# Numerical analysis of a plate-fin cross flow heat exchanger having plane triangular secondary fins and inline arrangement of rectangular wing vortex generator.

Introduction

One of the passive technique to augment the heat transfer characteristics is to employ the streamwise longitudinal vortex generator. The common vortex generators and the associated geometrical definitions are very well explained by Gentry and Jacobi [1]. The vortex generators are known as winglets when their chord is attached to the surface and wings when their trailing edge is fixed on the surface. These obstacles produce different type of secondary flows. The winglets generate single streamwise longitudinal vortices while the wing produce the vortices from both the side edges. The vortex generators are basically the obstacles in the flow which produce the pressure difference between the front surface and the back surface. This pressure difference causes the swirling of the fluid flow from the side edges. This rotating fluid enhances the exchange of fluid between the wall and the core region of the flow field, thereby disrupting the boundary layer. So the overall mixing of fluid takes place and the mean temperature of the fluid increases which causes the heat transfer enhancement. Literature shows that the study of the heat transfer enhancement by using the longitudinal vortex generator is carried out on various types of geometrical configurations. First geometry is the flat plate having wing or winglet type vortex generator as documented by many researchers [2-3]. Second is channel flow with different longitudinal vortex generator. In a channel flow, a favorable pressure gradient always exists which is missing in a flat plate flow. Biswas et al. [4] studied the flow structure and heat transfer in a channel flow with a built-in winglet vortex generator. Experiments are also conducted to verify the results. The results shows upto 65% enhancement in combined spanwise average Nusselt number over the case of a plane channel. Combined spanwise average Nusselt number is the average of local Nusselt number along the periphery and is a quantitative measure of the heat transfer performance. G. Biswas and H. Chattopadhyay [5] predicted the effect of wing type vortex generator in a channel flow. The combined spanwise average Nusselt number increases 34% even at the exit of the channel at an angle of attack of 26[degrees]. A higher heat transfer rate is observed at higher Reynolds number. Tigglebeck et al. [6] experimentally compared the four basic geometries of the longitudinal vortex generators in the Reynolds number range of 2000 to 8000 and angle of attack from 300 to 90[degrees]. The results described the winglets are better than wings and a pair of delta winglets is slightly better than a pair of rectangular winglets at angles more than 300and Reynolds number more than 3000. Hiravennavar et al. [7] investigated the flow structure and average Nusselt number in a rectangular channel using the built in winglet pair. Thickness of the winglet is also considered and is found that the overall heat transfer of the channel is increased up to 12.49% at the thickness and height ratio of 0.2485 as compared to without considering the thickness of the winglet. Many researchers have done numerical / experimental studies on different longitudinal vortex generators in the channel flow as documented in [8-9]. A considerable amount of study is related to the rectangular channel and of fin-tube heat exchangers. Tiwari et al.[10] predicted the heat transfer enhancement in cross flow heat exchangers using oval tubes and various configurations of the winglets pair. In common flow down configurations each extra winglet causes further enhancement of heat transfer. Pesteei et al. [11] conducted experiments to optimize the location of the winglet in fin-tube heat exchanger and observed that the maximum improvement is in the recirculation zone. In the same way variety of research is being done by so many researchers [12-13]. Vasudevan et al. [14] revealed the heat transfer characteristics in plate- fin cross flow heat exchanger having plane triangular secondary fin with single delta winglet as the vortex generator for two different thermal boundary conditions, one constant wall temperature and second constant heat flux. Heat transfer enhancement of 20-25% is achieved at the price of some pressure drop.

Our objective is to analyze the presence of inline arrangement of rectangular wing vortex generator in a plate-fin cross flow heat exchanger with plane triangular secondary fins. Flow structure and the heat transfer characteristics of the geometry are obtained. Additional loss in the static pressure is also determined. The thickness of the wing is not considered.

The numerical analysis model

Figure 1 shows the cross flow heat exchanger along with the triangular inserts and inline arrangement of the rectangular wing. Geometry for the computation without any vortex generator is same as Vasudevan [14]. Both the rectangular wings are identical and size of the wing is shown in figure 2. At all the three angles of attack i.e. 15[degrees], 20[degrees], and 26[degrees], the aspect ratio of both the wings is kept same i.e.0.2679.The trailing edge of the first wing is located at X = 2.77 and of second wing is at X = 4.75. The complete Navier-Stokes equations together with the governing equation of energy have been solved for the laminar flow at Reynolds number 100 and 200. The equations are discretized by the finite difference technique. Staggered grids are employed and the dimensions of the cells are dependent on the angle of attack of the wing and are given by the relation [beta] [DELTA]Y/[DELTA]X. The use of this relation ensures the plane of the wing passes through the U and V velocity nodes of the cell for any angle of attack of the wing. At the entrance of the channel, the axial flow i.e. U velocity is considered and the velocities on all the no-slip planes are zero. The plane of symmetry passes through the V and W velocity points of the staggered grid arrangement and U is symmetric across the plane. At the exit of the channel, the boundary condition given by Orlanski [15] is used. A modified version of Marker and Cell method by Harlow and Welch [16] and Hirt and Cook [17] is used to solve the governing equations. This method is explained by many researchers [4-5].

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Results and discussion Flow visualization

The fluid strikes the front of the wing and passes from both the side edges of the wing to go to the back of the wing. It causes the pressure difference. This pressure difference creates two main longitudinal vortexes, one counter rotating in the right side and the other in clockwise direction in the left side. The figure 3 shows the cross-stream velocity vectors along and after the first wing. The diminishing of velocity vectors is clear in figure. Along the second inline wing, same trends are obtained. The velocity vectors shown in figure 3 are for the wing at an angle of attack of 20[degrees] and Reynolds number 100.

[FIGURE 3 OMITTED]

Bulk temperature

As the cold fluid travels in the exchanger, it takes heat from the hot fluid thus raising the mean temperature along the length. The relation used to compute bulk temperature is [[theta].sub.b](x) = ([SIGMA]U[theta])*/([SIGMA]U). Figure 4 shows the variation of bulk temperature for the wings at 20[degrees] and Reynolds number 100 and 200. The vortex generated along the wing disturbs the boundary layer and mixes the fluid from the core cold region to hot fluid near the walls Thus there is a steep increase in the bulk temperature along both the wing locations. At higher Reynolds number, the velocity of the fluid increases so more fluid passes through the duct in the same interval. This extra fluid decreases the mean temperature. To keep the same bulk temperature at the exit, exchanger length can be reduced by having the vortex generator. To keep the exit bulk temperature 0.85 while the fluid is flowing at Reynolds number 100, the required length of the exchanger without any vortex generator is 7.78492, which is 35.77 % more than the required length of the exchanger having inline rectangular wings at an angle of attack of 26[degrees]. Similarly reduction of 21.51 % and 11.36 % in the length of the channel is possible with having the inline rectangular wings at 20[degrees] and 15[degrees] respectively.

Combined spanwise average Nusselt number

The vortex generator increases the mean temperature of the fluid but decreases the temperature at the surface causing the increases in temperature gradient at the surface. Thereby the Nusselt number also increases at both the locations of the wing. The combined spanwise average Nusselt number for the rectangular wing at an angle of attack of [beta] = 26[degrees] and Reynolds number 100 is 35.38 % higher than that of the plain duct at location X=2.24. Increasing the attack angles also increases the Nusselt number as shown in figure 5.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

At higher Reynolds number mass flow rate increases, so higher [Nu.sub.sa] is achieved as revealed in figure 6.

[FIGURE 6 OMITTED]

Pressure Loss Penalty

The enhancement in the heat transfer is at the cost of pressure drop. To keep the same exit pressure, there is more requirement of pressure at any axial locations while using the vortex generator and it increases with the increase in the angle of attack. The pressure difference for the wing at 20[degrees] is 10.79 % more as compare to the plain duct. To compensate this pressure loss, more pumping power is required. More inertia force is available with higher Reynolds number. It causes the less pressure drop as shown in figure 7. The inline wings at 20[degrees] and Reynolds number 200 has the maximum pressure difference 2.88428 while that of for the Reynolds number 100 is 4.62534, which is 60% more.

[FIGURE 7 OMITTED]

Concluding remarks

Use of the inline arrangement of the rectangular wing strongly enhances the heat transfer. Results shows that by increasing the angle of attack and Reynolds number, heat transfer can be increased substantially. This all is but at the expense of pressure drop so more pumping power is required. The analysis can be extended by making the stamped wing as the stamped wings are easy to manufacture and don't require any joining process. Furthermore thickness of the wing may also be considered.

Appendix

H Characteristic length dimension (Vertical Distance between the plates)

[Nu.sub.sa] Combined average spanwise Nusselt number

P Non-dimensional pressure

Re Reynolds number

T Temperature

Pr Prandtl number

q Heat flux

u,v,w axial, normal and spanwise component of velocity

U,V,W axial, normal and spanwise component of velocity (non-dimensional)

x,y,z axial, normal and span wise coordinates

X,Y,Z axial, normal and span wise coordinates (non-dimensional)

Greek symbols

[beta] Angle of attack of the vortex generators

v Kinematic viscosity of the fluid

[theta] Temperature (non-dimensional)

Subscript

w wall

b bulk condition

References

[1] Gentry, M.C., Jacobi, A.M., 2002. "Heat Transfer Enhancement by Delta Wing-Generated Tip Vortices in Flat Plate and Developing Channel Flows," Journal of Heat Transfer., Transactions of the ASME., 124, pp.-1158-1168.

[2] Turk, A.Y., and Junkhan, G. H., 1986. "Heat Transfer Enhancement Downstream of Vortex Generators on a Flat Plate," Heat Transfer 1986, Proceedings of the Eighth International Heat Transfer Conference., 6, pp. 2903-2908.

[3] Yanagihara, J. I., and Torii, K., 1993, "Heat Transfer Augmentation by Longitudinal Vortices Rows," Proceedings of the Third World Conference on Experimental Heat Transfer, 1., pp. 560-567.

[4] Biswas, G., Torii, K., Fujii, D., Nishino, K. 1996, "Numerical and experimental determination of flow structure and heat transfer effects of longitudinal vortices in a channel flow," International Journal of Heat and Mass Transfer., 39, pp.3441-3451

[5] Biswas, G., Chattopadhyay, H., 1992, "Heat transfer in a channel with built-in wing-type vortex generators," lnt. Journal of Heat Mass Transfer., 35(4), pp. 803-814.

[6] Tigglebeck. St., Mitra, N.K., Fiebig, M., 1994, "Comparison of wing type vortex generators for heat transfer enhancement in channel flows," Journal of heat transfer., 116, pp. 880-885.

[7] Hiravennavar, S.R., Tulapurkara, E.G. and Biswas, G., 2007, "A note on the flow and heat transfer enhancement in a channel with built-in winglet pair," International Journal of Heat and Fluid Flow, 28, pp. 299-305.

[8] Deb, P., Biswas, G. and Mitra, N.K., 1995, "Heat Transfer and flow structure in laminar and turbulent flows in a rectangular channel with longitudinal vortices," International journal of Heat Mass Transfer, 38, pp. 2427-2444.

[9] Yang, J.S., Lee, D.W., Choi, G.M.2008, " Numerical investigation of fluid flow and heat transfer characteristics by common flow up," lnt. Journal of Heat Mass Transfer,51,pp. 6332-6336.

[10] Tiwari, S., Maurya, D., Biswas, G., Eswaran, V., 2003, "Heat transfer enhancement in cross-flow heat exchangers using oval tubes and multiple delta winglets," lnt. Journal of Heat Mass Transfer, 46, pp. 2841-2856.

[11] Pesteei, S.M., Subbarao, P.M.V., R.S. Agarwal., 2005, "Experimental study of the effect of winglet location on heat transfer enhancement and pressure drop in fin-tube heat exchangers," Int J. of Applied Thermal Engineering, 25, pp.1684-1696

[12] Prabhakar, V., Biswas, G., Eswaran, V., 2003, "Numerical prediction of heat transfer in a channel with built in oval tube and various arrangements of the vortex generators," Numerical Heat Transfer, 44, pp. 315-333.

[13] Biswas, G., Mitra, N.K., Fiebig, M., 1994, "Heat transfer enhancement in fin-tube heat exchangers by winglet type vortex generators," J. Heal Mass Transfer, 37(2), pp. 283-291.

[14] Vasudevan, R., Eswaran, V., Biswas, G., 2000, "Winglet-type vortex generators for plate fin heat exchangers using Triangular fins," Numerical Heat Transfer, 58, pp.533-555.

[15] Orlanski, I., 1976, "A Simple Boundary Condition for unbounded Flows," J. Comput. Phys, 21, pp. 251-269.

[16] Harlow, F.H., Welch, J.E., 1965, "Numerical Calculation of Time Dependent Viscous Incompressible Flow of Fluid with Free surface," Phys. Fluids, 8, pp. 2182-2188.

[17] Hirt, C.W., Cook, J.L., 1972, " Calculating Three Dimensional Flows around Structures and over Rough Terrain," J. Comput. Phys, 10, pp. 324-340.

(1) Gulshan Sachdeva, (2) K.S. Kasana and (3) R. Vasudevan

(1,2) Department of Mechanical Engineering, N.I.T. Kurukshetra, India

(3) RCAM Lab, S.M.U. Dallas, U.S.A

(1) E-mail: gulshan4you@gmail.com

(2) E-mail: rvdevan27@gmail.com

(3) E-mail: kasanaks_nitkkr@rediffmail.com