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1111111111111I1~~lll~~I~~~II~II~~I~~1111111111111111 *30000002373864* UNIVERSITI TUN HUSSEIN ONN MALAYSIA BORANG PENGESAHAN STATUS TESIS' JUDUL: ANALYSIS OF FLOW AND HEAT TRANSFER OVER LOUVERED FINS IN COMPACT GEOMETRIES Saya SESI PENGAJIAN : 2007/2008 YONG KOK WEE (820516-06-5061) , mengaku membenarkan tesis (PSMISarjanaIDoktor Falsafah)' ini disimpan di Pcrpustakaan Universiti Tun Hussein Onn Malaysia dengan syarat-syarat kegunaan seperti berikut: I. Tesis adalah hakmilik Universiti Tun Hussein Onn Malaysia. 2. Perpustakaan dibenarkan membuat salinan untuk tujuan pengajian sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bah an pertukaran antara institusi pengajian tinggi. 4. .. Sila tandakan (>I' ) D SULIT D TERHAD (Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam AKTA RAHSIA RASMI 1972) (Mengandungi maklumat TERIIAD yang telah dilentukan oleh organisasi/badan di mana penyelidikan dijalankan) ~ TIDAK TERHAD Alamal Tetap: E-9-1!' BLOCK E PELANGI DAMANSARA 1 PJU 6 PERSIARAN SURIAN ;~ , 47800 PERTALING JA YA SELANGOR DARUL EHSAN. TARIKH: _-llOo.6..1lJ\,,-1aA.l:v~2u.OwOL.L7_ CATATAN: Potong yang tidak berkenaan. (TANDi.TjNGA tHNELIA) Prof. Dr. VIJA Y R.IiAGHA VAN ,". .' . T A RI K HI:.' __ --lIo6.6 .llJ\l.! A.A .YV...;2U.0UIJ07 .. Jika lesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasalorganisasi berkenaan dengan menyatakan sekali scbab dan dikelaskan sebagai SULIT atau TERHAD. Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara penyelidikan, alau disertai bagi pengajian secara kerja kursus dan penyelidikan atau Laporan Projek Sarjana Muda (PSM). "J declare that I have read this thesis and in my point of view this project is qualified in terms of scope and quality for the pilrpose of award of Master' s Degree of Mechanical Engineering (by research)". Signature Supervisor Date Signature Co-Supervisor Date GHA V AN ~".·t'""", : Prof. Dr. VIJAYR.RA Cl"'~'"'''''' J' .-,., " , •••• " •. t,." c' ,." I ! tHIJ" JI ~1," I'I,! ,j -\ ",1111 1 .., 'I l'oI .-:0" I'," i 00','" "_",,,, , ... . 2.D. ..... !! .... 4.Q~Z ............ . ~I \,\ I~ ....... \ ................................ . ANALYSIS OF FLOW AND HEAT TRANSFER OVER LOUVERED FINS IN COMPACT GEOMETRIES YONGKOKWEE A project submitted iu full fulfillment of the requirements for the award of the Master's Degree of Mechanical Engineering Faculty of Mechanical and Manufacturing Engineering University Tun Hussein Onn Malaysia June 2007 .. I declare that this project is the result 0/ my oll'lllI'ork except the ideas alld summaries/or which I have clarified their sources . .. Signature Writer's Name : YONG KOK WEE Date 11 iii ACKNOWLEGDEMENT I would like to express my heartiest gratitude to my supervisor, Prof. Dr. Vijay R. Raghavan for his assistance and guidance. With his valuable advice, ideas, support, encouragement and supervision throughout I have been able to complete this task successfully. Also, I would like to thank my teacher Mr. Wan Saiful Islam for his assistance and guidance in computer simulation. My appreciation and thanks to my parents who supported me in all the way of my life. Not to forget my sister and brothers for their love and respect. Thanks to all my beloved ones who have been supporting me and the Ministry of Science, Technology and Innovation (MOSTI) fund for its trust and support. iv ABSTRACT The louvered fin is most widely used in automotive applications. Compared to other geometrical parameters ofthe fin, the louver angle has a stronger effect on heat transfer. This study is carried out by computational method to determine the louver inclination of a rectangular channel heat exchanger that has the greatest influence on flow and heat transfer and invariant with other geometrical parameters. The meshed CAD model is validated with an established correlation in literature. In the earlier years of study, the mean flow angle was defined in two dimensional flows. ANSYS-CFD is capable of defining a mean flow angle was defined in three dimensional flows. The validation agrees weB, with about 5.39% of error. Various graphs are plotted to determine the optimized louver inclination. From the plotted graphs ofNusselt number and pumping power against the Reynolds Number, it is observed that the louver angle has a strong influence on the heat transfer rate. Then, a ratio of heat transfer rate to pumping power is used in the graphs as the non-dimensional number representation to determine the optimum angle. In addition to this study, a general correlation is developed to represent the behavior oflouver angle at different ranges of pumping power. With a practical range of Reynolds numbers and louver angles, the optimum angle is found to be 20 degrees. This numerical result has a high confidence level where a good agreement between the meshed models with the established finding is obtained. The study has succeeded in obtaining the result that was set out as the objective. \' ABSTRAK Louver fin adalah yang paling sesuai untuk aplikasi automotif. Berbanding dengan parameter yang lain, sudut louver fin adalah paling mendorong kepada perubahan aliran dan keboleh pindahan haba. Oalam tesis ini, kajian dilakukan secara simulasi berkomputer untuk menentukan sudut louver fin yang optimum dari segi keboleh pindahan dan ketelusan pengaliran udara. Model yang dimesh, telah menjalani peringkat pengesahan dengan formula dari kajian yang terdahulu. Oi awal kajian, defininasi adalah dalam aliran dua dimensi. Perisian ANSYS-CFO boleh memberi definisi dalam bentuk tiga dimensi. Pengesahan adalah sahih dalam 5.39% ralat. Pelbagai graftelah diplot dan didapati definisi pumping power adalah yang paling sesuai digunakan dalam optimisasi. Melalui graf-graf iaitu Nusselt number dan pumping power yang diplot berlawanan dengan Reynolds Number, ia didapati bahawa sudut louver mempunyai pengaruh yang kuat terhadap keupayaan pindah haba. Maka, satu nisbah antara keupayaan pindah haba kepada pumping power digunakan sebagai perwakilan nombor tidak berdimensi bagi menentukan sudut optimum louver. Sebagai tambahan kepada kajian ini, persamaan matematik yang merangkumi keseluruhan sifat sudut louver fin dengan pumping power dalam kaj ian juga dibinakan. Oalam lingkungan Re yang pratikal, sudut louver fin yang optimum adalah 20 degree. Hasil kajian ini adalah selari dengan hasilan dapatan dari Iiteratur oleh pengkaji yang terdahulu. vi TABLE OF CONTENTS TITLE DECLARATION ii ACKNOWLEDGEMENT iii ABSTRACT (ENGLISH) iv ABSTRACT (BAHASA MELA YU) v TABLE OF CONTENTS vi LIST OF TABLES ix LIST OF FIGURES x NOMENCLATURE xii LIST OF APPENDIX xiv I INTRODUCTION 1.1 Background 1.2 Importance of the Study 4 1.3 Rationale ofthe Study 4 1.4 Problem statement 6 1.5 Objectives 6 1.6 Scope 7 II LITERATURE REVIEW 2.1 Davenport's Observation 2.2 The Mean Flow Angle 2.3 Flow efficiency 2.4 The Relation of Flow Efficiency and Heat Transfer 2.5 The Relation of Flow Efficiency and Reynolds Number 2.6 The Relation of Flow Efficiency and Thickness Ratio 2.7 The Disagreements in Findings among the Researchers 2.8 Friction Factor Correlation 2.9 Thermal Wakes Effect 2.10 Assumption of Laminar Flow 2.II Summary of Literature Review ill METHODOLOGY 3.1 Introduction 3.2 Main Structure of the Methodology 3.2.1 Constructing the Analytical Model 3.2.2 Validation 3.2.3 Finding the Optimum Louver Angle 3.3 Solution Procedure 3.4 Numerical Analysis as the Tool IV ANALYSIS 4.1 Model Validation 4.2 Data and Result 4.2.1 The Required Pumping Power vs. Re 4.2.2 Heat Transfer Rate vs. Reynolds Number 4.2.3 Ratio of the Heat Transfer Rate to the Required Pumping Power vs. Reynolds number vii 8 9 IO II 12 I3 14 18 20 21 21 24 25 26 29 31 34 36 38 40 41 43 44 4.2.4 Ratio ofthe Heat Transfer rate to the Required Pumping Power vs. Angle 4.3 Evaluation method 4.4 Correlation Development V DISCUSSION AND CONCLUSION 5.1 5.2 5.3 Discussion Conclusion Future Work REFERENCE APPENDIX A. GGI and MFR Theory B. C. Estimation calculation of constant wall temperature Finding the louver angle: Flow and Heat transfer Data viii 45 47 49 51 54 55 56 60 65 66 ix LIST OF TABLES TABLE PAGE 4.1 Comparison between the predicted mean flow angle ofthis 39 study and the mean flow angle of Achaichia and Cowell (1988b) 4.2 Accuracy of equation 4.1 50 C1 Flow and Heat transfer Data - Inlet plane 64 C2 Flow and Heat transfer Data - North plane 65 C3 Flow and Heat transfer Data - East plane 67 C4 Flow and Heat transfer Data - south plane 68 C5 Heat transfer rate -Inlet, North, East and South plane 69 x LIST OF FIGURES FIGURE PAGE 1.1 Fonns of louvered fin-flat tube surface as illustrated by 2 Hesselgreaves (2001). 1.2 Section through louvered fin as illustrated by Achaichia and 3 Cowell {I 998a) 2.1 Mean flow angles in louver arrays from Achaichia and Cowell 9 (l988b). 2.2 (a) Critical Reynolds number versus louver angle; 16 (b) Flow efficiency versus Reynolds number by Zhang and Tafti (2003) 2.3 Comparison of flow efficiency predicted by researchers by 17 Zhang and Tafti (2003) 2.4 Geometrical parameters for Chang and Wang {I 997) 19 correlation. 3.1 Main structure ofthe methodology. 25 3.2 Dimensions of flat tube with rectangular channel and louver 26 fins. 3.3(a) 3-dimensional view of the fins stack 27 3.3(b) Side view ofthe fins stack 27 3.3(c) Fluid region as the control volume. 27 3.3 (d) The meshed control volume 28 3.4 Boundary conditions and regions. 29 3.5 Direction of air entering and leaving the control volume. 32 3.6 Solution procedure 35 XI 4.1 Relation of the required pumping power with Reynolds number 40 for different louver angles. 4.2 Vector plot showing the direction offlow in louver fins. 40 4.3 Relation ofNusselt number with Reynolds number for various 43 louver angles. 4.4(a) Relation ofthe ratio of heat transfer rate to the required 44 pumping power with Reynolds number for various louver angle (300 to 1000). 4.4(b) Relation of ratio heat transfer rate to pumping power with 45 Reynolds number for various louver angle. 4.5(a) Heat transfer over pumping power vs. louver angle at various 46 pumping power. 4.5(b) Heat transfer over pumping power vs. louver angle at various 47 mass flow rate. 4.6 The ratio of heat transfer over pumping power reference to 48 pumping power 0.001 watt vs. louver angle. 4.7 Ratio of heat transfer to pumping power reference to mass flow 48 rate 0.0002kg/s vs. louver angle. 4.8 Graph of the average ratio ofheat transfer rate to pumping 49 power vs. louver angle. 5.1 The schematic relation of truncation errors and round off errors 52 with number of steps. 5.2 Graph of flow efficiencies with different louver angles and fin 53 pitch ratios at a thickness ratio of 0.1 5.3 Graph of flow efficiencies vs. louver angles. 53 Symbols A b N Nu 'l 'lSI\' NOMENCLATURE Area Louver angle Thickness ratio (ratio of fin thickness over louver length) Mean flow angle specific heat capacity ideal distance if the flow were aligned with the louver characteristic flow efficiency length scale ratio Fin pitch or fin height Fin width Fin pitch ratio (ratio of fin pitch over louver length) Mass velocity heat transfer coefficient Average heat transfer coefficient Specific enthalpy conductivity Louver pitch or louver length Louver pitch ratio Lp= 1 Mass Mass flow rate Actual distance traveled by dye Nusselt number Flow efficiency Flow efficiency based on the finding of Sahnoun and Webb xii 'IWI 'IWI,max p ¢ p ReL Rein Rewl,c Sf T U u V v fir x Y L'l xiii Flow efficiency based on the finding of Webb and Trauger Flow efficiency at critical Re number based on the finding of Webb and Trauger Pressure Streamlines Mass density Reynolds number based on louver pitch Reynolds number based on inlet velocity Critical Reynolds number based on the finding of Webb and Trauger Stanton Number Temperature velocity in horizontal direction velocity in horizontal direction dynamic viscosity velocity in vertical direction pumping power x-direction y-direction difference A. B. C. LIST OF AT'PI::"!)JCES GGI and MrR Theory Estimation calculation of constant willi tcmrcratun: flow and Heat transfer Data '-,:'. CHAPTER I INTRODUCTION 1.1 Background Compact heat transfer surfaces play an important part in heat exchanger technology because they are lighter and more efficient. Newer surfaces are constantly evolving as a result of recent developments in compact heat exchangers. Of the many types of fins that have been studied in compact heat exchangers, such as strip fin, offset fin, wavy fin etc., the louvered fin is most widely used in automotive applications. The various forms of louvered fin flat-tube surface are shown in figure 1.1. According to Kraus et al. (2001), the design of or performance calculation for a compact heat exchanger for rejection of heat in automotive applications, such as a radiator, it is necessary to establish the heat transfer capability and the associated system resistances. The louvered fin is the preferred fin geometry in radiators because (i) it can be manufactured by automated process (ii) it can be accommodated in a small space, as compactness is important in an automobile, and (iii) unlike other types, it gives high heat duty which reduces the radiator frontal area, which is advantageous for the aerodynamics of the automobile. (.1 i 13111\Tt:d I1n llJl nUL IlIh: \\ ilh triangular dlall~H:l I h) I',"I~ and I"he 10'" ml lill gctHlI~Lry 2 {t.: I LlIU\r~J lin Oil nat tube \\ ttll rl'~tangllbr channd Figure 1.1: Forms oflouvered fin-flat tube surface as illustrated by Hesselgreaves (2001). The hydrodynamic characteristics of a stack of louvered fins have a complex dependence on a number of variables such as fin pitch, fin material, fin thickness, number of louvers, louver pitch, louver height and louver angle. The geometric parameters that can be varied include louver pitch L, louver length LL, louver angle a, and fin pitch F as shown in figure 1.2. Louver pitch is the same as louver length since it is the same length of the louver forming cuts in the metal. As describe by Shah and Sekulic (2003), such finning enhances heat transfer by a factor of2 or 3 compared with unlouvered surfaces. North face -----G> duct directed flow ----t> South face 3 Figure 1.2: Section through louvered fin as illustrated by Achaichia and Cowell (1998a) At first sight, the function of the louvered fins seems to be as turbulence generators. This was found not true because the louvered fms act rather by causing the fluid flow to be deflected from its incident direction and become aligned with the plane of the louvers which was shown by Beauvais (1965) in large-scale models. Thus, the louvered fins tend to act as multiple flat plates with their associated leading edge laminar boundary layers which enhance heat transfer without a disproportionate increase in flow resistance. According to Cowell et al (1995), this behavior of flow has been experimentally confirmed by many others- by Davenport (1980), using smoke traces; by Wong and Smith (1973) and Antoniou et al. (1990) using hot-wire anemometry; by Button et al. (1984), using LDA; and by others (Hiramatsu and Ota (1982), Tanaka et al. (1984), Tura (1986), Hiramatsu et al. (1990), Webb (1990) using water channels and flow visualization techniques. Further evidence of this behavior comes from the numerical analyses of flow through louvered arrays published by Achaichia and Cowell (1988a), Baldwin et al (1987), and Ikuta et al (1990). 1.2 Importance of the Study 4 Past studies have shown that the flow in the compact heat exchanger is strongly dependent on geometrical parameters. Thus, the optimum heat transfer rate could be obtained by manipUlating the geometrical parameters of the fm. In this study was done by selecting the most influential geometrical parameter. In general, the efficiency ofthe compact heat exchanger increases with air velocity and louver angle, while decreasing with fin pitch and thickness ratio. According to Zhang and Tafti (2003), louver angle has a stronger effect on heat transfer as compared to the other geometrical parameters. Therefore, selecting the louver inclination is a mean to reduce pressure loss without extensive modification in the design of the compact heat exchanger, yet achieve the required heat transfer duty with limited fan power. 1.3 Rationale of the Study The louvered fin on flat tube with rectangular channel (figure 1.1) is the preferred type of compact heat exchanger for automobile applications. Correlating the friction factor for such an important geometry was done by the past researcher as shown 5 in equations 2.18 to 2.24. However, these correlations are generalized and the percentage of deviation between these is as large as ± 15% and no consideration of the louver thickness parameter. Zhang and Tafti (2003) detennined that for small louver angles there is a significant thickness ratio effect on the heat transfer and the flow efficiency, defined in section 2.3. Detennining the optimum condition of the louver angle by using generalized correlations of Chang and Wang (1997) is unlikely to lead to the right answers. Therefore in this study the ratio of heat transfer rate to pumping power is considered to detennine the optimum angle. In a typical reliability test of a radiator, the air flow is conducted at 10 m1s (corresponding to a typical Reynolds number of 1000). Analogy of a real situation for such a reliability test is one where the heat load from engine becomes high when the automobile encounters a long upward slope. In such a case when the ram air velocity becomes low, the heat rejection of the radiator can no more depend on the ram air velocity, and has to depend on the fan. Below Reynolds number of about 300, Davenport (1980) noted that an inconsistency occurred in the heat transfer due to the thickness of the boundary layer developing on the louvers. This idea was also continned by the results of Achaichia and Cowell (1988). A review of the past literature, in section 2.7 of this thesis, showed that the heat transfer correlation is yet to have a continnation of which correlation has the strongest agreement. Besides, such a low Reynolds number is not in the practical range. To exclude this uncertainty, therefore, Reynolds numbers below 300 are not considered in this study. The importance of the thennal wake on the local heat transfer coefficients along a particular louver had been studied experimentally by Kurosaki et al. (1998), and numerically by Suga and Aoki (1991) and Zhang and Tafti (2001). Zhang and Tafti (2001) state that neglecting thennal wake effects at low flow efficiencies can introduce errors as high as 100% in the heat transfer. To perfonn such a study in large scale experiment would induce even more errors when the heating on louver fins is not unifonn. Therefore, to avoid such large errors, it is preferable to do this study fully by a computational method. Furthennore, errors are eliminated at validation stage. The 6 results are validated by comparison with previous published correlations. The purpose of validation is to verify that the mesh distribution and solution procedure are suitable before the study is carried further. 1.4 Problem Statement This study is carried out numerically to detennine the louver inclination that has the greatest influence on flow and heat transfer of the compact heat exchanger with rectangular channels, in which, other geometrical parameters are invariant. The study is directed towards automobile applications, although the results can be extended to other situations. 1.5 Objectives The objectives of this study are: (i) To develop a model using Computational Fluid Dynamics to analyze the flow and its heat transfer from compact louvered fins. 

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