HEAT TRANSFER AND FLUID FLOW AROUND AN ELLIPTIC CYLINDER IN CONVERGENT- DIVERGENT CHANNEL

International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 9, Sep 2018, pp. 979-989, Article ID: IJMET_09_09_107 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=9 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 IAEME Publication Scopus Indexed HEAT TRANSFER AND FLUID FLOW AROUND AN ELLIPTIC CYLINDER IN CONVERGENT- DIVERGENT CHANNEL Mechanical Engineering, Technical Institute of Dewaniya, Al-Furat Al-Awsat Technical University, Iraq ABSTRACT Forced convection heat transfer characteristics around isothermal cylinder with different axis ratio (E=0.3, 1) at the same cross section area, peak of convergentdivergent channel (s/h=0.071, 0.14, 0.21), (s), and Reynolds number (40 Re 1000) in steady, laminar cross-flow regime has been studied numerically. FLUENT is used to solve the fluid flow and energy equations the cylinder put in convergent divergent channel with different location. The pressure coefficient and Nusselt number have been studied. The results showed that, the pressure coefficient and Nusselt number around the tested cylinders was increased when using convergent divergent channel and with increasing the peak and Reynolds number. At E=0.3 (elliptic cylinder) the Nusselt number is highest than the circular cylinder (E=1) and case 2 is the best location of cylinder in convergent divergent channel. Keywords: CFD; FLUENT; Heat Transfer; Convergent-Divergent Channel; Elliptic Cylinder. Cite this Article:, Heat Transfer and Fluid Flow Around an Elliptic Cylinder In Convergent-Divergent Channel, International Journal of Mechanical Engineering and Technology (IJMET), 9(9), 2018, pp. 979-989. http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=9 1. INTRODUCTION Heat transfer and fluid flow around cylinder has been popular subject because of the cylinder with different cross suction importance iv variety of application such as heat exchanger, power generator, nuclear reaction et c. A series of experimental, analytical and numerical studies have been done to determine flow structure and heat transfer around cylinder. A previous study has examined the flow around the cylinder with different cross suctions as below. [1] Studied heat transfer and flow around heated circular cylinder numerically and experimentally. [2] Studied heat transfer around isothermal circular cylinder at Re (40-10000) numerically. Flow separation with different blockage ratio was studied numerically with Re (5-50) by [3-4] studied the flow and heat transfer around circular cylinder by using an integral http://www.iaeme.com/ijmet/index.asp 979 editor@iaeme.com

approach of BL analysis and using Von-Karman-Pohlhousen method to solve momentum and energy equations for both isothermal and is oflux boundary conditions. [5] studied flow and heat transfer for unsteady circular cylinder with Re (50-180) numerically. For fluid flow around square cylinder with different Re was studied numerically and experimentally by [8-9] and [10]. [11] Investigated heat transfer around hexagonal cylinder in laminar and turbulent region numerically with Re (100-50000). Many studies were done for fluid flow and heat transfer around an elliptic cylinder. [12] Studied heat transfer characteristic around hexagonal cylinder with different cross suctions (circular, square, rectangular, diamond and elliptic) experimentally under constant heat flux with Re (2200-22000), the results show that heat transfer increase with Re and highest Nusselt number was obtained for elliptic cylinder. [13] studied 2-D laminar force convection flow and heat transfer from elliptic cylinder with Re range (5-20), the results show that the range rate of Nu has closely to theoretical results Nu Pe 1/3. [14] Studied convection heat transfer from circular and elliptic cylinders with the same cross suction area numerically, the axis ratio (miner axis to major axis) (0 E 1), the results show that the heat transfers for elliptic cylinder greater than the circular cylinder. The unsteady state force convection heat. transfers from elliptic cylinder with different inclination α (0-90) at Re=50 and E (0.2-0.6) with Pr (0.01, 0.7 and 5) was study numerically by [15], the results that Nu decreases with decreases Pr and largest oscillation occur at attract angle 90 degree. The flow and heat transfer around an elliptic cylinder was study analytically by [16] with using integral method of B.L under isothermal and isoflux B.C, the results show that a good agreement with existing excremental and numerical data. The effect of aspect ratio on steady laminar fluid flow past an elliptic cylinder was investigated numerically by [17] at low Re (20-40), the results explained that no vortices exist behind the cylinder for aspect ratio (AR) < critical aspect ratio (ARc) and critical (ARc) depended on Re with ARc=0.5648 at Re=20 and ARc=0.4076 at Re=40 also pressure coefficient decrease only until ARc and then will be constant. [18] studied the characteristic of wake of flow of an elliptic cylinder with zero angle of attack experimentally, the results show that the trip wire has significant effect on flow characteristic and reaction in current force and it strongly depends on this lallation location of the wire on model. Also the reaction of the drag coefficient is directly related to increasing Nu. [19] Studied force convection heat transfer from a row of heated elliptic cylinders with aspect ratio 0.6and 0.8. The result shows that the drag coefficient due to flow friction changes with distance between tow elliptic cylinder also, heat transfer for small distance between cylinders has lower values compared to large distance, also dependent on aspect ratio of elliptic cylinder. By using Lattic Boltzmann (LB) method to simulate flow in 2-D laminar flow past elliptic cylinder was done by [20] with (0.25 E 0.5) and 5 Re 100, the results that the drag and lift coefficients increase with increasing of angle of incidence (ϴ) where 0 ϴ 90 and vortex shedding is not occurred at high Re at ϴ=0. [21] Studied 2-D laminar flow of power law over elliptic cylinder with the range of (0.2 E 5) on critical Re denoting on flow separation numerically. The results explained Re decreases with power law index for all values of axis ratio (E) and wake formation and vortex shedding in both shear-thinning and shear-thickening fluid are seen be delay to higher Re at the (E) increases from 0.2 to 5. [22] studied the steady flow around an elliptic cylinder with axis ratio (0.2, 0.5 0.8 and 1) at 0 α 90 with Re 40, the results explain that for thin cylinder at low incident, the separation bubble forms near the trailing tip and with increasing (α), the location of initial separation moves towered the leading tip. For thick cylinder the effect of (α) on the location of initial separation in however insignificant. Heat transfer characteristic of circular and elliptic cylinder at 7190 Re 50350 numerically and experimentally for inline cylinder backs was studied by [23], the result shows that a http://www.iaeme.com/ijmet/index.asp 980 editor@iaeme.com

Heat Transfer and Fluid Flow Around an Elliptic Cylinder In Convergent-Divergent Channel significant reduction of local Nu around front area 0 ϴ 40 for circular cylinder and 0 ϴ 20 for elliptic cylinder is observed and second raw cylinders also results indicated that elliptic cylinder has lower friction factor compared to circular cylinder and elliptic cylinder has small facial area compared with circular cylinder. [24] studied fluid flow and heat transfer in side convergent-divergent channel at 1000 Re 10000 with s/h range (0.013-0.052) and d/h range (0.33-0.6) for circular cylinder, the result shows that maximum heat transfer occurs at (s/h=0.053) and (d/h=0.46) at Re=5000. For present study heat transfer and pressure drop from an elliptic cylinder inside convergent-divergent channel with different location and different peak of convergentdivergent channel (s/h=0.071, 0.14 and 0.21) at the same length of peak (d) with two cases of axis ratio (E=0.3,1) with the same cross section area figure 1 is investigated numerically by using commercial CFD package FLUENT 6.1 which based on control volume (C.V) based technique to solve conservation of mass, momentum and energy equation. For each control volume, algebraic equations are yields the variables as temperature, pressure and velocity. The flow (u, p) and thermal (T) fields, in turn, are used to deduce the local and global characteristics like pressure coefficient, Nusselt number. Nusselt number and Reynolds number are based on the equivalent hydraulic diameter Dh, where Dh [12] is:- For circular cylinder (a=b=d) And for elliptic cylinder = [ ] = = [ ] Where =1 Figure (1) Schematic of flow around the elliptic cylinder for all cases 2. GRID GENERATION The rectangular computational domain is bounded by inlet, outlet and channel walls contain the cylinder. Two dimensional structured mesh of triangle method with quadrilateral mesh density is kept intense near the channel and cylinder walls for resolving B.L as shown in figure 2. http://www.iaeme.com/ijmet/index.asp 981 editor@iaeme.com

Figure (2) computational grid structure 3. GOVERNING EQUATION This study is for steady two dimensional flow of viscose incompressible Newtonian fluid past cylinder inside convergent-divergent channel. The length of cylinder is assumed to be long to have insignificant end effect. The equation of conservation is [19]: - Continuity equation: - -Momentum equation: - (1) Energy equation: - (2) Are solved with convergent criterion of 10-6 was found sufficiently accurate for this study Boundary conditions. For all cases, the following B.C were applied with no slip B.C for velocity on all solid wall are used. - inlet boundary A uniform velocity is defined normal to the inlet boundary with zero normal velocity component u=uinlet v=0 - exit boundary The exit B.C are unknown before solving the equation its works on the principle of zero except pressure sitting the first derivation equal to zero (3) http://www.iaeme.com/ijmet/index.asp 982 editor@iaeme.com

Heat Transfer and Fluid Flow Around an Elliptic Cylinder In Convergent-Divergent Channel =0 - Channel wall No slip B.C for velocity at the channel wall - cylinder No slip B.C for velocity at the cylinder wall with constant wall temperature. 4. RESUTS AND DISCUSSIONS Figure 3 shows the comparison between the present results with results obtained by [7] and [2] for change the value of local Nu around circular cylinder at Re=200, the results shows good agreement with previous studies. Figure (3) local Nu around circular cylinder at Re=200 Also figure 4 show distribution Nu around elliptic cylinder at Re=50 and compared with [15]. The results show a good agreement between the results. Figure (4) local Nu around elliptic cylinder at (E=0.3) at Re=5 The value of average Nu with Re range from (50-600) is compared with [2] and [6] are shown in figure 5. The results show good agreement with previous studies. Figure (5) Nu av with Re for circular cylinder Local Cp around cylinder at Re=40 compared with [17] for circular cylinder figure 6 and elliptic cylinder at (E=0.3) figure 7, the results shows excellent agreement. http://www.iaeme.com/ijmet/index.asp 983 editor@iaeme.com

Fig 6 Cp around circular cylinder at Re=40 Fig 7 Cp around elliptic cylinder at Re=40 Figure 8 shows the average Nu with Re range (40-1000) for elliptic cylinder at E=0.3 and compared with [16] also the results shows good agreement. Figure (8) Nu av with Re for cylinder at (E=0.3) Figure 9 (a,b) show the Flow topology at Re=40 for circular and elliptic cylinder respectively compared with [17], the flow show good agreement between them. Figure (9 a,b) flow topology at Re=40 Temperature contour around cylinders for all cases at Re=500 and (s/h=0.14) are shown in figure10, the effect of axis ratio (E=0.3, 1) and peak of convergent-divergent channel on temp. fields distribution are clearing and shows channel a relatively lower temperature zone is establish near the cylinder wall for all cases of convergent-divergent channel, this due to guidance the flow toward the cylinder surface. This effect was increases with increasing (s/h) as shown in figure 11 for case (3) (as example). http://www.iaeme.com/ijmet/index.asp 984 editor@iaeme.com

Heat Transfer and Fluid Flow Around an Elliptic Cylinder In Convergent-Divergent Channel Figure (10) temp. Contour around cylinder for all cases at Re=500 for (a) circular cylinder (E=1), (b) elliptic cylinder (E=0.3), (c) case1, (d) case2, (e) case3, (f) case4 Figure 12 shows the flow structures in the present study for cylinder at (E=1, 0.3) and different cases of elliptic cylinder at Re=500 and (s/h=0.14). It is easy detected by observing to the velocity vector plots that the velocity increases using convergent-divergent channel and the flow separation moves to the rear of cylinder also, thickness of B.L regain decreasing with increase (s/h). Figure (12) velocity vector around cylinder for all cases at Re=500 for (a) circular cylinder (E=1), (b) elliptic cylinder (E=0.3), (c) case1, (d) case2, (e) case3, (f) case4 http://www.iaeme.com/ijmet/index.asp 985 editor@iaeme.com

Local pressure coefficient (Cp) around cylinder at Re=200 and (E=0.3, 1) at (s/h=0.14) with different locations is shown in figure 13. The pressure drop across the cylinder will be increase with using convergent-divergent channel and maximum pressure drop on cylinder dependent on the location of cylinder in channel as shown. Local Nusselt number (Nu) at Re=200 and (E=0.3, 1) at (s/h=0.14) with different locations is shown in figure 14. From the figure can be shown that heat transfer increase when (E<1) and also increasing by using convergent-divergent channel, also Nu distribution dependent on the location of cylinder in the channel where in case 1 the flow sweeping the heat from front and rear of cylinder and the heat transfer increases by 7.4% compared with the case of straight channel, in case2 the sweeping start from the front part of cylinder until (ϴ=90) and heat transfer increasing by 18%, in case 3 heat transfer increase from front and rear area but maximum heat transfer be in mid of cylinder as a result of a large amount of fluid near the cyli9nder with high velocity and heat transfer by 17.3% but in case 4 the flow is directed towards rear of cylinder therefore higher heat removes be in the rear of cylinder with increasing by 16.1%. Fig 13 Cp around cylinder for all cases at Re=200 Fig 14 Nu around cylinder for all cases at Re=500 Figure 15 shows pressure drop around cylinder at (E=0.3) and Re=200 with different peaks (s/h). the results show that pressure drop increasing with increases peak (s/h) due to increasing velocity where the pressure decreases when increasing velocity. Figure (15) pressure drop around elliptic cylinder with different (s/h) Figure 16 shows heat transfer distribution around cylinder at (E=0.3) and Re=500 with different peak (s/h) where Nu increases with increasing (s/h) due to high heat sweeping from cylinder by high amount of fluid flow. Figure (16) Nu distribution around an elliptic cylinder at Re=500 http://www.iaeme.com/ijmet/index.asp 986 editor@iaeme.com

Heat Transfer and Fluid Flow Around an Elliptic Cylinder In Convergent-Divergent Channel The relation between average Nusselt number with Reynold number range from (100-1000), the result shows that heat transfer increases with increasing axis ratio (E), also increases with using convergent- divergent channel and case 2 was the best location of cylinder in convergent- divergent channel for increasing heat transfer especially at Re>600. 5. CONCLUSIONS In present study, a cylinder with different axis ratio (E=0.3, 1) with using convergent- divergent channel has been simulated. The study forecasts the steady, 2-D incompressible flow as well as the thermal behavior for cross flow past the cylinder numerically. The following conclusions can be drawn from this research. Increasing in heat transfer with decreasing axis ratio (E). Increasing in heat transfer with using convergent- divergent channel. Heat transfer also, increases with increasing Re. For elliptic cylinder (E=0.3), case 2 is the best location in convergent divergent channel. Pressure drop increases by using convergentdivergent channel and decreased with decreasing peak (s/h) and from the velocity vectors, the vortex arises in convergent- divergent channel and its grow with increasing peak (s/h). 6. NOMENCLATURE 2-D two dimension A the major axis length of the elliptic section m B the minor axis length of the elliptic section m B.C boundary condition B.L boundary layer CFD Computational Fluid Dynamics Cp Local pressure coefficient C.V control volume D circular cylinder diameter m D Length of base of peak M Dh hydraulic diameter m E axis ratio (b/a) H Channel height M H heat transfer coefficient " # $ K Thermal conductivity " #.$ L length of channel m Nu Local Nusselt number &' = ( ) P pressure & # Pe Peclt number Re Reynolds number based on hydraulic diameter +, ( *= - S peak of conv.-dive. Channel m T Temperature K U x component of velocity m/s V y component of velocity m/s http://www.iaeme.com/ijmet/index.asp 987 editor@iaeme.com

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