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Numerical and experimental analysis of composite fouling in corrugated plate heat exchangers
International Journal of Heat and Mass Transfer 63 (2013) 351–360
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Numerical and experimental analysis of composite fouling in corrugated plate heat exchangers Wei Li a,⇑, Hong-xia Li a, Guan-qiu Li a, Shi-chune Yao b a b
Department of Energy Engineering, Zhejiang University, Hangzhou 310027, PR China Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, United States
a r t i c l e
i n f o
Article history: Received 4 August 2012 Received in revised form 24 March 2013 Accepted 29 March 2013 Available online 1 May 2013 Keywords: Fouling Numerical simulation Von-Karman analogy Plate heat exchanger
a b s t r a c t This paper provides a numerical and experimental analysis on precipitation and particulate fouling in corrugated plate heat exchangers with different geometric parameters which are plate height, plate spacing, and plate angle. The Realizable j–e model with non-equilibrium wall functions is used in the 3D numerical simulation considering the realistic geometries of the flow channel to obtained Nusselt number and wall shear stress, while Von-Karman analogy is used to obtain mass transfer coefficient. Numerical analysis is verified by experimental study. The predicted influence of fluid velocity in fouling resistance is compatible with experimental data that it can help to optimize the design of plate heat exchangers. This investigation significantly simplifies the fouling analysis of complex flow fields and can be used to assess the fouling potential of corrugated plate heat exchangers. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Plate heat exchanger (PHE) has been widely used in many industrial applications, such as food, oil, heat-recovery etc., because of its outstanding heat transfer performance, easy maintenance, compactness, and convenience to increase heat transfer area etc. [1]. Corrugations in plate heat exchangers enhance heat transfer rate by increasing heat transfer area and increasing turbulence mixing at low flow rates. However, fouling brings many concerns in the applications of PHEs. The heat transfer coefficient of fouled PHEs can be even lower than the heat exchangers with no enhanced surfaces. Fouling is a comprehensive and complex problem, which has many influential factors. Many researchers have investigated the effects of geometry design and process conditions on fouling performance for tubes. In a number cases the fouling models were established. Kim and Webb conducted accelerated particulate fouling experiments in three repeated rib tubes and a plain tube. The mass transfer rate is assumed to control the particle transport process, and the wall shear stress is assumed to control the removal process [1]. Webb and Li [2] took 2 years to perform practical cooling tower water fouling in a series of a series of seven helical-rib tubes and a smooth tube. The j factor analogy was used to calculate the asymptotic fouling resistance [3]. Naess et al. [4] reported an experimental study of accelerated particulate fouling tests from real industrial gas streams on bare and finned tubes in cross flow. ⇑ Corresponding author. Tel./fax: +86 571 87952244. E-mail address: [email protected] (W. Li). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.03.073
Asymptotic fouling behavior was observed for both finned and unfinned tubes. The major part of the deposit was formed on the rear section of the tubes, where shear forces were low and protected from impaction of larger particles. Cho’s team continued to develop anti-fouling technology [5]. They investigated the effect of a selfcleaning filter on the performance of physical water treatment coil for the mitigation of mineral fouling in a concentric counter flow heat exchanger. Recent studies on fouling inside PHE are following. Merheb et al. [6] monitored the fouling inside PHE in real time, using multiple optimized non-intrusive sensors. Low-frequency acoustic waves propagated through the plates, and these waves were analyzed to detect fouling inside the PHE. Mahdi et al. [7] proposed a twodimensional dynamic model for milk fouling to predict the performance of a PHE using material balance equations. Their results showed fouling was highly dependent on the various process operating conditions. Lei et al. [8] tested the effects of surface roughness and textures of the PHE on calcium carbonate fouling, and found that the growth rate, the distribution and the crystal size of calcium carbonate fouling were strongly dependent on the surface texture and finish. Jun et al. [9] accounted for the hydrodynamics of fluid flow using a 2D model, which was capable of predicting the temperature distribution of flow with higher accuracy than a 1D model. Georgiadis and Macchietto [10] predicted the milk deposit patterns on the plate surfaces, which were expected to pave the way to organize and optimize the operating conditions for reducing the extra cost involved in fouling. Izadi et al. [11] tested the effects of different parameters, such as surface roughness, flow velocity, and concentration on the calcium carbonate scale formation process by using
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Nomenclature Ac B Cb C1, C2 Cp DAB Dh f Gj, Gb I j KB Km k, kt, kf L Nu p P Pr Re Rf Rf Sj, Se Sc Sh t
cross-section area, m2 time constant, 1/s bulk concentration, kg m3 constants specific heat, J/kg K Brownian diffusivity (DAB = (KBT)/(3ðìdp)), m2/s hydraulic diameter of plate heat exchangers, m fanning friction factor, dimensionless generation rates of turbulence kinetic energy due to the mean velocity gradients and to buoyancy, respectively turbulence intensity, dimensionless Colburn j-factor (¼ St P r2=3 ), dimensionless Boltzmann constant (=1.38E23), J/K the mass transfer coefficient, m/s thermal conductivity, turbulent thermal conductivity, thermal conductivity of fouling deposit, W/m K flow channel length inside plate heat exchangers, m Nusselt number, dimensionless pressure, Pa sticking probability, dimensionless Prandtl number, dimensionless Reynolds number, dimensionless fouling resistance of heat conduction, K/W asymptotic fouling resistance, K/W user-defined source terms Schmidt number (Sc = í/DAB), dimensionless Sherwood number, dimensionless time, s
a monitoring system. Balasubramanian and Puri [12] tested three coated plates, and Lectrofluor-641TM was the best of them, which was provided with the decrease in thermal energy consumption about 15.86% at the same flow rate. From the above understanding, it appears that further research is needed to strengthen the fouling characteristic of PHEs, especially in the influences of different geometry designs and flow velocities. With the development of CFD, numerical studies have been conducted recently to predict the heat transfer and fouling performance. Lozano et al. [13] analyzed the flow distribution in the PHE without considering the heat transfer by creating a 3D model which consists of a single channel. Galeazzo et al. [14] have conducted 3D modeling of an industrial PHE with non-chevron type in order to simplify computational efforts. They have investigated parallel and series flow arrangements and validated it with experimental data. Kho and Muèller-steinhagen [15] used their CFD code to simulate the flow and temperature distribution to predict the CaSO4 fouling performance in a flat PHE channel. The j–e model is capable of predicting the overall flow characteristics with reasonable accuracy and in relatively short CPU time. The studies of Ilulian et al. [16] considered more complex and realistic geometries of the fluid distribution regions, and assessed the laminar and twoequation turbulent models. Bonis and Ruocco [17] performed a two dimensional model for a single channel of PHE at laminar flow to investigate the influence of temperature and velocity on the fouling performance, and proved that CFD modeling results can be applied to geometry optimization. Literature is severely lacking for fouling models that are able to predict fouling potential in PHEs. From mass balance and numerical simulation in the investigation on the flow and heat transfer performance of plate heat exchangers, we use Von-Karman analogy to predict the fouling performance in three corrugated plate heat exchangers with different geometries. Additionally, the influences
T u ui, ui uT u0 y+
temperature, K average flow velocity through plates, m/s i-axis velocity component and time-averaged value, m/s the friction velocity, uT = (ôs/ñ)1/2 flow velocity in centrality of the PHE, m/s dimensionless wall distance (y+ = (uT y)/m)
Greek symbols DP pressure drop between inlet and outlet, Pa ss wall shear stress, Pa e turbulence kinetic energy dissipation rate j turbulence kinetic energy ì, ìt dynamic viscosity, turbulent dynamic viscosity, Pa s ñ, ñf density of fluid, density of fouling deposit, kg/m3 Ud fouling deposition rate, kg/m2 s Ur fouling removal rate, kg/m2 s r fouling process index, dimensionless ój, óe constants n the deposit bond strength, dimensionless m, mt kinematic viscosity, turbulent kinematic viscosity, m2/s Subscripts i, j refers to an axis (X, Y or Z) t turbulent r the reference point
of fluid velocity and geometries of PHEs have been discussed and compared with experimental data, which can be used to optimize the designs of PHE generally and broaden its further applications. 2. Fouling model Kern and Seaton [18] assumed deposit accumulation was result of two simultaneous opposing processes: fouling deposition and fouling removal. The deposition rate is proportional to mass transfer coefficient; the removal rate is directly related to wall shear stress:
Rf ¼ Rf 1 eBt ;
^s kf n ~f ; Rf ¼ K m PC b^i=o
^s =^i B¼o
ð1Þ
The asymptotic fouling resistance can be calculated through Eq. (1) providing that Km, P, ss and n are known. The Von Karman analogy is used to calculate Km. Reynolds analogy and Prandtl analogy do not consider the influence of buffer region, which may produce deviation. The three-region model of Von-Karman analogy is adopted for the analysis for better accuracy [19–21]:
~ DAB Sh ¼ K m Dh =n ¼ ðf =2ÞScRe=1 þ ðf =2Þ0:5 ½5ðSc 1Þ þ 5Lnðð5Sc þ 1Þ=6Þ
ð2Þ
The friction number is computed by Eq. (3):
~ u2 Þ f ¼ de DP=ð2Ln
ð3Þ
For smooth surfaces, wall shear stress is obtained using the friction factor (ss = fñu2/2). For rough surfaces, a fraction of the pressure drop may be due to profile drag on roughness elements. However in the fouling formation, the profile drag does not contribute to the removal process. Only wall shear stress is assumed to contribute to the removal of the particles from the wall according to Kern and Seaton [18]. Thus, it is necessary to quantify wall shear stress. Li et al.
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[19–21] investigated fouling in enhanced tubes. Experimental method was used to obtain wall shear stress. They assume that profile drag is small relative to wall shear stress in the tubes. Eq. (4) is used to compute ss. It is also mentioned that the surface shear stress is not proportional to pressure drop in the helically rib tubes, because of pressure drag caused by flow separation. Kim and Webb [1] proposed a four region model in Eq. (5) to quantify wall shear stress based on flow structure between the tube ribs (Fig. 1). In the Eq. (5), s1 and s3 are calculated from Lewis’s model [22], and s2 and s4 are obtained from the measurements by Lawallee and Popovich[23].
ss ¼ DPAc =Aw
ð4Þ
ss ¼ s1 A1 þ s2 A2 þ s3 A3 þ s4 A4
ð5Þ
In PHE, neither Li’s nor Kim’s method is valid because the flow structure is more complex in PHE than that in enhanced tubes. Flow separation and swirl happens at various places due to the compact and diversified channel. So the use of Eq. (4) to obtain ss in PHE may bring significant errors. In this study, numerical simulation is utilized to compute ss. In the numerical modeling of this paper, the centroid of the wall-adjacent cell falls within the logarithmic region of boundary layer, and wall shear stress ss can be solved by the Eqs. (6) and (7) [24]:
u=uT ¼ ðLnEðquT yuÞÞ=k
ð6Þ
^ s =n ~ Þ1=2 uT ¼ ðo
ð7Þ
swirl/rotation and with separation and reattachment of the boundary layer. For such flow field, the DNS or LES approaches are the most accurate but require large computational resources. To the best of our knowledge only two turbulence models have been considered suitable for a 3D simulation of a PHE: j–x SST [27] and Realizable j–e [28,29] models. For the Realizable j–e models, Iulian et al. [16] have tested three variants of wall treatment: standard wall functions, non-equilibrium wall functions, and enhanced wall treatment. Comparing the two models, the Realizable j–e model with non-equilibrium wall functions is adopted in this study. For the steady-state turbulent flow of an incompressible fluid, the equations of mass, momentum and energy are [30]:
@ðq ui Þ ¼0 @xi uj
2.2. Governing equations It is worth nothing that for a PHE channel flow, turbulence may occur even for a Reynolds number as low as 400 for a plate-angle U = 60° [26]. For higher Reynolds number, the flow is indeed turbulent. Previous studies [26,27] have shown that the flow in a PHE has a complex 3D structure, with streamline curvature,
@ðq TÞ @ @T ¼ ðk þ kt Þ @xj @xj @xj
ð9Þ
The equations for the kinetic turbulent energy j and the rate of dissipation of the turbulence kinetic energy e corresponding to the Realizable j–e model are:
uj
@ ðq jÞ @ ¼ @xj @xj
lþ
lt @ j þ Gj þ Gb q e Y M rj @xj
þ Sj
uj
The calculation domain is for one fluid passage confined between the plates. The exact geometry of the channels is considered in the modeling, i.e. the flow domain is extending up to the gaskets and from the inlets to the outlets, taking into accounting all geometrical details of the fluid entrance regions of the chevron plates. Table 1 shows the three different geometries of the commercially used corrugated PHEs, and more details are available on the website [25]. Take BRM01 PHE for example, in Fig. 2a, it can be noticed that the width, length and height of the channels are, respectively, aligned with the X, Y and Z axis. The plate dimensions are measured using the plate angle, plate height, corrugation pitch, and plate thickness marked in Fig. 2b. The values of the three different geometric parameters are shown in Table 1. The flow domain can be seen in Fig. 2c, in which it can be noticed that the inlet and exit ports for the fluid are located on the same side.
@ðq ui Þ @p @ @ui ¼ þ ðl þ lt Þ @xi @xi @xi @xj
C p uj
where u is the velocity parallel to the wall, y is the distance from the wall. k is the Von-Karman constant (0.4187) and E = 9.793. 2.1. Calculation domain
ð8Þ
@ ðq eÞ @ ¼ @xj @xj
ð10Þ
lþ
lt @ e e2 pffiffiffiffi þ q C 1 Se þ Gb q C 2 re @xj j þ m e ð11Þ
The problem under consideration is for steady-state flow. The fluid is considered to have constant specific heat, density, viscosity, and conductivity. Gravity forces are neglected. Therefore the hydrodynamic and thermal fields are coupled, and the effects of buoyancy are not taken into account. 2.3. Boundary conditions At the inlet the velocity and temperature of the water are specified according to the experiment conditions. For a boundary condition for the turbulence we chose the turbulence intensity and hydraulic diameter as the specification method. The hydraulic diameter Dh is the double of the gap between two consecutive plates and has a value shown in Table 1. The turbulence intensity was estimated using the following correlation:
I ¼ 0:16Re1=8
ð12Þ
For the outlets, the pressure outlet condition is used. The working fluid is water. The property parameters of the water is obtained using NIST-REFPROP from the average temperature and average pressure of the inlet and outlet in PHEs
Fig. 1. The four region wall shear stress model.
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Table 1 Geometry parameters of plate heat exchangers. Plate no.
Plate angle
Plate height (mm)
Corrugation pitch (mm)
Plate thickness (mm)
Dh
BRM01 BR05 BRM07
65° 60° 60°
2.0 2.5 2.0
7 10 8
0.5 0.5 0.5
4 5 4
Fig. 2. (a) View of the plates, dimensions and coordinate system; (b) Shape and dimensions of the corrugations; (c) The calculation flow domain.
2.4. Grid sensitivity analysis In general, an appropriate mesh for a simulation is dependent on the boundary conditions, geometry, and the chosen wall treatment. The Realizable j–e turbulence model states that, when using the wall functions, the first gird point should be in the logarithmic sublayer (30 < y+ < 300). In the case of a PHE modeling, it is extremely difficult to create a good mesh for the 30 < y+ < 300 conditions, because the geometry is complicated and the channel’s gap (the dimension along the Y axis) can be vary from 0.2 (where the almost touching points are located) to 2.5 mm (the maximum distance between the plates). The boundary layer thickness also varies and in some regions it presents flow separation and reattachment phenomena. In order to assess the influence of the gird resolution on the solution, 10 grids were created and tested by meshing the volumes with different interval sizes (1.5, 1.3, 1.2, 1.1, 1.0, 0.9, 0.7, 0.6, 0.5 and 0.4 mm). For each grid, one turbulent simulation is performed (0.2 m/s; Re = 3600, temperatures at the inlets is 50 °C). The mass conservation for the fluid and the overall energy balance for the heat exchanger were verified. These constrains were respected for all simulations with a maximum error of 0.08%. For the mass conservation, any trend with the reduction of the mesh interval cannot be observed. However, for the energy conservation, it was noticed that the energy balance improves with a decrease of the mesh size. Furthermore, we compared the evolutions of the average temperature of the fluid over the middle transversal sections along the length of the plate. Fig. 3 present the results for the com-
Fig. 3. Comparison of various grids for the average temperature.
parison at Re = 3600, for which the differences are more accentuated. In the simulated case, one can notice that 0.6 and 0.7 mm interval size grids give the most closed results. The maximum difference between results obtained with the 0.6 and 0.7 mm size grids is 0.0038 K. Furthermore, the trend near 0.6 mm size grid is smoother than anywhere else. The differences between the predictions of the 0.6 mm and the 1 mm grids are quite large: 0.005 K.
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355
(a)
(b) Fig. 4. A partial view of the final mesh.
Based on these results, the 0.6 mm spacing mesh has finally been chosen, which gives 8–11 nodes, i.e. 7–10 layers of cells between two consecutive plates. Such a density of cells is considered sufficient for capturing the gradients which exist in the flow and the thermal field. The other meshes are considered too coarse with respect to maximum space of 2.5 mm between the plates. Illustrations of the final mesh are shown in Fig. 4. Fig. 4a represents a portion of the chevron zone. One can notice the uniform spacing and mesh density. Because the shape of the corrugations is trapezoidal, the most contact region between the plates is actually a small parallelogram and not a single point. And there is only one grid between the plates in Fig. 4b which represents the final mesh over a cross-section through the channels (Y = 0 m). The total number of the mesh for BRM01, BR05 and BRM07 is respectively 1.1, 1.7 and 2.3 million. The speed of CPU used for the simulation is 2.66 GHz with 4 cores, and each case took about 8 h to reach the residual value 106 in the simulation.
3. Results and discussion In order to verify the reliability of the numerical results, an experimental rig has been established to test the heat transfer and fouling performance of the three PHEs. Fig. 5 shows the schematic of the test apparatus, which consists of four closed loops: (1) hot water loop which makes heat exchange with cold water in the test section, (2) cold water loop which contains the test foulant in fouling experiments, (3) vapor loop which obtains the necessary heating power to maintain the heat water inlet temperature, and (4) cooling water loop which makes the cold water temperature cooling down after heat exchange with the hot water in test section. The heat transfer tests are conducted at 57 °C hot water inlet temperature and 40 °C cold water inlet temperature for turbulent flow. The velocities of composite fouling tests have the average velocity of 0.2, 0.4 and 0.6 m/s. The composite fouling tests are the compound of precipitation fouling and particulate fouling, in
Fig. 5. Schematic drawing of the test rig.
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which precipitation foulants are NaHCO3 and CaCl2 and the particulate foulant is Al2O3 particles. These foulant are added in the cold water tank before experiment. After 30 h or more depending on the fouling process, the fouling heat resistance remain the same, that is the asymptotic Rf value.
The temperature, pressure and volume flow rate are taken by the data acquisition system. Experimental results are shown in Tables 2 and 3, also the photographs of the plates after fouling test can be seen in Fig. 6.
Rf ¼ Rtotal Rc Rh
3.1. The Nusselt number
ð13Þ
where Rh and Rc are the heat transfer resistance of hot water side and cold water side obtained in the clean test, the heat conduction resistance be ignored in the calculations. Rtotal could be calculated from Q and LMTD.
Rtotal ¼ LMTD=Q ¼ Rh þ Rw þ Rc
ð14Þ
LMTD ¼ ½ðT h;in T c;out Þ ðT h;out T c;in Þ=Ln½ðT h;in T c;out Þ=ðT h;out T c;in Þ
ð15Þ
Table 2 The experimental Nusselt number of the three PHEs. BRM01
BR05
BM07
Re
Nu/Pr0.3
Re
Nu/Pr0.3
Re
Nu/Pr0.3
825 1468 2222 3193 3495 5102 5372 6144 7141
22.53 32.96 43.48 57.45 53.99 67.75 67.96 74.17 74.64
1014 1788 2751 3710 4247 6045 6389 7332 8525
21.51 33.28 46.82 51.58 57.71 66.41 64.23 70.77 76.28
800 1532 2255 3210 3505 4994 5360 6098 7118
20.73 31.60 40.47 49.74 51.74 60.97 59.69 64.28 68.74
Table 3 The experimental fouling resistance of the three PHEs. PHE no.
Rf 104 K/W
3.2. Fouling performance
Test velocity m/s
BRM01 BR05 BRM07
The experimental results of Nusselt number at different Re are shown in Table 2. The comparison between the experimental and numerical Nusselt numbers is illustrated in Fig. 7. For the BRM07 PHE, the maximum and the average relative errors with respect to the experimental data are respectively 19.8% and 10.2%, the errors that can be qualified as satisfactory. The maximum and the average relative errors of the BR05 PHE are the smallest among the three, they are 12.8% and 8.2% respectively. But for the BRM01 PHE, the maximum and the average relative errors are too big to disregard indulgently, with the value of 28.7% and 20.9% respectively. So far as we know, the reason is that BRM01 has the smallest corrugation pitch and plate height, so a little difference between real PHE and the 3D model drawn by the commercial software Solidworks can make a big influence in numerical simulation. From the Fig. 7, BRM01 has the best heat transfer performance while BR05 PHE has the worst, as a result of the geometry and flow structure. To compare the flow patterns of the two PHE, a few streamlines are illustrated in Figs. 8 and 9. The streamline of BRM01 shows curvature, swirl/rotation near the inlet (Fig. 8a) and the flow turn back at the side wall of the PHE (Fig. 8b). In BR05, however, the strongly eddy happens far away from the inlet (Fig. 9a), and the flow does not reach the side wall (Fig. 9b) because its plate angle is 60°, smaller than 65°of BRM01. Also the corrugation pitch of BR05 is 10 mm larger than BRM01. That is why the eddy intensity of BR05 is smaller than BRM01. But it is a pity that the eddy intensity cannot be quantified by now. After all, the good heat transfer performance is due to the more compact structure design. All of the three PHE, the Nusselt number is increased with the flow velocity, but the increasing rate decreases with the velocity increase.
0.2
0.4
0.6
12.101 7.2391 4.8139
7.8288 5.0806 3.1344
5.99755 4.2754 2.4097
The Kern and Seaton model shows that the Rf is proportional to Km/ôs. In the present study, fouling performance is indirectly obtained by the Von-Karman analogy, in which heat transfer performance is obtained by numerical simulation instead of experiment study.
Fig. 6. The photographs of the clean PHE plate and after fouling test.
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(a) the bottom
(b) left side Fig. 8. The streamline in BRM01, (a) the bottom; (b) left side.
Fig. 7. Nusselt number of the PHE.
3.2.1. Numerical simulation result of Km and ôs According to Eqs. (4) and (5), the friction factor must be calculated in order to obtain Km. The numerical calculation result of f at different Re of the BRM01, BR05, and BRM07 respectively is
displayed in Fig. 10. From the comparison of numerical results and experimental data, large difference appears in the case of BRM01 for the same reason as discussed in the heat transfer performance. For BR05 and BRM07, the average error is 12.9%, 17.4% respectively. Finally, Km in BRM01, BR05, and BRM07 is shown in Fig. 11, and the correlations are as following:
K m ¼ 3E 11Re0:736 ; 0:720
¼ 3E 11Re
K m ¼ 3E 11Re0:698 ;
Km ð16Þ
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Fig. 10. The friction factor of the three PHE.
(a) the bottom
Fig. 11. The mass transfer coefficient of the three PHE.
(b) left side Fig. 9. The streamline in BR05, (a) the bottom; (b) left side. Fig. 12. The wall shear stress of three PHEs.
The wall shear stress calculated from the numerical simulation for the three PHE cases respectively is shown in Fig. 12. At the same time, the method [19–21] of using Eq. (4) to evaluate the wall shear stress is also attempted. Take the example of BRM07 at Re = 7800, the result from Eq. (4) is 49.29 Pa, while the numerical
simulation gives 18.91 Pa. The reason of the large difference is that the Eq. (4) is not appropriate for the PHE. The numerical data only shows the wall shear stress, which is only a small fraction of the total pressure drop. In addition to the friction loss, there are
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additional pressure drop due to the streamline curvature, swirl/ rotation, separation, and reattachment of the boundary layer in the PHE channel, and the sudden expansion or contraction at the entrance or exit.
359
From the Fig. 12, one can noticed that the BRM01 has the largest wall shear stress because of its compact geometry with the 65° plate angle and the smallest corrugation pitch of 7 mm. BM07 has the second large shear stress, and the BRM05 has the smallest shear stress, because its corrugation pitch is 10 mm, which is 3 and 2 mm larger than that of BRM01 and BM07 respectively. 3.2.2. Effect of fluid velocity on fouling performance This study is to explore the influence of velocity and geometry to the fouling behavior in PHEs. All the PHEs have same material and fouling water, when comparing their asymptotic fouling resistance by using the ratio of Rf⁄, the material’s influence can be counteracted, so the influence of velocity and geometry can been find obviously. According to Eq. (1), the Eq. (18) is obtained,
^ s =o ^sr Þ Rf =Rfr ¼ rðK m =K mr Þ=ðo
ð17Þ
Usually to ensure a good heat transfer performance, the Re number in PHE is usually set at higher than 1000, which is the reference Re in equation 18. The numerically evaluated fouling resistance at different Re (Re = 1000–8000) is illustrated in Fig. 13. The experimental data points in Table 3 are well matched by the numerical predictive line. For BRM01, BR05 and BRM07, the average relative errors with respect to the experimental data are 10.8%, 9.0% and 7.2% respectively. These errors are satisfactory. The fouling resistances of the PHEs are inversely proportional to the fluid velocity, which are shown on both numerical prediction and experimental data. Consider BRM01 in Fig. 13a as an example, the fouling resistances when Re number is 1600 are about 1.3–1.6 times the values when the Re is 3200; the fouling resistances when Re number is 3200 are about 1.1–1.7 times the values when the Re is 4800. The fouling resistance is reduced with the increase of velocity, but the reduction rate reduces when velocity increases. So in the operation of PHE, an optimum velocity may exist. If the velocity is too small, the fouling resistance can be too large to have a good heat transfer performance. And the continued increasing of velocity will demand a high pumping cost while has little improvement in fouling performance. 4. Conclusions This paper provides a numerical investigation of the heat transfer and fouling performance, including Nusselt number, friction factor, and fouling resistance for the three corrugated PHEs of different geometries. The Realizable j–e model with non-equilibrium wall functions was adopted. The 0.6 mm spacing mesh has been chosen through comparisons with different interval grid sizes. (1) The Nusselt numbers at turbulent flow (Re = 1000–8000) in BRM01, BR05, BRM07 are calculated by numerical simulation, and the average relative errors compared with the experimental data are 20.9%, 8.2%, 10.2% respectively. BRM01 has the best heat transfer performance because of its largest plate angle 65°and smallest corrugation pitch 7 mm, which caused strong eddy at the beginning of the inlet and the fluid flow can extend to the side wall of the PHE.
Fig. 13. The compare of predictive line and the experimental data of the fouling resistance in PHE.
(2) The fouling resistance is reduced with the increase of velocity, but the reduction rate reduces at high velocity. So in the use of PHE, an optimum velocity may exist. For BRM01, BR05 and BRM07, the average relative errors with respect to the experimental data are respectively 10.8%, 9.0%, 7.2%, errors that can be considered as satisfactory. (3) The numerical simulation result gives good predictions, which can be generally used for the actual applications and to provide directions for a better PHE design. The
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numerical analysis is verified by experimental study. The investigation significantly simplifies the fouling analysis of complex flow fields and can be used to assess the fouling potential of corrugated plate heat exchangers.
Acknowledgments This work was supported by the National Science Foundation of China (No. 51210011 and No. 51076070) and the National Key Technology R&D Program ‘‘Highly-Effective Energy-Saving Techniques for Combined Buildings’’ (2012BAA10B01). We would like to delicate this work to the memory of Dr. Ralph Webb.
References [1] R.L. Webb, N.H. Kim, Principles of Enhanced Heat Transfer, second ed., Taylor & Francis Group, New York, 2004. [2] R.L. Webb, W. Li, Fouling in enhanced tubes using cooling tower water: part I: long-term fouling data, Int. J. Heat Mass Transfer 43 (2000) 3567–3578. [3] Wei Li, The internal surface area basis, a key issue of modeling fouling in enhanced heat transfer tubes, Int. J. Heat Mass Transfer 46 (2003) 4345–4349. [4] E. Naess, T. Slungaard, O.K. Sonju, Experimental investigation of particulate fouling in waste heat recovery from the aluminum industry, in: The 13th International Heat and Mass Transfer Conference in Sydney, 2006. [5] Yong Yang, Hyoungsup Kim, Alexander Fridman, Young I. Cho, Effect of a plasma-assisted self-cleaning filter on the performance of PWT coil for the mitigation of mineral fouling in a heat exchanger, Int. J. Heat Mass Transfer 53 (2010) 412–422. [6] B. Merheb, G. Nassar, B. Nongaillard, G. Delaplace, J.C. Leuliet, Design and performance of a low-frequency non-intrusive acoustic technique for monitoring fouling in plate heat exchangers, J. Food Eng. 82 (2007) 518–527. [7] Y. Mahdi, A. Mouheb, L. Oufer, A dynamic model for milk fouling in a plate heat exchanger, Appl. Math. Model. 33 (2009) 648–662. [8] Chengwang Lei, Zhongxiao Peng, Thomas Day, Xinping Yan, Xiuqin Bai, Chengqing Yuan, Experimental observation of surface morphology effect on crystallization fouling inplate heat exchangers, Int. Commun. Heat Mass Transfer 38 (2011) 25–30. [9] S. Jun, V.M. Puri, R.F. Roberts, A dynamic model for thermal performance of plate heat exchangers, Trans. ASAE 47 (2003) 213–222. [10] M.C. Georgiadis, S. Macchietto, Dynamic modelling and simulation of plate heat exchangers under milk fouling, Chem. Eng. Sci. 55 (2000) 1605–1619. [11] M. Izadi, D.K. Aidun, P. Marzocca, H. Lee, Integrated experimental investigation of seawater composite fouling effect on the 90/10 Cu/Ni tube, Appl. Therm. Eng. J. 31 (2011) 2464–2473.
[12] S. Balasubramanian, V.M. Puri, Thermal energy savings in pilot-scale plate heat exchanger system during product processing using modified surfaces, J. Food Eng. 91 (2009) 608–611. [13] A. Lozano, F. Barreras, N. Fueyo, S. Santodomingo, The flow in an oil/water plate heat exchanger for the automotive industry, Appl. Therm. Eng. 28 (2008) 1109–1117. [14] F.C.C. Galeazzo, R.Y. Miura, J.A.W. Gut, C.C. Tadini, Experimental and numerical heat transfer in a plate heat exchanger, Chem. Eng. Sci. 61 (2006) 7133–7138. [15] T. Kho, H. Muller-Steenhagen, An experimental and numerical investigation of heat transfer fouling and fluid flow in flat plate heat exchangers, Inst. Chem. Eng. Trans. IChemE 77 (1999) 124–130. [16] Iulian Gherasim, Nicolas Galanis, Cong Tam Nguyen, Heat transfer and fluid flow in a plate heat exchanger Part II: assessment of laminar and two-equation turbulent models, Int. J. Therm. Sci. 50 (2011) 1499–1511. [17] Maria Valeria De Bonis, Gianpaolo Ruocco, Conjugate fluid flow and kinetics modeling for heat exchanger fouling simulation, Int. J. Therm. Sci. 48 (2009) 2006–2012. [18] D.Q. Kern, R.A.A. Seaton, Theoretical analysis of thermal surface fouling, Br. Chem. Eng. 4 (1959) 258–262. [19] Wei Li, Guan-qiu Li, Zhengjiang Zhang, Xu Zhiming, Modeling cooling tower fouling in helical- rib tubes based on Von-Karman analogy, Int. J. Heat Mass Transfers 53 (2010) 2715–2721. [20] Wei Li, Guan-qiu Li, Zhike Wang, Zhengjiang Zhang, Xu Zhiming, Analysis of cooling tower fouling in enhanced tubes based on Prandtl analogy, J. Enhanced Heat Transfer 18 (2011) 513–526. [21] Wei Li, Guan-qiu Li, Zhengjiang Zhang, Zhiming Xu, Analysis of fouling characteristic in enhanced tubes using multiple analogies, in: The 14th International Heat Transfer Congress, IHTC14-22529, Washington D.C., USA, 2010. [22] M.J. Lewis, An elementary analysis for predicting the momentum and heat transfer characteristics of a hydraulically rough surface, ASME J. Heat Transfer 97 (1975) 249–254. [23] H.C. Lavallee, A.T. Popovich, Fluid flow near roughness elements investigated by photolysis method, Chem. Eng. Sci. 29 (1974) 49–59. [24] Frank M. White, Fluid Mechanics, McGraw Hill Higher Education Press, New York, 2003. pp. 356–360. [25] http://www.shnanhua.zcom/en/proshow.asp?classid=16&id=447. [26] W.W. Focke, J. Zachariades, I. Olivier, The effect of the corrugation inclinat handbook ion angle on the thermo-hydraulic performance of plate heat exchangers, Int. J. Heat Mass Transfer 28 (1985) 1469–1479. [27] A.G. Kanaris, A.A. Mouza, S.V. Paras, Flow and heat transfer prediction in a corrugated plate heat exchanger using a CFD code, Chem. Eng. Technol. 29 (2006) 923–930. [28] Y.C. Tsai, F.B. Liu, P.T. Shen, Investigations of the pressure drop and flow distribution in a chevron-type plate heat exchanger, Int. Commun. Heat Mass Transfer 36 (2009) 574–578. [29] S. Jain, A. Joshi, P.K. Bansal, A new approach to numerical simulation of small sized plate heat exchangers with chevron plates, J. Heat Transfer 129 (2007) 291–297. [30] W.J. Minkowycz, E.M. Sparrow, J.Y. Murthy, Handbook of Numerical Heat Transfer, Wiley Press, Hoboken, 2006. pp. 191–224.
Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Numerical and experimental analysis of composite fouling in corrugated plate heat exchangers Wei Li a,⇑, Hong-xia Li a, Guan-qiu Li a, Shi-chune Yao b a b
Department of Energy Engineering, Zhejiang University, Hangzhou 310027, PR China Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, United States
a r t i c l e
i n f o
Article history: Received 4 August 2012 Received in revised form 24 March 2013 Accepted 29 March 2013 Available online 1 May 2013 Keywords: Fouling Numerical simulation Von-Karman analogy Plate heat exchanger
a b s t r a c t This paper provides a numerical and experimental analysis on precipitation and particulate fouling in corrugated plate heat exchangers with different geometric parameters which are plate height, plate spacing, and plate angle. The Realizable j–e model with non-equilibrium wall functions is used in the 3D numerical simulation considering the realistic geometries of the flow channel to obtained Nusselt number and wall shear stress, while Von-Karman analogy is used to obtain mass transfer coefficient. Numerical analysis is verified by experimental study. The predicted influence of fluid velocity in fouling resistance is compatible with experimental data that it can help to optimize the design of plate heat exchangers. This investigation significantly simplifies the fouling analysis of complex flow fields and can be used to assess the fouling potential of corrugated plate heat exchangers. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Plate heat exchanger (PHE) has been widely used in many industrial applications, such as food, oil, heat-recovery etc., because of its outstanding heat transfer performance, easy maintenance, compactness, and convenience to increase heat transfer area etc. [1]. Corrugations in plate heat exchangers enhance heat transfer rate by increasing heat transfer area and increasing turbulence mixing at low flow rates. However, fouling brings many concerns in the applications of PHEs. The heat transfer coefficient of fouled PHEs can be even lower than the heat exchangers with no enhanced surfaces. Fouling is a comprehensive and complex problem, which has many influential factors. Many researchers have investigated the effects of geometry design and process conditions on fouling performance for tubes. In a number cases the fouling models were established. Kim and Webb conducted accelerated particulate fouling experiments in three repeated rib tubes and a plain tube. The mass transfer rate is assumed to control the particle transport process, and the wall shear stress is assumed to control the removal process [1]. Webb and Li [2] took 2 years to perform practical cooling tower water fouling in a series of a series of seven helical-rib tubes and a smooth tube. The j factor analogy was used to calculate the asymptotic fouling resistance [3]. Naess et al. [4] reported an experimental study of accelerated particulate fouling tests from real industrial gas streams on bare and finned tubes in cross flow. ⇑ Corresponding author. Tel./fax: +86 571 87952244. E-mail address: [email protected] (W. Li). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.03.073
Asymptotic fouling behavior was observed for both finned and unfinned tubes. The major part of the deposit was formed on the rear section of the tubes, where shear forces were low and protected from impaction of larger particles. Cho’s team continued to develop anti-fouling technology [5]. They investigated the effect of a selfcleaning filter on the performance of physical water treatment coil for the mitigation of mineral fouling in a concentric counter flow heat exchanger. Recent studies on fouling inside PHE are following. Merheb et al. [6] monitored the fouling inside PHE in real time, using multiple optimized non-intrusive sensors. Low-frequency acoustic waves propagated through the plates, and these waves were analyzed to detect fouling inside the PHE. Mahdi et al. [7] proposed a twodimensional dynamic model for milk fouling to predict the performance of a PHE using material balance equations. Their results showed fouling was highly dependent on the various process operating conditions. Lei et al. [8] tested the effects of surface roughness and textures of the PHE on calcium carbonate fouling, and found that the growth rate, the distribution and the crystal size of calcium carbonate fouling were strongly dependent on the surface texture and finish. Jun et al. [9] accounted for the hydrodynamics of fluid flow using a 2D model, which was capable of predicting the temperature distribution of flow with higher accuracy than a 1D model. Georgiadis and Macchietto [10] predicted the milk deposit patterns on the plate surfaces, which were expected to pave the way to organize and optimize the operating conditions for reducing the extra cost involved in fouling. Izadi et al. [11] tested the effects of different parameters, such as surface roughness, flow velocity, and concentration on the calcium carbonate scale formation process by using
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Nomenclature Ac B Cb C1, C2 Cp DAB Dh f Gj, Gb I j KB Km k, kt, kf L Nu p P Pr Re Rf Rf Sj, Se Sc Sh t
cross-section area, m2 time constant, 1/s bulk concentration, kg m3 constants specific heat, J/kg K Brownian diffusivity (DAB = (KBT)/(3ðìdp)), m2/s hydraulic diameter of plate heat exchangers, m fanning friction factor, dimensionless generation rates of turbulence kinetic energy due to the mean velocity gradients and to buoyancy, respectively turbulence intensity, dimensionless Colburn j-factor (¼ St P r2=3 ), dimensionless Boltzmann constant (=1.38E23), J/K the mass transfer coefficient, m/s thermal conductivity, turbulent thermal conductivity, thermal conductivity of fouling deposit, W/m K flow channel length inside plate heat exchangers, m Nusselt number, dimensionless pressure, Pa sticking probability, dimensionless Prandtl number, dimensionless Reynolds number, dimensionless fouling resistance of heat conduction, K/W asymptotic fouling resistance, K/W user-defined source terms Schmidt number (Sc = í/DAB), dimensionless Sherwood number, dimensionless time, s
a monitoring system. Balasubramanian and Puri [12] tested three coated plates, and Lectrofluor-641TM was the best of them, which was provided with the decrease in thermal energy consumption about 15.86% at the same flow rate. From the above understanding, it appears that further research is needed to strengthen the fouling characteristic of PHEs, especially in the influences of different geometry designs and flow velocities. With the development of CFD, numerical studies have been conducted recently to predict the heat transfer and fouling performance. Lozano et al. [13] analyzed the flow distribution in the PHE without considering the heat transfer by creating a 3D model which consists of a single channel. Galeazzo et al. [14] have conducted 3D modeling of an industrial PHE with non-chevron type in order to simplify computational efforts. They have investigated parallel and series flow arrangements and validated it with experimental data. Kho and Muèller-steinhagen [15] used their CFD code to simulate the flow and temperature distribution to predict the CaSO4 fouling performance in a flat PHE channel. The j–e model is capable of predicting the overall flow characteristics with reasonable accuracy and in relatively short CPU time. The studies of Ilulian et al. [16] considered more complex and realistic geometries of the fluid distribution regions, and assessed the laminar and twoequation turbulent models. Bonis and Ruocco [17] performed a two dimensional model for a single channel of PHE at laminar flow to investigate the influence of temperature and velocity on the fouling performance, and proved that CFD modeling results can be applied to geometry optimization. Literature is severely lacking for fouling models that are able to predict fouling potential in PHEs. From mass balance and numerical simulation in the investigation on the flow and heat transfer performance of plate heat exchangers, we use Von-Karman analogy to predict the fouling performance in three corrugated plate heat exchangers with different geometries. Additionally, the influences
T u ui, ui uT u0 y+
temperature, K average flow velocity through plates, m/s i-axis velocity component and time-averaged value, m/s the friction velocity, uT = (ôs/ñ)1/2 flow velocity in centrality of the PHE, m/s dimensionless wall distance (y+ = (uT y)/m)
Greek symbols DP pressure drop between inlet and outlet, Pa ss wall shear stress, Pa e turbulence kinetic energy dissipation rate j turbulence kinetic energy ì, ìt dynamic viscosity, turbulent dynamic viscosity, Pa s ñ, ñf density of fluid, density of fouling deposit, kg/m3 Ud fouling deposition rate, kg/m2 s Ur fouling removal rate, kg/m2 s r fouling process index, dimensionless ój, óe constants n the deposit bond strength, dimensionless m, mt kinematic viscosity, turbulent kinematic viscosity, m2/s Subscripts i, j refers to an axis (X, Y or Z) t turbulent r the reference point
of fluid velocity and geometries of PHEs have been discussed and compared with experimental data, which can be used to optimize the designs of PHE generally and broaden its further applications. 2. Fouling model Kern and Seaton [18] assumed deposit accumulation was result of two simultaneous opposing processes: fouling deposition and fouling removal. The deposition rate is proportional to mass transfer coefficient; the removal rate is directly related to wall shear stress:
Rf ¼ Rf 1 eBt ;
^s kf n ~f ; Rf ¼ K m PC b^i=o
^s =^i B¼o
ð1Þ
The asymptotic fouling resistance can be calculated through Eq. (1) providing that Km, P, ss and n are known. The Von Karman analogy is used to calculate Km. Reynolds analogy and Prandtl analogy do not consider the influence of buffer region, which may produce deviation. The three-region model of Von-Karman analogy is adopted for the analysis for better accuracy [19–21]:
~ DAB Sh ¼ K m Dh =n ¼ ðf =2ÞScRe=1 þ ðf =2Þ0:5 ½5ðSc 1Þ þ 5Lnðð5Sc þ 1Þ=6Þ
ð2Þ
The friction number is computed by Eq. (3):
~ u2 Þ f ¼ de DP=ð2Ln
ð3Þ
For smooth surfaces, wall shear stress is obtained using the friction factor (ss = fñu2/2). For rough surfaces, a fraction of the pressure drop may be due to profile drag on roughness elements. However in the fouling formation, the profile drag does not contribute to the removal process. Only wall shear stress is assumed to contribute to the removal of the particles from the wall according to Kern and Seaton [18]. Thus, it is necessary to quantify wall shear stress. Li et al.
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[19–21] investigated fouling in enhanced tubes. Experimental method was used to obtain wall shear stress. They assume that profile drag is small relative to wall shear stress in the tubes. Eq. (4) is used to compute ss. It is also mentioned that the surface shear stress is not proportional to pressure drop in the helically rib tubes, because of pressure drag caused by flow separation. Kim and Webb [1] proposed a four region model in Eq. (5) to quantify wall shear stress based on flow structure between the tube ribs (Fig. 1). In the Eq. (5), s1 and s3 are calculated from Lewis’s model [22], and s2 and s4 are obtained from the measurements by Lawallee and Popovich[23].
ss ¼ DPAc =Aw
ð4Þ
ss ¼ s1 A1 þ s2 A2 þ s3 A3 þ s4 A4
ð5Þ
In PHE, neither Li’s nor Kim’s method is valid because the flow structure is more complex in PHE than that in enhanced tubes. Flow separation and swirl happens at various places due to the compact and diversified channel. So the use of Eq. (4) to obtain ss in PHE may bring significant errors. In this study, numerical simulation is utilized to compute ss. In the numerical modeling of this paper, the centroid of the wall-adjacent cell falls within the logarithmic region of boundary layer, and wall shear stress ss can be solved by the Eqs. (6) and (7) [24]:
u=uT ¼ ðLnEðquT yuÞÞ=k
ð6Þ
^ s =n ~ Þ1=2 uT ¼ ðo
ð7Þ
swirl/rotation and with separation and reattachment of the boundary layer. For such flow field, the DNS or LES approaches are the most accurate but require large computational resources. To the best of our knowledge only two turbulence models have been considered suitable for a 3D simulation of a PHE: j–x SST [27] and Realizable j–e [28,29] models. For the Realizable j–e models, Iulian et al. [16] have tested three variants of wall treatment: standard wall functions, non-equilibrium wall functions, and enhanced wall treatment. Comparing the two models, the Realizable j–e model with non-equilibrium wall functions is adopted in this study. For the steady-state turbulent flow of an incompressible fluid, the equations of mass, momentum and energy are [30]:
@ðq ui Þ ¼0 @xi uj
2.2. Governing equations It is worth nothing that for a PHE channel flow, turbulence may occur even for a Reynolds number as low as 400 for a plate-angle U = 60° [26]. For higher Reynolds number, the flow is indeed turbulent. Previous studies [26,27] have shown that the flow in a PHE has a complex 3D structure, with streamline curvature,
@ðq TÞ @ @T ¼ ðk þ kt Þ @xj @xj @xj
ð9Þ
The equations for the kinetic turbulent energy j and the rate of dissipation of the turbulence kinetic energy e corresponding to the Realizable j–e model are:
uj
@ ðq jÞ @ ¼ @xj @xj
lþ
lt @ j þ Gj þ Gb q e Y M rj @xj
þ Sj
uj
The calculation domain is for one fluid passage confined between the plates. The exact geometry of the channels is considered in the modeling, i.e. the flow domain is extending up to the gaskets and from the inlets to the outlets, taking into accounting all geometrical details of the fluid entrance regions of the chevron plates. Table 1 shows the three different geometries of the commercially used corrugated PHEs, and more details are available on the website [25]. Take BRM01 PHE for example, in Fig. 2a, it can be noticed that the width, length and height of the channels are, respectively, aligned with the X, Y and Z axis. The plate dimensions are measured using the plate angle, plate height, corrugation pitch, and plate thickness marked in Fig. 2b. The values of the three different geometric parameters are shown in Table 1. The flow domain can be seen in Fig. 2c, in which it can be noticed that the inlet and exit ports for the fluid are located on the same side.
@ðq ui Þ @p @ @ui ¼ þ ðl þ lt Þ @xi @xi @xi @xj
C p uj
where u is the velocity parallel to the wall, y is the distance from the wall. k is the Von-Karman constant (0.4187) and E = 9.793. 2.1. Calculation domain
ð8Þ
@ ðq eÞ @ ¼ @xj @xj
ð10Þ
lþ
lt @ e e2 pffiffiffiffi þ q C 1 Se þ Gb q C 2 re @xj j þ m e ð11Þ
The problem under consideration is for steady-state flow. The fluid is considered to have constant specific heat, density, viscosity, and conductivity. Gravity forces are neglected. Therefore the hydrodynamic and thermal fields are coupled, and the effects of buoyancy are not taken into account. 2.3. Boundary conditions At the inlet the velocity and temperature of the water are specified according to the experiment conditions. For a boundary condition for the turbulence we chose the turbulence intensity and hydraulic diameter as the specification method. The hydraulic diameter Dh is the double of the gap between two consecutive plates and has a value shown in Table 1. The turbulence intensity was estimated using the following correlation:
I ¼ 0:16Re1=8
ð12Þ
For the outlets, the pressure outlet condition is used. The working fluid is water. The property parameters of the water is obtained using NIST-REFPROP from the average temperature and average pressure of the inlet and outlet in PHEs
Fig. 1. The four region wall shear stress model.
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Table 1 Geometry parameters of plate heat exchangers. Plate no.
Plate angle
Plate height (mm)
Corrugation pitch (mm)
Plate thickness (mm)
Dh
BRM01 BR05 BRM07
65° 60° 60°
2.0 2.5 2.0
7 10 8
0.5 0.5 0.5
4 5 4
Fig. 2. (a) View of the plates, dimensions and coordinate system; (b) Shape and dimensions of the corrugations; (c) The calculation flow domain.
2.4. Grid sensitivity analysis In general, an appropriate mesh for a simulation is dependent on the boundary conditions, geometry, and the chosen wall treatment. The Realizable j–e turbulence model states that, when using the wall functions, the first gird point should be in the logarithmic sublayer (30 < y+ < 300). In the case of a PHE modeling, it is extremely difficult to create a good mesh for the 30 < y+ < 300 conditions, because the geometry is complicated and the channel’s gap (the dimension along the Y axis) can be vary from 0.2 (where the almost touching points are located) to 2.5 mm (the maximum distance between the plates). The boundary layer thickness also varies and in some regions it presents flow separation and reattachment phenomena. In order to assess the influence of the gird resolution on the solution, 10 grids were created and tested by meshing the volumes with different interval sizes (1.5, 1.3, 1.2, 1.1, 1.0, 0.9, 0.7, 0.6, 0.5 and 0.4 mm). For each grid, one turbulent simulation is performed (0.2 m/s; Re = 3600, temperatures at the inlets is 50 °C). The mass conservation for the fluid and the overall energy balance for the heat exchanger were verified. These constrains were respected for all simulations with a maximum error of 0.08%. For the mass conservation, any trend with the reduction of the mesh interval cannot be observed. However, for the energy conservation, it was noticed that the energy balance improves with a decrease of the mesh size. Furthermore, we compared the evolutions of the average temperature of the fluid over the middle transversal sections along the length of the plate. Fig. 3 present the results for the com-
Fig. 3. Comparison of various grids for the average temperature.
parison at Re = 3600, for which the differences are more accentuated. In the simulated case, one can notice that 0.6 and 0.7 mm interval size grids give the most closed results. The maximum difference between results obtained with the 0.6 and 0.7 mm size grids is 0.0038 K. Furthermore, the trend near 0.6 mm size grid is smoother than anywhere else. The differences between the predictions of the 0.6 mm and the 1 mm grids are quite large: 0.005 K.
W. Li et al. / International Journal of Heat and Mass Transfer 63 (2013) 351–360
355
(a)
(b) Fig. 4. A partial view of the final mesh.
Based on these results, the 0.6 mm spacing mesh has finally been chosen, which gives 8–11 nodes, i.e. 7–10 layers of cells between two consecutive plates. Such a density of cells is considered sufficient for capturing the gradients which exist in the flow and the thermal field. The other meshes are considered too coarse with respect to maximum space of 2.5 mm between the plates. Illustrations of the final mesh are shown in Fig. 4. Fig. 4a represents a portion of the chevron zone. One can notice the uniform spacing and mesh density. Because the shape of the corrugations is trapezoidal, the most contact region between the plates is actually a small parallelogram and not a single point. And there is only one grid between the plates in Fig. 4b which represents the final mesh over a cross-section through the channels (Y = 0 m). The total number of the mesh for BRM01, BR05 and BRM07 is respectively 1.1, 1.7 and 2.3 million. The speed of CPU used for the simulation is 2.66 GHz with 4 cores, and each case took about 8 h to reach the residual value 106 in the simulation.
3. Results and discussion In order to verify the reliability of the numerical results, an experimental rig has been established to test the heat transfer and fouling performance of the three PHEs. Fig. 5 shows the schematic of the test apparatus, which consists of four closed loops: (1) hot water loop which makes heat exchange with cold water in the test section, (2) cold water loop which contains the test foulant in fouling experiments, (3) vapor loop which obtains the necessary heating power to maintain the heat water inlet temperature, and (4) cooling water loop which makes the cold water temperature cooling down after heat exchange with the hot water in test section. The heat transfer tests are conducted at 57 °C hot water inlet temperature and 40 °C cold water inlet temperature for turbulent flow. The velocities of composite fouling tests have the average velocity of 0.2, 0.4 and 0.6 m/s. The composite fouling tests are the compound of precipitation fouling and particulate fouling, in
Fig. 5. Schematic drawing of the test rig.
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which precipitation foulants are NaHCO3 and CaCl2 and the particulate foulant is Al2O3 particles. These foulant are added in the cold water tank before experiment. After 30 h or more depending on the fouling process, the fouling heat resistance remain the same, that is the asymptotic Rf value.
The temperature, pressure and volume flow rate are taken by the data acquisition system. Experimental results are shown in Tables 2 and 3, also the photographs of the plates after fouling test can be seen in Fig. 6.
Rf ¼ Rtotal Rc Rh
3.1. The Nusselt number
ð13Þ
where Rh and Rc are the heat transfer resistance of hot water side and cold water side obtained in the clean test, the heat conduction resistance be ignored in the calculations. Rtotal could be calculated from Q and LMTD.
Rtotal ¼ LMTD=Q ¼ Rh þ Rw þ Rc
ð14Þ
LMTD ¼ ½ðT h;in T c;out Þ ðT h;out T c;in Þ=Ln½ðT h;in T c;out Þ=ðT h;out T c;in Þ
ð15Þ
Table 2 The experimental Nusselt number of the three PHEs. BRM01
BR05
BM07
Re
Nu/Pr0.3
Re
Nu/Pr0.3
Re
Nu/Pr0.3
825 1468 2222 3193 3495 5102 5372 6144 7141
22.53 32.96 43.48 57.45 53.99 67.75 67.96 74.17 74.64
1014 1788 2751 3710 4247 6045 6389 7332 8525
21.51 33.28 46.82 51.58 57.71 66.41 64.23 70.77 76.28
800 1532 2255 3210 3505 4994 5360 6098 7118
20.73 31.60 40.47 49.74 51.74 60.97 59.69 64.28 68.74
Table 3 The experimental fouling resistance of the three PHEs. PHE no.
Rf 104 K/W
3.2. Fouling performance
Test velocity m/s
BRM01 BR05 BRM07
The experimental results of Nusselt number at different Re are shown in Table 2. The comparison between the experimental and numerical Nusselt numbers is illustrated in Fig. 7. For the BRM07 PHE, the maximum and the average relative errors with respect to the experimental data are respectively 19.8% and 10.2%, the errors that can be qualified as satisfactory. The maximum and the average relative errors of the BR05 PHE are the smallest among the three, they are 12.8% and 8.2% respectively. But for the BRM01 PHE, the maximum and the average relative errors are too big to disregard indulgently, with the value of 28.7% and 20.9% respectively. So far as we know, the reason is that BRM01 has the smallest corrugation pitch and plate height, so a little difference between real PHE and the 3D model drawn by the commercial software Solidworks can make a big influence in numerical simulation. From the Fig. 7, BRM01 has the best heat transfer performance while BR05 PHE has the worst, as a result of the geometry and flow structure. To compare the flow patterns of the two PHE, a few streamlines are illustrated in Figs. 8 and 9. The streamline of BRM01 shows curvature, swirl/rotation near the inlet (Fig. 8a) and the flow turn back at the side wall of the PHE (Fig. 8b). In BR05, however, the strongly eddy happens far away from the inlet (Fig. 9a), and the flow does not reach the side wall (Fig. 9b) because its plate angle is 60°, smaller than 65°of BRM01. Also the corrugation pitch of BR05 is 10 mm larger than BRM01. That is why the eddy intensity of BR05 is smaller than BRM01. But it is a pity that the eddy intensity cannot be quantified by now. After all, the good heat transfer performance is due to the more compact structure design. All of the three PHE, the Nusselt number is increased with the flow velocity, but the increasing rate decreases with the velocity increase.
0.2
0.4
0.6
12.101 7.2391 4.8139
7.8288 5.0806 3.1344
5.99755 4.2754 2.4097
The Kern and Seaton model shows that the Rf is proportional to Km/ôs. In the present study, fouling performance is indirectly obtained by the Von-Karman analogy, in which heat transfer performance is obtained by numerical simulation instead of experiment study.
Fig. 6. The photographs of the clean PHE plate and after fouling test.
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(a) the bottom
(b) left side Fig. 8. The streamline in BRM01, (a) the bottom; (b) left side.
Fig. 7. Nusselt number of the PHE.
3.2.1. Numerical simulation result of Km and ôs According to Eqs. (4) and (5), the friction factor must be calculated in order to obtain Km. The numerical calculation result of f at different Re of the BRM01, BR05, and BRM07 respectively is
displayed in Fig. 10. From the comparison of numerical results and experimental data, large difference appears in the case of BRM01 for the same reason as discussed in the heat transfer performance. For BR05 and BRM07, the average error is 12.9%, 17.4% respectively. Finally, Km in BRM01, BR05, and BRM07 is shown in Fig. 11, and the correlations are as following:
K m ¼ 3E 11Re0:736 ; 0:720
¼ 3E 11Re
K m ¼ 3E 11Re0:698 ;
Km ð16Þ
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Fig. 10. The friction factor of the three PHE.
(a) the bottom
Fig. 11. The mass transfer coefficient of the three PHE.
(b) left side Fig. 9. The streamline in BR05, (a) the bottom; (b) left side. Fig. 12. The wall shear stress of three PHEs.
The wall shear stress calculated from the numerical simulation for the three PHE cases respectively is shown in Fig. 12. At the same time, the method [19–21] of using Eq. (4) to evaluate the wall shear stress is also attempted. Take the example of BRM07 at Re = 7800, the result from Eq. (4) is 49.29 Pa, while the numerical
simulation gives 18.91 Pa. The reason of the large difference is that the Eq. (4) is not appropriate for the PHE. The numerical data only shows the wall shear stress, which is only a small fraction of the total pressure drop. In addition to the friction loss, there are
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additional pressure drop due to the streamline curvature, swirl/ rotation, separation, and reattachment of the boundary layer in the PHE channel, and the sudden expansion or contraction at the entrance or exit.
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From the Fig. 12, one can noticed that the BRM01 has the largest wall shear stress because of its compact geometry with the 65° plate angle and the smallest corrugation pitch of 7 mm. BM07 has the second large shear stress, and the BRM05 has the smallest shear stress, because its corrugation pitch is 10 mm, which is 3 and 2 mm larger than that of BRM01 and BM07 respectively. 3.2.2. Effect of fluid velocity on fouling performance This study is to explore the influence of velocity and geometry to the fouling behavior in PHEs. All the PHEs have same material and fouling water, when comparing their asymptotic fouling resistance by using the ratio of Rf⁄, the material’s influence can be counteracted, so the influence of velocity and geometry can been find obviously. According to Eq. (1), the Eq. (18) is obtained,
^ s =o ^sr Þ Rf =Rfr ¼ rðK m =K mr Þ=ðo
ð17Þ
Usually to ensure a good heat transfer performance, the Re number in PHE is usually set at higher than 1000, which is the reference Re in equation 18. The numerically evaluated fouling resistance at different Re (Re = 1000–8000) is illustrated in Fig. 13. The experimental data points in Table 3 are well matched by the numerical predictive line. For BRM01, BR05 and BRM07, the average relative errors with respect to the experimental data are 10.8%, 9.0% and 7.2% respectively. These errors are satisfactory. The fouling resistances of the PHEs are inversely proportional to the fluid velocity, which are shown on both numerical prediction and experimental data. Consider BRM01 in Fig. 13a as an example, the fouling resistances when Re number is 1600 are about 1.3–1.6 times the values when the Re is 3200; the fouling resistances when Re number is 3200 are about 1.1–1.7 times the values when the Re is 4800. The fouling resistance is reduced with the increase of velocity, but the reduction rate reduces when velocity increases. So in the operation of PHE, an optimum velocity may exist. If the velocity is too small, the fouling resistance can be too large to have a good heat transfer performance. And the continued increasing of velocity will demand a high pumping cost while has little improvement in fouling performance. 4. Conclusions This paper provides a numerical investigation of the heat transfer and fouling performance, including Nusselt number, friction factor, and fouling resistance for the three corrugated PHEs of different geometries. The Realizable j–e model with non-equilibrium wall functions was adopted. The 0.6 mm spacing mesh has been chosen through comparisons with different interval grid sizes. (1) The Nusselt numbers at turbulent flow (Re = 1000–8000) in BRM01, BR05, BRM07 are calculated by numerical simulation, and the average relative errors compared with the experimental data are 20.9%, 8.2%, 10.2% respectively. BRM01 has the best heat transfer performance because of its largest plate angle 65°and smallest corrugation pitch 7 mm, which caused strong eddy at the beginning of the inlet and the fluid flow can extend to the side wall of the PHE.
Fig. 13. The compare of predictive line and the experimental data of the fouling resistance in PHE.
(2) The fouling resistance is reduced with the increase of velocity, but the reduction rate reduces at high velocity. So in the use of PHE, an optimum velocity may exist. For BRM01, BR05 and BRM07, the average relative errors with respect to the experimental data are respectively 10.8%, 9.0%, 7.2%, errors that can be considered as satisfactory. (3) The numerical simulation result gives good predictions, which can be generally used for the actual applications and to provide directions for a better PHE design. The
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numerical analysis is verified by experimental study. The investigation significantly simplifies the fouling analysis of complex flow fields and can be used to assess the fouling potential of corrugated plate heat exchangers.
Acknowledgments This work was supported by the National Science Foundation of China (No. 51210011 and No. 51076070) and the National Key Technology R&D Program ‘‘Highly-Effective Energy-Saving Techniques for Combined Buildings’’ (2012BAA10B01). We would like to delicate this work to the memory of Dr. Ralph Webb.
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