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Experimental and numerical investigation on particulate fouling characteristics of vortex generators with a hole
International Journal of Heat and Mass Transfer 148 (2020) 119130
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Experimental and numerical investigation on particulate fouling characteristics of vortex generators with a hole Zhimin Han, Zhiming Xu∗ School of Energy and Power Engineering, Northeast Electric Power University, Jilin City, Jilin Province, China
a r t i c l e
i n f o
Article history: Received 8 September 2019 Revised 23 November 2019 Accepted 26 November 2019
Keywords: Vortex generator Punched holes CFD Experimental investigation Fouling characteristic
a b s t r a c t In this study, the particulate fouling characteristics in a heat exchange channel with a rectangular wing vortex generator were investigated both experimentally and numerically. First, the fouling and flow resistance characteristics of the smooth channel, vortex generator without a hole, and vortex generator with a hole were compared experimentally. Subsequently, the fouling characteristics of the rectangular vortex generator with and without a hole were compared under turbulent conditions via numerical simulations. Finally, the effects of the hole diameter, and the lateral and vertical hole distances in the vortex generator on the particulate fouling characteristics were evaluated. The results show that both the vortex generator with a hole and without a hole could inhibit the formation of particles on the heat transfer surface. Compared with the vortex generator without a hole, the vortex generator with a hole could better inhibit particulate fouling, and it had a low flow resistance loss. The asymptotic fouling resistance decreased first and then increased with increasing hole diameter, it decreased as the lateral distance of the hole increased, and increased as the vertical distance of the hole increased. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction The heat transfer enhancement and fouling characteristics of heat exchangers have generally been of marked research interest. Heat transfer surface fouling inevitably causes heat loss to the heat exchange equipment, which compromises the safe operation of the heat exchange equipment. Beside deterioration of heat transfer, the growing fouling layer is leading to a reduction of channels crosssection that increase the pressure loss in the heat exchanger [1]. Vortex generators (VGs), as the most representative heat transfer enhancement component, have been the focus of significant global study [2]. Currently, many studies have indicated that vortex generators can enhance the heat transfer ability of the heat transfer surface [3–6]. However, a literature survey found that regardless of the type of vortex generator used, a certain pressure drop loss occurs while enhancing the heat transfer ability of the channel. For example, Chu et al. [7] studied the effects of a triangular winglet vortex generator on the heat transfer of a finned elliptical tube heat exchanger under laminar flow. It was found that the triangular winglets increased the average Nusselt number of the heat exchanger by 13.6%–32.9%, but the pressure loss also increased
∗
Corresponding author. E-mail address: [email protected] (Z. Xu).
https://doi.org/10.1016/j.ijheatmasstransfer.2019.119130 0017-9310/© 2019 Elsevier Ltd. All rights reserved.
by 29.2%–40.6%. Chen et al. [8] studied the heat transfer characteristics in rectangular micro-channels with different number of pairs and dimensions longitudinal vortex generators. It was found that the heat transfer performance of the micro-channels with vortex generators was enhanced by 12.3–73.8% and 3.4–45.4% for microchannels with aspect ratios of 0.0667 and 0.25, respectively, while the pressure losses were increased by 40.3–158.6% and 6.5– 47.7%, respectively. Gallegos and Sharma [9] investigated the heat transfer characteristics of rectangular channels equipped with a flapping flag as a vortex generator. Their results showed that the inclusion of a flapping flag in the channel leads to a Nusselt number enhancement as high as 1.34 to 1.62 times the bare channel levels, and the friction factor was as high as 1.39 to 3.56 times the bare channel levels. To ensure the heat transfer enhancement of the vortex generator while reducing the flow resistance, many new designs have been proposed for the vortex generator. Tang et al. [10] proposed various types of vortex generators, compared with the commonflow-down configuration, the Nusselt number of the commonflow-up configuration increase by 2.7–2.9% and the friction factors reduced by 7.8–10.0%. Biswas and Chattopadhyay [11] determined that punching holes under the airfoil vortex generator would have an effect on the heat transfer and resistance characteristics. Wu et al. [12] found that the structure was not only easy to implement by arranging the rectangular vortex generator with punched holes on the surface of the fin heat exchanger but also helped to im-
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Nomenclatures a b c CMgO C∞ C+ d DB DT dp e J k mf m˙ f m˙ d m˙ r p Rf S Sp T Tl t U ud v xf y
length of the vortex generator (m) height of the vortex generator (m) hole vertical direction distance (m) particle concentration (kg/m3 ) bulk particle concentration (kg/m3 ) dimensionless particle concentration hole diameter (m) Brownian diffusivity (m2 /s) turbulent diffusivity (m2 /s) particle diameter (m) hole lateral direction distance (m) deposition flux (kg/(m2 •s)) removal constant (–) fouling mass per unit area (kg/m2 ) total mass rate (kg/(m2 •s)) deposition mass rate (kg/(m2 •s)) removal mass rate (kg/(m2 •s)) pressure (Pa) fouling resistance (m2 •K/W) particle-fluid density ratio (–) sticking portability (–) temperature (K) Lagrangian integral time scale (s) fouling time (s) velocity vector (–) particle deposition velocity (m/s) fluid velocity (m/s) thickness of fouling layer (m) distance from wall (m)
Greek symbols ε deposit porosity (–) λ thermal conductivity (W/(m•K)) λf thermal conductivity of the deposit (W/(m•K)) μ dynamic viscosity (kg/(m•s)) v kinematic viscosity (m2 /s) ρ density (kg/m3 ) ρ dep density of the deposit (kg/m3 ) τp particle relaxation time (s) τw wall shear stress (MPa) ψ the bond strength factor (–) Subscripts d deposition f fouling in inlet l liquid phase out outlet p particle phase r removal
prove the overall heat transfer and reduce pressure loss. He et al. [13] studied the effects of the enhanced heat transfer on a perforated winglet vortex generator in a finned tube heat exchanger. Their results showed that a significant increase of up to 33.8–70.6% in the heat transfer coefficient was achieved and was accompanied by a pressure drop of 43.4–97.2% for the 30° case compared to the plain fin. The performances of plane and curved winglet vortex generators with and without punched holes have been investigated experimentally by Zhou and Feng [14]. Their results showed that punched holes could enhance the heat transfer in both the laminar and turbulent flow regions and decrease the flow resistance. Qi et al. [15] investigate the effects of round hole diam-
eter and pitch-row on thermal and hydrodynamic characteristics of nanofluids based on triangular tubes with perforated turbulator inserted, and apply thermal and exergy efficiency to assess the comprehensive thermal and hydrodynamic characteristics. Jeong et al. [16] proposed a crescent-shaped protrusion was mounted as a vortex generator on the downstream of the dimple. The dimpled channel with a vortex generator shows better normalized thermoperformances than the general dimpled channel. Experimental and numerical of vortex heat transfer in turbulent air flow around the plate with permeable transverse rectangular ribs have been made by Kong et al. [17]. It is shown that the presence of a slit can eliminate secondary separation zones on the plate and decrease recirculation flow regions behind a rib. Vortex generators have been extensively studied for heat transfer enhancement, however, research on fouling is relatively sparse. Hasan et al. [18] studied the crystallization fouling characteristics of the delta-wing vortex generator, and proposed that the structural design of the vortex generator should be considered in conjunction with antifouling and pressure drop. Zhang et al. [19] proved experimentally that the vortex generator could effectively improve the heat transfer coefficient and also destroy the boundary layer near the wall surface, thus inhibiting fouling. Furthermore, our recent work [20] demonstrated that induced vortexes could inhibit fouling formation. Therefore, in this work, the fouling characteristics of a new type of vortex generator with a hole were studied experimentally and numerically. First, a comparison of a rectangular vortex generator with and without a hole was carried out. Then, the effects of the hole diameter, and the lateral and vertical hole distances of the VGs on the particulate fouling characteristics were studied. 2. Experimental procedure A schematic diagram of the experimental system is shown in Fig. 1 [21]. The system was composed of a working fluid circulation loop, a cooling cycle loop, and a data acquisition system. The temperature in the experimental section was controlled using a Pt100 thermal resistance and thermostat control. All the relevant experimental data were collected through the data acquisition system and sent to a computer. The test section used a rectangular channel with a size of 10 0 0 mm × 100 mm × 8.5 mm. The test section consisted of a polypropylene (PP) plastic plate, a silica gel sheet, and a 304 stainless steel plate. The thickness of the stainless steel plate was 0.5 mm, which was the main heat exchange surface for the test section, and the fouling was mainly deposited on it. Its geometrical dimensions were 10 0 0 mm × 10 0 mm as shown in Fig. 2. The PP plastic plate was anti-hygroscopic, had acid and alkali corrosion resistance, and was resistant to oxidation under high temperature conditions. Therefore, the surface materials were constructed using PP plastic plates. The silica gel sheet had large elastic deformation because of its soft texture and pressure, and therefore had good sealing abilities and functioned as a seal in the test section. The test section was well insulated to minimize the heat loss. The schematic diagram of the test section and vortex generator with a hole is shown in Fig. 2. The arrow indicates the direction of fluid flow. The VGs with two rows and nine columns were placed in the channel at an attack angle of 90°. The first VG pair was located 150 mm from the leading edge. The lateral spacing between two VGs was 20 mm. The longitudinal spacing between the two VGs was 90 mm. The sizes of rectangular VGs with a hole are shown in Fig. 2(a). The VGs were made of a steel plate with a = 25 mm long and b = 6 mm high. A hole was punched on the VG surfaces at different positions. The height from the center of the hole to the bottom edge was c. The width from the center of hole to the side edge was e. The diameter of the punched hole was
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Fig. 1. Diagram of the experimental system.
Fig. 2. Schematic diagram of the test section and vortex generator with a hole. (a) The sizes of the vortex generator with a hole. (b) The hole direction distance of vortex generator.
d. Table 1 lists the geometrical dimensions of the rectangular VGs used, and Fig. 2(b) shows the hole direction distance of VGs in this study. To ensure the accuracy of the results, multiple experiments on the rectangular channels without vortex generators were carried out. The root mean square method was used to calculate the er-
ror. The temperature measurement error of resistive thermometer was 0.206%, and the flow measurement error of electromagnetic flowmeter was 0.503%. Furthermore, the uncertainties of the results were evaluated based upon the analysis of errors in the experimental measurements. The results show that the two groups of experiment results were basically the same and the relative error
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Fig. 3. Mesh generation for the rectangular channel of the VGs with a hole. Table 1 Geometrical dimension of VGs with a hole. Name
Symbol
Size (mm)
Dimensionless dimension
The hole diameters The hole vertical direction distance The hole lateral direction distance
d c e
2, 3, 4, 5, 6 1.5, 2.25, 3, 3.75, 4.5 1.5, 7, 12.5, 18, 23.5
d/b=0.33, 0.5, 0.67, 0.83, 1 c/b=0.25, 0.375, 0.5, 0.625, 0.75 e/a=0.06, 0.28, 0.5, 0.72, 0.94
of the fouling resistance was less than 5%, thus meeting engineering requirements. Moreover, the measurement errors of temperature, pressure drop, and volumetric flow rate of test bed are less than ±1%. A detailed error analysis can be found in Ref. [20]. 3. Numerical methods and procedure Numerical simulations were conducted using the finite volume method (FVM) with the assistance of a commercial CFD package (ANSYS Fluent). For the convective and diffusive terms, the second order upwind method was used while the SIMPLE procedure was introduced for the velocity-pressure coupling. The discretization of the pressure equation was completed using the standard scheme. The residual criteria for the continuity, momentum, and energy equations were set to 10−6 . The ICEM software was used to construct the 3D computational domain. The model was discretized using an unstructured mesh. The grid was refined in key areas of interest such as the regions close to the wall and the VGs. 3.1. Physical model The geometry of the rectangular channel and vortex generators were the same as the test section used in the experiments. The computational domain was extended 150 mm from the entrance and the exit to ensure a uniform velocity distribution of the entrance flow and avoid recirculation of the outflow [22]. The thickness of the VGs was often neglected for simplification in most of the simulations. The generation of a mesh in the rectangular channel with rectangular VGs is shown in Fig. 3. The grid independence study was applied to the rectangular channel with VGs. Different grid system sizes were used to ensure grid independence and validate the results. When the grid number increased further, changes in the deposition velocity were less than 1%, and the final adopted grid number was 1,589,598. 3.2. Governing equations The simulated flow was unsteady, and the fluid was assumed to be incompressible. The velocity inlet was specified as 0.5 m/s in the numerical simulation part, which corresponded to a Reynolds number of 10,703. The RNG k–ε turbulent model was employed in this study. The Eulerian-Eulerian model solves two sets of conservation equations, one for each phase. The governing equations of continuity, momentum, and energy in the computational domain are as follows [23]: Continuity equation:
∇U = 0
(1)
Momentum equation:
∂U + ρU · ∇ U = −∇ p + μ∇ 2U ∂t
(2)
Energy equation:
∂T λ 2 + U · ∇T = ∇ T ∂t ρ cp
(3)
where U is the velocity vector, t is the time, ρ is the fluid density, μ is the fluid dynamic viscosity, p is the pressure, T is the temperature, cp is the specific heat capacity, and λ is the thermal conductivity. The RNG k-ε turbulence model:
∂ ( ρ k ) ∂ ( ρ kui ) ∂ ∂k + = +Gk − ρε σμ ∂t ∂ xi ∂ xj k eff ∂ xj ∂ (ρε ) ∂ (ρε ui ) ∂ ∂ε ε ε2 + = +C1∗ε Gk − C2ε ρ σk μeff ∂t ∂ xi ∂ xj ∂ xj k k
(4)
(5)
where μe f f = μ + μt , μt = ρCμ k2 /ε , and Cμ =0.0845; σ k and σ ε are the Prandtl numbers corresponding to the kinetic energy k and the dissipation rate ε , respectively, σ k =σ ε =1.39; C1∗ε = η (1−η/η0 , C1ε =1.42 and C2ε =1.68,η = (2Eij · Eij )1/2 k/ε , Eij = 1+βη3 ∂ uj 1 ∂ ui 2 ( ∂ xj + ∂ xi ); η 0 =4.377 and β =0.012.
C1ε −
The boundary conditions imposed on the computational domain are shown in Table 2. 3.3. Fouling model The deposition mass rate m˙ d was calculated using the following equation [24]:
m˙ d = Sp · ud · C∞
(6)
where Sp is the probability of sticking and C∞ is the bulk particle concentration. In this study, the fluid had a constant particle concentration and the sticking probability was assumed to be Sp = 1. The particulate deposition velocity ud was expressed as following [25]:
ud =
J ∂C+ μ = − ( DB + εp ) − DT C∞ ∂y ρl T
∂ v 2 py ∂T × C + − τp × C+ ∂y ∂y (7)
where the right hand of the equation are the Brownian and eddy diffusion terms, the thermophoretic deposition term, and finally turbophoretic deposition term. DB is the Brownian diffusivity, and
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Table 2 Boundary conditions. Boundary condition
Assumption
Inlet Outlet Bottom wall (no-slip condition) Inlet and outlet extended section (adiabatic) Remaining walls and Vortex generator (adiabatic)
εp is the particulate eddy diffusivity [26],
uin =0.5 m/s, v=w=0, Tin =298 K
∂ u/∂ x=∂ v/∂ x=∂ w/∂ x=0, ∇ T=0 u=v=w=0, Tw =318 K u=v=w=0, ∇ T=0 u=v=w=0, ∇ T=0
εp τp −1 vt = (1 + Tl ) , were
Tl is the Lagrangian time scale of the fluid, Tl = vt /v 2 y , v 2 y is the root-mean-square (RMS) of the local wall-normal velocity fluctuations, vt is the turbulent eddy viscosity, and τ p is the partiSd2 Cc
cle relaxation time, τp = 18p v , DT is the thermal diffusion coefficient [27], ∂ T/∂ y is the temperature gradient perpendicular to the surface and is calculated by the CFD program, C+ is the nondimensional concentration, v 2 py is the intensity of the particulate wall normal velocity fluctuations, which can be approximately esT
timated according to Johansen [26], v 2 py = v 2 y ( τp +l T ). l
The mass removal rate m˙ r of the fouling is expressed as [28]:
m˙ r = k
τ w
ψ
xf
(8)
where k is the removal constant, ψ is the bond strength factor of the deposit layer, τ w is the wall shear force, and xf is the fouling thickness. According to Ref. [28], k/ψ are combined to obtain a constant, which was 0.084. According to Kern and Seaton [29], the fouling is the result of a deposition and removal process and can be calculated as:
m˙ f = m˙ d − m˙ r
(9)
The fouling resistance represents the heat transfer thermal resistance caused by a buildup of deposit on the surfaces of the heat exchangers, and can then be calculated as [30]:
Rf = mf /
ρdep λf
(10)
where mf is the total fouling mass; ρ dep is the density of the deposit, ρdep = ρp (1 − ε ) + ρl ε ; λf is the thermal conductivity of the deposit, λf = (1 − ε )λp + λl ε ; ε is the deposit porosity [31]. 4. Results and discussion There is prior work [32] showing that the stable existence of the Mg2+ and Ca2+ ions in urban sewage cause are Magnesium Oxide and Calcium Carbonate fouling, after two stage treatment. Therefore, pure water containing magnesium oxide nanoparticles was selected as the working fluid in this study. The nanoparticles could be well suspended in water. The particles were spherical and had a size of 50 nm, a concentration of 0.4 kg/m3 , and their specific surface area was 30–50 m2 /g. 4.1. Experimental results The variation in the fouling resistance with time at the VGs with and without a hole, and in the smooth channel is shown in Fig. 4. For the VG with a hole, the hole was punched in its center, i.e., e = 12.5 mm and d = 3.0 mm. The velocity, magnesium oxide concentration, inlet temperature of the solution, and waterbath temperature were maintained at 0.1 m/s, 0.4 kg/m3 , 298 K, and 318 K, respectively. As shown in Fig. 4, the fouling resistance curves for the three experiments were asymptotic, and the asymptotic fouling resistance of the smooth rectangular channel was the maximum, followed by the VG without a hole, and VG with a hole was the lowest. This shows that a rectangular-wing VG with and
Fig. 4. Variation in fouling resistance with time.
without a hole can inhibit the formation of particulate fouling. This is because the working fluid that passes through the vortex generator produces a strong longitudinal vortex. A strong longitudinal vortex increases the removal and shear effects of the fluid on the wall, thus inhibiting the formation of particulate fouling on the heat transfer surface. Furthermore, compared with the VG without a hole, the VGs with a hole had better antifouling performance. This is because the VG with a hole could improve the flow characteristics in the backflow area of the rectangular-wing VG, and an example is shown in Fig. 5, which shows a visualization of the fouling deposition for the VGs without and with a hole. Fig. 5 shows that the fouling layer behind the rectangularwing VGs with a hole was thin, and had two distinct jet traces behind it. It also can be seen that the local fouling layer with the jet disturbances was relatively thinner. These results are consistent with those previously reported in literature [14]. This process leads to a large shear force and increases the removal rate in this area. Therefore, the antifouling performance of the VGs with a hole was better than the one without a hole The variation in the pressure drop with the Reynolds number of the VG with and without a hole, and for the smooth channel is shown in Fig. 6. It can be seen that as the Reynolds number changes, the pressure drop for the VG without a hole and for the VG with a hole was higher than for the smooth channel. Furthermore, the pressure drop for the VG with a hole was less than for the VG without a hole. There are two main reasons for this: the first is that the VG without a hole has a larger flow area than the VG with a hole, so the pressure drop that occurs when the working fluid flows through the vortex generator is relatively large; the second was that when the fluid flows through the VG with a hole, a part of the working fluid passes through the hole to generate a jet action, and this part of the working fluid retains the original flow trajectory and reduces the flow resistance. The experimental results show that the flow resistance loss of the VGs with a hole was less than that for the VGs without a hole.
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Fig. 7. Comparison of the experimental results and numerical results.
Fig. 5. Visualization of fouling deposition.
Fig. 8. Variation of the fouling resistance with time.
Fig. 6. Pressure drop with the variation of Re.
4.2. Numerical results 4.2.1. Comparison with experimental results To validate the reliability of the numerical method, the experimental and numerical results of the smooth channel and the VG channel with a hole were selected for verification. Fig. 7 shows that except for the large error caused by the simulation neglecting the fouling induction period in the early stage, the experimental results and numerical results were in close agreement. However, the focus of this study was on the late stable stage. Therefore, the good agreement between the experimental and numerical results at the later stage indicates that the numerical approach adopted was reliable. Turbulent flow is mostly dominant in actual industrial equipment. Hence, in the simulation part, the fluid velocity was increased by 0.5 m/s. For comparison in this section, the inlet
velocity, magnesium oxide concentration, inlet solution temperature, and water-bath temperature were maintained at 0.5 m/s, 0.4 kg/m3 , 298 K, and 318 K, respectively. The fouling characteristics of the rectangular channel of the VGs with and without a hole were studied. The variation of the fouling resistance with time is shown in Fig. 8. From the results in Fig. 8, the conclusion that the fouling resistance of the VGs with a hole is smaller than that the VGs without a hole can be reached, and the maximum reduction was 2.97%. From Fig. 5, it was determined that as the working fluid passes through the VG with a hole, a part of the fluid forms a jet through the circular hole. To better verify this point, the velocity contour of the rectangular wing VGs with and without a hole are given, as shown in Fig. 9. It can be seen that for the VG with a hole, a distinct jet is formed at the hole. The high-speed jet not only destroys the low-speed stagnation zone, but also increases the flow rate of the working fluid. At the same time, this process increases the wall shear force and the removal rate in this area. Therefore, the VGs with a hole have better antifouling performance than the VGs without a hole. 4.2.2. Effects of the hole diameters The effect of the hole diameters (d/b = 0.33, 0.50, 0.67, 0.83, 1.00) are studied at a lateral hole distance of e = 6 mm (e/a = 0.50) and a vertical distance of c = 3 mm (c/b = 0.50). The change
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Fig. 9. Near-wall velocity contour of the rectangular wing VGs with and without a hole. (a) XY section. (b) XZ section.
Fig. 10. Variation of fouling resistance with the hole diameter.
in the fouling resistance with time for the different hole diameters are shown in Fig. 10. It can be seen that the asymptotic fouling resistance of the VGs with a hole decreases first and then increased as the hole diameter increased. The asymptotic fouling resistance curve had a minimum value at d/b = 0.5. The reason for this was that when the fluid flows through the vortex generator, an end vortex can be generated at the end of the vortex generator. These vortices continue to develop along the flow direction and sweep the working fluid at the wall surface, thinning or destroying the boundary layer. However, as the hole diameters of the VGs increase, on the one hand, the formed jet increases the scouring area of the backflow stagnation zone behind the rectangular wing because of the increased hole size, which further reduces the mass deposition rate; on the other hand, a larger hole results in a smaller intensity of the jet formed, and the strength of the vortex formed at the end of the VGs is lower, which reduces the mass removal rate. Since the above two effects are opposed, the fouling resistance will have a minimum value, which is why the value of the asymptotic fouling resistance first decreases and then increases as the hole diameter increases. Fig. 11 shows the near-wall velocity contours of the VGs with different hole diameters. It can be clearly seen from the figure that as the hole diameter increases, the area of the low-speed stagnation area behind the vortex generator continuously decreases. However, the velocity of the end vor-
Fig. 11. Near-wall velocity contours with different hole diameter.
tex on both sides of the vortex generator became smaller. Hence, these two phenomena verify the above explanation. 4.2.3. Effects of the hole lateral direction distance The effect of the lateral hole distance (e/a = 0.06, 0.28, 0.50, 0.72, 0.94) was studied for a hole diameter of d = 3 mm (d/b = 0.50), and the vertical hole distance was c = 3 mm (c/b = 0.50). The fouling resistances changed with time under the different lateral hole distances, as shown in Fig. 12. It can be seen from Fig. 12 that the asymptotic fouling resistance of the VG with a hole decreases as the lateral hole distance increases, and a minimum was obtained when the hole lateral direction distance was 0.94. This was because when the hole was located near the side wall, the area of the low velocity region after the vortex generator was reduced, so that the mass deposition rate reduced. This can be clearly seen from the near-wall velocity contours of the VGs with
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Fig. 14. Variation of fouling resistance with the vertical hole distance. Fig. 12. Variation of fouling resistance with the lateral hole distance.
Fig. 15. Near-wall velocity contours of VGs with different vertical hole distances.
Fig. 13. Near-wall velocity contours of VGs with different lateral hole distances.
different lateral hole distances, as shown in Fig. 13. Moreover, it also can be seen from the figure that when the lateral hole position was e/a = 0.06, i.e., the hole was close to the inner edge, since the lateral distance (20 mm) of the two vortex generators was limited, the jets formed by the hole were superimposed on each other, and the area that can be affected becomes small. Therefore, compared with the other lateral hole positions, the fouling resistance value at e/a = 0.06 was the largest. 4.2.4. Effects of the hole vertical direction distance The effect of the hole vertical distance (c/b = 0.25, 0.375, 0.50, 0.625, 0.75) was studied when the hole diameter was d = 3 mm (d/b = 0.50), and the hole lateral direction distance was e = 12.5 mm (e/a = 0.50). The fouling resistance changed with time for the different vertical hole distances, as shown in Fig. 14. It can be seen that the asymptotic fouling resistance of the VGs with a hole increased as the vertical hole distance increased. The hole vertical direction distance of c/b = 0.25, i.e., the value of the asymptotic fouling resistance reached a maximum value when the hole was close to the upper wall surface; the vertical hole distance
c/b = 0.75, i.e., the value of the asymptotic resistance had a minimum value when the hole was close to the bottom surface. Fig. 15 shows the near-wall velocity contours of the VG with different vertical hole distances. It can be clearly seen from the figure that when the vertical hole distance was c/b = 0.25 (near the bottom surface), the jet formed on the bottom surface of the VG directly flushes the bottom surface because of the punched hole, thereby destroying the stagnation zone. When c/b = 0.75 (close to the upper wall), while the hole could increase the vortex area, its effect is not as clear as for directly destroying the stagnation area. Therefore, as the vertical hole distance increases, i.e., the hole gradually moves away from the bottom surface, the value of the asymptotic fouling resistance of the channel gradually decreases, which can explain the trend in Fig. 14 well. 5. Conclusions In this work, experimental and numerical studies of the particulate fouling characteristics in a channel with a rectangular wing vortex generator were investigated. The main conclusions can be summarized as follows: (1) The rectangular wing VG with a hole and without a hole could both inhibit the formation of magnesium oxide nanoparticles on the heat transfer surface. Compared with VGs without a hole, the VGs with a hole could better inhibit
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particulate fouling. Moreover, the flow resistance loss of the VGs with a hole was less than that of the VGs without a hole. (2) The good agreement between the experimental and numerical results with the adopted numerical approach indicated that the results were reliable. For turbulent flow, the fouling resistance of the VGs with a hole was also smaller than that of the VGs without a hole, and a maximum reduction of 12.97% was obtained. (3) In the simulation range, the asymptotic fouling resistance of the VGs with a hole first decreased and then increased with increasing hole diameter. The asymptotic fouling resistance of the VGs with a hole decreased with increasing lateral hole distance, and increased with the increasing vertical hole distance. Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled,“Experimental and numerical investigation on particulate fouling characteristics of vortex generators with a hole”. CRediT authorship contribution statement Zhimin Han: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing. Zhiming Xu: Conceptualization, Resources, Supervision, Project administration, Funding acquisition. Acknowledgement The financial support of the National Natural Science Foundation of China (Nos. 51476025 and 51706038) is gratefully acknowledged. References [1] P.O. Kapustenko, J.J. Klemeš, O.I. Matsegora, P.Y. Arsenyev, O.P. Arsenyeva, Accounting for local thermal and hydraulic parameters of water fouling development in plate heat exchanger, Energy 174 (2019) 1049–1059. [2] Y.L. He, Y.W. Zhang, Advances and outlooks of heat transfer enhancement by longitudinal vortex generators, Adv. Heat Transf. 44 (2012) 119–185. [3] P. Promvonge, T. Chompookham, S. Kwankaomeng, C. Thianpong, Enhanced heat transfer in a triangular ribbed channel with longitudinal vortex generators, Energy Convers. Manag. 51 (6) (2010) 1242–1249. [4] C. Qi, N. Zhao, X. Cui, T.T. Chen, J.D. Hu, Effects of half spherical bulges on heat transfer characteristics of CPU cooled by TiO2 -water nanofluids, Int. J. Heat Mass Transf. 123 (2018) 320–330. [5] Z.M. Xu, Z.M. Han, J.T. Wang, Z.D. Liu, The characteristics of heat transfer and flow resistance in a rectangular channel with vortex generators, Int. J. Heat Mass Transf. 116 (2018) 61–72. [6] P.J. Bezbaruah, R.S. Das, B.K. Sarkar, Thermo-hydraulic performance augmentation of solar air duct using modified forms of conical vortex generators, Heat Mass Transf 55 (5) (2019) 1387–1403.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Experimental and numerical investigation on particulate fouling characteristics of vortex generators with a hole Zhimin Han, Zhiming Xu∗ School of Energy and Power Engineering, Northeast Electric Power University, Jilin City, Jilin Province, China
a r t i c l e
i n f o
Article history: Received 8 September 2019 Revised 23 November 2019 Accepted 26 November 2019
Keywords: Vortex generator Punched holes CFD Experimental investigation Fouling characteristic
a b s t r a c t In this study, the particulate fouling characteristics in a heat exchange channel with a rectangular wing vortex generator were investigated both experimentally and numerically. First, the fouling and flow resistance characteristics of the smooth channel, vortex generator without a hole, and vortex generator with a hole were compared experimentally. Subsequently, the fouling characteristics of the rectangular vortex generator with and without a hole were compared under turbulent conditions via numerical simulations. Finally, the effects of the hole diameter, and the lateral and vertical hole distances in the vortex generator on the particulate fouling characteristics were evaluated. The results show that both the vortex generator with a hole and without a hole could inhibit the formation of particles on the heat transfer surface. Compared with the vortex generator without a hole, the vortex generator with a hole could better inhibit particulate fouling, and it had a low flow resistance loss. The asymptotic fouling resistance decreased first and then increased with increasing hole diameter, it decreased as the lateral distance of the hole increased, and increased as the vertical distance of the hole increased. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction The heat transfer enhancement and fouling characteristics of heat exchangers have generally been of marked research interest. Heat transfer surface fouling inevitably causes heat loss to the heat exchange equipment, which compromises the safe operation of the heat exchange equipment. Beside deterioration of heat transfer, the growing fouling layer is leading to a reduction of channels crosssection that increase the pressure loss in the heat exchanger [1]. Vortex generators (VGs), as the most representative heat transfer enhancement component, have been the focus of significant global study [2]. Currently, many studies have indicated that vortex generators can enhance the heat transfer ability of the heat transfer surface [3–6]. However, a literature survey found that regardless of the type of vortex generator used, a certain pressure drop loss occurs while enhancing the heat transfer ability of the channel. For example, Chu et al. [7] studied the effects of a triangular winglet vortex generator on the heat transfer of a finned elliptical tube heat exchanger under laminar flow. It was found that the triangular winglets increased the average Nusselt number of the heat exchanger by 13.6%–32.9%, but the pressure loss also increased
∗
Corresponding author. E-mail address: [email protected] (Z. Xu).
https://doi.org/10.1016/j.ijheatmasstransfer.2019.119130 0017-9310/© 2019 Elsevier Ltd. All rights reserved.
by 29.2%–40.6%. Chen et al. [8] studied the heat transfer characteristics in rectangular micro-channels with different number of pairs and dimensions longitudinal vortex generators. It was found that the heat transfer performance of the micro-channels with vortex generators was enhanced by 12.3–73.8% and 3.4–45.4% for microchannels with aspect ratios of 0.0667 and 0.25, respectively, while the pressure losses were increased by 40.3–158.6% and 6.5– 47.7%, respectively. Gallegos and Sharma [9] investigated the heat transfer characteristics of rectangular channels equipped with a flapping flag as a vortex generator. Their results showed that the inclusion of a flapping flag in the channel leads to a Nusselt number enhancement as high as 1.34 to 1.62 times the bare channel levels, and the friction factor was as high as 1.39 to 3.56 times the bare channel levels. To ensure the heat transfer enhancement of the vortex generator while reducing the flow resistance, many new designs have been proposed for the vortex generator. Tang et al. [10] proposed various types of vortex generators, compared with the commonflow-down configuration, the Nusselt number of the commonflow-up configuration increase by 2.7–2.9% and the friction factors reduced by 7.8–10.0%. Biswas and Chattopadhyay [11] determined that punching holes under the airfoil vortex generator would have an effect on the heat transfer and resistance characteristics. Wu et al. [12] found that the structure was not only easy to implement by arranging the rectangular vortex generator with punched holes on the surface of the fin heat exchanger but also helped to im-
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Nomenclatures a b c CMgO C∞ C+ d DB DT dp e J k mf m˙ f m˙ d m˙ r p Rf S Sp T Tl t U ud v xf y
length of the vortex generator (m) height of the vortex generator (m) hole vertical direction distance (m) particle concentration (kg/m3 ) bulk particle concentration (kg/m3 ) dimensionless particle concentration hole diameter (m) Brownian diffusivity (m2 /s) turbulent diffusivity (m2 /s) particle diameter (m) hole lateral direction distance (m) deposition flux (kg/(m2 •s)) removal constant (–) fouling mass per unit area (kg/m2 ) total mass rate (kg/(m2 •s)) deposition mass rate (kg/(m2 •s)) removal mass rate (kg/(m2 •s)) pressure (Pa) fouling resistance (m2 •K/W) particle-fluid density ratio (–) sticking portability (–) temperature (K) Lagrangian integral time scale (s) fouling time (s) velocity vector (–) particle deposition velocity (m/s) fluid velocity (m/s) thickness of fouling layer (m) distance from wall (m)
Greek symbols ε deposit porosity (–) λ thermal conductivity (W/(m•K)) λf thermal conductivity of the deposit (W/(m•K)) μ dynamic viscosity (kg/(m•s)) v kinematic viscosity (m2 /s) ρ density (kg/m3 ) ρ dep density of the deposit (kg/m3 ) τp particle relaxation time (s) τw wall shear stress (MPa) ψ the bond strength factor (–) Subscripts d deposition f fouling in inlet l liquid phase out outlet p particle phase r removal
prove the overall heat transfer and reduce pressure loss. He et al. [13] studied the effects of the enhanced heat transfer on a perforated winglet vortex generator in a finned tube heat exchanger. Their results showed that a significant increase of up to 33.8–70.6% in the heat transfer coefficient was achieved and was accompanied by a pressure drop of 43.4–97.2% for the 30° case compared to the plain fin. The performances of plane and curved winglet vortex generators with and without punched holes have been investigated experimentally by Zhou and Feng [14]. Their results showed that punched holes could enhance the heat transfer in both the laminar and turbulent flow regions and decrease the flow resistance. Qi et al. [15] investigate the effects of round hole diam-
eter and pitch-row on thermal and hydrodynamic characteristics of nanofluids based on triangular tubes with perforated turbulator inserted, and apply thermal and exergy efficiency to assess the comprehensive thermal and hydrodynamic characteristics. Jeong et al. [16] proposed a crescent-shaped protrusion was mounted as a vortex generator on the downstream of the dimple. The dimpled channel with a vortex generator shows better normalized thermoperformances than the general dimpled channel. Experimental and numerical of vortex heat transfer in turbulent air flow around the plate with permeable transverse rectangular ribs have been made by Kong et al. [17]. It is shown that the presence of a slit can eliminate secondary separation zones on the plate and decrease recirculation flow regions behind a rib. Vortex generators have been extensively studied for heat transfer enhancement, however, research on fouling is relatively sparse. Hasan et al. [18] studied the crystallization fouling characteristics of the delta-wing vortex generator, and proposed that the structural design of the vortex generator should be considered in conjunction with antifouling and pressure drop. Zhang et al. [19] proved experimentally that the vortex generator could effectively improve the heat transfer coefficient and also destroy the boundary layer near the wall surface, thus inhibiting fouling. Furthermore, our recent work [20] demonstrated that induced vortexes could inhibit fouling formation. Therefore, in this work, the fouling characteristics of a new type of vortex generator with a hole were studied experimentally and numerically. First, a comparison of a rectangular vortex generator with and without a hole was carried out. Then, the effects of the hole diameter, and the lateral and vertical hole distances of the VGs on the particulate fouling characteristics were studied. 2. Experimental procedure A schematic diagram of the experimental system is shown in Fig. 1 [21]. The system was composed of a working fluid circulation loop, a cooling cycle loop, and a data acquisition system. The temperature in the experimental section was controlled using a Pt100 thermal resistance and thermostat control. All the relevant experimental data were collected through the data acquisition system and sent to a computer. The test section used a rectangular channel with a size of 10 0 0 mm × 100 mm × 8.5 mm. The test section consisted of a polypropylene (PP) plastic plate, a silica gel sheet, and a 304 stainless steel plate. The thickness of the stainless steel plate was 0.5 mm, which was the main heat exchange surface for the test section, and the fouling was mainly deposited on it. Its geometrical dimensions were 10 0 0 mm × 10 0 mm as shown in Fig. 2. The PP plastic plate was anti-hygroscopic, had acid and alkali corrosion resistance, and was resistant to oxidation under high temperature conditions. Therefore, the surface materials were constructed using PP plastic plates. The silica gel sheet had large elastic deformation because of its soft texture and pressure, and therefore had good sealing abilities and functioned as a seal in the test section. The test section was well insulated to minimize the heat loss. The schematic diagram of the test section and vortex generator with a hole is shown in Fig. 2. The arrow indicates the direction of fluid flow. The VGs with two rows and nine columns were placed in the channel at an attack angle of 90°. The first VG pair was located 150 mm from the leading edge. The lateral spacing between two VGs was 20 mm. The longitudinal spacing between the two VGs was 90 mm. The sizes of rectangular VGs with a hole are shown in Fig. 2(a). The VGs were made of a steel plate with a = 25 mm long and b = 6 mm high. A hole was punched on the VG surfaces at different positions. The height from the center of the hole to the bottom edge was c. The width from the center of hole to the side edge was e. The diameter of the punched hole was
Z. Han and Z. Xu / International Journal of Heat and Mass Transfer 148 (2020) 119130
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Fig. 1. Diagram of the experimental system.
Fig. 2. Schematic diagram of the test section and vortex generator with a hole. (a) The sizes of the vortex generator with a hole. (b) The hole direction distance of vortex generator.
d. Table 1 lists the geometrical dimensions of the rectangular VGs used, and Fig. 2(b) shows the hole direction distance of VGs in this study. To ensure the accuracy of the results, multiple experiments on the rectangular channels without vortex generators were carried out. The root mean square method was used to calculate the er-
ror. The temperature measurement error of resistive thermometer was 0.206%, and the flow measurement error of electromagnetic flowmeter was 0.503%. Furthermore, the uncertainties of the results were evaluated based upon the analysis of errors in the experimental measurements. The results show that the two groups of experiment results were basically the same and the relative error
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Fig. 3. Mesh generation for the rectangular channel of the VGs with a hole. Table 1 Geometrical dimension of VGs with a hole. Name
Symbol
Size (mm)
Dimensionless dimension
The hole diameters The hole vertical direction distance The hole lateral direction distance
d c e
2, 3, 4, 5, 6 1.5, 2.25, 3, 3.75, 4.5 1.5, 7, 12.5, 18, 23.5
d/b=0.33, 0.5, 0.67, 0.83, 1 c/b=0.25, 0.375, 0.5, 0.625, 0.75 e/a=0.06, 0.28, 0.5, 0.72, 0.94
of the fouling resistance was less than 5%, thus meeting engineering requirements. Moreover, the measurement errors of temperature, pressure drop, and volumetric flow rate of test bed are less than ±1%. A detailed error analysis can be found in Ref. [20]. 3. Numerical methods and procedure Numerical simulations were conducted using the finite volume method (FVM) with the assistance of a commercial CFD package (ANSYS Fluent). For the convective and diffusive terms, the second order upwind method was used while the SIMPLE procedure was introduced for the velocity-pressure coupling. The discretization of the pressure equation was completed using the standard scheme. The residual criteria for the continuity, momentum, and energy equations were set to 10−6 . The ICEM software was used to construct the 3D computational domain. The model was discretized using an unstructured mesh. The grid was refined in key areas of interest such as the regions close to the wall and the VGs. 3.1. Physical model The geometry of the rectangular channel and vortex generators were the same as the test section used in the experiments. The computational domain was extended 150 mm from the entrance and the exit to ensure a uniform velocity distribution of the entrance flow and avoid recirculation of the outflow [22]. The thickness of the VGs was often neglected for simplification in most of the simulations. The generation of a mesh in the rectangular channel with rectangular VGs is shown in Fig. 3. The grid independence study was applied to the rectangular channel with VGs. Different grid system sizes were used to ensure grid independence and validate the results. When the grid number increased further, changes in the deposition velocity were less than 1%, and the final adopted grid number was 1,589,598. 3.2. Governing equations The simulated flow was unsteady, and the fluid was assumed to be incompressible. The velocity inlet was specified as 0.5 m/s in the numerical simulation part, which corresponded to a Reynolds number of 10,703. The RNG k–ε turbulent model was employed in this study. The Eulerian-Eulerian model solves two sets of conservation equations, one for each phase. The governing equations of continuity, momentum, and energy in the computational domain are as follows [23]: Continuity equation:
∇U = 0
(1)
Momentum equation:
∂U + ρU · ∇ U = −∇ p + μ∇ 2U ∂t
(2)
Energy equation:
∂T λ 2 + U · ∇T = ∇ T ∂t ρ cp
(3)
where U is the velocity vector, t is the time, ρ is the fluid density, μ is the fluid dynamic viscosity, p is the pressure, T is the temperature, cp is the specific heat capacity, and λ is the thermal conductivity. The RNG k-ε turbulence model:
∂ ( ρ k ) ∂ ( ρ kui ) ∂ ∂k + = +Gk − ρε σμ ∂t ∂ xi ∂ xj k eff ∂ xj ∂ (ρε ) ∂ (ρε ui ) ∂ ∂ε ε ε2 + = +C1∗ε Gk − C2ε ρ σk μeff ∂t ∂ xi ∂ xj ∂ xj k k
(4)
(5)
where μe f f = μ + μt , μt = ρCμ k2 /ε , and Cμ =0.0845; σ k and σ ε are the Prandtl numbers corresponding to the kinetic energy k and the dissipation rate ε , respectively, σ k =σ ε =1.39; C1∗ε = η (1−η/η0 , C1ε =1.42 and C2ε =1.68,η = (2Eij · Eij )1/2 k/ε , Eij = 1+βη3 ∂ uj 1 ∂ ui 2 ( ∂ xj + ∂ xi ); η 0 =4.377 and β =0.012.
C1ε −
The boundary conditions imposed on the computational domain are shown in Table 2. 3.3. Fouling model The deposition mass rate m˙ d was calculated using the following equation [24]:
m˙ d = Sp · ud · C∞
(6)
where Sp is the probability of sticking and C∞ is the bulk particle concentration. In this study, the fluid had a constant particle concentration and the sticking probability was assumed to be Sp = 1. The particulate deposition velocity ud was expressed as following [25]:
ud =
J ∂C+ μ = − ( DB + εp ) − DT C∞ ∂y ρl T
∂ v 2 py ∂T × C + − τp × C+ ∂y ∂y (7)
where the right hand of the equation are the Brownian and eddy diffusion terms, the thermophoretic deposition term, and finally turbophoretic deposition term. DB is the Brownian diffusivity, and
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Table 2 Boundary conditions. Boundary condition
Assumption
Inlet Outlet Bottom wall (no-slip condition) Inlet and outlet extended section (adiabatic) Remaining walls and Vortex generator (adiabatic)
εp is the particulate eddy diffusivity [26],
uin =0.5 m/s, v=w=0, Tin =298 K
∂ u/∂ x=∂ v/∂ x=∂ w/∂ x=0, ∇ T=0 u=v=w=0, Tw =318 K u=v=w=0, ∇ T=0 u=v=w=0, ∇ T=0
εp τp −1 vt = (1 + Tl ) , were
Tl is the Lagrangian time scale of the fluid, Tl = vt /v 2 y , v 2 y is the root-mean-square (RMS) of the local wall-normal velocity fluctuations, vt is the turbulent eddy viscosity, and τ p is the partiSd2 Cc
cle relaxation time, τp = 18p v , DT is the thermal diffusion coefficient [27], ∂ T/∂ y is the temperature gradient perpendicular to the surface and is calculated by the CFD program, C+ is the nondimensional concentration, v 2 py is the intensity of the particulate wall normal velocity fluctuations, which can be approximately esT
timated according to Johansen [26], v 2 py = v 2 y ( τp +l T ). l
The mass removal rate m˙ r of the fouling is expressed as [28]:
m˙ r = k
τ w
ψ
xf
(8)
where k is the removal constant, ψ is the bond strength factor of the deposit layer, τ w is the wall shear force, and xf is the fouling thickness. According to Ref. [28], k/ψ are combined to obtain a constant, which was 0.084. According to Kern and Seaton [29], the fouling is the result of a deposition and removal process and can be calculated as:
m˙ f = m˙ d − m˙ r
(9)
The fouling resistance represents the heat transfer thermal resistance caused by a buildup of deposit on the surfaces of the heat exchangers, and can then be calculated as [30]:
Rf = mf /
ρdep λf
(10)
where mf is the total fouling mass; ρ dep is the density of the deposit, ρdep = ρp (1 − ε ) + ρl ε ; λf is the thermal conductivity of the deposit, λf = (1 − ε )λp + λl ε ; ε is the deposit porosity [31]. 4. Results and discussion There is prior work [32] showing that the stable existence of the Mg2+ and Ca2+ ions in urban sewage cause are Magnesium Oxide and Calcium Carbonate fouling, after two stage treatment. Therefore, pure water containing magnesium oxide nanoparticles was selected as the working fluid in this study. The nanoparticles could be well suspended in water. The particles were spherical and had a size of 50 nm, a concentration of 0.4 kg/m3 , and their specific surface area was 30–50 m2 /g. 4.1. Experimental results The variation in the fouling resistance with time at the VGs with and without a hole, and in the smooth channel is shown in Fig. 4. For the VG with a hole, the hole was punched in its center, i.e., e = 12.5 mm and d = 3.0 mm. The velocity, magnesium oxide concentration, inlet temperature of the solution, and waterbath temperature were maintained at 0.1 m/s, 0.4 kg/m3 , 298 K, and 318 K, respectively. As shown in Fig. 4, the fouling resistance curves for the three experiments were asymptotic, and the asymptotic fouling resistance of the smooth rectangular channel was the maximum, followed by the VG without a hole, and VG with a hole was the lowest. This shows that a rectangular-wing VG with and
Fig. 4. Variation in fouling resistance with time.
without a hole can inhibit the formation of particulate fouling. This is because the working fluid that passes through the vortex generator produces a strong longitudinal vortex. A strong longitudinal vortex increases the removal and shear effects of the fluid on the wall, thus inhibiting the formation of particulate fouling on the heat transfer surface. Furthermore, compared with the VG without a hole, the VGs with a hole had better antifouling performance. This is because the VG with a hole could improve the flow characteristics in the backflow area of the rectangular-wing VG, and an example is shown in Fig. 5, which shows a visualization of the fouling deposition for the VGs without and with a hole. Fig. 5 shows that the fouling layer behind the rectangularwing VGs with a hole was thin, and had two distinct jet traces behind it. It also can be seen that the local fouling layer with the jet disturbances was relatively thinner. These results are consistent with those previously reported in literature [14]. This process leads to a large shear force and increases the removal rate in this area. Therefore, the antifouling performance of the VGs with a hole was better than the one without a hole The variation in the pressure drop with the Reynolds number of the VG with and without a hole, and for the smooth channel is shown in Fig. 6. It can be seen that as the Reynolds number changes, the pressure drop for the VG without a hole and for the VG with a hole was higher than for the smooth channel. Furthermore, the pressure drop for the VG with a hole was less than for the VG without a hole. There are two main reasons for this: the first is that the VG without a hole has a larger flow area than the VG with a hole, so the pressure drop that occurs when the working fluid flows through the vortex generator is relatively large; the second was that when the fluid flows through the VG with a hole, a part of the working fluid passes through the hole to generate a jet action, and this part of the working fluid retains the original flow trajectory and reduces the flow resistance. The experimental results show that the flow resistance loss of the VGs with a hole was less than that for the VGs without a hole.
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Z. Han and Z. Xu / International Journal of Heat and Mass Transfer 148 (2020) 119130
Fig. 7. Comparison of the experimental results and numerical results.
Fig. 5. Visualization of fouling deposition.
Fig. 8. Variation of the fouling resistance with time.
Fig. 6. Pressure drop with the variation of Re.
4.2. Numerical results 4.2.1. Comparison with experimental results To validate the reliability of the numerical method, the experimental and numerical results of the smooth channel and the VG channel with a hole were selected for verification. Fig. 7 shows that except for the large error caused by the simulation neglecting the fouling induction period in the early stage, the experimental results and numerical results were in close agreement. However, the focus of this study was on the late stable stage. Therefore, the good agreement between the experimental and numerical results at the later stage indicates that the numerical approach adopted was reliable. Turbulent flow is mostly dominant in actual industrial equipment. Hence, in the simulation part, the fluid velocity was increased by 0.5 m/s. For comparison in this section, the inlet
velocity, magnesium oxide concentration, inlet solution temperature, and water-bath temperature were maintained at 0.5 m/s, 0.4 kg/m3 , 298 K, and 318 K, respectively. The fouling characteristics of the rectangular channel of the VGs with and without a hole were studied. The variation of the fouling resistance with time is shown in Fig. 8. From the results in Fig. 8, the conclusion that the fouling resistance of the VGs with a hole is smaller than that the VGs without a hole can be reached, and the maximum reduction was 2.97%. From Fig. 5, it was determined that as the working fluid passes through the VG with a hole, a part of the fluid forms a jet through the circular hole. To better verify this point, the velocity contour of the rectangular wing VGs with and without a hole are given, as shown in Fig. 9. It can be seen that for the VG with a hole, a distinct jet is formed at the hole. The high-speed jet not only destroys the low-speed stagnation zone, but also increases the flow rate of the working fluid. At the same time, this process increases the wall shear force and the removal rate in this area. Therefore, the VGs with a hole have better antifouling performance than the VGs without a hole. 4.2.2. Effects of the hole diameters The effect of the hole diameters (d/b = 0.33, 0.50, 0.67, 0.83, 1.00) are studied at a lateral hole distance of e = 6 mm (e/a = 0.50) and a vertical distance of c = 3 mm (c/b = 0.50). The change
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Fig. 9. Near-wall velocity contour of the rectangular wing VGs with and without a hole. (a) XY section. (b) XZ section.
Fig. 10. Variation of fouling resistance with the hole diameter.
in the fouling resistance with time for the different hole diameters are shown in Fig. 10. It can be seen that the asymptotic fouling resistance of the VGs with a hole decreases first and then increased as the hole diameter increased. The asymptotic fouling resistance curve had a minimum value at d/b = 0.5. The reason for this was that when the fluid flows through the vortex generator, an end vortex can be generated at the end of the vortex generator. These vortices continue to develop along the flow direction and sweep the working fluid at the wall surface, thinning or destroying the boundary layer. However, as the hole diameters of the VGs increase, on the one hand, the formed jet increases the scouring area of the backflow stagnation zone behind the rectangular wing because of the increased hole size, which further reduces the mass deposition rate; on the other hand, a larger hole results in a smaller intensity of the jet formed, and the strength of the vortex formed at the end of the VGs is lower, which reduces the mass removal rate. Since the above two effects are opposed, the fouling resistance will have a minimum value, which is why the value of the asymptotic fouling resistance first decreases and then increases as the hole diameter increases. Fig. 11 shows the near-wall velocity contours of the VGs with different hole diameters. It can be clearly seen from the figure that as the hole diameter increases, the area of the low-speed stagnation area behind the vortex generator continuously decreases. However, the velocity of the end vor-
Fig. 11. Near-wall velocity contours with different hole diameter.
tex on both sides of the vortex generator became smaller. Hence, these two phenomena verify the above explanation. 4.2.3. Effects of the hole lateral direction distance The effect of the lateral hole distance (e/a = 0.06, 0.28, 0.50, 0.72, 0.94) was studied for a hole diameter of d = 3 mm (d/b = 0.50), and the vertical hole distance was c = 3 mm (c/b = 0.50). The fouling resistances changed with time under the different lateral hole distances, as shown in Fig. 12. It can be seen from Fig. 12 that the asymptotic fouling resistance of the VG with a hole decreases as the lateral hole distance increases, and a minimum was obtained when the hole lateral direction distance was 0.94. This was because when the hole was located near the side wall, the area of the low velocity region after the vortex generator was reduced, so that the mass deposition rate reduced. This can be clearly seen from the near-wall velocity contours of the VGs with
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Z. Han and Z. Xu / International Journal of Heat and Mass Transfer 148 (2020) 119130
Fig. 14. Variation of fouling resistance with the vertical hole distance. Fig. 12. Variation of fouling resistance with the lateral hole distance.
Fig. 15. Near-wall velocity contours of VGs with different vertical hole distances.
Fig. 13. Near-wall velocity contours of VGs with different lateral hole distances.
different lateral hole distances, as shown in Fig. 13. Moreover, it also can be seen from the figure that when the lateral hole position was e/a = 0.06, i.e., the hole was close to the inner edge, since the lateral distance (20 mm) of the two vortex generators was limited, the jets formed by the hole were superimposed on each other, and the area that can be affected becomes small. Therefore, compared with the other lateral hole positions, the fouling resistance value at e/a = 0.06 was the largest. 4.2.4. Effects of the hole vertical direction distance The effect of the hole vertical distance (c/b = 0.25, 0.375, 0.50, 0.625, 0.75) was studied when the hole diameter was d = 3 mm (d/b = 0.50), and the hole lateral direction distance was e = 12.5 mm (e/a = 0.50). The fouling resistance changed with time for the different vertical hole distances, as shown in Fig. 14. It can be seen that the asymptotic fouling resistance of the VGs with a hole increased as the vertical hole distance increased. The hole vertical direction distance of c/b = 0.25, i.e., the value of the asymptotic fouling resistance reached a maximum value when the hole was close to the upper wall surface; the vertical hole distance
c/b = 0.75, i.e., the value of the asymptotic resistance had a minimum value when the hole was close to the bottom surface. Fig. 15 shows the near-wall velocity contours of the VG with different vertical hole distances. It can be clearly seen from the figure that when the vertical hole distance was c/b = 0.25 (near the bottom surface), the jet formed on the bottom surface of the VG directly flushes the bottom surface because of the punched hole, thereby destroying the stagnation zone. When c/b = 0.75 (close to the upper wall), while the hole could increase the vortex area, its effect is not as clear as for directly destroying the stagnation area. Therefore, as the vertical hole distance increases, i.e., the hole gradually moves away from the bottom surface, the value of the asymptotic fouling resistance of the channel gradually decreases, which can explain the trend in Fig. 14 well. 5. Conclusions In this work, experimental and numerical studies of the particulate fouling characteristics in a channel with a rectangular wing vortex generator were investigated. The main conclusions can be summarized as follows: (1) The rectangular wing VG with a hole and without a hole could both inhibit the formation of magnesium oxide nanoparticles on the heat transfer surface. Compared with VGs without a hole, the VGs with a hole could better inhibit
Z. Han and Z. Xu / International Journal of Heat and Mass Transfer 148 (2020) 119130
particulate fouling. Moreover, the flow resistance loss of the VGs with a hole was less than that of the VGs without a hole. (2) The good agreement between the experimental and numerical results with the adopted numerical approach indicated that the results were reliable. For turbulent flow, the fouling resistance of the VGs with a hole was also smaller than that of the VGs without a hole, and a maximum reduction of 12.97% was obtained. (3) In the simulation range, the asymptotic fouling resistance of the VGs with a hole first decreased and then increased with increasing hole diameter. The asymptotic fouling resistance of the VGs with a hole decreased with increasing lateral hole distance, and increased with the increasing vertical hole distance. Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled,“Experimental and numerical investigation on particulate fouling characteristics of vortex generators with a hole”. CRediT authorship contribution statement Zhimin Han: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Writing - review & editing. Zhiming Xu: Conceptualization, Resources, Supervision, Project administration, Funding acquisition. Acknowledgement The financial support of the National Natural Science Foundation of China (Nos. 51476025 and 51706038) is gratefully acknowledged. References [1] P.O. Kapustenko, J.J. Klemeš, O.I. Matsegora, P.Y. Arsenyev, O.P. Arsenyeva, Accounting for local thermal and hydraulic parameters of water fouling development in plate heat exchanger, Energy 174 (2019) 1049–1059. [2] Y.L. He, Y.W. Zhang, Advances and outlooks of heat transfer enhancement by longitudinal vortex generators, Adv. Heat Transf. 44 (2012) 119–185. [3] P. Promvonge, T. Chompookham, S. Kwankaomeng, C. Thianpong, Enhanced heat transfer in a triangular ribbed channel with longitudinal vortex generators, Energy Convers. Manag. 51 (6) (2010) 1242–1249. [4] C. Qi, N. Zhao, X. Cui, T.T. Chen, J.D. Hu, Effects of half spherical bulges on heat transfer characteristics of CPU cooled by TiO2 -water nanofluids, Int. J. Heat Mass Transf. 123 (2018) 320–330. [5] Z.M. Xu, Z.M. Han, J.T. Wang, Z.D. Liu, The characteristics of heat transfer and flow resistance in a rectangular channel with vortex generators, Int. J. Heat Mass Transf. 116 (2018) 61–72. [6] P.J. Bezbaruah, R.S. Das, B.K. Sarkar, Thermo-hydraulic performance augmentation of solar air duct using modified forms of conical vortex generators, Heat Mass Transf 55 (5) (2019) 1387–1403.
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