization fouling of CaSO4 on the flat heat transfer surfaces based on models for the mass deposition and removal rates, and used the model to calculate the fouling process under different conditions. Mwaba et al. [10] evaluated the changes that resulting from a non-uniform fouling layer in the heat flow distribution, and simulated a case where calcium sulfate fouling forms on for a heated plate subjected to a shear flow. Zhang et al. [11] studied a new computational fluid dynamics (CFD) model and developed the method how to characterize a crystallization fouling process mathematically. Pääkkönen et al. [12] used CFD to simulate the CaCO3 crystallization fouling on an idealized heat exchanger, and then used to analyze further the crystallization fouling mechanism. The most papers show that the researches were committed to the simple geometric model to mainly study the crystallization fouling mechanism. Recently, the vortex generators (VGs) as a new heat transfer enhancement technique, has received more and more attention. It was a passive heat transfer element by a special type of extended
surface that was possible to generate vortices with parallel to the flow direction [13]. The vortex generators which can produce longitudinal vortices were widely used in the field of the heat transfer enhancement, because the longitudinal vortices can thin and destroy the wall boundary layer and then to achieve heat transfer enhancement [14-18]. In this paper, CFD was often used to model the CaSO4 crystallization fouling on the rectangular channel with half-cylinder vortex generators. The fouling characteristics under different operation conditions and structures such as the concentration of CaSO4, the wall temperature, the inlet velocity, the length, the radius and the spacing of the halfcylinder vortex generators were investigated.
2. Mathematical model 2.1 Geometry description The rectangular channel with half-cylinder vortex generators was shown in Fig. 1. The channel has a length L=420mm, height H=10mm, and width B=30mm. In order to keep the inlet velocity stability, and to avoid the backflow of the outlet, the actual calculation region was expanded to include an inlet extending zone of E=50mm; and the out extending zone of F=150mm. The half-cylinder vortex generators were equally distributed along the base of the rectangular channel. The spacing between two vortex generators was G. The length of the vortex generator was A, and the radius was R.
Fig.1 Rectangular channel with half-cylinder vortex generators
2.2 Mathematical formulation The governing equations in physical space for continuity, momentum, energy and species equations in the calculation region can be expressed generally as follows [19]:
∂ ( ρφ ) ∂t
+ div ( ρU φ ) = div ( Γφ gradφ ) + Sφ
（1）
where ρ was the density of the fluid, t was time, φ was generalized variable, it represents the variables of u, v, w, T etc.. Γφ was generalized diffusion coefficient. Sφ was generalized source term. The extended equations applied in this paper were presented more detailed in references [12]. FLUENT has provided many choices of turbulence models [20]. Whereas the standard k-ε turbulence model was usually developed for fully turbulent flows, and the RNG k-ε turbulence model was better adapted to low Reynolds numbers. In the present work, the flow regime in the set-up was turbulent in the studied conditions with the bulk Reynolds numbers between 8,900 and 23,900. Therefore, the standard k-ε turbulent model was adopted in the calculation region [21].
2.3 Crystallization fouling model In this paper, the following crystallization fouling model of Brahim [9]and Krause [22] was carried out to CFD: 1 1 k 2 k 2 1 kt m d = kt + ∆c − t + t ∆c 4 k R k R 2 kR
（2）
where ∆c was the total concentration difference: ∆c = c F -cS . cF was the mainstream concentration of salt solution and cS was the saturation concentration and was calculated as a function of Tf [9, 23].
log(cs )=-
∆c ∆LH 0 + p ⋅ log ( T f ) + C 2.3 ⋅ h ⋅ T f h
（3）
The mass transfer coefficient was kt , which can be determined as:
kt =
ShD . dh
（4）
Sherwood number can be calculated by the following semi-empirical approach according to Lammers [23]:
Sh = 0.034Re0.875 Sc1/3 where Re =
ρud h η , Sc = . D can be obtained by the Bird [24]: η ρD T 1 1 D = D1 2 exp 380 − T1 T1 T2
where when T1 =355.5K, the mass diffusion coefficient D1=1.0633×10-7m2/s.
（5）
-
The surface reaction rate constant kR can be calculated by Arrhenius law: k R = k R0 e
E RoT f
.
where kRo was the reaction constant, kRo=7.07m4/(kg·s), and E was the reaction activation energy, E=37143J/(mol·k) [9]. Tf was the surface temperature of the fouling layer. Ro was the universal gas constant.
The model of the removal mass rate of CaSO4 fouling was given by [9, 25]:
m r =
1/3 K ρ f (1 + δ∆T ) dP ( ρ 2η g ) x f u 2 P
（6）
The measurement methods based on Krause’s measurements was used for the calculation of P/K [22]:
P = 83.2 ⋅ u 0.54 . K The average density of fouling layer as: ρ f =
m . xf
The fluid velocity u above the fouling layer as: u = u0
H . H − xf
The thickness of the fouling layer was calculated as the total deposit mass per surface area divided by the density ρf of the fouling layer: x f =
m t + ∆t
ρf
.
where (1+δ∆T) which describes the temperature stresses in the fouling layer. ∆T was the temperature gradient in the fouling layer, δ was the linear expansion coefficient. According to Krause [22], dp was the average diameter of crystal for CaSO4 solution, which was about 36 micrometer, xf was the mean thickness of the fouling layer.
The total mass rate was calculated as:
dm dmd dmr = − ⇒ m = m d − m r dt dt dt
（7）
The thermal resistance of the fouling layer can be modelled as:
Rf = m / ( ρ f λf
)
（8）
where λf was the thermal conductivity of fouling layer.
2.4 Boundary conditions Pääkkönen et al. [26] found that the surface integration was controlled the crystallization fouling process. Therefore, during numerical simulation process, the heated wall was applied to the constant surface temperature
boundary condition. The temperature at the bottom of the channel was from 320 K to 340 K. The other surfaces and extending area of the channel were considered as insulated. The channel walls and the vortex generators were adopted at no-slip boundary conditions. The velocity inlet condition was used for the inlet boundary condition, and the outflow was used for the outlet boundary condition. The inlet boundary was specified flow velocity, salt concentration and temperature. The temperature of the fluid at the inlet was 300 K, the inlet velocity was changes from 0.4 m/s to 0.8 m/s, and the concentration was from 2.0 kg/m3 to 4.0 kg/m3. The range of Reynolds number in the set-up was between 8,900 and 23,900 with the given flow velocity range.
3. Numerical method and validation In this paper, the commercial software package CFD software ANSYS FLUENT 14.0 was used to formulate and solve the process. The calculation region was discretized by using a structured mesh generated with the software of ICEM. In order to capture the characteristics of the fluid flow, the hexahedron grids filling the majority of the volume were used. In addition, the local grid refinement was applied in the vicinity of the bottom of the channel and the vortex generators. Three-dimensional double separate of FLUENT software was used for solver. The SIMPLE algorithm was used to couple the pressure and velocity in the momentum equation. The standard scheme was used to couple the discretization of the pressure, and the continuity, momentum, energy and species equation were performed by the second-order upwind scheme. The convergence criterion of the residual of continuity, momentum, energy and species equations was set to be 10-6. A 400 h fouling process was simulated with the time step ∆t specified as 1h [10]. The grid independent test was applied in half-cylinder vortex generators in the rectangular channel. At the fluid inlet, the concentration and the temperature of CaSO4 solution were, respectively Cin =3.0 kg/m3 and Tf = 300 K. The inlet velocity u was 0.5 m/s and the constant surface temperature Tw was 330K.The grid number increases from 201,152 to 1,172,720, the mass deposition rate with the change of the grid number was illustrated in Fig. 2. The results indicate that the mass deposition rate no longer changes, when the grid number of the computing area was larger than 0.9 million. This finding demonstrates that the grid system with 1,068,704 elements was adequately enough for the simulations.
201152 409542 647328 815796 927080 1068704 1172720
1.983
-7
2
Mass deposition rate [10 kg/m s]
1.986
u : 0.5m/s, Tw : 330K
1.980
Tf : 300K, CF : 3.0kg/m2
1.977 1.974 1.971 1.968
0
100
200
300
Time [h] Fig.2 Verify of grid independence
Fig.3 Schematic diagram of experimental system
In order to verify the accuracy of the calculation model and numerical method, it was necessary to compare with experimental data. Fig. 3 shows the schematic diagram of the experimental system used for the fouling experiments.
The specific experimental steps and principles applied in this paper were presented more detailed in references [27]. The specific process was: the manually formulated CaSO4 solution was heated at a heater controlled temperature, and then through the circulating water pump from the low water tank into the high water tank. In the high water tank need to control the water level, when the water level exceeds the specified water level will flow back from the overflow pipe to the low water tank. This will make the high water tank in the working fluid to ensure that a certain flow rate through the experimental channel for heat transfer, and then the working fluid flow through the flow meter, valves, etc., and finally flow back to the low water tank. The flow rate of the
working fluid can be adjusted by means of flow meters and valves. The temperature in the experimental section was controlled by thermal resistance and thermostat control. At last, all relevant experimental data are collected through the data acquisition system and entered into the computer. The calculated mass deposition rate from the smooth channel was compared to the experimental results on the same size channel, in the same conditions. These numerical validations have widely been applied for the compact heat exchanger [28-31], which were most reliable and accurate with wide applicable ranges considering a smooth channel (without vortex generators). The comparison result for the mass deposition rate for a smooth channel was shown in Fig. 4. It shows that the relative error between the computational data and the experimental data was within 15%. For now, the error range was acceptable in the field of fouling calculation. 100 90
Experimental Simulation
6.0
80 Relative error [%]
-5
2
Fouling resistance [10 m K/W]
7.5
4.5 u : 0.1 m/s Tf : 323 K
3.0
CF: 2.1 g/L
1.5
70 60 50 40 30 20 10
0.0
0
50
100
150
200
0
0
50
Time [h]
100
150
200
Time / h
Fig.4 Verification results for the mass deposition rate for a smooth channel
4 Results and discussion 4.1 Effect of operating conditions on fouling resistance evolution 4.1.1 Effect of the inlet velocity The variation of the mass deposition rate and the mass removal rate with time at various flow velocities were shown in Fig. 5. The concentration of CaSO4, inlet temperatures and surface temperatures of the solution were conducted at 3.0 kg/m3, 300 K, and 330 K, respectively. It can be observed from Fig. 5 that the mass deposition rate of CaSO4 fouling curve was almost coincident due to the relationship of the vertical coordinate. However, after the vertical coordinates were enlarged, the variation of the mass deposition rate with time was shown in the partial amplification. It shows that the mass deposition rate of CaSO4 fouling increases with the increase of velocity. This was because from the Eq. (2) that, the mass deposition rate was in proportion to the mass transfer coefficient, and the mass transfer coefficient was indirectly proportion to the velocity. So the increase of the velocity will lead to mass
deposition rate increases. It also can be seen from Fig.4 that the mass removal rate increases with the increase of velocity. It can be explained by the model of mass removal rate Eq. (6) that the size of the mass removal rate was associated with the flow velocity of fluid. A higher shear force and a larger flushing action were formed with the increase of flow velocity at the interface of the fouling layer and the solution [26].
2.4 2.0
-7
-7
2.0
2.8
2
2.4
Mass removal rate 0.4 m/s 0.5 m/s 0.6 m/s 0.7 m/s 0.8 m/s
Mass removal rate [10 kg/m s]
Mass deposition rate 0.4 m/s 0.5 m/s 0.6 m/s 0.7 m/s 0.8 m/s
2
Mass deposition rate [10 kg/m s]
2.8
1.6 2.00
-7
2
Mass deposition rate [10 kg/m s]
1.6 1.2 0.8 D : 40 mm, R : 6 mm A : 8/8 H, Tw: 330 K
0.4
1.99
1.2
1.98
0.8
1.97 0
0.0
Tf : 300 K, CF: 3.0 kg/m
0
100
100
200
300
400
0.4
Time [h]
3
(The partial amplification)
200
300
400
0.0
Time [h]
Fig.5 Effect of inlet velocity on the mass deposition rate and the mass removal rate The variation of the fouling resistance with time at various flow velocities were shown in Fig. 6. It can be seen that the fouling resistance decreased with the increase in the flow velocity. This was because that the fouling resistance was derived from the mass deposition rate and the mass removal rate. And the increment of mass removal rate was much higher than the increment of mass deposition rate. So the fouling resistance decreases with the increase of flow velocity. Pääkkönen et al. [32] and Yang et al. [33] studied that at a constant surface temperature, the fouling resistance increased and the asymptotic fouling period decreased with the increased of the velocity because of the increased number of foulant ions. 0.4m/s 0.6m/s 0.8m/s
0.5m/s 0.7m/s
6
-6
2
Fouling resistance [10 m K/W]
8
4 D : 40 mm, R : 6 mm A : 8/8 H, Tw: 330K
2
3
T f: 300K, CF: 3.0kg/m
0
0
100
200
300
400
Time [h] Fig.6 Effect of inlet velocity on the mass deposition rate and the mass removal rate
4.1.2 Effect of the CaSO4 concentration The variation of the mass deposition rate and the mass removal rate with time at various CaSO4 concentrations were shown in Fig. 7. The inlet velocity, inlet temperatures and surface temperatures of the solution were maintained at 0.5m/s, 300K, and 330K, respectively. It can be seen that, the mass deposition rate increases with the increase of CaSO4 concentration. This was because the concentration in the main flow region increases with the increase of CaSO4 concentration in the fluid. And the boundary concentration was remains unchanged by the change of saturated fluid. Therefore, the concentration difference becomes large between the main flow region and boundary layer nearby. The mass deposition rate increases with increase of CaSO4 concentration. It also can be seen from Fig.6 that the mass removal rate increases with the increase of CaSO4 concentration. The main reason was that the size of the mass removal rate will be affected by thickness of fouling layer. On the one hand, the mass deposition increase with the increase of the concentration, it will increase the thickness of fouling layer. On the other hand, the increase of the thickness of fouling layer may cause the increase of the velocity. It will increase the scouring action of the fouling layer in the fluid. Therefore, the mass removal rate increases with the increase of concentration.
3
3.0 kg/m
4
3
2.5 kg/m
2.0 kg/m
3
3
3.5 kg/m
3.0 kg/m
3
3
2.5 kg/m
3
3.5 kg/m
3
4.0 kg/m
4
4.0 kg/m
-7
2
Mass deposition rate [10 kg/m s]
2.0 kg/m
5
Mass removal rate 3
3
3
2
2
1
1
0
D: 40 mm， R : 6 mm， A : 8/8 H u : 0.5 m/s ， Tf : 300 K， Tw: 330 K
0
100
200
300
400
2
3
-7
Mass deposition rate
Mass removal rate [10 kg/m s]
5
0
Time [h]
Fig.7 Effect of CaSO4 concentration on the mass deposition rate and the mass removal rate The variation of the fouling resistance with time at various CaSO4 concentrations was shown in Fig. 8. It can be seen that the fouling resistance increases with the increase of CaSO4 concentration. The main reason was that the fouling resistance was derived from the mass deposition rate and the mass removal rate. Before the asymptotic fouling period, the increasing slope of the fouling resistance increases with the increase of CaSO4 concentration [34,35], and this was because the increased reaction rate with the increased number of foulant ions led to a higher deposition rate [36].
3
2.0kg/m
3
2.5kg/m
3
3.0kg/m
3
3.5kg/m
8
3
2
Fouling resistance [10 m K/W]
10
-6
4.0kg/m 6
4
D : 40 mm, R : 6 mm A : 8/8 H, u : 0.5 m/s Tf : 300 K, Tw: 330 K
2
0 0
100
200
300
400
Time [h]
Fig.8 Effect of CaSO4 concentration on the fouling reswastance 4.1.3 Effect of the surface temperature The variation of the mass deposition rate and the mass removal rate with time at various surface temperatures were shown in Fig. 9. The concentration of CaSO4, inlet temperatures and inlet velocity of the solution were maintained at 3.0kg/m3, 300K, and 0.5m/s, respectively. It can be observed from Fig. 9 that the mass deposition rate of CaSO4 fouling increases with the increase of surface temperature. The reason was that the change in the mass deposition rate was affected by the total concentration gradient, which can be seen by the model of mass deposition rate Eq. (2). As CaSO4 was a kind of sulfate shows inverse solubility, the solubility of CaSO4 decreases with the increase of the solution temperature. Therefore, the total concentration gradient increases with the increase of surface temperature, and more CaSO4 precipitates from the cycle working fluid. It also can be seen from Fig. 9 that the mass removal rate increases with the increase of the surface temperature of the fluid. This was because the mass removal rate mainly affected by the thickness of the fouling layer. As can be seen from the foregoing, the increase of deposition amount will increase the thickness of fouling layer. Meanwhile, the mass removal rate of fouling will increase with the increase of the surface temperature. The variation of the fouling resistance with time at various surface temperatures was shown in Fig. 10. It can be seen that the fouling resistance increases with the increase of surface temperature. Yang et al. [33] reported that the increase of the surface temperature will increase the reaction rate constant. So the fouling resistance increases with increase of surface temperature. The increasing slope of the fouling resistance increases with the increase of surface temperature because of the increasing deposition rate with the higher surface temperature. While the decreasing solubility at higher solution temperatures leads to the increase of the asymptotic fouling period.
2
Mass deposition rate Mass removal rate 320 K 320 K 325 K 325 K 330 K 330 K 335 K 335 K 340 K 340 K
1.5
1.0
1.0
D : 40 mm, R : 6 mm A : 8/8 H, u : 0.5 m/s Tf : 300 K, CF: 3.0 kg/m3
0.5
0.0
1.5
0
100
200
300
0.5
400
-7
-7
Mass removal rate [10 kg/m s]
2.0
2
Mass deposition rate [10 kg/m s]
2.0
0.0
Time [h]
320 K 325 K 330 K 335 K 340 K
6
-6
2
Fouling resistance [10 m K/W]
Fig.9 Effect of surface temperatures on the mass deposition rate and the mass removal rate
4 D : 40 mm, R : 6 mm A : 8/8 H, u : 0.5 m/s Tf : 300 K, CF : 3.0 kg/m3
2
0
0
100
200
300
400
Time [h]
Fig.10 Effect of surface temperatures on the fouling resistance
4.2 Effect of vortex generators structures on fouling resistance evolution 4.2.1 Effect of the length of VGs The variation of the mass deposition rate and the mass removal rate with time at various lengths of VGs were shown in Fig.11. The variation of the fouling resistance with time at various lengths was shown in Fig.12. The radius and spacing of the half-cylinder vortex generators were conducted at 5 mm and 15 mm, respectively. It can be seen from Fig.11 that the mass deposition rate has a minimum value at 4/8H and a maximum value at 8/8H in rectangular channel with vortex generators. This was because the fluid near the wall was completely separated by the vortex generators when the length of generator arrived at 8/8H, and it produces a large backflow stagnation zone. That was
beneficial to the fouling deposition. Simultaneously, the vortex and the disturbance of the fluid was smaller obvious compared with the length of generator was 4/8H. This to a certain extent reduces the mass removal rate which can be observed from Fig. 11. So it can be seen from Fig.12 that, the fouling resistance increase at first and then decreases and has a larger value at 4/8H with the increase of the generator length. The fouling resistance has a larger value at 4/8H and a maximum value at 8/8H in rectangular channel with vortex generators. Mass deposition rate 8/8 H 7/8 H 5/8 H 4/8 H 3/8 H 2/8 H 1/8 H
1.985
2.0 6/8 H
1.6
Mass removal rate 7/8 H 6/8 H 3/8 H 2/8 H
8/8 H 4/8 H
5/8 H 1/8 H
1.2 1.980 D : 15 mm, R : 5 mm, u : 0.5 m/s Tw: 330 K, Tf : 300 K, CF: 3.0 kg/m3
1.975
0.8 0.4
1.970 0
100
200
300
400
Mass removal rate [10 -7 kg/m 2 s]
Mass deposition rate [10 -7kg/m 2 s]
1.990
0.0
Time [h] Fig.11 Effect of length of VGs on the mass deposition rate and the mass removal rate
5.8
Length
2
4
-6
-6
2
Fouling resistance [10 m K/W]
6
Fouling resistance [10 m k/w]
8/8 H 7/8 H 6/8 H 5/8 H 4/8 H 3/8 H 2/8 H 1/8 H
D : 15 mm, R : 5 mm u : 0.5 m/s, Tw : 330 K
2
3
Tf : 300 K, CF : 3.0 kg/m
5.7
5.6
5.5 1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/8
Length [mm]
0 0
100
200
300
400
Time [h]
Fig.12 Effect of length of VGs on the fouling resistance 4.2.2 Effect of the spacing of VGs The variation of the mass deposition rate and the mass removal rate with time at various spacing of VGs were shown in Fig.13. The variation of the fouling resistance with time at various spacing was shown in Fig.14.The radius and length of the half-cylinder vortex generators were maintained at 5 mm and 4/8H, respectively. It can be seen from
Fig.13 that the mass deposition increases and the increase amplitude smaller with the increase of the spacing of VGs. And when the spacing over 55 mm the change of the mass deposition rate was very small. The reason was that the 55 mm was a single half-cylinder vortex generator produced by longitudinal vortex effect can achieve the longest distance. It also can be seen from Fig.13 that, the mass removal rate increases with the increase of spacing of VGs. The main reason was that the vortex generated by the two adjacent vortex generators cannot overlay with each other, which reduce the region affected by the vortex. So the fluid turbulence near wall will generally decline, and the fouling particles to the surface's ability to transport process gradually increase. Therefore, the fouling mass deposition increases in the rectangular channel with vortex generators with the increase of the spacing. The good validation of this point was shown in Fig. 14. The fouling resistance was increase with the increase of the spacing of VGs. Mass deposition rate 15 mm 25 mm 35 mm 45 mm 55 mm 65 mm 75 mm
1.988
2.0 Mass removal rate 15 mm 25 mm 45 mm 55 mm 75 mm
35 mm 65 mm
1.5
1.981
1.0 A : 4/8 H, R : 5 mm u : 0.5 m/s, Tw : 330 K
1.974
0.5
Tf : 300 K, CF : 3.0 kg/m3
1.967 0
100
200
300
400
Mass removal rate [10 -7 kg/m 2 s]
Mass deposition rate [10 -7 kg/m 2 s]
1.995
0.0
Time [h] Fig.13 Effect of spacing of VGs on the mass deposition rate and the mass removal rate 15 mm 25 mm 35 mm 45 mm 55 mm 65 mm 75 mm
4
5.9
2
-6
2
Spacing
Fouling resistance [10 m k/w]
-6
2
Fouling resistance [10 m K/W]
6
5.8 5.7
A : 4/8 H, R : 5 mm u : 0.5 m/s, Tw : 330 K
5.6
3
Tf : 300 K, CF : 3.0 kg/m
5.5 10
20
30
40
50
60
70
80
Spacing [mm]
0
0
100
200
300
400
Time [h]
Fig.14 Effect of spacing of VGs on the fouling resistance
4.2.3 Effect of the radius of VGs The variation of the mass deposition rate and the mass removal rate with time at various radiuses of VGs were shown in Fig.15. The variation of the fouling resistance with time at various radiuses was shown in Fig.16.The spacing and length of the half-cylinder vortex generators was maintained at 15 mm and 4/8H, respectively. It can be observed from Fig. 15 that the mass deposition decreases and the decrease amplitude was larger with the increase of the radius of VGs. This was because the minimum section area of rectangular channel decreases with the increase of the generator radius. So the larger vortex and disturbance of the fluid increase with the increase of the velocity. Therefore, it disturbed the fouling particles to the surface of the deposition process, thus more effectively reduce the fouling mass deposition. It also can be seen from Fig.15 that the mass removal rate decreases with the increase of radius of VGs. Because the size of the mass removal rate was affected by the mass deposition rate, the less mass deposition, the less removal rate. Comprehensive the above two parts, it knows that the fouling resistance decreases with the increase of the radius of VGs. And it can be observed from Fig. 16.
1.98
2
1.0
1.97
1.96
1.5
-7
-7
1.99
2.0
0.5
0
100
200
300
400
Mass removal rate [10 kg/m s]
Mass deposition rate D: 15 mm A: 4/8 H u: 0.5m/s Tw: 330 K 2.5 mm 3.0 mm T : 300 K C : 3 kg/m3 F 3.5 mm 4.0 mm f 4.5 mm 5.0 mm Mass removal rate 5.5 mm 2.5 mm 3.0 mm 3.5 mm 4.0 mm 4.5 mm 5.0 mm 5.5 mm
2
Mass deposition rate [10 kg/m s]
2.00
0.0
Time [h]
Fig.15 Effect of radius of VGs on the mass deposition rate and the mass removal rate
2.5 mm 3.0 mm 3.5 mm 4.0 mm 4.5 mm 5.0 mm 5.5 mm
4
5.9 5.8
-6
2
Fouling resistance [10 m k/w]
-6
2
Fouling resistance [10 m K/W]
6
2
D : 15 mm, A : 4/8 H u : 0.5 m/s, Tw : 330 K Tf : 300 K, CF : 3 kg/m3
5.7
Radius
5.6 5.5 5.4 5.3 2.5
3.0
3.5
4.0
4.5
5.0
5.5
Radius [mm]
0 0
100
200
300
400
Time [h] Fig.16 Effect of radius of VGs on the fouling resistance
5. Conclusions (1) The mass deposition rate and the mass removal rate of CaSO4 fouling increases and the fouling resistance decreases with the increase of inlet velocity. The mass deposition rate, mass removal rate and fouling resistance all increase with the increase of CaSO4 concentration. The mass deposition rate, mass removal rate and fouling resistance all increase with the increase of surface temperature. Comparing the influence of the fouling resistance of four kinds of operation conditions: the effect of concentration on fouling resistance was the maximum, and that of the surface temperature was the minimum. (2) The mass deposition rate, mass removal rate and fouling resistance have the same variation that decreases firstly and then increases with the increase of the length. The value of fouling resistance reaches the minimum when the length was 4/8H. The mass deposition rate, mass removal rate and fouling resistance increases with the increase of the spacing. The value of fouling resistance reaches the maximum when the spacing was more than 55mm, and the fouling characteristics tends to be similar as the situation without the vortex generators. The mass deposition rate, mass removal rate and fouling resistance decreases with the increase of the radius.
Acknowledgement The financial support of the National Natural Science Foundation of China (Grant No.51476025) was gratefully acknowledged.
References [1] X. Zhao, X.D Chen, A critical review of basic crystallography to salt crystallization fouling in heat exchangers, Heat Transf. Eng. 34 (2013) 719-732. [2] N. Andritsos, A. Karabelas, Calcium carbonate scaling in a plate heat exchanger in the presence of particles, Heat Mass Transfer. 46 (2003) 4613-4627. [3] D. Kern, R. Seaton, A theoretical analysis of thermal surface fouling, Br. Chem. Eng. 4 (1959) 258-262. [4] Hasson D, Avriel M, Resnick W, Calcium carbonate scale deposition on heat transfer surfaces, Desalination. 5 (1) (1968) 107-119. [5] W. Augustin, M. Bohnet, Influence of the ratio of free hydrogen ions on crystallization fouling, Chem. Eng. Process. 34 (1995) 79-85. [6] F. Fahiminia, A.P. Watkinson, N. Epstein, Early events in the precipitation fouling of calcium sulphate dehydrate under sensible heating conditions, Can. J. Chem. Eng. 85 (2007) 679-691. [7] M. Mayer, J. Bucko, W. Benzinger, et al, The impact of crystallization fouling on a microscale heat exchanger, Exp. Therm. Fluid Sci. 40 (2012) 126-131. [8] G. M Zhang, G. Q Li, W. Li, Z. Zhang, X. L Leng, Particulate fouling and composite fouling assessment in corrugated plate heat exchangers, Int. J. Heat Mass Transf. 60 (2013) 263-273. [9] F. Brahim, W. Augustin, M. Bohnet, Numerical simulation of the fouling process, Int. J. Therm. Sci. 42 (2003) 323-334. [10]M. Mwaba, C. Rindt, A. Van Steenhoven, et al, Validated numerical analysis of CaSO4 fouling, Heat Transfer Eng. 27 (7) (2006) 50-62. [11]F. Zhang, J. Xiao, X.D. Chen, Towards predictive modeling of crystallization fouling: a pseudo-dynamic approach, Food Bioprod. Process. 93 (2014) 188-196. [12]T.M. Pääkkönen, U. Ojaniemi, T. Pättikangas, CFD modelling of CaCO3 crystallization fouling on heat transfer surfaces, Int. J. Heat Mass Transf. 97 (2016) 618-630. [13]M Fiebig, Vortices generators and heat transfer, Trans. Inst. Chem. Eng. 76 (2) (1998) 108-123. [14]K.M. Kwak, K. Torii, K. Nwashino, Heat transfer and pressure loss penalty for the number of tube rows of staggered finned-tube bundles with a single transverse row of winglets, Int. J. Heat Mass Transf. 46 (02) (2003) 175-180. [15]S.M. Pesteei, P.M.V. Subbarao, R.S. Agarwal, Experimental study of the effect of winglet location on heat
transfer enhancement and pressure drop in fin-tube heat exchangers, Appl. Therm. Eng. 25 (11-12) (2005) 1684-1696. [16]L.O. Salviano, D.J. Dezan, J.I. Yanagihara, Optimization of winglet-type vortex generator positions and angles in plate-fin compact heat exchanger: response surface methodology and direct optimization, Int. J. Heat Mass Transf. 82 (2015) 373-387. [17]C.M. Velte, M.O.L. Hansen, V.L. Okulov, Multiple vortex structures in the wake of a rectangular winglet in ground effect, Exp. Therm. Fluid Sci. 72 (2016) 31-39. [18]B Lotfi, B Sundén, Q W Wang, An investigation of the thermo-hydraulic performance of the smooth wavy fin-and-elliptical tube heat exchangers utilizing new type vortex generators, Appl. Energ. 162 (2016) 12821302. [19]W Q Tao, Numerical Heat Transfer, Second Edition, Xi'an Jiaotong University, 2011. [20]FLUENT Incorporation, FLUENT User's Guide. USA: FLUENT Incorporated Lebanon NH, 2011. [21]V. Yakhot, S.A. Orszag, Renormalization group analysis of turbulence. I. Basic theory, J. Sci. Comput. 1 (1) (1986) 3-51. [22]S. Krause, Fouling of heat transfer surfaces by crystallization and sedimentation, Int. Chem. Eng. 33 (3) (1993) 335-401. [23]J. Lammers, Zur Krwastallwasation von Calciumsulfat bei der Verkrustung von Heizflächen, Dwass. TU Berlin, 1972. [24]Bird R B, Transport phenomena, New York: Wiley, 1960. [25]M. Bohnet, Fouling of heat transfer surfaces, Chem. Eng. Technol. 10 (2) (1987) 113-125. [26]T.M. Pääkkönen, M. Riihimäki, C.J. Simonson, et al, Modeling CaCO3 crystallization fouling on a heat exchanger surface-definition of fouling layer properties and model parameters, Int. J. Heat Mass Transf. 83 (2015) 84-98. [27]Liu Zuodong. Experimental investigation on the vortex generator CaSO4 fouling characteristic of crystallization, Ji Lin: Northeast Dianli University, 2012. [28]S.W. Hwang, D.H. Kim, J.K. Min, J.H. Jeong, CFD analysis of fin tube heat exchanger with a pair of delta winglet vortex generators, J. Mech. Sci. Technol. 26 (2012) 2949-2958. [29]L.O. Salviano, J.D. Dezan, J.I. Yanagihara, Optimization of winglet-type vortex generator positions and angles in plate-fin compact heat exchanger: response surface methodology and direct optimization, Int. J. Heat Mass Transf. 82 (2015) 373-387.
[30]Gaofeng Lu, Guobing Zhou, Numerical simulation on performances of plane and curved winglet type vortex generator pairs with punched holes. Int. J. Heat Mass Transf. 102 (2016) 679-690. [31]Ting Zhang, Zhe Q. Huang, Xiao B. Zhang, Numerical investigation of heat transfer using a novel punched vortex generator. Numer. Heat Transf. A-Appl. 69 10 (2016): 1150-1168. [32]T.M. Pääkkönen, M. Riihimäki, C.J. Simonson, et al, Crystallization fouling of CaCO3-analyswas of experimental thermal reswastance and its uncertainty. Heat Mass Transf. 55 (2012) 6927-6937. [33]Q. Yang, Y. Liu, A. Gu, et al, Investigation of induction period and morphology of CaCO3 fouling on heated surface, Chem. Eng. Sci. 57 (2002) 921-931. [34]B. Bansal, H. Müller-Steinhagen, X.D. Chen, Performance of plate heat exchangers during calcium sulphate fouling-investigation with an in-line filter, Chem. Eng. Process. Process-Inten. 39 (2000) 507-519. [35]T. Kho, H.U. Zettler, H. Müller-Steinhagen, et al, Effect of flow distribution on scale formation in plate and frame heat exchangers, Chem. Eng. Res. Design. 75 (1997) 635-640. [36]Eungchan Lee, Jaemyeong Jeon, Hoon Kang, et al, Thermal resistance in corrugated plate heat exchangers under crystallization fouling of calcium sulfate (CaSO4), Int. J. Heat Mass Transf. 78 (2014) 908-916.
Highlights 1. 2. 3. 4.
A numerical simulation method was used to study the fouling characteristics. The crystallization fouling of CaSO4 was analyzed in the rectangular channel with half-cylinder vortex generators. The effects of different operating conditions and structures on the fouling resistance were investigated. The simulated results were validated based on the experimental dates.
S1359-4311(17)33043-0 http://dx.doi.org/10.1016/j.applthermaleng.2017.09.051 ATE 11108
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
4 May 2017 3 September 2017 11 September 2017
Please cite this article as: Z. Han, Z. Xu, J. Wang, CaSO4 fouling characteristics on the rectangular channel with half-cylinder vortex generators, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/ j.applthermaleng.2017.09.051
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
CaSO4 fouling characteristics on the rectangular channel with halfcylinder vortex generators Zhimin Han, Zhiming Xu*, Jingtao Wang
College of Energy and Power Engineering, Northeast Electric Power University, Jilin, Jilin Province, China * （ Corresponding Author: [email protected]）
ABSTRACT In order to study the fouling characteristics on the rectangular channel with half-cylinder vortex generators, the deposition process of CaSO4 fouling were studied by numerical simulation method. The fouling characteristics under different operation conditions and structures such as the concentration of CaSO4, the wall temperature, the inlet velocity, the length, the radius and the spacing of the half-cylinder vortex generators were investigated. The results show that the asymptotic value of fouling resistance increases with the increase of the surface temperature and the concentration, and decreases with the increase of the inlet velocity. The value of fouling resistance first decreases and then increases with the increase of the length. The value of fouling resistance reaches the minimum when the length was 4/8H. The value of fouling resistance increases with the increase of the spacing. The value of fouling resistance reaches the maximum when the spacing was more than 55mm, and the fouling characteristics tends to be similar as the situation without the vortex generators. The value of fouling resistance decreases with the increase of the radius.
KEYWORDS: Vortex generator, Fouling resistance, Numerical simulation, CaSO4 fouling
1. Introduction Fouling, was the accumulation of solid matter on a heat transfer surface, which reduces the heat transfer rate and increases the pressure drop of equipment, such as evaporators, heat exchangers, crystallizers, membranes etc.. It can cause a decline in operating efficiency of heat exchangers, power plants and other chemical industries [1]. In heat exchangers, the fouling was usually caused by supersaturation of the fluid due to a change in temperature [2]. The principal mode of calcium sulfate deposition was referred to as crystallization fouling. The normal
Nomenclatures A the length of the vortex generator (m) B width of the rectangular channel (m) cF concentration of salt solution (kg/m3) cS saturation concentration (kg/m3)
Cin
inlet concentration (kg/m3) 2
D dh dp
E, F G H, L
diffusion coefficient (m /s) hydraulic diameter (m) mean crystal diameter (m) inlet, outlet extending zone (m) spacing between two vortex generators (m) height, length of the rectangular channel (m)
P/K kt kR
cohesion coefficient ( kg·m/s2) mass transfer coefficient (m/s) rate of reaction (m4·kg/s)
Re Sh Sc Tf
Reynolds number Sherwood number Schmidt number temperature of fouling layer surface (K)
Tw
temperature of heat transfer surface (K)
∆T temperature gradient (K) ∆t computing time step (s) source term Sφ u,v,w velocity component (m2/s) xf thickness of crystal layer (m) Greek Symbols ρ density of salt solution (kg/m3) ρf density of fouling layer (kg/m3 ) λf thermal conductivity of fouling layer (W/(m· K)) ᵟ linear expansion coefficient generalized variable φ diffusion coefficient Γφ ƞ dynamic viscosity (kg/m·s)
total mass (kg/m2) m d deposition mass rate (kg/m2·s) removal mass rate (kg/m2·s) m r R radius (m) Rf fouling resistance (m2· K/W) solubility salts scales on cold surfaces, while the inverse solubility salts causes the scaling on heated surfaces. The
m
calcium sulfate was belongs to inverse solubility salts. The fouling model of heat transfer surfaces was established often based on the approach of Kern and Seaton [3] in which the difference between the mass deposition rate and the mass removal rate was the overall mass deposited on the surface. Hasson [4] as the founder of crystallization fouling research, proposed a classical ion diffusion model in study of CaCO3 fouling problems. Afterward, many scholars have done a lot of research on this basis [5-8]. In order to account the temporal and spatial variations in the fluid properties of complex heat exchangers, the Computational Fluid Dynamics (CFD) can be used [9-12]. Brahim et al. [9] in a preliminary simulation the case of the crystallization fouling of CaSO4 on the flat heat transfer surfaces based on models for the mass deposition and removal rates, and used the model to calculate the fouling process under different conditions. Mwaba et al. [10] evaluated the changes that resulting from a non-uniform fouling layer in the heat flow distribution, and simulated a case where calcium sulfate fouling forms on for a heated plate subjected to a shear flow. Zhang et al. [11] studied a new computational fluid dynamics (CFD) model and developed the method how to characterize a crystallization fouling process mathematically. Pääkkönen et al. [12] used CFD to simulate the CaCO3 crystallization fouling on an idealized heat exchanger, and then used to analyze further the crystallization fouling mechanism. The most papers show that the researches were committed to the simple geometric model to mainly study the crystallization fouling mechanism. Recently, the vortex generators (VGs) as a new heat transfer enhancement technique, has received more and more attention. It was a passive heat transfer element by a special type of extended
surface that was possible to generate vortices with parallel to the flow direction [13]. The vortex generators which can produce longitudinal vortices were widely used in the field of the heat transfer enhancement, because the longitudinal vortices can thin and destroy the wall boundary layer and then to achieve heat transfer enhancement [14-18]. In this paper, CFD was often used to model the CaSO4 crystallization fouling on the rectangular channel with half-cylinder vortex generators. The fouling characteristics under different operation conditions and structures such as the concentration of CaSO4, the wall temperature, the inlet velocity, the length, the radius and the spacing of the halfcylinder vortex generators were investigated.
2. Mathematical model 2.1 Geometry description The rectangular channel with half-cylinder vortex generators was shown in Fig. 1. The channel has a length L=420mm, height H=10mm, and width B=30mm. In order to keep the inlet velocity stability, and to avoid the backflow of the outlet, the actual calculation region was expanded to include an inlet extending zone of E=50mm; and the out extending zone of F=150mm. The half-cylinder vortex generators were equally distributed along the base of the rectangular channel. The spacing between two vortex generators was G. The length of the vortex generator was A, and the radius was R.
Fig.1 Rectangular channel with half-cylinder vortex generators
2.2 Mathematical formulation The governing equations in physical space for continuity, momentum, energy and species equations in the calculation region can be expressed generally as follows [19]:
∂ ( ρφ ) ∂t
+ div ( ρU φ ) = div ( Γφ gradφ ) + Sφ
（1）
where ρ was the density of the fluid, t was time, φ was generalized variable, it represents the variables of u, v, w, T etc.. Γφ was generalized diffusion coefficient. Sφ was generalized source term. The extended equations applied in this paper were presented more detailed in references [12]. FLUENT has provided many choices of turbulence models [20]. Whereas the standard k-ε turbulence model was usually developed for fully turbulent flows, and the RNG k-ε turbulence model was better adapted to low Reynolds numbers. In the present work, the flow regime in the set-up was turbulent in the studied conditions with the bulk Reynolds numbers between 8,900 and 23,900. Therefore, the standard k-ε turbulent model was adopted in the calculation region [21].
2.3 Crystallization fouling model In this paper, the following crystallization fouling model of Brahim [9]and Krause [22] was carried out to CFD: 1 1 k 2 k 2 1 kt m d = kt + ∆c − t + t ∆c 4 k R k R 2 kR
（2）
where ∆c was the total concentration difference: ∆c = c F -cS . cF was the mainstream concentration of salt solution and cS was the saturation concentration and was calculated as a function of Tf [9, 23].
log(cs )=-
∆c ∆LH 0 + p ⋅ log ( T f ) + C 2.3 ⋅ h ⋅ T f h
（3）
The mass transfer coefficient was kt , which can be determined as:
kt =
ShD . dh
（4）
Sherwood number can be calculated by the following semi-empirical approach according to Lammers [23]:
Sh = 0.034Re0.875 Sc1/3 where Re =
ρud h η , Sc = . D can be obtained by the Bird [24]: η ρD T 1 1 D = D1 2 exp 380 − T1 T1 T2
where when T1 =355.5K, the mass diffusion coefficient D1=1.0633×10-7m2/s.
（5）
-
The surface reaction rate constant kR can be calculated by Arrhenius law: k R = k R0 e
E RoT f
.
where kRo was the reaction constant, kRo=7.07m4/(kg·s), and E was the reaction activation energy, E=37143J/(mol·k) [9]. Tf was the surface temperature of the fouling layer. Ro was the universal gas constant.
The model of the removal mass rate of CaSO4 fouling was given by [9, 25]:
m r =
1/3 K ρ f (1 + δ∆T ) dP ( ρ 2η g ) x f u 2 P
（6）
The measurement methods based on Krause’s measurements was used for the calculation of P/K [22]:
P = 83.2 ⋅ u 0.54 . K The average density of fouling layer as: ρ f =
m . xf
The fluid velocity u above the fouling layer as: u = u0
H . H − xf
The thickness of the fouling layer was calculated as the total deposit mass per surface area divided by the density ρf of the fouling layer: x f =
m t + ∆t
ρf
.
where (1+δ∆T) which describes the temperature stresses in the fouling layer. ∆T was the temperature gradient in the fouling layer, δ was the linear expansion coefficient. According to Krause [22], dp was the average diameter of crystal for CaSO4 solution, which was about 36 micrometer, xf was the mean thickness of the fouling layer.
The total mass rate was calculated as:
dm dmd dmr = − ⇒ m = m d − m r dt dt dt
（7）
The thermal resistance of the fouling layer can be modelled as:
Rf = m / ( ρ f λf
)
（8）
where λf was the thermal conductivity of fouling layer.
2.4 Boundary conditions Pääkkönen et al. [26] found that the surface integration was controlled the crystallization fouling process. Therefore, during numerical simulation process, the heated wall was applied to the constant surface temperature
boundary condition. The temperature at the bottom of the channel was from 320 K to 340 K. The other surfaces and extending area of the channel were considered as insulated. The channel walls and the vortex generators were adopted at no-slip boundary conditions. The velocity inlet condition was used for the inlet boundary condition, and the outflow was used for the outlet boundary condition. The inlet boundary was specified flow velocity, salt concentration and temperature. The temperature of the fluid at the inlet was 300 K, the inlet velocity was changes from 0.4 m/s to 0.8 m/s, and the concentration was from 2.0 kg/m3 to 4.0 kg/m3. The range of Reynolds number in the set-up was between 8,900 and 23,900 with the given flow velocity range.
3. Numerical method and validation In this paper, the commercial software package CFD software ANSYS FLUENT 14.0 was used to formulate and solve the process. The calculation region was discretized by using a structured mesh generated with the software of ICEM. In order to capture the characteristics of the fluid flow, the hexahedron grids filling the majority of the volume were used. In addition, the local grid refinement was applied in the vicinity of the bottom of the channel and the vortex generators. Three-dimensional double separate of FLUENT software was used for solver. The SIMPLE algorithm was used to couple the pressure and velocity in the momentum equation. The standard scheme was used to couple the discretization of the pressure, and the continuity, momentum, energy and species equation were performed by the second-order upwind scheme. The convergence criterion of the residual of continuity, momentum, energy and species equations was set to be 10-6. A 400 h fouling process was simulated with the time step ∆t specified as 1h [10]. The grid independent test was applied in half-cylinder vortex generators in the rectangular channel. At the fluid inlet, the concentration and the temperature of CaSO4 solution were, respectively Cin =3.0 kg/m3 and Tf = 300 K. The inlet velocity u was 0.5 m/s and the constant surface temperature Tw was 330K.The grid number increases from 201,152 to 1,172,720, the mass deposition rate with the change of the grid number was illustrated in Fig. 2. The results indicate that the mass deposition rate no longer changes, when the grid number of the computing area was larger than 0.9 million. This finding demonstrates that the grid system with 1,068,704 elements was adequately enough for the simulations.
201152 409542 647328 815796 927080 1068704 1172720
1.983
-7
2
Mass deposition rate [10 kg/m s]
1.986
u : 0.5m/s, Tw : 330K
1.980
Tf : 300K, CF : 3.0kg/m2
1.977 1.974 1.971 1.968
0
100
200
300
Time [h] Fig.2 Verify of grid independence
Fig.3 Schematic diagram of experimental system
In order to verify the accuracy of the calculation model and numerical method, it was necessary to compare with experimental data. Fig. 3 shows the schematic diagram of the experimental system used for the fouling experiments.
The specific experimental steps and principles applied in this paper were presented more detailed in references [27]. The specific process was: the manually formulated CaSO4 solution was heated at a heater controlled temperature, and then through the circulating water pump from the low water tank into the high water tank. In the high water tank need to control the water level, when the water level exceeds the specified water level will flow back from the overflow pipe to the low water tank. This will make the high water tank in the working fluid to ensure that a certain flow rate through the experimental channel for heat transfer, and then the working fluid flow through the flow meter, valves, etc., and finally flow back to the low water tank. The flow rate of the
working fluid can be adjusted by means of flow meters and valves. The temperature in the experimental section was controlled by thermal resistance and thermostat control. At last, all relevant experimental data are collected through the data acquisition system and entered into the computer. The calculated mass deposition rate from the smooth channel was compared to the experimental results on the same size channel, in the same conditions. These numerical validations have widely been applied for the compact heat exchanger [28-31], which were most reliable and accurate with wide applicable ranges considering a smooth channel (without vortex generators). The comparison result for the mass deposition rate for a smooth channel was shown in Fig. 4. It shows that the relative error between the computational data and the experimental data was within 15%. For now, the error range was acceptable in the field of fouling calculation. 100 90
Experimental Simulation
6.0
80 Relative error [%]
-5
2
Fouling resistance [10 m K/W]
7.5
4.5 u : 0.1 m/s Tf : 323 K
3.0
CF: 2.1 g/L
1.5
70 60 50 40 30 20 10
0.0
0
50
100
150
200
0
0
50
Time [h]
100
150
200
Time / h
Fig.4 Verification results for the mass deposition rate for a smooth channel
4 Results and discussion 4.1 Effect of operating conditions on fouling resistance evolution 4.1.1 Effect of the inlet velocity The variation of the mass deposition rate and the mass removal rate with time at various flow velocities were shown in Fig. 5. The concentration of CaSO4, inlet temperatures and surface temperatures of the solution were conducted at 3.0 kg/m3, 300 K, and 330 K, respectively. It can be observed from Fig. 5 that the mass deposition rate of CaSO4 fouling curve was almost coincident due to the relationship of the vertical coordinate. However, after the vertical coordinates were enlarged, the variation of the mass deposition rate with time was shown in the partial amplification. It shows that the mass deposition rate of CaSO4 fouling increases with the increase of velocity. This was because from the Eq. (2) that, the mass deposition rate was in proportion to the mass transfer coefficient, and the mass transfer coefficient was indirectly proportion to the velocity. So the increase of the velocity will lead to mass
deposition rate increases. It also can be seen from Fig.4 that the mass removal rate increases with the increase of velocity. It can be explained by the model of mass removal rate Eq. (6) that the size of the mass removal rate was associated with the flow velocity of fluid. A higher shear force and a larger flushing action were formed with the increase of flow velocity at the interface of the fouling layer and the solution [26].
2.4 2.0
-7
-7
2.0
2.8
2
2.4
Mass removal rate 0.4 m/s 0.5 m/s 0.6 m/s 0.7 m/s 0.8 m/s
Mass removal rate [10 kg/m s]
Mass deposition rate 0.4 m/s 0.5 m/s 0.6 m/s 0.7 m/s 0.8 m/s
2
Mass deposition rate [10 kg/m s]
2.8
1.6 2.00
-7
2
Mass deposition rate [10 kg/m s]
1.6 1.2 0.8 D : 40 mm, R : 6 mm A : 8/8 H, Tw: 330 K
0.4
1.99
1.2
1.98
0.8
1.97 0
0.0
Tf : 300 K, CF: 3.0 kg/m
0
100
100
200
300
400
0.4
Time [h]
3
(The partial amplification)
200
300
400
0.0
Time [h]
Fig.5 Effect of inlet velocity on the mass deposition rate and the mass removal rate The variation of the fouling resistance with time at various flow velocities were shown in Fig. 6. It can be seen that the fouling resistance decreased with the increase in the flow velocity. This was because that the fouling resistance was derived from the mass deposition rate and the mass removal rate. And the increment of mass removal rate was much higher than the increment of mass deposition rate. So the fouling resistance decreases with the increase of flow velocity. Pääkkönen et al. [32] and Yang et al. [33] studied that at a constant surface temperature, the fouling resistance increased and the asymptotic fouling period decreased with the increased of the velocity because of the increased number of foulant ions. 0.4m/s 0.6m/s 0.8m/s
0.5m/s 0.7m/s
6
-6
2
Fouling resistance [10 m K/W]
8
4 D : 40 mm, R : 6 mm A : 8/8 H, Tw: 330K
2
3
T f: 300K, CF: 3.0kg/m
0
0
100
200
300
400
Time [h] Fig.6 Effect of inlet velocity on the mass deposition rate and the mass removal rate
4.1.2 Effect of the CaSO4 concentration The variation of the mass deposition rate and the mass removal rate with time at various CaSO4 concentrations were shown in Fig. 7. The inlet velocity, inlet temperatures and surface temperatures of the solution were maintained at 0.5m/s, 300K, and 330K, respectively. It can be seen that, the mass deposition rate increases with the increase of CaSO4 concentration. This was because the concentration in the main flow region increases with the increase of CaSO4 concentration in the fluid. And the boundary concentration was remains unchanged by the change of saturated fluid. Therefore, the concentration difference becomes large between the main flow region and boundary layer nearby. The mass deposition rate increases with increase of CaSO4 concentration. It also can be seen from Fig.6 that the mass removal rate increases with the increase of CaSO4 concentration. The main reason was that the size of the mass removal rate will be affected by thickness of fouling layer. On the one hand, the mass deposition increase with the increase of the concentration, it will increase the thickness of fouling layer. On the other hand, the increase of the thickness of fouling layer may cause the increase of the velocity. It will increase the scouring action of the fouling layer in the fluid. Therefore, the mass removal rate increases with the increase of concentration.
3
3.0 kg/m
4
3
2.5 kg/m
2.0 kg/m
3
3
3.5 kg/m
3.0 kg/m
3
3
2.5 kg/m
3
3.5 kg/m
3
4.0 kg/m
4
4.0 kg/m
-7
2
Mass deposition rate [10 kg/m s]
2.0 kg/m
5
Mass removal rate 3
3
3
2
2
1
1
0
D: 40 mm， R : 6 mm， A : 8/8 H u : 0.5 m/s ， Tf : 300 K， Tw: 330 K
0
100
200
300
400
2
3
-7
Mass deposition rate
Mass removal rate [10 kg/m s]
5
0
Time [h]
Fig.7 Effect of CaSO4 concentration on the mass deposition rate and the mass removal rate The variation of the fouling resistance with time at various CaSO4 concentrations was shown in Fig. 8. It can be seen that the fouling resistance increases with the increase of CaSO4 concentration. The main reason was that the fouling resistance was derived from the mass deposition rate and the mass removal rate. Before the asymptotic fouling period, the increasing slope of the fouling resistance increases with the increase of CaSO4 concentration [34,35], and this was because the increased reaction rate with the increased number of foulant ions led to a higher deposition rate [36].
3
2.0kg/m
3
2.5kg/m
3
3.0kg/m
3
3.5kg/m
8
3
2
Fouling resistance [10 m K/W]
10
-6
4.0kg/m 6
4
D : 40 mm, R : 6 mm A : 8/8 H, u : 0.5 m/s Tf : 300 K, Tw: 330 K
2
0 0
100
200
300
400
Time [h]
Fig.8 Effect of CaSO4 concentration on the fouling reswastance 4.1.3 Effect of the surface temperature The variation of the mass deposition rate and the mass removal rate with time at various surface temperatures were shown in Fig. 9. The concentration of CaSO4, inlet temperatures and inlet velocity of the solution were maintained at 3.0kg/m3, 300K, and 0.5m/s, respectively. It can be observed from Fig. 9 that the mass deposition rate of CaSO4 fouling increases with the increase of surface temperature. The reason was that the change in the mass deposition rate was affected by the total concentration gradient, which can be seen by the model of mass deposition rate Eq. (2). As CaSO4 was a kind of sulfate shows inverse solubility, the solubility of CaSO4 decreases with the increase of the solution temperature. Therefore, the total concentration gradient increases with the increase of surface temperature, and more CaSO4 precipitates from the cycle working fluid. It also can be seen from Fig. 9 that the mass removal rate increases with the increase of the surface temperature of the fluid. This was because the mass removal rate mainly affected by the thickness of the fouling layer. As can be seen from the foregoing, the increase of deposition amount will increase the thickness of fouling layer. Meanwhile, the mass removal rate of fouling will increase with the increase of the surface temperature. The variation of the fouling resistance with time at various surface temperatures was shown in Fig. 10. It can be seen that the fouling resistance increases with the increase of surface temperature. Yang et al. [33] reported that the increase of the surface temperature will increase the reaction rate constant. So the fouling resistance increases with increase of surface temperature. The increasing slope of the fouling resistance increases with the increase of surface temperature because of the increasing deposition rate with the higher surface temperature. While the decreasing solubility at higher solution temperatures leads to the increase of the asymptotic fouling period.
2
Mass deposition rate Mass removal rate 320 K 320 K 325 K 325 K 330 K 330 K 335 K 335 K 340 K 340 K
1.5
1.0
1.0
D : 40 mm, R : 6 mm A : 8/8 H, u : 0.5 m/s Tf : 300 K, CF: 3.0 kg/m3
0.5
0.0
1.5
0
100
200
300
0.5
400
-7
-7
Mass removal rate [10 kg/m s]
2.0
2
Mass deposition rate [10 kg/m s]
2.0
0.0
Time [h]
320 K 325 K 330 K 335 K 340 K
6
-6
2
Fouling resistance [10 m K/W]
Fig.9 Effect of surface temperatures on the mass deposition rate and the mass removal rate
4 D : 40 mm, R : 6 mm A : 8/8 H, u : 0.5 m/s Tf : 300 K, CF : 3.0 kg/m3
2
0
0
100
200
300
400
Time [h]
Fig.10 Effect of surface temperatures on the fouling resistance
4.2 Effect of vortex generators structures on fouling resistance evolution 4.2.1 Effect of the length of VGs The variation of the mass deposition rate and the mass removal rate with time at various lengths of VGs were shown in Fig.11. The variation of the fouling resistance with time at various lengths was shown in Fig.12. The radius and spacing of the half-cylinder vortex generators were conducted at 5 mm and 15 mm, respectively. It can be seen from Fig.11 that the mass deposition rate has a minimum value at 4/8H and a maximum value at 8/8H in rectangular channel with vortex generators. This was because the fluid near the wall was completely separated by the vortex generators when the length of generator arrived at 8/8H, and it produces a large backflow stagnation zone. That was
beneficial to the fouling deposition. Simultaneously, the vortex and the disturbance of the fluid was smaller obvious compared with the length of generator was 4/8H. This to a certain extent reduces the mass removal rate which can be observed from Fig. 11. So it can be seen from Fig.12 that, the fouling resistance increase at first and then decreases and has a larger value at 4/8H with the increase of the generator length. The fouling resistance has a larger value at 4/8H and a maximum value at 8/8H in rectangular channel with vortex generators. Mass deposition rate 8/8 H 7/8 H 5/8 H 4/8 H 3/8 H 2/8 H 1/8 H
1.985
2.0 6/8 H
1.6
Mass removal rate 7/8 H 6/8 H 3/8 H 2/8 H
8/8 H 4/8 H
5/8 H 1/8 H
1.2 1.980 D : 15 mm, R : 5 mm, u : 0.5 m/s Tw: 330 K, Tf : 300 K, CF: 3.0 kg/m3
1.975
0.8 0.4
1.970 0
100
200
300
400
Mass removal rate [10 -7 kg/m 2 s]
Mass deposition rate [10 -7kg/m 2 s]
1.990
0.0
Time [h] Fig.11 Effect of length of VGs on the mass deposition rate and the mass removal rate
5.8
Length
2
4
-6
-6
2
Fouling resistance [10 m K/W]
6
Fouling resistance [10 m k/w]
8/8 H 7/8 H 6/8 H 5/8 H 4/8 H 3/8 H 2/8 H 1/8 H
D : 15 mm, R : 5 mm u : 0.5 m/s, Tw : 330 K
2
3
Tf : 300 K, CF : 3.0 kg/m
5.7
5.6
5.5 1/8
2/8
3/8
4/8
5/8
6/8
7/8
8/8
Length [mm]
0 0
100
200
300
400
Time [h]
Fig.12 Effect of length of VGs on the fouling resistance 4.2.2 Effect of the spacing of VGs The variation of the mass deposition rate and the mass removal rate with time at various spacing of VGs were shown in Fig.13. The variation of the fouling resistance with time at various spacing was shown in Fig.14.The radius and length of the half-cylinder vortex generators were maintained at 5 mm and 4/8H, respectively. It can be seen from
Fig.13 that the mass deposition increases and the increase amplitude smaller with the increase of the spacing of VGs. And when the spacing over 55 mm the change of the mass deposition rate was very small. The reason was that the 55 mm was a single half-cylinder vortex generator produced by longitudinal vortex effect can achieve the longest distance. It also can be seen from Fig.13 that, the mass removal rate increases with the increase of spacing of VGs. The main reason was that the vortex generated by the two adjacent vortex generators cannot overlay with each other, which reduce the region affected by the vortex. So the fluid turbulence near wall will generally decline, and the fouling particles to the surface's ability to transport process gradually increase. Therefore, the fouling mass deposition increases in the rectangular channel with vortex generators with the increase of the spacing. The good validation of this point was shown in Fig. 14. The fouling resistance was increase with the increase of the spacing of VGs. Mass deposition rate 15 mm 25 mm 35 mm 45 mm 55 mm 65 mm 75 mm
1.988
2.0 Mass removal rate 15 mm 25 mm 45 mm 55 mm 75 mm
35 mm 65 mm
1.5
1.981
1.0 A : 4/8 H, R : 5 mm u : 0.5 m/s, Tw : 330 K
1.974
0.5
Tf : 300 K, CF : 3.0 kg/m3
1.967 0
100
200
300
400
Mass removal rate [10 -7 kg/m 2 s]
Mass deposition rate [10 -7 kg/m 2 s]
1.995
0.0
Time [h] Fig.13 Effect of spacing of VGs on the mass deposition rate and the mass removal rate 15 mm 25 mm 35 mm 45 mm 55 mm 65 mm 75 mm
4
5.9
2
-6
2
Spacing
Fouling resistance [10 m k/w]
-6
2
Fouling resistance [10 m K/W]
6
5.8 5.7
A : 4/8 H, R : 5 mm u : 0.5 m/s, Tw : 330 K
5.6
3
Tf : 300 K, CF : 3.0 kg/m
5.5 10
20
30
40
50
60
70
80
Spacing [mm]
0
0
100
200
300
400
Time [h]
Fig.14 Effect of spacing of VGs on the fouling resistance
4.2.3 Effect of the radius of VGs The variation of the mass deposition rate and the mass removal rate with time at various radiuses of VGs were shown in Fig.15. The variation of the fouling resistance with time at various radiuses was shown in Fig.16.The spacing and length of the half-cylinder vortex generators was maintained at 15 mm and 4/8H, respectively. It can be observed from Fig. 15 that the mass deposition decreases and the decrease amplitude was larger with the increase of the radius of VGs. This was because the minimum section area of rectangular channel decreases with the increase of the generator radius. So the larger vortex and disturbance of the fluid increase with the increase of the velocity. Therefore, it disturbed the fouling particles to the surface of the deposition process, thus more effectively reduce the fouling mass deposition. It also can be seen from Fig.15 that the mass removal rate decreases with the increase of radius of VGs. Because the size of the mass removal rate was affected by the mass deposition rate, the less mass deposition, the less removal rate. Comprehensive the above two parts, it knows that the fouling resistance decreases with the increase of the radius of VGs. And it can be observed from Fig. 16.
1.98
2
1.0
1.97
1.96
1.5
-7
-7
1.99
2.0
0.5
0
100
200
300
400
Mass removal rate [10 kg/m s]
Mass deposition rate D: 15 mm A: 4/8 H u: 0.5m/s Tw: 330 K 2.5 mm 3.0 mm T : 300 K C : 3 kg/m3 F 3.5 mm 4.0 mm f 4.5 mm 5.0 mm Mass removal rate 5.5 mm 2.5 mm 3.0 mm 3.5 mm 4.0 mm 4.5 mm 5.0 mm 5.5 mm
2
Mass deposition rate [10 kg/m s]
2.00
0.0
Time [h]
Fig.15 Effect of radius of VGs on the mass deposition rate and the mass removal rate
2.5 mm 3.0 mm 3.5 mm 4.0 mm 4.5 mm 5.0 mm 5.5 mm
4
5.9 5.8
-6
2
Fouling resistance [10 m k/w]
-6
2
Fouling resistance [10 m K/W]
6
2
D : 15 mm, A : 4/8 H u : 0.5 m/s, Tw : 330 K Tf : 300 K, CF : 3 kg/m3
5.7
Radius
5.6 5.5 5.4 5.3 2.5
3.0
3.5
4.0
4.5
5.0
5.5
Radius [mm]
0 0
100
200
300
400
Time [h] Fig.16 Effect of radius of VGs on the fouling resistance
5. Conclusions (1) The mass deposition rate and the mass removal rate of CaSO4 fouling increases and the fouling resistance decreases with the increase of inlet velocity. The mass deposition rate, mass removal rate and fouling resistance all increase with the increase of CaSO4 concentration. The mass deposition rate, mass removal rate and fouling resistance all increase with the increase of surface temperature. Comparing the influence of the fouling resistance of four kinds of operation conditions: the effect of concentration on fouling resistance was the maximum, and that of the surface temperature was the minimum. (2) The mass deposition rate, mass removal rate and fouling resistance have the same variation that decreases firstly and then increases with the increase of the length. The value of fouling resistance reaches the minimum when the length was 4/8H. The mass deposition rate, mass removal rate and fouling resistance increases with the increase of the spacing. The value of fouling resistance reaches the maximum when the spacing was more than 55mm, and the fouling characteristics tends to be similar as the situation without the vortex generators. The mass deposition rate, mass removal rate and fouling resistance decreases with the increase of the radius.
Acknowledgement The financial support of the National Natural Science Foundation of China (Grant No.51476025) was gratefully acknowledged.
References [1] X. Zhao, X.D Chen, A critical review of basic crystallography to salt crystallization fouling in heat exchangers, Heat Transf. Eng. 34 (2013) 719-732. [2] N. Andritsos, A. Karabelas, Calcium carbonate scaling in a plate heat exchanger in the presence of particles, Heat Mass Transfer. 46 (2003) 4613-4627. [3] D. Kern, R. Seaton, A theoretical analysis of thermal surface fouling, Br. Chem. Eng. 4 (1959) 258-262. [4] Hasson D, Avriel M, Resnick W, Calcium carbonate scale deposition on heat transfer surfaces, Desalination. 5 (1) (1968) 107-119. [5] W. Augustin, M. Bohnet, Influence of the ratio of free hydrogen ions on crystallization fouling, Chem. Eng. Process. 34 (1995) 79-85. [6] F. Fahiminia, A.P. Watkinson, N. Epstein, Early events in the precipitation fouling of calcium sulphate dehydrate under sensible heating conditions, Can. J. Chem. Eng. 85 (2007) 679-691. [7] M. Mayer, J. Bucko, W. Benzinger, et al, The impact of crystallization fouling on a microscale heat exchanger, Exp. Therm. Fluid Sci. 40 (2012) 126-131. [8] G. M Zhang, G. Q Li, W. Li, Z. Zhang, X. L Leng, Particulate fouling and composite fouling assessment in corrugated plate heat exchangers, Int. J. Heat Mass Transf. 60 (2013) 263-273. [9] F. Brahim, W. Augustin, M. Bohnet, Numerical simulation of the fouling process, Int. J. Therm. Sci. 42 (2003) 323-334. [10]M. Mwaba, C. Rindt, A. Van Steenhoven, et al, Validated numerical analysis of CaSO4 fouling, Heat Transfer Eng. 27 (7) (2006) 50-62. [11]F. Zhang, J. Xiao, X.D. Chen, Towards predictive modeling of crystallization fouling: a pseudo-dynamic approach, Food Bioprod. Process. 93 (2014) 188-196. [12]T.M. Pääkkönen, U. Ojaniemi, T. Pättikangas, CFD modelling of CaCO3 crystallization fouling on heat transfer surfaces, Int. J. Heat Mass Transf. 97 (2016) 618-630. [13]M Fiebig, Vortices generators and heat transfer, Trans. Inst. Chem. Eng. 76 (2) (1998) 108-123. [14]K.M. Kwak, K. Torii, K. Nwashino, Heat transfer and pressure loss penalty for the number of tube rows of staggered finned-tube bundles with a single transverse row of winglets, Int. J. Heat Mass Transf. 46 (02) (2003) 175-180. [15]S.M. Pesteei, P.M.V. Subbarao, R.S. Agarwal, Experimental study of the effect of winglet location on heat
transfer enhancement and pressure drop in fin-tube heat exchangers, Appl. Therm. Eng. 25 (11-12) (2005) 1684-1696. [16]L.O. Salviano, D.J. Dezan, J.I. Yanagihara, Optimization of winglet-type vortex generator positions and angles in plate-fin compact heat exchanger: response surface methodology and direct optimization, Int. J. Heat Mass Transf. 82 (2015) 373-387. [17]C.M. Velte, M.O.L. Hansen, V.L. Okulov, Multiple vortex structures in the wake of a rectangular winglet in ground effect, Exp. Therm. Fluid Sci. 72 (2016) 31-39. [18]B Lotfi, B Sundén, Q W Wang, An investigation of the thermo-hydraulic performance of the smooth wavy fin-and-elliptical tube heat exchangers utilizing new type vortex generators, Appl. Energ. 162 (2016) 12821302. [19]W Q Tao, Numerical Heat Transfer, Second Edition, Xi'an Jiaotong University, 2011. [20]FLUENT Incorporation, FLUENT User's Guide. USA: FLUENT Incorporated Lebanon NH, 2011. [21]V. Yakhot, S.A. Orszag, Renormalization group analysis of turbulence. I. Basic theory, J. Sci. Comput. 1 (1) (1986) 3-51. [22]S. Krause, Fouling of heat transfer surfaces by crystallization and sedimentation, Int. Chem. Eng. 33 (3) (1993) 335-401. [23]J. Lammers, Zur Krwastallwasation von Calciumsulfat bei der Verkrustung von Heizflächen, Dwass. TU Berlin, 1972. [24]Bird R B, Transport phenomena, New York: Wiley, 1960. [25]M. Bohnet, Fouling of heat transfer surfaces, Chem. Eng. Technol. 10 (2) (1987) 113-125. [26]T.M. Pääkkönen, M. Riihimäki, C.J. Simonson, et al, Modeling CaCO3 crystallization fouling on a heat exchanger surface-definition of fouling layer properties and model parameters, Int. J. Heat Mass Transf. 83 (2015) 84-98. [27]Liu Zuodong. Experimental investigation on the vortex generator CaSO4 fouling characteristic of crystallization, Ji Lin: Northeast Dianli University, 2012. [28]S.W. Hwang, D.H. Kim, J.K. Min, J.H. Jeong, CFD analysis of fin tube heat exchanger with a pair of delta winglet vortex generators, J. Mech. Sci. Technol. 26 (2012) 2949-2958. [29]L.O. Salviano, J.D. Dezan, J.I. Yanagihara, Optimization of winglet-type vortex generator positions and angles in plate-fin compact heat exchanger: response surface methodology and direct optimization, Int. J. Heat Mass Transf. 82 (2015) 373-387.
[30]Gaofeng Lu, Guobing Zhou, Numerical simulation on performances of plane and curved winglet type vortex generator pairs with punched holes. Int. J. Heat Mass Transf. 102 (2016) 679-690. [31]Ting Zhang, Zhe Q. Huang, Xiao B. Zhang, Numerical investigation of heat transfer using a novel punched vortex generator. Numer. Heat Transf. A-Appl. 69 10 (2016): 1150-1168. [32]T.M. Pääkkönen, M. Riihimäki, C.J. Simonson, et al, Crystallization fouling of CaCO3-analyswas of experimental thermal reswastance and its uncertainty. Heat Mass Transf. 55 (2012) 6927-6937. [33]Q. Yang, Y. Liu, A. Gu, et al, Investigation of induction period and morphology of CaCO3 fouling on heated surface, Chem. Eng. Sci. 57 (2002) 921-931. [34]B. Bansal, H. Müller-Steinhagen, X.D. Chen, Performance of plate heat exchangers during calcium sulphate fouling-investigation with an in-line filter, Chem. Eng. Process. Process-Inten. 39 (2000) 507-519. [35]T. Kho, H.U. Zettler, H. Müller-Steinhagen, et al, Effect of flow distribution on scale formation in plate and frame heat exchangers, Chem. Eng. Res. Design. 75 (1997) 635-640. [36]Eungchan Lee, Jaemyeong Jeon, Hoon Kang, et al, Thermal resistance in corrugated plate heat exchangers under crystallization fouling of calcium sulfate (CaSO4), Int. J. Heat Mass Transf. 78 (2014) 908-916.
Highlights 1. 2. 3. 4.
A numerical simulation method was used to study the fouling characteristics. The crystallization fouling of CaSO4 was analyzed in the rectangular channel with half-cylinder vortex generators. The effects of different operating conditions and structures on the fouling resistance were investigated. The simulated results were validated based on the experimental dates.