Parametric investigation of heat transfer enhancement and pressure loss in louvered fins with longitudinal vortex generators

International Journal of Thermal Sciences 135 (2019) 533–545

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Parametric investigation of heat transfer enhancement and pressure loss in louvered fins with longitudinal vortex generators

T

Daniel Jonas Dezana,∗, Jurandir Itizo Yanagiharab, Guilherme Jenovencioc, Leandro Oliveira Salvianod a

Energy Engineering, Federal University of ABC, Santo Andre, Sao Paulo, Brazil Department of Mechanical Engineering, Polytechnic School, University of Sao Paulo, Sao Paulo, Sao Paulo, Brazil c Angewandte Mechanik, EU Researcher, University of Munchen, Munchen, Germany d Department of Mechanical Engineering, Sao Paulo State University, Ilha Solteira, Sao Paulo, Brazil b

ARTICLE INFO

ABSTRACT

Keywords: Louvered fin Longitudinal vortex generators Heat transfer enhancement Screening analysis Smoothing spline ANOVA method Computational fluid dynamics Thermal-hydraulic performance

The present work aims to perform a parametric study of heat transfer enhancement and the associated pressure loss applied to louvered fins with rectangular winglet vortex generators (RWL). The contributions of a set of design variables on heat transfer and pressure drop are evaluated for two geometry types, L1 and L2. The procedure to investigate the relative importance of the geometrical design variables on thermal-hydraulic performance is enabled by a Design of Simulations (DOS) method called Latin Hypercube Sampling (LHS) in association with a modern non-parametric statistical method (Smoothing Spline ANOVA method) and Computational Fluid Dynamics. Outcomes from the screening analyses turned out that the louver angle is the unique contributor to friction factor for both geometry types and this behaviour is independent of Reynolds number. With respect to heat transfer, the contributions of the input variables are different for both geometry types and Reynolds numbers. For ReDh = 120 , no important two-factor interaction effects were observed for both L1 and L2, in the same way as occurred in terms of friction factor. Conversely, for ReDh = 240 one relevant interaction effect was observed.

1. Introduction In the last decades, the researchers have focused much effort to understand the heat transfer mechanisms in louvered fin arrays and longitudinal vortex generators (LVG). As described in Bergles [1], the concomitant application of two or more enhancement techniques could provide heat transfer intensification larger than that observed when the techniques are used separately. In this paper, a parametric investigation of a compound heat transfer enhancement technique composed by louvered fins with rectangular winglet vortex generators (RWL) for relatively low Reynolds numbers is accomplished. Multilouvered fins are very popular passive heat transfer enhancement technique used especially for air-side heat transfer enhancement. The use of this fin type is of particular importance in the automotive industry due to restrictions on space, weight and costs [2]. The louvered fins also find widespread use in ventilation, heating and air-conditioning industries [3], as well as in applications under frosting and wet conditions [4–6]. Fig. 1 shows an example of a typical multilouvered fin geometry.

∗

This type of extended surface increases the heat transfer coefficient several times if compared to plain fin, with associated high-pressure penalty. In simple terms, the heat transfer characteristics and flow loss penalty of a louvered fins are highly dependent of geometric parameters and Reynolds number. With regard to geometrical parameters of the louvered fins, the convection heat transfer normally increases for small fin pitches, large louver pitches, large louver angles and thin louvers. The combination of these geometrical characteristics and high Reynolds numbers are conductive to louver-directed flow. In this case, the boundary layers become thinner and the flow goes through the gap between adjacent louvers, increasing the heat transfer. Conversely, large fin pitches, small louver pitches, small louver angles, thick louvers and low Reynolds numbers lead to a duct-directed flow, which normally presents very low convection heat transfer coefficients. Fig. 2 illustrates the louver and duct-directed flows. DeJong and Jacobi [9] evaluated the importance of geometrical parameters and Reynolds number for a louvered fin on pressure loss and heat transfer enhancement, and as consequence, on flow efficiency. They suggested that the vortex shedding has low impact on heat

Corresponding author. E-mail address: [email protected] (D.J. Dezan).

https://doi.org/10.1016/j.ijthermalsci.2018.09.039 Received 17 July 2017; Received in revised form 26 September 2018; Accepted 30 September 2018 1290-0729/ © 2018 Published by Elsevier Masson SAS.

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Nomenclature

ANOVA AC A0 Afr

Analysis of variance method Minimum flow cross-sectional area (m2) Total surface area (m2) Fin frontal area (m2)

Dh = DOE DOS DWL E f FD FH FP j LH LP LVG

Hydraulic diameter (m) Design of Experiments Design of Simulations Delta winglet vortex generator Wetted perimeter (m) Friction factor Flow depth (mm) Fin height (mm) Fin pitch (mm) Colburn factor Louver height (mm) Louver pitch (mm) Longitudinal vortex generators

4Afr E

Rectangular winglet vortex generator RWL ReDh Reynolds number based on hydraulic diameter SS ANOVA Smoothing Spline ANOVA method TP Transverse tube pitch (mm) UAfr UC = A Maximum air velocity (m/s) C x LVG streamwise position (mm) Greek symbols Louver angle (º) LVG angle of attack (º) Subscripts

1, 2, 3, 4 LVG nomenclature Inlet; in out Outlet; w Tube and fin walls

transfer and pressure drop. An investigation of the mean flow effects on thermal-hydraulic performance for a hybrid fin (combination of slit fin and louvered fin) is reported by T'Joen et al. [10]. For low Reynolds numbers, the hybrid fin offered some benefits when compared to louvered and slit fins used separately. In their work, Dogan et al. [11] estimated the performance of a heat exchanger composed by two and three louvered arrays between the flat-tubes. The authors examined transient and steady state temperatures of the fluids (cold and hot sides) of the heat exchangers and suggested that the correlations to predict the pressure drop and heat transfer of standard louvered fins cannot be applied to the cases when two or three fins rows are placed between the tubes. Karthik et al. [12] presented the effect of fin pitch, transverse tube pitch, longitudinal tube pitch, louver pitch and louver angle on heat transfer, pressure drop and goodness factor of the flat-tube louvered fin heat exchanger for turbulent flow. Qi et al. [13] indicated that the number of louvers, flow depth and fin pitch to fin thickness ratio are the most relevant parameters that could be monitored in the preliminary design assessment of a louvered fin. Sizing optimization of flattube louvered fin heat exchangers by using genetic algorithm can be observed on the work from Yadav et al. [14]. The parametric study showed that the heat transfer rate is very affected by louver angle, louver height and fin frequency. In the numerical study by Zuoqin et al. [15], a parametric analysis was performed to estimate the impact of design parameters on the performance of a round-tube louvered fin heat exchanger were investigated. From the data reduction, the authors proposed correlations for Nusselt number and pressure drop. In the open literature there are a considerable amount of studies

focused on flow patterns and heat transfer characteristics of heat exchangers using many types of longitudinal vortex generators. A comprehensive coverage of the different aspects of the heat transfer surfaces with vortex generators has been systematically presented by Torii and Yanagihara [16], Torii and Yanagihara [17], Yanagihara and Torii [18] and Fiebig [19]. The longitudinal vortex generators (LVGs) generate intentionally large secondary flow structures to improve the heat transfer coefficient. The secondary flow structures are recognized to be three-dimensional and their propagation occurs along the main flow direction. The great advantage of the LVGs is that they lead to heat transfer enhancement with associated small increase of pressure penalty. The vortices created by an LVG cause flow destabilization and swirling, disruption and modification in the boundary layer and heavy bulk fluid mixing (especially due to heat exchange between the near wall region and the secondary flow) [16] [17], [18]. The researches about this subject indicate that the performance is strongly linked to LVG aspect ratio, LVG type, LVG frontal area, angle of attack of the LVG and Reynolds number [19–24]. The basic vortex structures formed by a rectangular winglet vortex generator (RWL) can be seen in Fig. 3 and they are described in details on the studies from Velte et al. [25]. A complex vortex system is created when the flow passes through the RWL, which is composed by two mechanisms: (i). A basic vortex system and; (ii). A secondary vortex structure. The basic vortex system is constituted by the primary vortex, also known as main vortex, and the corner vortices. The main vortex is a result of the flow separation at the tip of the RWL and rolling up due to the lower pressure in the back side of the RWL; the corner vortices are

Fig. 2. Section showing the two extreme flow regimes in a typical louver array [8].

Fig. 1. Typical multilouvered fin geometry [7]. 534

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Fig. 3. Vortical structures generated by flow passing through RWL: (a) Sketch of basic vortex system and (b) Combination of basic vortex system and secondary vortex structure - adapted from Velte et al. [25].

parameters of a round-tube louvered fin heat exchanger with DWL is tightly related to flow conditions. In this sense, at low Reynolds numbers the geometry of DWLs are important in terms of heat transfer and pressure drop; at high Reynolds numbers, louver angle and fin pitch have a high effect on heat transfer and pressure drop. Studies about the interaction effects between design parameters of a round-tube louvered fin heat exchanger with DWLs can be seen in the work from Ameel et al. [35]. Results indicated that the interaction effects are as important as the main effects. Dezan et al. [22] used a non-parametric statistical method to assess the contributions of input parameters on heat transfer and pressure drop applied to louvered fins with delta-winglets. From that research, none substantial two-factor interaction effects between louver angle and DWL parameters (frontal area, streamwise position and angle of attack) was observed. Dezan et al. [23] proposed an optimization procedure for maximization of the heat transfer for a flat-tube louvered fin compact heat exchanger with DWLs under laminar flow conditions. The optimization procedure found a maximum heat transfer about 20% higher than baseline case (louvered fin without DWLs). Whereas numerous investigations of louvered fins and longitudinal vortex generators on compact heat exchangers are available, only few works deal with numerical investigations of thermal-hydraulic performance of louvered fins combined with longitudinal vortex generators. Moreover, it was not found any research considering the effect of geometrical parameters of flat-tube louvered fin heat exchangers with RWL on heat transfer and pressure drop, for relatively low Reynolds number. The present research aims at using a statistical method to assess the impact of louver angle, RWL angles of attack and RWL streamwise positions on the dimensionless heat transfer (Colburn factor) and the dimensionless pressure gradient (friction factor) for two different geometries. The main and interaction effects for the proposed compound heat transfer enhancement technique (flat-tube louvered fin and rectangular winglet vortex generators) are investigated. The identification of the relative importance of the design variables will be enabled by a Design of Simulations (DOS) method combined with a semi-parametric statistical method based on ANOVA decomposition, known as Smoothing Spline ANOVA. Two rows of RWL are placed in the computational domain and the three-dimensional numerical simulations are performed using the Finite Volume Method. The Reynolds numbers used to conduct the numerical simulations are 120 and 240 (based on the hydraulic diameter), corresponding to inlet velocities of 1 m/s and 2 m/s, respectively. Smoothing Spline ANOVA Method (SS-ANOVA) Due to the complexity of the flow phenomena involving heat transfer, the relationship among the design variables and the outputs (convection heat transfer coefficient, Nusselt number, Colburn fator, pressure drop, friction fator, etc) may not be delineated by using parametric regression models. In

horseshoe-like vortices, occurring on both sides of the RWL, and they are created in the junction between the front side of the RWL and the fin-plate. It is important to note that the corner vortex does not necessarily appears in all flow regimes. Up to a limit condition, where the primary vortex becomes very stronger, a discrete vortex can be generated because of the detachment occurred by the continuously growth of separation region. The secondary vortex structure, also known as induced vortex, is created by local separation of the boundary layer in the lateral direction between the main and corner vortices. In Fig. 3 (b), the two corner vortices are not shown because the main vortex, at earlier stage of its formation, normally overlaps the corner vortex generated on the suction side of the RWL. Saha et al. [26] performed a comparison of winglet-type vortex generators arranged in pairs and the results turned out that the heat transfer enhancement from RWL pair is more effective that from the DWL. However, the RWL pair develops slightly higher pressure drop than the DWL pair. Li et al. [27] also reported that the heat transfer enhancement by the RWL is more significant than that from the DWL. On the other hand, the higher thermal-hydraulic performance was observed for a DWL with angle of attack equal to 45°. Min et al. [28] proposed a modification on the standard RWL geometry and the authors showed that the highest Nusselt number was achieved for an angle of attack of 55°. He et al. [29] analysed the heat transfer enhancement of a fin-and-tube heat exchangers with RWL, under low Reynolds number flow conditions. From that research, the authors concluded that the additions of RWLs pairs can enhance the heat transfer performance of that type of heat exchangers with moderate pressure drop increasing. Filgueira et al. [30] focused their research to accomplish a parametric investigation of low-profile RWL and the authors showed that the height of the RWL affects the non-dimensional vorticity peak generated downstream of the RWL. The effect of surface modification of an RWL on thermal-hydraulic performance was numerically investigated by Kashyap et al. [31]. The authors considered convex and concave shaped surfaces at the leading and trailing edges of the RWLs. The main conclusion was that multiple concave shapes at the leading edges and single convex shapes at the trailing edges produce an increasing of the primary vortex strength. The investigation of Zhang et al. [32] indicated a heat transfer enhancement when an RWL pair is placed in a rectangular channel and that the longitudinal vortices augmented the local Nusselt number in spanwise direction. In the next paragraphs is presented a review about researches related to louvered fins combined to longitudinal vortex generators. Sanders and Thole [33] used Taguchi method to quantify the impact of Reynolds number and design variables on the performance of louvered fins with DWLs. The presence of the DWLs increased the heat transfer about 39% with an associated pressure drop augmentation of 23%. Huisseune et al. [34] suggested that the contribution of the design 535

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as [36].

Table 1 Air properties at inlet temperature of 311K. Fluid property

Value 3

Density (kg/m ), ρ Specific heat (J/kg.K), cp Thermal conductivity (W/m.K), k Dynamic viscosity (kg/m.s), μ Prandtl number (−), Pr

i

(ri , r ) r 2

=

(2)

where ri and r are column vectors of length n. The relationship between these two vectors, based on the function of ANOVA decomposition of a trained model assessed at the sampling points, is written according to Eq. (3)

1.1348 1006.8 0.02693 1.91.10−5 0.7124

k

r =

this sense, nonparametric regression models could provide a better fit curve to understand the contribution of the input parameters on heat transfer and pressure drop. One of the most popular nonparametric regression methods which has arising from statistical literature is the Smoothing Spline ANOVA model (SS-ANOVA). The SS-ANOVA is considered a suitable nonparametric technique for modelling or to estimate both univariate and multivariate functions. In this method, the function F is reproduced by kernel Hilbert space and this function has an ANOVA decomposition in which

F (t ) = X +

f (t ) +

f (t , t ) <

ri

(3)

i=1

If the ri are approximately orthogonal to each other, the value of i provides the percentage decomposition of variance into the statistical model, i.e., each term of the ANOVA decomposition represents the percentage of the relative contribution to the global variance. Thus, lower values of i indicate negligible terms; in turn, higher values of i reveal essential terms that must be kept in the statistical model. Ricco [37] applied the Smoothing Spline ANOVA approach to measure the robustness and reliability of the method. The results from SS-ANOVA were well aligned with a set of benchmark tests. Dezan et al. [22] also used the SS-ANOVA for parameters selection analysis of louvered fins with DWL and the results were in accordance with known flow patterns and heat transfer characteristics for those geometry types.

(1)

where X is the mean, f is most contributor effects and f is the twofactor interaction effects. In this approach, three-factor interaction effects and higher order of interactions are typically excluded from the ANOVA decomposition to reduce the computational efforts and to improve the interpretability the results from the regression model. After fitting a SS-ANOVA, i.e, the model was trained over a given sample data, it is important to perform some diagnostics of the model quality. A useful diagnostic tool to assess the quality of the model is the collinearity index. In order to guarantee that the column vectors are not parallel (at least nearly orthogonal) to each other, the collinearity indices must be close to 1.0. On the other hand, if the column vectors are highly correlated, the collinearity indices can present values much higher than 1.0. In order to avoid this issue, some recommendations could be addressed: (i). Selection of good sampling points; (ii). Adequate amount of sampling points in the design space and; (iii). Do not use dependent input variables, e.g, linearly dependent variables. A great ability of the SS-ANOVA methods is the visualization of some relationships among the input variables, which is not easily observed when parametric regression methods are used. However, this statistical method normally requires high computational resources, which is a function of both problem complexity and sample size. The effect of the different input variables composing the statistical model can be evaluated by means of the contribution index, calculated

2. Model description Numerical Model and Boundary Conditions. In this work, the governing equations have been solved by using a Finite Volume Method. ANSYS Fluent v.14.5 software is used as solver. As the flow is assumed to be steady laminar flow with constant physical properties, incompressible and three-dimensional, the equations of continuity, momentum and energy can be expressed as follows. Continuity equation:

xi

( ui ) = 0

(4)

Momentum equation (for j = 1, 2, 3):

xi

( ui uj ) =

xi

µ

uj xi

p xj

(5)

Energy equation:

xi

( ui T ) =

k T x i cP x i

(6)

Air is used as working fluid and Table 1 summarizes the values of the air properties for the numerical simulations. The properties of the

Fig. 4. Numerical domain and boundary conditions used in the present research. 536

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Fig. 5. Sketch of the louvered fin with RWL: (a) Top view of the L1 geometry; (b) Top view of the L2 geometry and; (c) section A-A of the L1 showing the louvers sticking into the flow space for a louver angle of 45°. Table 2 Constant parameters of the core domain. Input parameter

Constant values

Fin pitch (FP ) Fin height (FH ) Flow depth (FD ) Louver pitch (LP ) Transverse tube pitch (TP ) RWL height RWL area on L1 RWL area on L2

1.10 mm 9.54 mm 10.3 mm 0.9 mm 11.04 mm 0.66 mm 1.31 mm2 1.16 mm2

aluminium fin and flat-tubes are assumed to be constant (ρ = 2719 kg/ m3, cp = 871 J/kg.K, k = 203 W/m.K). The numerical domain (Fig. 4) consists of the core region, upstreamextended domain and downstream extended domain. In the core region, two RWLs are placed on each side of the louver array. The upstreamextended domain has 10.3 mm length and the downstream-extended domain has 41.2 mm length. Non-uniform meshes are used in the core region being fine enough in the regions with higher velocity and temperature gradients. In the extensions, the meshes are as coarse as

Fig. 6. Input parameters and the reference node (0,0,0).

Table 3 Parameters of the L1 and L2 to be evaluated and their operating ranges. Input parameter Louver angle RWL1 angle of attack RWL2 angle of attack RWL1streamwise position RWL2 streamwise position

Symbol

1 2

x1 x2

537

Operating range for L1

Operating range for L2

15º 45º 45º 45º 1 45º 45º 2 1.109 mm x1 4.060 mm 6.240 mm x2 9.210 mm

15º 45º 45º 45º 1 45º 45º 2 0.980 mm x1 4.170 mm 6.130 mm x2 9.320 mm

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rectangular winglets is equal to 60% of the fin pitch for both geometries. Table 2 lists the constant parameters adopted for the core region. The thicknesses of the louvered fin and RWLs are neglected for the numerical simulations. For L1 and L2, the louver array comprises an entrance louver, six louvers, a turnaround louver and an exit louver. The spanwise positions of the RWLs are coincident with the symmetry line between flat-tubes and louvers. In Table 3 are shown the input parameters and their operating ranges used in the non-parametric statistical analyses. It is observed in Table 3 that there is a slight difference in the operating ranges of the L1 and L2 streamwise positions to cover a design space as large as possible and to prevent unfeasible designs. The streamwise positions of the RWL3 and RWL4 are similar of the RWL1 and RWL2, respectively. Moreover, with respect to the angle of attack of the RWLs, 3 = 1 and 4 = 2. Fig. 6 shows the input parameters arranged in the core region of the computational domain, which contains the node (0,0,0). This reference node matches the fixed node located on the half chord of the RWL. Based on this node, all RWL are moved in the core domain. Parameter Definitions. For single phase forced convection, the flow condition is determined by the Reynolds number, and the heat transfer and pressure drop can be assessed by Colburn factor, j , and friction factor, f . The dimensionless numbers above can be written as

Table 4 Grid Convergence Index (GCI) for the fine mesh at the core region.

Cells number, n Refinement factor, r GCI

f

ReDh = 120 ReDh = 120

Fine grid

Intermediate grid

Coarse grid

7,935,518 –

2,805,202 1.414

1,024,836 1.399

0.124% 0.924% 0.450% 1.007%

possible to reduce the computational efforts. For the estimation of the flow and heat transfer behaviour, Eqs (4)–(6) combined with the boundary conditions are solved simultaneously. The boundary conditions set to the three regions of the computational domain are described below: ➢ At the inlet boundary: U= Uin = const , V= W= 0 , T= Tin = 311K ➢ At the louvered fin and tube regions: Tfin = Ttube = 373K , U = V = W = 0 ➢ At the RWLs: Q = 0 (adiabatic ) ➢ At the right and left sides of the domain: U W T = y =0, V=0, y =0 y ➢ At the top and bottom sides of the domain: U (x , y, 0) = U (x , y, FP ) , V (x , y, 0) = V (x , y , FP ) , W (x , y, 0)

ReDh =

= W (x , y, FP ) , T (x , y , 0) = T (x , y, FP ) U V W T ➢ At the outlet boundary: x = x = x = x = 0

h Pr 2/3 UC cp

j=

The SIMPLE algorithm is used for pressure-velocity coupling and the discretisation of the convection and diffusion terms in the governing equations is done by second-order upwind scheme. In this research, two types of geometries, L1 and L2, containing louvered fins and two pairs of rectangular winglets are investigated, as displayed in Fig. 5. From Fig. 5, it can be noted that the louver height of the L1 geometry (5.54 mm) is smaller than in geometry L2 (8.00 mm). Another difference between L1 and L2 is that the rectangular winglet chord is 1.98 mm on L1 and 1.76 mm on L2. The height of the

UC Dh µ

(7) (8)

where

h=

Q A 0 Tln

(9)

The total heat transfer rate is calculated as

Q = mcP Tln where the log-mean temperature difference is

Fig. 7. Parameter contributions on friction factor for ReDh = 120 . 538

(10)

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Fig. 8. Velocity contours along the main flow direction with Φ = 45° and θ1 = θ2 = 45° for (a) L1 and (b) L2.

Fig. 9. Parameter contributions on Colburn factor for ReDh = 120 .

Fig. 10. Temperature contours along the main flow direction at ReDh = 120 : (a) L1 and (b) L2.

539

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However, it is expected that the flow pattern and the thermal behaviour of flat-tube louvered fin with RWLs may not be similar of those presented on flat-tube louvered fins. To ensure that the numerical results are independent of the grid refinement, the grids used in the numerical validation by Dezan et al. [22] and Dezan et al. [23] were tested in the current computational domain. The Grid Convergence Index (GCI) proposed by Roache [39] has been used to obtain an estimate of the friction factor ( f ) and Colburn factor ( j ) at zero grid spacing. The geometrical parameters of the L1 geometry selected to perform the GCI analysis are: = 45º , 1 = 45º , 2 = 45º, x1 = 1.109 mm and x2 = 6.240 mm . The results from the GCI for the fine mesh at the core region are shown in Table 4. From that, it can be noted that the grid discretisation errors due to the grid refinement for f and j are estimated to be about 1% for both Reynolds numbers, which indicates that the intermediate mesh is acceptable to run the numerical simulations. 3. Results and discussions

Fig. 11. Temperature contours in the spanwise direction for ReDh = 120 : (a) L1 and (b) L2.

Tln =

T¯in)(TW

(TW

and T¯ =

ln

(

TW T¯in TW T¯out

)

The amount of design sets generated via Latin Hypercubes Sampling (LHS) was 25 designs per input variable. The selected outputs were Colburn factor ( j ) and friction factor ( f ). With regard to collinearity indices, they were assessed and all indices were very close 1.0; therefore, the statistical analyses can be considered reliable. Dezan et al. [22] reported the contribution of the same input parameters and operating conditions of this work but using louvered fins with DWL instead of RWL. On that research, it was investigated two types of geometries, GEO1 and GEO2, which are equivalent to the geometries L1 and L2, respectively. The present results are compared to those from Dezan et al. [22] as well as from other works available in the open literature. Reynolds number of 120. The contributions of the input parameters on friction factor are illustrated in Fig. 7, which reveals that the effect of the louver angle ( ) is predominant for L1 and L2 geometries. The higher contribution of the louver angle on friction factor is because of the flow phenomena inherent to louvered fins. For low values of , the flow is generally duct-directed; otherwise, the flow with higher values of are generally louver-directed. With regard to friction loss, the main difference between duct-directed and louver-directed flows is

T¯out ) (11)

UTdA A A

UdA

A 2 P f= C A0 UC2

with P = P¯in

(12)

P¯out and. P¯ =

PdA A A

dA

Grid Dependency Study and Numerical Validation. The numerical model and boundary conditions are similar to previous works from Dezan et al. [22] and Dezan et al. [23], where the results of the numerical model were compared to results from Kim and Bullard [38] for flat-tube louvered fin heat exchangers. Three grid sizes (coarse, intermediate and fine) were used for the numerical validation. Based on experimental results from Kim and Bullard [38], the intermediate grid could be considered suitable to perform the numerical simulations in the current research.

Fig. 12. Parameter contributions on friction factor for ReDh = 240 . 540

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Fig. 13. Parameter contributions on Colburn factor for ReDh = 240 .

Fig. 14. Streamlines starting from the rectangular winglets with θ1 = θ2 = 45°: (a) L1 and (b) L2.

that in the last the fluid goes through the louvers for long distances, increasing the pressure drop of the flow. It is clear that the contribution of is very high even when DWL is used as longitudinal vortex generator. The frontal areas of the RWL on L1 and L2 are 34% and 50% higher than the frontal areas of DWL, used by Dezan et al. [22] on GEO1 and GEO2, respectively. Thus, the results have indicated that the impact of the louver angle on friction factor is independent from louver height (or louver area), LVG type and LVG frontal area. The physical explanation for this behaviour is illustrated by Fig. 8, which shows the velocity contours for various cross-sections along the main flow direction. It can be seen from Fig. 8 that the air flow velocity on louver array is slightly higher than the flow velocity on plain fin region (where the RWLs are mounted), which is more evident on L2

(Fig. 8 (b)). In addition, since it was not observed any important interaction effect, the flow passing through the louvers is not mixed with the flow from the plain fin region; therefore, the pressure drop due to the louvers is much higher than that from RWLs or DWLs. Also related to Fig. 8, a great acceleration of the air flow can be seen on the first louver after the inlet louver and on the first louver after the turnaround louver. The explanation is that the flow in the near-wall region is characterized by large separation zones, especially in louvers just after the inlet louver and the turnaround louver. This result is consistent with the experimental results of DeJong and Jacobi [40] who investigated the flow phenomena of louvered fins in near wall regions. The contributions of the input parameters on Colburn factor are presented in Fig. 9. Similar to the results for friction factor, the most important parameter for heat transfer is the louver angle. The results 541

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Fig. 15. Streamlines and velocity magnitude at a XY-plane positioned at Z = 1.1 mm for different values of Φ, θ1 and θ2.

also show that the effect of the parameters and 1 on heat transfer is dependent on the louver height (or louver area) and LVG type since the contribution of those parameters changes according to LVG type. Moreover, the contribution of the other input parameters on heat transfer can be assumed negligible. The contribution of the parameter 1 for L1 and L2 was about 10% of the overall contribution to heat transfer. The effect of 1 is very limited because of the small temperature difference between heat surfaces, i.e., fin and flat-tubes, and bulk flow at the second half of the fin. In order to explain the contribution of 1 on heat transfer, Fig. 10 displays the temperature contours along the main flow direction for L1 and L2. As the Reynolds number is very low, the bulk flow temperature in second half of the louvered array is nearly equally of the temperature of the heated parts, which can also be confirmed by Fig. 11. Thus, the mass flowing through the second row of RWL does not have a big contribution to the overall heat transfer of the fin for two reasons: (i) it represents only a small fraction of the mass flow passing through the RWL and; (ii) the temperature gradient between bulk flow and heated surfaces on that region is very small. As stated in the previous paragraphs, at ReDh = 120 the RWL parameters are clearly of no importance on heat transfer enhancement. This

outcome corroborated with the results from Sanders and Thole [33]. The most noteworthy conclusion from statistical analysis is that no important interaction effects were observed, in the same way as occurred in terms of friction factor. This means that the combination of both heat transfer enhancement techniques could be treated separately, for Reynolds number of 120. Reynolds number of 240. From an examination of Fig. 12, which presents the contribution of the input parameters on friction factor, the overriding influential parameter is the louver angle, corresponding to about 90% of the overall contribution to friction factor for both L1 and L2. Fig. 12 also reveals that similar trends are observed with regard to DWLs. These results corroborate with the previous study from Ameel et al. [35] for Reynolds numbers ranging from 235 to 300. Therefore, the conclusion that follows is that the louver angle is the unique contributor to friction factor independently of the Reynolds number and geometry type. Conversely, the contribution of the input variables on heat transfer is strongly dependent of geometry type and LVG type, as shown in Fig. 13. The most important contributor for both L1 and L2 is the parameter 1, followed by . It is also evident that the parameter 2 plays an important role in the overall heat transfer. 542

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Fig. 16. Temperature contour diagram at a XY-plane positioned at Z = 1.1 mm for different values of Φ, θ1 and θ2.

An increase in Reynolds number from 120 to 240 results in higher decreasing on contribution of the parameter on heat transfer. This occurs because, as the Reynolds number is augmented, the boundary layers formed in the louver surface are thinner and the flow is more aligned to the louvers. As a consequence, the heat transfer increases and the effect of on the Colburn factor is mitigated. The contributions of 1 and 2 on the Colburn factor (for both L1 and L2) are due to the longitudinal vortices formed when the flow passes through the LVGs (Fig. 14). The increase of the angle of the LVGs up to a limit also increases the vortices strength, causing a heavy bulk fluid mixing between wall and the secondary flow. The parameter 2 has another effect as the second row of RWL strengthens the longitudinal vortices generated by the first row of RWL, as also illustrated in Fig. 14. This behaviour was also identified when two rows of DWL are mounted in a louvered fin heat exchanger with DWLs [22]. When the Reynolds number increases from ReDh = 120 to ReDh = 240 , the contributions of 1 and 2 show a distinct behaviour for both L1 and L2. For ReDh = 240 , the strength of the longitudinal vortices

grows more intensely with the angle of attack augmentations than on ReDh = 120 . Based on the results from Fig. 13(a), it can be inferred that an important interaction effect between parameters 1 and is identified for L1, being this interaction effect negligible for DWL. In order to get a better understanding of how the interaction effect 1* occurs, Fig. 15 shows the streamlines along the flow direction at a XY-plane at Z = 1.1 mm. Note that a fraction of mass flow from the first row of RWL is deflected towards the turnaround louver and, as and 1 are increased, the velocity of the fluid on that region is augmented as well as the mass flowing through the louvers. As consequence of this, the fluid temperature on the turnaround louver region is increased (Fig. 16). It is worthwhile to mention that the presence of the second row of RWL does not introduce a significant blockage effect that could promote a direct impingement of the flow on the second half of the louver array, as evidenced by the very small interaction effect * 2 . For Reynolds number of 240, the results from screening analysis have indicated that the effects of the louver angle and angle of attack of 543

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the first row of RWL on heat transfer are different of those observed by Ameel [35], showing that the heat transfer characteristics for louvered fins with flat-tube have a particular behaviour. Finally, as shown by the statistical results, important interaction effect was identified only for ReDh = 240 , which is different from that observed for ReDh = 120 . This is an evidence that other relevant interactions could appear for higher Reynolds numbers.

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4. Concluding remarks The present research investigated the contribution of five parameters on the thermal-hydraulic performance of flat-tube louvered fin heat exchanger with rectangular winglet vortex generators, for ReDh = 120 and ReDh = 240 . Two rows of RWLs are placed between louvers and flat-tubes. The identification of the relative importance of the parameters were enabled by a Design of Simulations (DOS) method combined with a non-parametric statistical method based on NOVA decomposition, known as Smoothing Spline ANOVA (SS-ANOVA). To this end, SS- ANOVA was utilized to quantify the percentage of contribution of the input parameters on the dimensionless heat transfer (Colburn factor) and the dimensionless pressure gradient (friction factor) for two different geometry types, named L1 and L2. The numerical simulations were performed by using the Finite Volume Method. The randomly sample generation was accomplished by a DOS (Design of Simulations) known as Latin Hypercube Sampling (LHS) method. The outcomes of the present research were compared to the results for similar louvered fin geometries but with DWL instead of RWL, since it was not found any research about louvered fins with RWLs. Based on the results, the following main conclusions can be drawn: ➢ Related to friction factor, the louver angle is the unique contributor to friction factor independently of the Reynolds number and geometry type; ➢ For L1 and L2 geometries, the louver angle is the major contributor to heat transfer at ReDh = 120 .; ➢ None important two-factor interaction effects were identified at ReDh = 120 .; ➢ With regard to heat transfer, the contribution of the input parameters is meaningly affected by Reynolds number and LVG type; ➢ At ReDh = 240 , only one relevant interaction effect (between louver angle and angle of attack of the first row of RWL) was observed for L1 geometry. In turn, none substantial two-factor interaction effects were observed for L2 geometry; ➢ The importance of the parameter θ2 becomes considerable at ReDh = 240 ; ➢ In terms of pressure drop, the contributions of the louvered fins with RWL behave nearly equal to those presented for louvered fins with DWL; ➢ The results from screening analysis indicated that the geometry type and LVG type can drastically change the contribution of input parameters on heat transfer, especially the parameters 1 and Φ. Conflicts of interest The authors have no financial or other relationship that might be perceived as leading to a conflict of interest that could affect authors’ objectivity. Acknowledgements The authors would like to acknowledge FAPESP (Sao Paulo State Research Foundation) for Grant No. 2017/06978-3 and 2016/14620-9, CNPq (National Council for Scientific and Technological Development) for Grant No. 307421/2014-7 and ESSS (Engineering Simulation and Scientific Software) for technical support. 544

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