SIMULATION OF FLOW STRUCTURE AND HEAT TRANSFER ENHANCEMENT IN A TRIANGULAR DUCT WITH RECTANGULAR WING

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1 International Journal of Engineering and Management Research, Vol. 2, Issue-3, JUNE 2012 ISSN No.: Pages: SIMULATION OF FLOW STRUCTURE AND HEAT TRANSFER ENHANCEMENT IN A TRIANGULAR DUCT WITH RECTANGULAR WING Balvinder Budania 1, Harshdeep Shergill 2 1 Student of Master in Technology, RIEIT Ropar. 2 Department of Mechanical Engineering, RIEIT Ropar. 1 balvinderbudania@gmail.com, 2 harshdeep.shergill@gmail.com ABSTRACT The improvement of the performance of heat exchangers with gas as the working fluid becomes particularly important due to the high thermal resistance offered by gases in general. In order to compensate for the poor heat transfer properties of gases, the surface area density of plate heat exchangers can be increased by making use of the secondary fins such as, off -set fins, triangular fins, wavy fins, louvered fins etc. In addition, a promising technique for the enhancement of heat transfer is the use of longitudinal vortex generators. The longitudinal vortices are produced due to the pressure difference generated between the front and back surface of the vortex generator. The longitudinal vortices facilitate the exchange of fluid near the walls with the fluid in the core and hence, the boundary layer is disturbed. It causes the increase in temperature gradient at the surface which leads to the augmentation in heat transfer. An innovative design of triangular shaped secondary fins with rectangular delta wing vortex generator mounted on bottom surface of the channel for enhancing the heat transfer rate in plate-fin heat exchanger is proposed. The computational details have been given for analysis of problem in the FLUENT 6.3 which mainly describes about the solution algorithm and solution schemes as well as the underrelaxation factors required for the present problem. As the solution is converged after certain number of iterations, the values of pressure drop and Nusselt number, Average temperature, friction factor are calculated for different angle of attack and for different locations at β=30o and compared for the same parameter of plain channel without rectangular wing. Keywords Fluent, Heat Exchanger, Rectangular Wing, Reynolds Number. I. INTRODUCTION Heat exchangers are mechanical device which provides the surface area necessary to transfer heat energy from one fluid to another fluid stream. While flowing fluid through the exchanger, the temperature of both fluids may change.as a result of the gradual change in the temperature levels in an exchanger, the temperature difference across the heat transfer barrier vary over the length of the exchanger. There is no external work and heat interaction in heat exchanger. There are varieties of application of heat exchangers like heating and cooling of stream concerned and condensation or evaporation of single or multi component stream concerned. In some other applications the target is to recover and reject heat or sterilize, pasteurize or control a fluid process. Heat augmentation techniques play a vital role for laminar flow, since the heat transfer coefficient is generally low in plain tubes. During recent years, serious attempts have been made to apply different active and passive mechanisms for heat transfer enhancement in compact heat exchangers for the automotive industry, air-conditioning and refrigerant applications, internal cooling for gas turbine blades, electrical circuits in electronic chipsets, etc. Achieving higher heat transfer rates through various augmentation techniques can result in substantial energy savings, more compact and less expensive apparatus with higher thermal efficiency. II. METHODOLOGY STATE OF PROBLEM The geometry of the computational domain is described in the Figure. 1 below which shows the triangular duct with the Rectangular wing type vortex generator. The rectangular wing is join to the bottom surface by welding, brazing etc, techniques known as built in vortex generators. This vortex generator is kept at an angle on the bottom of the duct by the flow attack to 24

2 this at an angle, which is known as angle of attack (β). 2-D view of the geometry is shown in Figure.2. Figure 1: plate fin heat exchanger with rectangular wing votrex generators COMPUTATIONAL DOMAIN Computation is performed on a three-dimensional channel which is formed by two neighboring fins o f a plate fin compact heat exchanger. Obstacles in the form of wing type LVGs are mounted on floor the of this channel to enhance the heat transfer. Figure.3 presents the physical model and relevant parameters of the channel attached with LVGs. The height of the channel is H; the length of the channel (L) equals 8H. As shown in Figure. 1 flow is described in a coordinate system (x, y, z), in which x, y, z are stream wise, normal, and span wise coordinates, respectively. Additionally, y stands for the fin pitch direction. Figure 2: Computational domain in case of built in rectangular wing GOVERNING EQUATIONS AND BOUNDARY CONDITIONS The Reynolds number uses for the study are equal to 200, which makes the flow to be laminar. Air is used as a working fluid and treated as a steady incompressible, laminar and three dimensional flows. The governing equations including continuity, momentum and energy equations can be expressed as follows: Continuity equation: ( ρui ) = 0. xi Momentum equation: (3.1) u j p ( ρ uu i j) = µ. xi xi xi xj (3.2) Energy equation: k u j ( ρut i ) =. xi x i Cp x i (3.3) General transport equation (for scalars): 25

3 ( ρuiφ) φ = Γ φ + S xi xi xi φ (3.4) The general equations 3.1 to 3.4 are used in the CFD computations to calculate the flow field for both thermal and fluid (air) dynamics, solving for heat transfer and pressure drop. These are discretised and solved by the finite volume method. These equations are solved on staggered grid using solvers for Laminar Flow Models. To ensure coupling between velocity and pressure, the SIMPLE or SIMPLEC algorithm is used. Because the governing equation are elliptic in special coordinates the boundary condition are required for all boundaries of the computational domain. The required boundary conditions are described as follows: Boundary Conditions at Inlet: There is direction of the flow at the inlet is axial. Therefore, the components of velocity at inlet are given as: factors for pressure = , momentum = ,. The residuals of continuity equation, components of velocity are 10-5, whereas for the energy it is below 10-7 for convergence of solution. The periodic conditions are imposed at inlet and outlet of flow domain. Mass flow rate and upstream bulk flow are given as input to inlet/outlet periodic boundary condition. Boundary Conditions at no Slip Surfaces: The wall of the channel has no slip surfaces, hence Boundary Condition at the Channel Outlet: The Pressure at the channel outlet is assumed to be atmospheric, hence P outlet =P atm. =0 Boundary Condition at the Extended Surface: The extended surface is also treated as a wall, hence no slip surface Figure 3: Algorithm of numerical approach used by simulation software s V=0 COMPUTATIONAL DETAILS The software FLUENT6.3 is used for the numerical solution of Nervier Strokes and Energy equations. Fluent uses a control volume based technique to convert the governing equations into algebraic equations which can be solved numerically. This involves subdividing the fluid flow region into finite number of control volumes so that equations can be integrated numerically to produce discrete algebraic equations. Segregated steady state solver is used for numerical simulations. The SIMPLE/SIMPLEC algorithm is used for pressure and velocity coupling. A second order up winding scheme is used for space discretisation of momentum, turbulence and energy equations. The under-relaxation III. PRIOR APPROACH In general, a lot of work on heat exchanger is successfully done; still a lot of work has to be done. The work already done on the topic is presented below: Fiebig M, Valencia A, Mitra N. K [1993] employed wing type VGs to investigate its effect on plate fin and tube heat exchanger for staggered and inline configurations The experiments show that the single pair of delta wing behind each tube significantly improves the gas side heat transfer characteristics. For inclined arrangement the heat transfer augmentation is around 55-65% with VGs mounted behind each tube whereas increase in friction factor was around 20% in Re = The corresponding increase for staggered arrangement is lower. Fiebig M, Valencia A, Mitra N.K [1994] determine the local heat transfer in case of plate and tube 26

4 fin heat exchanger in staggered arrangement. The use of vortex generator can enhance the heat transfer for flat tube by a factor of two or more. Similarly pressure loss also increase by a factor of two or more. The flow losses are 50% smaller in case of flat tube and VGs compared to round ones. Overall 2.6 % of the total surface is needed to be modified for the purpose of heat transfer enhancement. J.Y. Jang, M.C. Wu, W.J. Chang [1995] carried out experimental and computational studies on laminar flow heat transfer on plate fin heat exchangers for various different kinds of geometrical parameters having Re = It is found that for staggered arrangement the heat transfer coefficient is 15 % - 27 % higher than that of inline arrangement whereas the pressure drop is 20 % - 27 % higher than that of in-line arrangement. The numbers of tube rows have a small effect on average heat transfer. C.C. Wang, Y.J. Chang [1996] presented their experimental study on 15 different cases of plate fin and tube-fin heat exchanger with different geometrical parameters which include number of tube rows, fin spacing and fin thickness. The results are presented in terms of fanning friction factor f plotted against the Reynolds number. It has been fairly reported that heat transfer is independent of fin spacing while number of tube rows as well as fin thickness has minimal effect on frictional characteristics. The maximum value of colburn factor is said to occur at low Reynolds number value with large number of tube rows and smaller fin spacing. Also a negligible effect of fin spacing is observed on heat transfer at high Reynolds number for plate tube and fin heat exchanger. Lee et al[7] numerically simulated heat transfer characteristics and turbulent structure in a three-dimensional turbulent boundary layer with delta wing type longitudinal vortices. The study found that longitudinal vortices are capable of disturbing the turbulent and thermal boundary layer, which caused anisotropy of turbulent intensity and augmentation of heat transfer. Gentry and Jacobi [8], [9] experimentally studied the heat transfer enhancement performance of delta wings in a flat plate flow by a naphthalene sublimation technique. The results indicated that the average heat and mass transfer could be increased by 50 60% at low Reynolds number conditions in comparison with the original configuration C.C. Wang, K.Y. Chi, Y.J. Chang, Y.P. Chang [1997] conducted the experimental studies on louver fin and tube heat exchangers to know about their frictional and heat transfer characteristics and found that number of tube rows does not affect the friction factor for Re > Heat transfer performance also decreases for Re < 2000 for six rows coils. The fin pitch has negligible effect on heat transfer characteristics for Re >1000 also heat transfer performance decreases with fin pitch for Re < C.C. Wang, K.Y.Chi [1999] display air side performance of fin and tube heat exchanger with plain fin configuration for 18 cases tested experimentally. The effect of number of tube rows, fin pitch, tube diameter on thermal hydraulic characteristics was examined. For number of tube rows N = 1 and N = 2 the heat transfer performance increases with increase in fin pitch whereas for N > 4 and Re = 2000, heat transfer becomes independent of fin pitch. The effect of number of rows on frictional characteristics is very small. The effect of number of tube rows on heat transfer is especially prominent at low Reynolds number value, Wherever the number of tube rows is more and the fin pitch is small, the variation in frictional performance is negligible. The effect of tube diameter on heat transfer is rather small at low fin pitch. Y. Kim & Y. Kim [2004] produced the technical data based upon experimental performance of 22 plate fin and heat exchangers having variation in geometrical parameters like fin pitch, number of tube rows and tube alignment. Heat transfer coefficient decrease as the fin pitch reduces and number of tube rows increases. For the decrease in fin pitch from 15.0 mm to 7.5 mm over the Re = , the heat transfer coefficient reduction is approximately around 10 %. As the number of tube rows increases from 1 to 4, the heat transfer coefficient decreases for the given fixed fin pitches for all rows of tube. It also discusses about the improved heat transfer performance of staggered arrangement compared to inline tube row arrangement by more than 10 %. These trends become more obvious as the frontal air velocity increases as well increases in number of tube rows. Biswas et al. [15] carried out numerical and experimental studies of flow structure and heat transfer effects of longitudinal vortices behind a delta winglet placed in a fully developed laminar channel flow. They found that the delta winglet produce a main vortex, a corner vortex and an induced vortex. A.Lemouedda, M.Breuer, E. Franz, T.Botsch and A.Delgado[2011] conducted a study of delta winglet VGs used to enhance the heat transfer between the energy carrying fluid and the heat transfer surface in plate fin and tube banks. In this study optimal angle of attack of delta winglet are investigated based on the pareto optimal strategy. It is based on CFD analysis. The Delta winglet pair mounted behind each tube is varied between β = 90 and +90. The flow structure and heat transfer behavior is analyzed in detail for certain cases and compared. Finally, for each of these arrangements, the optimal sets of angle of attack for different Reynolds numbers are presented. IV. OUR APPROACH 1. To simulate the fluid flow and heat transfer for flat plate fin heat exchanger 2. To compare the results from simulated case with the experimental results for round plate-fin heat exchanger available from literature 3. To compare the simulated results for different angle of attacks. 27

5 4. To find the optimum angle of attack and locations, at which heat transfer is maximum. The problem is solved using FLUENT 6.3 and results are obtained from the same. The results are presented graphically. The post processing of results are done in the FLUENT itself. the pressure drop through the channel. Figure 5. shows the variation of the pressure Drop along the main flow direction at different angle of attack for Re = 200.The comparison is done in the form of graphs. It is shown from the Figure5. that the pressure drop is maximum when wing is mounted at β = 45 o. A sharp increase in pressure drop is shown along the wing location. V. RESULT AND DISCUSSIONS FLOW STRUCTURE The flow structure for channel with rectangular wing is analyzed with angle of attack 20 o, 30 o and 45. The incoming fluid strikes the rectangular wing and flowing through the both edges of the wing. It creates the secondary vortices in the channel. The development of the secondary velocities is shown in Figure 4 at four cross sections of the channel (x/h = 2.0, 2.3, 2.6and 2.9) for β= 45 o and Re = 200. The velocity vectors shown in Figure 4 are in the yz direction which shows the secondary flow. This secondary flow is also known as the vortex flow of flowing fluid in the channel. The locations x/h = 2.0 is before the wing, x/h= 2.3 and 2.6 are on the wing and x/h=2.9 is after the wing. From the above, it is found that the strength of the vortices increases as the angle of attack increase. For the current study angle of attack are taken as 20 o, 30 o and45. It is found that the strength of the vortices is maximum at β = 45 o for rectangular wing vortex generator. Figure 5: Variation of the pressure Drop along the main flow direction at different angle of attack for Re = 200 Figure 4: Secondary velocity vectors at different locations along the main flow direction for Re = 200. PRESSURE DROP THROUGH THE CHANNEL The pressure drop for the triangular duct with rectangular wing is shown in the Figure 5 and Figure 6. The pumping power is required for flowing the fluid through the channel; this pumping power is proportional to Figure 6: Variation of the pressure Drop along the main flow direction at different locations of Rectangular wing at β= 30 o for Re = 200 HEAT FLUX (Q) FOR BOTTOM WALL OF THE CHANNEL 28

6 The efficiency of the heat exchanger is calculated by Nusselt number. Nusselt number is a dimensionless heat transfer coefficient which gives a measure of the ratio of the heat transfer rate to the rate at which heat would be conducted within the fluid under a temperature gradient ΔT/L. Figure 7: Variation of the heat flux of the Bottom wall at different angle of attack For Re = 200. Figure 9: Variation of Average Nusselt number at different angle of attack Figure 8: variations in the heat flux for different locations at β = 30 o Average Heat fl ux (Q) on the bottom channel walls at different angle of attack and for different locations shown in Figure 7 and 8 for Re = 200. Variation in heat flux in Figure 7, shows that the, there is an increment in the heat flux on the location at which wing is mounted. From the graph, it is clearly shown that the variation is maximum for β = 45 o. As the value of angle of attack increases, the variation in the heat flux also increases due to increase in the strength of the vortices. Figure 8. shows the variations in the local heat flux for different locations at β = 30oby which it is concluded that the variation in heat flux is almost same at different locations. The value of heat flux for the wing placed near the inlet is increases up to 29% in comparison to plain channel without wing. While if wing is placed at a location 77 mm from inlet the increment in heat flux is 29.5% which is not much higher. So for reducing the length of the channel wing must place near inlet of the channel. SPAN WISE AVERAGE NUSSELT NUMBER Figureure10: Variation of Average Nusselt number at o different locations at β=30 To the downstream of the channel, the heat transfer from the isothermal walls decreases continuously due to increase in the temperature of the flowing fluid. Further, it is found that the thermal boundary layer decreases the temperature gradient near the isothermal surfaces and hence, the combined span wise average nusselt number decrease. Along the length X<2.0, the temperature difference between the incoming cold fluid 29

7 and the walls of the channel is high, therefore the combined span wise nusselt number is very high in this region. Since the thermal boundary layer is also thin in this region, the effect of wingis mainly observed downstream of the wing. The wing churns and mixes the fluid near the walls with comparatively colder fluid in the core region. Hence, the temperature gradient near the walls increases and consequently, the combined span wise average Nusselt number also increases. Figure 9 and 10 shows the variation of the combined span wise average nusselt number for different angle of attack and for different locations respectively.the above Figure shows that the variation in combined span wise nusselt is maximum for the channel with wing at β=45 o in comparison to the plain channel without wing. It is clearly shown from the Figure that there is sudden increase and decrease in the combined span wise average nusselt number. This decrease in combined span wise nusselt number is due to wake region generated near the trailing edge of the wing. In this wake region, temperature of the fluid increases which decreases the temperature gradient, therefore there is a decrease in the combined span wise nusselt number is found. It is interesting to note that the value of nusselt number for channel with wing is high in comparison to the plain channel without wing at the exit. The value of combined average span wise nusselt number for channel with wing at β=45 o is increases up to 34% in comparison with plain channel without wing. VI. CONCLUSION The overall performance of the channel with single Rectangular wing type vortex generator mounted at different angle of attack and different locations in the triangular channel is compared with the plain triangular channel without wing. The results are analyzed from the point view of the field synergy principle. In plate fin triangular heat exchanger, the use of the rectangular wing also provide additional heat transfer enhancement on extended surfaces. Increasing the angle of attack of the wing considerably increases both the combined span wise average nusselt number and average temperature of the working fluid. The average local heat flux also increases with increase in the angle of attach of the rectangular wing. It is concluded that the value of combined span wise average nusselt number is increases up to 11.25% for β=20 o, 17.31% for β=30 o and up to 34% for β=45 o in comparison with plain channel without wing. Similarly, the values of the average temperature increases for channel with wing for different angle of attack are 11.1% for β=20 o, 17.6% for β=30 o and 28.96% for β=45 o. The pressure loss and friction factor also increases with increase in angle of attack. Pressure loss increases for β=20 o, β=30 o, and β=45 o are 8.5%, 13.8% and 33% respectively. However, the compactness and the increased heat transfer, strongly compensate the pressure loss penalty. The effect of wing placed at different location is that by placing the wing near the inlet of the channel we can reduced the length of the channel by which cost of the heat exchanger reduced because there is value of combined nusselt number and bulk temperature is more in case of wing mounted near the inlet. Also the pressure loss is increases for the same case. The study in current model is done for using single rectangular wing and from the study it is concluded that the heat transfer characteristics for triangular duct with rectangular wing type vortex generator is maximum for the angle of attack β=45 o and for economical design of the heat exchanger, wing location near the inlet of the channel is best. REFERENCES [1] Achaichia, A., and Cowell, T. W., 1988, Heat Transfer and Pressure Drop Characteristics of Flat Tube and Louvered Plate-Fin Surfaces, Experimental Thermal and Fluid Science, Vol. 1, pp [2] A. Joardar, A.M. Jacobi, [46] Heat transfer enhancement by winglet-type vortex generator arrays in compact plain-fin-and-tube heat exchangers international journal of refrigeration (2007). [3] A.M. Jacobi, R.K. Shah, Heat transfer surface enhancement through the use of longitudinal vortices: a review of recent progress, Experimental Thermal and Fluid Science 11 (1995) [4] A. Sohankar, Heat transfer augmentation in a rectangular channel with a vee-shaped vortex generators, International Journal of Heat and Fluid Flow 28 (2007) [5] Biswas,G. and H. Chattopadhyay, 1992, "Heat Transfer in a Channel with Built-in Wing-Type Vortex Generators," International Journal of Heat and Mass Transfer, Vol. 35, pp [6] Biswas G.,N.K. Mitra, and M. Fiebig, 1989, "Computation of Laminar Mixed Convection Flow: in a Channel with Wing-Type Built-in Obstacles," Journal of Thermophysics, Vol. 3,No.4, [7] Biswas, G., N.K. Mitra, and M. Fiebig, 1994, "Heat Transfer Enhancement in Fin-Tube heat Exchangers by Winglet Vortex Generators," International Journal of Heat and Mass Transfer, Vol. 37, pp [8] Book of Heat and Mass transfer, Rajput. R.k, S.Chand & Sons Publication. [9] Brockmeier, U., M. Fiebig, T. Guntermannand N.K. Mitra, 1989, Heat Transfer Enhancement in Fin-Plate Heat Exchangers by Wing Type Vortex Generators," Chemical Engineering Technology, Vol. 12, pp [10] C.B. Allison, B.B. Dally, [47] effect of a delta-winglet vortex pair on the performance of a tube fin heat exchanger, International Journal of Heat and Mass Transfer (2007). 30

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