an efficient method to predict the heat transfer performance of a louver fin radiator in an...

Journal of Mechanical Science and Technology 28 (1) (2014) 145~155

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-013-0951-8

An efficient method to predict the heat transfer performance

of a louver fin radiator in an automotive power system† Sang Hyuk Lee1,2, Nahmkeon Hur1,3,* and Seongwon Kang1,3

1Multi-phenomena CFD Engineering Research Center (ERC), Sogang University, Sinsoo 1, Mapo, Seoul, 121-742, Korea 2Department of Nuclear Equipment and Machinery Research, Korea Institute of Machinery & Materials, Yuseong, Daejeon, 305-343, Korea

3Department of Mechanical Engineering, Sogang University, Sinsoo 1, Mapo, Seoul, 121-742, Korea

(Manuscript Received February 7, 2013; Revised July 23, 2013; Accepted August 6, 2013)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract A numerical method to efficiently predict heat transfer phenomena of a louver fin radiator was presented – multi-scale semimicro-

scopic heat exchange (SHE) method. This method consists of microscopic analysis and semimicroscopic analysis. To predict heat trans-fer characteristics of a louver fin element, the microscopic analysis employs modeling of the detailed geometry of a fin element. Numeri-cal models for the heat transfer rate and flow friction derived from the microscopic analysis are then used for simulations of the full radia-tor model in semimicroscopic analysis. In the semimicroscopic analysis, conjugate heat transfer is analyzed for the domain with the ra-diator whose louver fin area is replaced by a porous media. The results with the proposed method show a good agreement with the ex-perimental data. The proposed method can be used to predict flow and heat transfer characteristics of a realistic louver fin radiator with a reduced cost and sufficient accuracy.

Keywords: Automotive radiator; Louver fin; Porous medium; Conjugate heat transfer; CFD ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

Automotive cooling devices, such as radiators, condensers and evaporators, have a significant effect on a vehicle’s effi-ciency. Especially, a radiator exhausting heat from the engine is closely related to the engine performance and mechanical failure. To enhance efficiency of a radiator, various studies have been done on the additional devices such as a rectangular fin [1], a plate [2, 3], a circular tube [4, 5], a flat tube [6], an elliptic tube [7] and a louver fin [8]. Among various types of radiators, louver fin radiators are often used in commercial vehicles. A louver fin radiator provides a high heat transfer rate but results in a significant friction loss due to the complex coolant passage. So far, significant efforts have been made to predict the characteristics of heat transfer and flow friction in a louver fin radiator.

The louver fin radiator is characterized by two geometric features: complex flow passages to enhance heat transfer and a very large difference in geometric scales between the radiator and a fin element. Because these geometric features from lou-vers, fins and tubes pose a great difficulty in a numerical anal-ysis, many previous studies were done with experiments.

Webb and Jung [9] reported that the heat exchanger using a louver fin has a better performance compared to a plate fin. Davenport [10] performed an experimental study on the heat transfer and flow characteristics of a louver fin radiator. In this study, empirical relationships for the heat transfer rate and flow friction were derived from the experimental data of 32 different louver fin models with a triangular shaped channel. Kays and London [11] documented the empirical formulas for the heat transfer rate and flow friction for various louver fin radiators. Chang and Wang [12] and Chang et al. [13] ana-lyzed 91 and 45 different louver fin radiators and derived cor-relations for the heat transfer rate and flow friction, respec-tively. These studies provided the overall heat transfer and flow friction characteristics of louver fin radiators. However, they have limitations in terms of investigating detailed flow features. Also, these experimental studies must be expensive because of many cases from several design parameters for the louver, fin and tube.

In literature, there are also several theoretical and numerical analyses for a louver fin radiator. Song et al. [14] simulated a louver fin radiator by modeling the louver fin region by a po-rous medium. Perrotin and Clodic [15] and Vorayos and Kiat-siriroat [16] did simulations of heat transfer in a detailed lou-ver fin geometry resolved by the mesh. Hsien and Jang [17] performed 3D simulations of a flow over a radiator and engine

*Corresponding author. Tel.: +82 2 705 8637, Fax.: +82 2 713 8637 E-mail address: [email protected]

† Recommended by Editor Dongshin Shin © KSME & Springer 2014

146 S. H. Lee et al. / Journal of Mechanical Science and Technology 28 (1) (2014) 145~155

room. Jung and Assanis [18] analyzed a heat transfer problem in a louver fin radiator with correlations suggested by Chang and Wang [12]. Hur et al. [19] developed a semimicroscopic heat exchange (SHE) method for a heat transfer problem in an automotive radiator. With the SHE method, a simulation with the air, coolant, louver fin and tube regions resolved in detail is possible with a reduced computational cost, and the results from test cases with conjugated heat transfer showed a good agreement with various experimental data. However, the SHE method requires correlations for the heat transfer rate and flow friction from an experiment, which is not practical for a new louver fin design. The numerical studies mentioned so far focused on either very small or large geometric scales in a louver fin radiator. The studies on the microscopic geometries investigated very small louver fin elements and can provide the data for a group of combined louver fins. However, they have a limitation in extending their methods to an entire lou-ver fin radiator. In contrast, the previous studies on large geo-metric scales considered the entire cooling system in an auto-mobile. However, they require either experimental or empiri-cal correlations for the heat transfer rate and flow friction to model the louver fin region with very small geometric features.

We present a numerical method with a reduced cost and sufficient accuracy to analyze a full-scale louver fin radiator for underhood thermal management in an automobile. This method is based on the SHE method of Hur et al. [19], but we eliminated the need for the experimental correlations that limit its usefulness. As a result, the modified method is easily ap-plied to new design of a louver fin radiator while retaining the advantage of the original method that the full-scale radiator with high geometric complexity is efficiently handled.

In the next section, the louver fin radiator considered in the present study is presented, and the non-dimensional parame-ters generally used in the previous studies for heat transfer and flow characteristics are introduced. In Sec. 3, the SHE method and the modification based on multi-scale simulations are presented. In Secs. 4 and 5, the results from the microscopic and semimicroscopic analyses including a simulation of a full-scale louver fin radiator for underhood thermal management in an automobile are provided, followed by the conclusions.

2. Louver fin heat exchanger

In the present study, flow and heat transfer phenomena in a louver fin radiator shown in Fig. 1(a) were numerically ana-lyzed using a commercial CFD software, STAR-CD V4.14 [20]. In Fig. 1(a), the coolant heated by the engine enters the radiator from the upper pipe and is distributed to tube passages. Then, the temperature of the coolant is reduced by heat trans-fer to the ambient air. In a louver fin radiator, two techniques are used to enhance heat transfer in the passages: (i) fins to increase the surface area, and (ii) louvers around the tubes to increase flow instability. Among various types of louver fin radiator, the present study is focused in the corrugated louver fin model with the rectangular channel. For an element of the

corrugated louver fin radiator in Fig. 1(b), the sizes of the heat transfer rate and flow friction depend on several geometric parameters as shown in the figure. The corrugated fin with the pitch pF , length lF , depth dF and thickness fd was lo-cated between tubes with the pitch pT and depth dT . In the planar fin, the specific region with the pitch pL and length

lL was twisted with the angle q to form the inclined louver. The values of the geometric parameters are listed in Table 1. The selected radiator is one of the models used in the paramet-ric study by Chang and Wang [12].

The performance of the louver fin radiator is affected also by the operating conditions, the most important of which is the Reynolds number based on the louver pitch:

Re a in pLp

a

V Lrm

= . (1)

Many previous studies on heat exchangers used non-

dimensionalized parameters to quantify performance in terms of the heat transfer rate and pressure drop. We use the Colburn j-factor as a measure for the heat transfer rate and the Fanning f-factor for the pressure drop. To define the Colburn j-factor,

Table 1. Geometric parameters of the louver fin radiator.

Louver angle q 28 degree Louver pitch pL 1.42 mm

Louver length lL 17.18 mm Fin thickness fd 0.16 mm

Fin pitch pF 1.8 mm Fin length lF 19 mm

Fin depth dF 22 mm Hydraulic diameter hD 3.041 mm

Tube pitch pT 24 mm Tube depth dT 22 mm

(a) Geometry of the louver fin radiator

(b) Geometric parameters of the louver fin radiator

Fig. 1. 3-D models of the louver fin radiator.

S. H. Lee et al. / Journal of Mechanical Science and Technology 28 (1) (2014) 145~155 147

following relationships for the heat transfer rate are necessary:

( ) ( ), , ,s c a m p a out a inQ hA T T mc T T= - = -& (2)

( ), , , / 2a m a out a inT T T= + . (3)

With these relationships, the heat transfer coefficient h can

be computed from the temperature values at the inlet, outlet and wall of the tubes. Then, the Colburn j-factor is defined as:

2 / 3

,2 / 3

max ,

Pr p a a

a p a

chj StV c k

mr

æ ö= × = ç ÷

è ø. (4)

In several previous studies on louver fin radiators, various

empirical formulas for the j-factor have been proposed. Among them, the j-factor (for 100< ReLp <3000) suggested by Chang and Wang [12] is:

0.14 0.29 0.230.27

0.49

0.68 0.28 0.05

Re90

p l dLp

p p p

p fl

p p p

F F TjL L L

TLL L L

q

d

- - -

-

- -

æ ö æ ö æ öæ ö= ç ÷ ç ÷ ç ÷ç ÷ ç ÷ ç ÷ ç ÷è ø è ø è ø è ø

æ ö æ ö æ öç ÷ ç ÷ ç ÷ç ÷ ç ÷ ç ÷è ø è ø è ø

. (5)

The empirical correlation of j-factor based on the 91 sam-

ples of louver fin radiator shows that the experimental data are correlated within ±15%.

As a measure for performance in terms of the pressure drop, the Fanning f-factor is defined as follows:

2max

2 c

a s

p AfV ArD

= . (6)

Among several empirical correlations in literature, the f-

factor (for 150< ReLp <5000) proposed by Chang et al. [13] is as follows:

1 2 3f f f f= ´ ´ (7)

( )( )20.527

0.50.6049 1.064 /1 4.97Re log / 0.9Lp e f pf Fq d-

- æ ö= +ç ÷è ø

(8)

( ) ( )( ) ( ) ( )2.966 0.7931 /2 / log 0.3Re / p hT T

h p e Lp p lf D L F F- -

= (9)

( ) ( )( )3.553

0.0446 1.4 0.4773 / log 1.2 /p m e p pf T D L F q-

- -æ ö= +ç ÷è ø

. (10)

The empirical correlation of f-factor based on the 45 sam-

ples shows that 89.91% of experimental data are correlated within ±15%.

3. SHE (semimicroscopic heat exchange) method and

an extension to multi-scale simulation

The SHE method is characterized by a conjugate heat trans-

fer analysis for the domain composed of the coolant in a tube, tube wall, region where air passes through the louver fins and ambient air. The louver fin region where heat transfer occurs was modeled by a porous media occupied by the air and solid. In the literature, the numerical technique for the porous media is widely used for not only the complex pore structure of arbi-trary shapes but also the complex spatial structure of periodic patterns [21-23]. For the louver fin radiator, the porous media is also useful to model the complex periodic structure [19]. By modeling the louver fin region with the porous media, the flow and pressure in the porous media region were predicted using the Darcy equation. In the present study, the Darcy equation modified by Brinkman-Forchheimer was used:

21/ 2 .

DD D

eff ED D D D i

i

U U Ut

p CU U U U fx K K

re

m m r re

¶æ ö+ ×Ñç ÷¶è ø¶

= - + Ñ - - +¶

(11)

For the flow friction through the porous media in the sem-

imicroscopic analysis, the f-factor in Eq. (6) from a previous study can be used to model the third and fourth terms in the RHS.

There are two methods to predict the temperature in the po-rous media: one-medium and two-media model. The one-medium model does not consider the effect of local heat trans-fer between air and the louver fin because they use only one porous medium with a prescribed heat source. In the two me-dia model, however, the heat source/sink is computed from the local temperature difference between the fluid and solid porous media. The energy equation for the two-media model is written as:

Fluid phase:

( )

( ) ( ) ( ), 2

fD f

f eff df s f

p pf f

TU T

t

k haD T T Tc ce r e r

¶+ ×Ñ

¶æ öç ÷= + Ñ + -ç ÷ç ÷è ø

. (12)

Solid phase:

( )( ) ( )( ) ( ), 2

1 1s effs

s s fp ps s

kT haT T Tt c ce r e r

æ ö¶ ç ÷= Ñ + -ç ÷¶ - -è ø

. (13)

The size of heat transfer between the fluid and solid media

was calculated by the heat transfer coefficient h and the tem-perature difference between two porous media. The j-factor in Eq. (4) from a previous experimental or numerical study can be used to compute the heat transfer coefficient.

In Eqs. (12) and (13), ,f effk and ,s effk are the effective thermal conductivities of the fluid and solid porous media, respectively. In the present study, the effective thermal con-ductivity proposed by Song et al. [14] was used. The effective


thermal conductivity is assumed as a function of the geometry of the louver fin:

Air thermal conductivity: ( ), 1 /f eff f t p fk k F F ke= = - (14)

Fin thermal conductivity: ( ) ( ), 1 /s eff s t p sk k F F ke= - = .

(15) As mentioned before, a disadvantage of the SHE method is

that it depends on the previous study for correlations such as j- and f-factors. Although these values are available for certain types of louver fins such as those considered in Davenport [10] and Chang and Wang [12], a method that does not require the data from the previous studies may be desirable for a new louver fin design or time-varying operational condition. A modification to the SHE method to resolve this issue is pre-sented in Fig. 2. The modified method is a combination of microscopic and semimicroscopic analyses. In the micro-scopic analysis, simulations with the detailed geometry of a louver fin element are carried out and correlations for the heat transfer rate and flow friction are derived from the results. In the semimicroscopic analysis, the louver fin region is modeled using the correlations from the microscopic analysis, and de-tails of all parts except for the louver fins are resolved in the mesh. The effect of a specific geometry in the louver fin re-gion is considered in the microscopic analysis. By employing the correlations in the louver fin region, the number of mesh points required for an accurate semimicroscopic analysis can be significantly reduced. Accuracy of this multi-scale simula-tion is improved by exchanging the operational and boundary conditions between two analyses with different length scales. In the present study, the flow fields in both analyses are steady, partly because of turbulence modeling (RANS) used in the present study. The steady state and the use of the non-dimensional parameters (j- and f-factors) greatly simplify the process of data exchange in the example of the present study.

4. Microscopic analysis

In the present numerical method, correlations for the heat transfer rate and flow friction are obtained in the microscopic analysis in which simulations for a louver fin element are car-ried out. The computational domain for the microscopic anal-ysis is shown in Fig. 3. The symmetric and cyclic boundary conditions are used in the lateral sides of the computational domain. A constant temperature is assumed at the regions with the wall boundary condition. Heat is transferred to the air through the louver fin. To obtain the correlations, several sim-ulations were done with the air inlet velocities varying from 1 m/s (ReLp = 95) to 30 m/s (ReLp = 2,836) and the tube wall temperatures varying from 343 K to 373 K. By examining sensitivity to the mesh density as shown in Fig. 4, the compu-tational models with the tetrahedral meshes of 4,500,000 among which 4,100,000 cells are in the fluid region and 400,000 cells in the solid region were adopted throughout the present microscopic analysis. It took about 10 hours per case using 1 CPU of a Linux server with a 2.4 GHz AMD Opteron 64 bit processor.

Figs. 5 and 6 and Table 2 show the simulation results with the air inlet velocity set to 1 m/s and the tube wall temperature varying from 343 K to 373 K. Different tube wall tempera-tures lead to different temperature fields of the air and louver fin regions (Fig. 6). However, the velocity and pressure fields are only marginally affected by the difference in the wall tem-perature (Fig. 5). From the parametric study with varying temperature, the Colburn j-factor defined in Eqs. (2)-(4) was obtained and listed in Table 2. It is observed the value of the j-

Fig. 2. Comparison between the SHE and modified multi-scale SHE method.

Fig. 3. Geometry and boundary conditions for the microscopic analysis of the louver fin radiator.

Fig. 4. Mesh sensitivity test for the microscopic analysis of the fin radiator (ReLp = 95).


factor is almost constant for different wall temperatures. The same trend is found also for the f-factor.

To see the effect of the inlet velocity, simulations with the inlet velocities varying from 1 m/s to 30 m/s were performed with the tube wall temperature set to 358 K. The temperature and pressure fields with different inlet velocities are shown in Fig. 7. The outlet temperature of air with a higher inlet veloc-ity is lower than the temperature with a lower inlet velocity because of a larger velocity and temperature gradient near the louver fin. A large velocity has a positive effect on heat trans-fer but can increase the flow friction and pressure drop. The pressure fields show that the pressure drop increases rapidly as the inlet velocity increases.

The values of Colburn j-factor and the Fanning f-factor from the varying inlet velocity are shown in Fig. 8. The j-factor and f-factor are influenced by the inlet velocity and

louver fin geometry. Since these correlations are functions of the Reynolds number for a fixed louver fin geometry, j- and f-factor can be expressed as:

2

1 ReCLpj C= , 4

3 ReCLpf C= . (16)

The coefficients of these correlations were obtained by a

curve fitting method:

0.6030.9461ReLpj -= (17) 0.3881.1112ReLpf -= . (18)

These numerical correlations were compared with the em-

pirical correlations of the j-factor (Eq. (5)) proposed by Chang and Wang [12] and the f-factor (Eqs. (7)-(10)) proposed by Chang et al. [13]. In Fig. 8, the correlations of the present study are similar to the empirical correlations of the present study. As the Reynolds number increases, the values of j- and f-factor decrease. These values become independent of the Reynolds number at a sufficiently high Reynolds number. The numerical result of the j-factor shows a better agreement with the empirical correlation than the f-factor. Since the empirical correlations were obtained by experiments with 91 and 45 different louver fin models, a difference between the numeri-cal and empirical correlations may exist. Another reason for the difference in the f-factor between the present study and Chang et al. [13] is a possible discrepancy in the velocity boundary conditions.

5. Semimicroscopic analysis

To analyze the entire louver fin radiator, the SHE method employs numerical or the empirical correlations for the j- and f-factor. In the present study, louver fin radiators in a previous wind tunnel test and a full automotive vehicle were considered in the semimicroscopic analysis.

5.1 Validation of SHE method

To validate the SHE method, the results from the SHE method were compared with the results from the microscopic analysis. The computational domain and boundary condition for the SHE method are shown in Fig. 9. The computational domains for the fluid and solid regions are separately modeled because of the two-media model mentioned in the previous section. The computational model was generated with the hexahedral meshes of 520,000 among which 450,000 cells are in the fluid region and 70,000 cells in the solid region. It took about 1 hour per case using 1 CPU of a Linux server with a 2.4 GHz AMD Opteron 64 bit processor.

Fig. 10 shows the contours of the temperature using the SHE method for different Reynolds numbers. The small figure above each figure shows the result from the microscopic anal-ysis. The temperature in the downstream of the louver fin decreases as the Reynolds number increases, because the in-

Table 2. Heat transfer and friction characteristics with various wall temperature.

Twall 343.0 K 358.0 K 373.0 K

Tin 298.0 K 298.0 K 298.0 K

Tout 338.8 K 352.5 K 366.1 K

j-factor 0.0528 0.0530 0.0530

dp 10.03 Pa 10.03 Pa 10.03 Pa

f-factor 0.319 0.319 0.319

(a) Velocity magnitude (b) Pressure Fig. 5. Contours of the velocity magnitude and pressure from the mi-croscopic analysis (ReLp = 95).

(a) Twall = 343 K

(b) Twall = 358 K

(c) Twall = 373 K

Fig. 6. Contours of the temperature with various wall temperature (ReLp = 95).


crease in the mass rate of the fluid is relatively larger than the increase in the amount of heat transfer between the fluid and solid. The temperature fields from the SHE method and the corresponding microscopic analysis are qualitatively similar.

To further validate the SHE method, the j-factor and f-factor were calculated from the results of the SHE method and com-

pared with the results from the microscopic analysis. Fig. 11 shows a comparison of the j-factor and f-factor from two anal-yses. The j-factor from the SHE method agrees well with the correlation from the microscopic analysis, which makes sense considering that the SHE method uses the correlation. Both methods produce similar results also in the f-factor. However,

(a) ReLp = 95 (b) ReLp = 378 (c) ReLp = 945

(d) ReLp = 1,607 (e) ReLp = 2,269 (f) ReLp = 2,836 Fig. 7. Contours of the temperature and pressure with various Reynolds numbers.

(a) Colbum f-factor (b) Fanning f-factor Fig. 8. Comparison of the j-factor and f-factor from the microscopic analysis with the empirical correlations.


a larger difference was observed as the Reynolds number de-creases. The difference seems to originate from the Darcy equation, which models the complex geometry as a porous media, especially from the quadratic flow resistance term in Eq. (11).

As shown in Table 3, an advantage of the SHE method is the reduced computational cost compared to the microscopic analysis. In the examples of this section, the SHE method requires about 1/10-th of the computational meshes and time for the microscopic analysis and produces similar results. Us-

Fig. 9. Geometry and boundary conditions for the semimicroscopic analysis.

(a) ReLp = 95 (b) ReLp = 378 (c) ReLp = 945

(d) ReLp = 1,607 (e) ReLp = 2,269 (f) ReLp = 2,836 Fig. 10. Contours of the temperature from the microscopic and semimicroscopic analyses.

(a) Colbum j-factor (b) Fanning f-factor Fig. 11. Comparison of the j-factor and f-factor from the semimicroscopic analysis with the numerical correlation.


ing accurate correlations either from experiments or micro-scopic analyses, the SHE method can be applied efficiently to a louver fin radiator for underhood thermal management in an automobile.

5.2 Application to underhood thermal management

In this section, the SHE method is used to analyze a louver fin radiator in a realistic vehicle model. Using the correlations from the microscopic analysis in the previous sections, we analyzed the flow and temperature fields in the domain includ-ing the full vehicle model as well as the radiator with the SHE method.

Fig. 12 shows the computational domain and meshes used for the SHE method. The geometric parameters of the louver

fin radiator inside the vehicle are listed in Table 1. The total number of the coolant passages is 67. The computational model was generated with the trimmed meshes of 7,000,000. The computational domain is divided into two regions: the louver fin radiator and the ambient air. The region of the lou-ver fin radiator consists of the louver fins, tubes and coolant passages. The region of the ambient air consists of the air passing through the louver fins and the ambient air. Using the two-media method, the regions of the air passing through the louver fins and the solid louver fins were modeled as porous media. In these regions, the temperature field was modeled using Eqs. (12) and (13) with the thermal conductivities in Eqs. (14) and (15), and the flow field was modeled using the Darcy equation (Eq. (11)). The employed temperature model in-cludes the effect from conjugate heat transfer by considering the temperature difference between two porous media occupy-ing the same space. In the computational domain except for two porous regions, the regular momentum and energy equa-tions were used to simulate the velocity and temperature fields. It took about one day per case by using 4 CPU of a Linux server with a 2.4 GHz AMD Opteron 64 bit processor.

We analyzed the performance of the louver fin radiator with the vehicle speeds varying from 10 m/s to 30 m/s. The vehicle speed significantly affects the velocity of the air passing through the louver fin radiator and the heat transfer rate to the air.

Fig. 13 shows the contours of the temperature in several parts of the computational domain with various vehicle speeds. The heat transfer rate is proportional to the temperature differ-ence between two porous regions of the fluid and solid (Figs. 13(a) and (b)). The temperatures in two porous regions are strongly affected by the temperature fields of the coolant and ambient air (Figs. 13 (c) and (d)). The temperatures at all parts of the radiator and at the exit of the coolant decrease as the vehicle speed increases. Therefore, the heat generated from the engine can be easily exhausted at a high vehicle speed.

Table 4 shows the temperature values of the air at the inlet and the coolant at the inlet and outlet with the heat transfer rate for different vehicle speeds. The exit temperature of the coolant decreases and the heat transfer rate increases as the vehicle speed increases.

To summarize, the present numerical approach can be used efficiently to design a louver fin radiator for underhood ther-mal management. Most previous numerical studies on the full model of a louver fin radiator employed some empirical corre-lations for the heat transfer rate and flow friction. In the pre-

Table 3. Comparison of computational costs for the microscopic and semimicroscopic analyses.

Microscopic analysis Semimicroscopic analysis

Computational meshes Total Fluid region Solid region

4.46 x 106 cells 4.10 x 106 cells 0.36 x 106 cells

0.52 x 106 cells 0.45 x 106 cells 0.07 x 106 cells

Computational time* Average

39,294 sec

3,647 sec

* By using 1 CPU of a Linux server with a 2.4 GHz AMD Opteron 64 bit processor.

Fig. 12. Computational domain and mesh for the application of the SHE method to underhood thermal management.

Table 4. Heat transfer characteristics of the louver fin radiator for underhood thermal management.

Vvehicle 10 m/s 20 m/s 30 m/s

Tair,in 313.0 K 313.0 K 313.0 K

Tcoolant,in 380.0 K 380.0 K 380.0 K

Tcoolant,out 372.0 K 371.3 K 370.9 K

Q 18.26 kW 20.31 kW 21.42 kW


sent method, a microscopic analysis uses a louver fin element with identical dimensions to that of the full model for obtain-ing the correlations, which can result in more accurate and consistent results in the simulations of the full model. The present method can be also used for various types of heat ex-changer having a complex geometry. Although the corrugated and complex geometry generally leads to disturbed flow, the previous models for the porous media seem to damp out the disturbance. Therefore, the present method appears to be more effective for a heat exchanger with the structure of smaller

geometric scales.

6. Conclusions

A numerical approach was introduced to analyze a louver fin radiator for underhood thermal management accurately and efficiently. The present method consists of microscopic and semimicroscopic analyses. In the microscopic analysis, the heat transfer rate and flow friction of a louver fin element were predicted and correlations for the non-dimensionalized j-

(a) Fluid in the porous region

(b) Solid in the porous region

(c) Coolant

(d) Cooling fan

(e) Side view of the engine room

Fig. 13. Contours of the temperature of automotive underhood model with various vehicle speeds.


factor and f-factor were obtained. Using the correlations from the microscopic analysis, the conjugate heat transfer problem in the full radiator model was simulated in the semimicro-scopic analysis referred to as the SHE method. The proposed multi-scale SHE method becomes very efficient because com-plex microscopic structures in the louver fin region are mod-eled as porous media to reduce the computational costs. An accurate simulation of the full model is possible by modeling properties of the porous media such as the heat transfer rate and flow friction using the correlations from the microscopic analysis. The present method is useful for the accurate and efficient prediction of flow and heat transfer for the design of a louver fin radiator in a realistic vehicle model for underhood thermal management. Furthermore, the present method can be applied to various types of heat exchanger with the complex structures of small geometric scales.

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant No. 2009-0083510 funded by the Korea Government (MEST) through Multi-phenomena CFD Engineering Research Center.

Nomenclature------------------------------------------------------------------------

cA : Cross-sectional area [m2] sA : Surface area [m2]

a : Ratio of surface area to volume [m-1] pc : Specific heat capacity [J/K] hD : Hydraulic diameter of fin array [mm]

f : Fanning f-factor dF : Fin depth [mm] lF : Fin length [mm] pF : Fin pitch [mm]

h : Heat transfer coefficient [W/m2K] j : Colburn j-factor k : Thermal conductivity [W/mK]

hL : Louver height [mm] lL : Louver length [mm] pL : Louver pitch [mm]

Pr : Prandtl number ReLp : Reynolds number based on louver pitch St : Stanton number T : Temperature [K]

dT : Tube depth [mm] pT : Tube pitch [mm]

Q : Heat transfer rate [W] V : Velocity [m/s]

DU : Darcian velocity [m/s] pD : Pressure drop [Pa] r : Density [kg/m3] m : Viscosity [kg/ms] e : Porosity q : Louver angle [degree]

fd : Fin thickness [mm]

Subscript

a : Air c : Coolant eff : Effective f : Fluid in : Inlet max : Maximum out : Outlet s : Solid

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Sang Hyuk Lee is a Senior Researcher in the Department of Nuclear Equipment and Machinery Research at Korea Insti-tute of Machinery & Materials. He re-ceived his Ph.D. from Sogang Univer-sity in 2012, and worked as a Post-Doctoral Researcher in Multi-phenomena CFD Engineering Research Center

(ERC). Currently, his research interests include multiphysics computational fluid dynamics.

Nahmkeon Hur is a Professor in the Department of Mechanical Engineering of Sogang University in Seoul, Korea and a director of Multi-phenomena CFD Engineering Research Center (ERC) funded by National Research Founda-tion of Korea. He received his Ph.D. from Stevens Institute of Technology in

1988. His research interests include multiphysics and multi-dynamics CFD and its application.

Seongwon Kang is an Assistant Profes-sor in the Department of Mechanical Engineering at Sogang University. He received his Ph.D. from Stanford Uni-versity in 2008 and joined Sogang Uni-versity in 2010. His research interests include numerical methods for a com-plex geometry and turbulent flows with

combustion.