International Journal of Engineering Research & Science (IJOER) ISSN: [ ] [Vol-3, Issue-8, August- 2017]

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1 Numerical Aalysis of Heat Trasfer i Usteady Naofluids i a Small Pipe with Pulse Pressure Cheol Park 1, Juhyo Kim 2, Jugpil Noh 3, Suchul Huh 4, Byeogkeu Choi 5, hashik Chug 6, *HyoMi Jeog 7 1 Departmet of Eergy ad Mechaical Egieerig, Gyeogsag Natioal Uiversity. Istitute of Marie Idustry, Cheodaegukchi-Gil 38, Togyeog, Gyeogam, 65-16, South Korea 2 Departmet of Marie Egieerig, Mokpo Natioal MaritimeUiversity,61 dorim-ri, 1666 Yeogsa-ro. cheoggye-myeo, Mua-gu, jeoam, South Korea 3,4,5,6,7 Departmet of Eergy ad Mechaical Egieerig, Gyeogsag Natioal Uiversity Istitute of Marie Idustry, Cheodaegukchi-Gil 38, Togyeog, Gyeogam, 65-16, South Korea Abstract I the preset paper, developig turbulece forced covectio flows were umerically ivestigated by usig water-al 2 O 3 ao-fluid through a circular compact pipe which has 4.5mm diameter. Each model has a steady state ad uiform heat flux (UHF) at the wall. The whole umerical experimets were processed uder the RPM 1 to 5 ad the ao-fluid models were made by the Alumia volume fractio. Sigle-phase fluid models were defied through ao-fluid physical ad thermal properties calculatios, Two-phase models (mixture graular model) were processed i 1m diameter. The results show that compariso of usselt umber ad heat trasfer rate are improved as the Al 2 O 3 volume fractio icreased. All of the umerical flow simulatios are processed by the FLUENT. The results show a icrease from volume fractio cocetratio ad a icrease i heat trasfer coefficiet with icreasig RPM. Keywords aofluid, mixture, alumia, usselt umber, heat trasfer coefficiet, Pulsatio pressure. I. INTRODUCTION Heat trasfer fluids play a importat role i may idustries, icludig power plats; productio processes, trasportatio ad electroics, ad the heat trasfer characteristics of thermal fluids play a importat role i the developmet of eergy efficiet heat trasfer devices. Past improvemets have bee based o structural chages ad the additio of heat trasfer areas, vibratios o the surface of the heat, ijectio or ihalatio of fluids ad the applicatio of electros or magetic fields. These ehacemet techiques rarely meet the icrease i heat trasfer coefficiet ad, i this coectio; there is a strog demad for the developmet of advaced heat trasfer fluids with higher heat trasfer properties. Therefore, a umber of recet studies o aofluids for experimetal covective heat trasfer through circular tubes have bee coducted by seior scholars. However, aofluid research is still i the hot debate ad ivestigatio. I additio, research o the pulse pressure has bee actively carried out all over the world, ad may research results have bee published especially i the field of oise vibratio. No-steady pulsatig flow pheomea will be geerated by iteral smoke ad reciprocatig compressors. The pulsatig pressure i the iteral combustio egie will be the silecer part. The fuctio of this silecer is to reduce the pulsatio pressure iside the silecer as well as to reduce the back pressure. Maxwell [1,2] has demostrated that icreasig the volume fractio of solid particles ca icrease the thermal coductivity of the mixture. The particle diameter curretly available for particle maufacturig techology developmet is smaller tha 1 m, called ao-size. This effort allows the particle mixig fluid to icrease the thermal coductivity of the heat trasfer fluid by icreasig the critical thermal coductivity. I additio, solid aoparticle colloids are very stable ad do ot exhibit sigificat sedimetatio uder static coditios after weeks or moths. I additio, solid colloids float easily whe you reduce particle size. Therefore, aofluidic techology is expected to be suitable for heat trasfer fluids. Mohamad ad viskata [3] studied the abormal atural covectio for a low pradtl umber of fluids i the cavity, ad patterso ad Imberger [4] coducted a study o the abormal atural circulatio i a square cavity. Hellims ad Churchill [5] umerically studied the atural covectio i a usteady state i a closed vessel. Therefore, this study focuses o the aofluid oly for pulsatig pressure i a small tube with a pulse pressure. The purpose of this study is to verify the Page 63

2 umerical aalysis techique i terms of the fluidity of the aofluids i a small tube with a pulsatig pressure through umerical aalysis. The purpose is to secure the data. II. MATHEMATICAL MODELING 2.1 Geometry ad boudary coditio Fig. 1a shows the actual model of geometry ad Fig. 1b is the part of the Two-dimesioal Mesh. Oe of the mai purpose of this simulatio is tryig to uderstad the ear wall behavior of ao-particles, velocity distributio perpedicular to the pipe surface ad drag coefficiet at the ear of pipe wall, so the relatively cocetrated mesh i the ear wall area is eeded. As a result, the mesh has a o-uiform quadratic mesh. The bottom horizotal lie is a axis which makes Three-dimesioal pipe model at the asymmetric eviromet. The upper horizotal lie is a wall with Uiform heat flux. The tube cosisted with a diameter (D) of 4.5 mm ad a legth (L) of 1.17 m. Naofluids is composed of Al 2 O 3 particles ad water have the physical properties such as Table.1[6]. The total flow rate for each fluid model is iput at a costat temperature of 293K ad the axial velocity is defied as pressure chage over time at 1,3,5RPM ad the wall surface has a Heat flux of 5 (w / m2). Chemical formula FIGURE 1. PART OF THE MESH OF COMPUTATIONAL CELL. 8 X 8 WITH.96 RATIO 2.2 Goverig equatio TABLE 1 Al 2 O 3 NANOPARTICLE AT TEMPERATURE OF 293K The sigle-phase model is ivestigated for the compariso of mixture model as prescribed. Followig equatios are represetig the mathematical formulatio of the sigle-phase model ad of the cotiuous phase of the mixture model. The exact k-ε equatios cotai may ukow ad u-measurable term [6-8] Eergy equatio: Desity kg m 3 Heat coductivity W mk Specific heat J kgk Spherical diameter m Al 2 O Page 64

3 turbulet kietic eergy k div ρvcpt = div kgradt + S e (1) (ρk ) t + (ρk u i) x i = x j μ t k + 2μ ς k x t E ij E ij ρε (2) j dissipatio ε (ρε ) t + (ρε u i) x i = x j μ t ε ς ε x j + C 1ε 2μ t E ij E ij C 2ε ρ ε2 k (3) Ad k- ε equatio of represets velocity compoet i correspodig directio (u i ), represets compoet of rate of deformatio(e ij ), represets eddy viscosity(μ t ) (Rate of chage of k or ε +Trasport of k or ε by covectio = Trasport of k or ε by diffusio + Rate of productio of k or ε Rate of destructio of k or ε) Coservatio of mass: δρ m δt + ρ m u m = (4) Where u m is the mass-averaged velocity? u m = k=1 α k ρ k u k ρ m (5) ad ρ m is the mixture desity with α k volume fractio of phase k: ρ m = k=1 α k ρ k (6) Mometum equatio for sigle-phase: div ρvv = grad P + μ V + S m (7) Mometum equatio for multi-phase: k=1 α k ρ k u k u k = ρ m u m u m + α k ρ k u Mk u Mk k=1 (8) The compressio ad viscous lose by heat are assumed to be excluded i the eergy equatio. The source/sik terms S m ad S e represet the uitize effects of eergy ad mometum exchage with base fluid. These are zero value i the sigle-phase model. Mometum equatio of multi-phase are affected by volume fractio (α), velocity of phase (u k ), diffusio velocity (u Mk ). The determiatios of particle motio are particle mass (m p ), cross-sectioal area of the particle(a p ), drag coefficiet(c D ), slip velocity(u cp ). The drag force i this study is followig Clift et al equatio (7) for sigle rigid spherical particle i a fluid: 2.3 Numerical approach F D = 1 2 A pρ c C D u Cp u Cp 1 2 V pρ c du Cp dt 6γ p 2 πρ c μ c t du Cp ds t s ds (9) The computatioal fluid dyamic code FLUENT 16.1 is employed to solve the preset problem. The goverig Eqs. (1)-(3) are solved by cotrol volume approach. The algebraic discretize equatios, resultig from spatial iter-fractio process, are sequetially solved throughout the physical domai cosidered. ANSYS Fluet 16.1 solves the systems resultig from discretizatio schemes usig a umerical method. For the covective ad diffusive terms, a secod order upwid method was used. Pressure ad velocity were coupled usig Semi Implicit Method for Pressure Liked Equatios (SIMPLE) i siglephase. To calculate the pulse pressure, Figure 2. The PISO algorithm was used to calculate the aomalous state as a complete egative solutio. The cotiuity equatio ad the mometum equatio are used to calculate the pressure iside the small tube. Page 65

4 The turbulece model is based o the stadard model k -ε model which has already proved its egieerig validity. The covergece judgmet of the residuals was regarded as covergece whe the residual value reached 1 or less. FIGURE 2. FLOW CHART OF PISO ALGORITHM As already see for the SIMPLE algorithm, the steps 4 ad 5 ca be repeated for a prescribed umber of times to correct for o-orthogoality. III. RESULTS The I this work a umber of umerical simulatios have bee performed to study forced covective heat trasfer of Al 2 O 3 - water i a circular tube uder turbulece flow ad results were coducted to employig the sigle phase ad mixture model for φ= to 4%, 1to5RPM as q=5 W m^2 with a costat state. I all cases the size of the spherical particles is 1 m. Thermal etrace legth depeds o Pradtl umber.[9] So whe cocetratio icreases Pr umber also icreases ad cosequetly, thermal etrace legth becomes greater. 8 1 h (w/m2*k) 6 4 1RPM % 4% Nu RPM % 4% (a) (b) FIGURE 3.(A) 1RPM, HEAT TRANSFER COEFFICIENT FOR Al 2 O 3 -WATER, (B)1RPM, NUSSELT NUMBER As show i Fig. 3 (a), the differece betwee % ad seems to be isigificat i the rage of.1x / Lmm, but the heat trasfer rate of 4% Al 2 O 3 is 2 times larger tha, Respectively. Likewise, i figure (b) Page 66

5 The trasmissio rate of ad Al 2 O 3 is less tha 1, but 4% aofluids ca be see to have more tha twice the Nusselt umber RPM % 15 4% 5RPM % 4% h (w/m2*k) 1 Nu (a) (b) FIGURE 4.(a) 5RPM, HEAT TRANSFER COEFFICIENT FOR Al 2 O 3 -WATER, (b) 5RPM, NUSSELT NUMBER I Fig. 4 (a), ulike 1RPM, the pheomea appearig more tha twice as much as %, ad 4% are ot show i the figure. This pheomeo ca be grasped by icreasig the iteral pressure at 5 RPM. Also, i Fig. (B), the Nusselt umber seems to be closer to Al 2 O 3 tha 4% Al23-water () 1RPM 3RPM 5RPM h (w/m2*k) 6 4 Nu Al23-water () 1RPM 3RPM 5RPM (a) (b) FIGURE 5.(a) Al 2 O 3 -WATER, HEAT TRANSFER COEFFICIENT FOR 1 TO 5RPM, (B) Al 2 O 3 -WATER, NUSSELT NUMBER FOR 1 TO 5RPM Figures 3 ad 4 shows the differece i heat trasfer coefficiet ad umber of us i the aofluid for each RPM. 5 (a) ad (b), however, the heat trasfer coefficiet ad the umber of uclei for RPM chages of the same Al 2 O 3 ca be cofirmed. The heat trasfer rate ad the umber of usselts are sigificatly lower tha those of 3 ad 5 RPM. However, at 3 RPM, it ca be cofirmed that the heat trasfer coefficiet ad the umber are higher tha 5 RPM i the early stage. IV. CONCLUSION Numerical aalysis of the heat trasfer of the aofluid i the usteady state i the small tube ito which the pulsatig pressure is itroduced showed that the effect of the cotet of Al 2 O 3, which is a aofluid, was further icreased i the low 1 RPM. I additio, it was cofirmed that the aofluids of % ad compared to % ad of Al 2 O 3 have a data differece of more tha 2 times. I 5 RPM, the differece i cotet is ot sigificat compared to 1 RPM, but aofluids with high Al 2 O 3 The heat trasfer coefficiet ad the umber of us were better. Ad the icrease i the heat trasfer coefficiet of the aofluid to the RPM chage shows better results as the RPM icreases. Therefore, aofluid with Page 67

6 high Al 2 O 3 cotet ad high RPM ca improve the thermoelectric coefficiet ad icrease the umber of uts. But the CFD should be progressed with costat ad trasiet umerical ivestigatio parallel. Basically, It would be pace with the experimet especially differet model scale study. Also, uiform heat flux sample, wall shear stress, body force researches does ot iclude this paper. This compact size model is ot usual model o the ao-fluid CFD study so these factors eed to be proved. ACKNOWLEDGEMENTS This research was supported by Basic Sciece Research Program through the Natioal Research Foudatio of Korea (NRF) fuded by the Miistry of Sciece, ICT ad future Plaig (No. 217R1A2B4762). REFERENCES [1] J. C. Maxwell, A Treatise o Electrictiy ad Magetism, Oxford Uiversity Press, Cambridge, 1881J. Clerk Maxwell, A Treatise o Electricity ad Magetism, 3rd ed., vol. 2. Oxford: Claredo, 1892, pp [2] Q. Li, Y. Xua, Heat trasfer ehacemet of aofluids, Iteratioal Joural 21, pp.58-64, 2. [3] A.A Mohamad, ad R.Viskata: It. J. Numerical Method i Fluid, 12, 61-81(1991) [4] Sughoo kim,hyemi So,JaeCheo Lee, The effect of eccetricity betwee gear ad housig i ivolute gear pump, Joural of the Korea Society of Marie Egieerig 37(6) 213.9, [5] Yagwoo Mo,YougTae Yoo,GeeDae Na,JiHwa Kim, A Characteristics of Impedace Propagatio by the Usteady Flow i a Hydraulic Pipelie, Joural of the Korea Society of Maufacturig Techology Egieers 13(6), 24.12, [6] M. Nazififard, M. Nematollahi, K. Jafarpur, K. Y. Suh, Numerical Simulatio of Water-Based Alumia Naofluid i Subchael Geometry, Sciece ad Techology of Nuclear Istallatios, Vol 212, 212 [7] ANSYS Fluet Theroy Guide, pp. 51, November 213 [8] V. Biaco, F. Chiacchio, O. Maca, S. Nardii, Numerical ivestigatio of aofluids forced covectio i circular tubes, Applied Thermal Egieerig 29, pp , 29 [9] V. Biaco, F. Chiacchio, O. Maca, ad S. Nardii, Numerical ivestigatio o aofluids turbulet covectio heat trasfer iside a circular tube, Iteratioal Joural of Thermal Scieces, vol. 5, o. 3, pp , 211 [1] Chugseub Yi,kyuji shim,wada ali akbar,hashik chug,hyomi Jeog, study o the Pressure Variatio i a Chamber Caused by Pulsatio Pressure, Trasactio of Korea Society of Automotive Egieers 15(4),27.7, (7pages) Page 68