An Efficient Method to Predict the Heat Transfer Performance of a Louver Fin Radiator in an Automotive Power System

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 Hur 1,3,* and Seongwon Kang1,3 1

Multi-pheno Multi-phenomena mena CFD Engine Engineering ering Research Research Center Center (ERC), (ERC), Sogang Sogang Universit University, y, Sinsoo Sinsoo 1, Mapo, Seoul, Seoul, 121-742, 121-742, Korea Department Department of of Nuclear Nuclear Equipme Equipment nt and and Machinery Machinery Research, Research, Korea Korea Institute Institute of Machinery Machinery & Materials Materials,, Yuseong, Yuseong, Daejeon Daejeon,, 305-343, 305-343, Korea 3 Department Department of Mechanica Mechanicall Engineerin Engineering, g, Sogang Sogang Univers University, ity, Sinsoo Sinsoo 1, Mapo, Mapo, Seoul, Seoul, 121-742 121-742,, Korea Korea

2

(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 semimicroscopic heat exchange (SHE) method. This method consists of microscopic analysis and semimicroscopic analysis. To predict heat transfer characteristics of a louver fin element, the microscopic analysis employs modeling of the detailed geometry of a fin element. Numerical models for the heat transfer rate and flow friction derived from the microscopic analysis are then used for simulations of the full radiator model in semimicroscopic analysis. In the semimicroscopic analysis, conjugate heat transfer is analyzed for the domain with the radiator whose louver fin area is replaced by a porous media. The results with the proposed method show a good agreement with the ex perimen perimental tal data. data. The proposed proposed method method can can be used used to predic predictt flow flow and and heat heat transfer transfer charact characteris eristics tics of a reali realistic stic louve louverr fin radiator radiator with a reduced cost and sufficient accuracy. Keywords 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 efficiency. 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 predict the characteris characteristics tics of heat heat transfer transfer and flow flow frictio friction n 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 louvers, fins and tubes pose a great difficulty in a numerical analysis, many previous studies were done with experiments. *

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

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] analyzed 91 and 45 different louver fin radiators and derived correlations for the heat transfer rate and flow friction, respectively. 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 because of many cases cases from several several design design parameters parameters for 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 porous medium. Perrotin and Clodic [15] and Vorayos and Kiatsiriroat [16] did simulations of heat transfer in a detailed louver fin geometry resolved by the mesh. Hsien and Jang [17] performed performed 3D simulations simulations of a flow flow over over a radiator radiator and engine engine

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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 louver fin radiator. In contrast, the previous studies on large geometric scales considered the entire cooling system in an automobile. However, they require either experimental or empirical 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 parameters 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 fullscale 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 analyzed 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 transfer 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

Table 1. Geometric parameters of the louver fin radiator. Louver angle q

28 degree

Louver pitch L p

1.42 mm

Louver length Ll 17.18 mm

Fin thickness d f

0.16 mm

Fin pitch F p

1.8 mm

Fin length F l

19 mm

Fin depth F d

22 mm

Hydraulic diameter Dh

3.041 mm

Tube pitch T p

24 mm

Tube depth T d

22 mm

(a) Geometry of the louver fin radiator

(b) Geometric parameters of the louver fin radiator Fig. 1. 3-D models of t he louver fin radiator.

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 F p , length F l , depth F d and thickness d f was located between tubes with the pitch T p and depth T d . In the planar fin, the specific region with the pitch L p 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 parametric 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 Lp =

r aVin L p m a

.

(1)

Many previous studies on heat exchangers used nondimensionalized 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,

147


following relationships for the heat transfer rate are necessary:

& p ( Ta ,out - Ta ,in ) Q = hA s ( Tc - Ta , m ) = mc

(2)

Ta , m = ( Ta ,out + T a ,in ) / 2 .

(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:

j = St × Pr

2/3

æ c p , a m a ö = ç ÷ r aVmax c p , a è k ø h

2/3

.

(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< Re Lp <3000) suggested by Chang and Wang [12] is:

-0.49

j = Re Lp

æ Ll ö ç ÷ ç L p ÷ è ø

æ q ö ç ÷ è 90 ø

0.68

æ F p ç ç L p è

0.27

æ T p ö ç ÷ ç Lp ÷ è ø

-0.28

ö ÷ ÷ ø

-0.14

æ d f ö ç ÷ ç Lp ÷ è ø

æ Fl ö ç ÷ ç Lp ÷ è ø

-0.29

æ T d ö ç ÷ ç Lp ÷ è ø

2D p 2 max

r aV

Ac

.

-0.05

(5)

.

As

(6)

Among several empirical correlations in literature, the f factor (for 150< Re Lp <5000) proposed by Chang et al. [13] is as follows: f = f 1 ´ f 2 ´ f 3

(7)

0.6049 -1.064/ q 2

f 1 = 4.97 Re Lp

f 2

=

0.5 æ ö ç log e ( d f / F p ) + 0.9 ÷ è ø

(

( ( D / L ) log ( 0.3Re ) ) h

(

f 3 = T p / Dm

p

)

e

-0.0446

Lp

)

2.966

-

(F

p

/ F l

)

)

-0.527

(

0 .79 31 Tp / T h

-

1.4 æ ö ç loge 1.2 + ( Lp / F p ) ÷ è ø

(

r æ ¶U D

ö ç ¶ + U D × ÑU D ÷ e è t ø ¶ p m eff 2 m r C E =+ Ñ U D - U D - 1/ 2 U D U D + r fi . ¶ xi e K K

(11)

-0.23

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: f =

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 arbitrary 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:

)

(8)

(9)

-3.553

q -

0.477

. (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-

For the flow friction through the porous media in the semimicroscopic 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 porous media: one-medium and two-media model. The onemedium model does not consider the effect of local heat transfer between air and the louver fin because they use only one porous medium with a prescribed heat source. In the two media 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: ¶T f + ( U D × ÑT f ) ¶t . æ k ö ha f , eff d ÷ 2 ç = + D Ñ T f + ( Ts - T f ) çç e ( r c ) ÷÷ e ( rc p ) p f f è ø

(12)

Solid phase: k s , eff ¶T s æç = ¶t ç ( 1 - e ) ( r c p ) s è

ö ha ÷ Ñ 2T s + ( Ts - T f ) . ÷ 1 - e ) ( rcp ) ( s 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), k f , eff and k s , eff are the effective thermal conductivities of the fluid and solid porous media, respectively. In the present study, the effective thermal conductivity proposed by Song et al. [14] was used. The effective

148


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

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

thermal conductivity is assumed as a function of the geometry of the louver fin: Air thermal conductivity: k f , eff = e k f = ( 1 - Ft / Fp ) k f (14)

Fin thermal conductivity: k s , eff = ( 1 - e ) ks = ( Ft / Fp ) k s .

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

(15) As mentioned before, a disadvantage of the SHE method is that it depends on the previous study for correlations such as jand 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 presented in Fig. 2. The modified method is a combination of microscopic and semimicroscopic analyses. In the microscopic 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 details of all parts except for the louver fins are resolved in the mesh. The effect of a specific geometry in the louver fin region 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 simulation 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 nondimensional 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 carried out. The computational domain for the microscopic analysis 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 simulations were done with the air inlet velocities varying from 1 m/s (Re Lp = 95) to 30 m/s (Re Lp = 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 computational 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 temperatures 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-


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

343.0 K

358.0 K

373.0 K

T in

298.0 K

298.0 K

298.0 K

T out

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

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: C 2 j = C 1 Re Lp , f

C 4 C 3 Re Lp .

=

-0.603

-0.388

f = 1.1112Re Lp

(b) Pressure

Fig. 5. Contours of the velocity magnitude and pressure from the microscopic analysis (Re Lp = 95).

(a) T wall = 343 K

(b) T wall = 358 K

(16)

The coefficients of these correlations were obtained by a curve fitting method: j = 0.9461Re Lp

(a) Velocity magnitude

149

.

(17) (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 numerical 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

(c) T wall = 373 K Fig. 6. Contours of the temperature with various wall temperature (Re Lp = 95).

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

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 velocity 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 transfer 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 jfactor and f -factor are influenced by the inlet velocity and

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 analysis. The temperature in the downstream of the louver fin decreases as the Reynolds number increases, because the in-

150


(a) Re Lp = 95

(b) Re Lp = 378

(d) Re Lp = 1,607

(c) Re Lp = 945

(e) Re Lp = 2,269

(f) Re Lp = 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.

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 analyses. 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,


151

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

(a) Re Lp = 95

(b) Re Lp = 378

(d) Re Lp = 1,607

(c) Re Lp = 945

(e) Re Lp = 2,269

(f) Re Lp = 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.

a larger difference was observed as the Reynolds number decreases. 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-

152


Table 3. Comparison of computational costs for the microscopic and semimicroscopic analyses. Microscopic analysis Computational meshes Total Fluid region Solid region Computational time* Average

Semimicroscopic analysis

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

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.

ing accurate correlations either from experiments or microscopic 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 including 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

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

10 m/s

20 m/s

30 m/s

T air,in

313.0 K

313.0 K

313.0 K

T coolant,in

380.0 K

380.0 K

380.0 K

T coolant,out

372.0 K

371.3 K

370.9 K

Q

18.26 kW

20.31 kW

21.42 kW

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 louver 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 includes the effect from conjugate heat transfer by considering the temperature difference between two porous media occupying the same space. In the computational domain except for two porous regions, the regular momentum and energy equations 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 difference 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 thermal management. Most previous numerical studies on the full model of a louver fin radiator employed some empirical correlations for the heat transfer rate and flow friction. In the pre-


153

(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.

sent method, a microscopic analysis uses a louver fin element with identical dimensions to that of the full model for obtaining 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 exchanger 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-

154


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 semimicroscopic 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 modeled 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 Foundation of Korea (NRF) grant No. 2009-0083510 funded by the Korea Government (MEST) through Multi-phenomena CFD Engineering Research Center.

Nomenclature----------------------------------------------------------------------- Ac A s a c p Dh f F d F l F p h j k Lh Ll L p Pr Re Lp St T T d T p Q V U D D p r m e q

2

: Cross-sectional area [m ] 2 : Surface area [m ] -1 : Ratio of surface area to volume [m ] : Specific heat capacity [J/K] : Hydraulic diameter of fin array [mm] : Fanning f -factor : Fin depth [mm] : Fin length [mm] : Fin pitch [mm] 2 : Heat transfer coefficient [W/m K] : Colburn j-factor : Thermal conductivity [W/mK] : Louver height [mm] : Louver length [mm] : Louver pitch [mm] : Prandtl number : Reynolds number based on louver pitch : Stanton number : Temperature [K] : Tube depth [mm] : Tube pitch [mm] : Heat transfer rate [W] : Velocity [m/s] : Darcian velocity [m/s] : Pressure drop [Pa] 3 : Density [kg/m ] : Viscosity [kg/ms] : Porosity : Louver angle [degree]

d f

: Fin thickness [mm]

Subscript a c eff f in max out s

: Air : Coolant : Effective : Fluid : Inlet : Maximum : Outlet : Solid

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Sang Hyuk Lee is a Senior Researcher in the Department of Nuclear Equipment and Machinery Research at Korea Institute of Machinery & Materials. He received his Ph.D. from Sogang University in 2012, and worked as a PostDoctoral 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 Foundation of Korea. He received his Ph.D. from Stevens Institute of Technology in 1988. His research interests include multiphysics and multidynamics CFD and its application. Seongwon Kang is an Assistant Professor in the Department of Mechanical Engineering at Sogang University. He received his Ph.D. from Stanford University in 2008 and joined Sogang University in 2010. His research interests include numerical methods for a com plex geometry and turbulent flows with

combustion.

An Efficient Method to Predict the Heat Transfer Performance of a Louver Fin Radiator in an Automotive Power System

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