RESULTS AND DISCUSSIONS
2.2 Effect of Number of Vortex Generators
4.3.2 Effect of Reynolds Number
53
Reynolds number, Re
500 600 700 800
Heat transfer coefficient/pressure drop
0.5 1.0 1.5 2.0
2.5
Circular-CFUCircular-CFD Oval-CFU Oval-CFD
Oval-(CFU+CFD) Oval-Staggered
Figure 48-Performance parameter (h/p ratio) for a range of Re numbers at 15º angle of attack with 7VG
54 Figure 49- velocity contours for circular tubes at X=98 mm for 7 vortex generator configuration at a) Re=500 b) Re=700 c) Re=850 at angle of attack of 15º
The Reynolds number has a significant impact on heat transfer distribution. Increasing Reynolds number defines a higher velocity of the fluid as seen by the color contours. The deepest brown color indicates the highest velocity under stated condition which tends more fluid to go to the central tube region and thereby intensifies the mixing.
Temperature Contours at Exit Plane
Figure 50- Temperature contours for oval tubes at Exit plane for 7 VGs at a) Re= 500 b) Re=
700 c) Re= 850 at angle of attack of 15º
It is observed that increasing Reynolds number increases heat transfer coefficient for all the stated cases. Oval tube with 7 vortex generators at Higher Reynolds number shows a higher heat transfer capacity than that of oval tubes at low Reynolds number. Suppose, oval tubes at Re=850 shows a good heat transfer region at the tube portion (the blue color gradually fades away) than that of Re=500 and Re=700.
Figure 51 shows the variation of streamline with Reynolds number. It is seen that increasing Reynolds number increases velocity. Oval tube with Re=850 shows a higher velocity region (indicated by red portion) than that of oval tubes with 700 Reynolds number. Figure 51(c) depicts a lower velocity region. The flow recirculation region appears quite similarly for all the cases.
a.
b.
c.
FLOW
55 c) Streamline Distribution at YZ Plane
Figure 51- Streamline distribution for oval tubes at x=89.5mm for 7 vortex generators at a) Re=850 b) Re= 700 c) Re=500 at angle of attack of 15º
Effect of Reynolds numbers on Variation of Velocity and Temperature Profile (For Oval tube)
a.
b.
c.
Width,Y(m)
0.000 0.005 0.010 0.015 0.020 0.025
Velocity(ms-1 )0 1 2 3 4
Re=500 Re=700 Re=850
FLOW
FLOW
56
Figure 52- Velocity distribution along the midline of YZ plane at a distance X=98mm for oval tubes (AR=1.80) at different Reynolds number and 15ºangle of attack
Figure 53- Temperature distribution along the midline of YZ plane at a distance X=98mm for oval tubes (AR=1.80) at different Reynolds number and 15ºangle of attack
From Figure 2 it is clearly observed that velocity increases with the increment of Reynolds number and the peak velocity is obtained for Re=850. Nearly zero velocity is investigated at the tube surface while it gradually increases towards the wall of the channel.
From Figure 53 it is seen that temperature variation is clearly evident at the tube surface with the change of Reynolds numbers. The highest possible heat transfer is obtained for Re=850 as suggested by the temperature value of approximately 300K near the tube surface.
Figure 54(a) shows the variation of heat transfer coefficient with Reynolds number. It is seen that increasing Reynolds number increases heat transfer coefficient for all the stated cases.
Circular tube with vortex generators shows a higher heat transfer capacity than that of oval tubes but considering the pressure drops from Figure 54(b) the overall performance of oval tube is better than the circular ones. For illustration, oval tubes with 7 vortex generators gives the identical heat transfer to circular tubes of 3 VGs but reduces the pressure drop of approximately 6 Pa at Re=850.
Width,Y(m)
0.000 0.005 0.010 0.015 0.020 0.025
Temperature(k)
295 300 305 310 315
Re=500 Re=700 Re=850
57 Variation of Heat transfer Coefficient and Pressure drop with Reynolds number
Reynolds number, Re
500 600 700 800
H eat transf er coef ficien t, h( W m
-2k
-1)
20 25 30 35 40 45 50
55 Circular Baseline
1VG 3VG7VG
Oval tubes Baseline 1VG3VG
7VG
Reynolds number, Re
500 600 700 800
Pre ssur e dr op , dP (P a)
0 10 20 30 40
50 Circular tube Baseline
1VG3VG 7VG
Oval tubes Baseline 1VG
3VG7VG
Figure 54- Performance parameter (a) heat transfer coefficient and (b) pressure drop variations with Reynolds number for CFU configuration of VG at 15ºangle of attack.
Variation of Heat Transfer Coefficient and Pressure Drop
Figure 55 shows the variation of Pressure drop and heat transfer coefficient with Reynolds number. It is seen that increasing Reynolds number increases pressure drop and heat transfer coefficient for all the stated cases. Circular tube with vortex generators shows a higher heat
(a)
(b)
58 transfer capacity than that of oval tubes at higher Aspect ratios but considering the pressure drops , the overall performance of oval tube at AR=1.8,2.34 is better than the circular ones.
Reynolds number, Re
500 600 700 800
Heat transfer coefficient,h(Wm-2 k-1 ) 25 30 35 40 45 50
55 Circular
Oval(AR=1.24) Oval(AR=1.54) Oval(AR=1.8) Oval(AR=2.34)
Figure 55- Variation of heat transfer coefficient and pressure drop with Reynolds number for different aspect ratios of oval tubes at 15ºangle of attack
Reynolds number, Re
500 600 700 800
Pressure drop,dP(Pa)
10 15 20 25 30 35 40 45
50 Circular
Oval(AR=1.24) Oval(AR=1.54) Oval(AR=1.8) Oval(AR=2.34)
59 At the same time, It is also observed that, oval tubes with AR=1.8 gives h=43 at a pressure drop of nearly 28 Pa (h/p=1.535) while circular tube shows a h/p=1.136 for the same case.
Heat Transfer Coefficient and Pressure Drop for Angle of Attack
As stated earlier, angle of attack has a significant influence on vortices distribution and thereby its impact on heat transfer is so important. It is observed that increasing Reynolds number increases heat transfer coefficient for higher angle of attack for all the stated cases because a large volume of fluid goes through the narrow passage offered by the large angle of attack. Circular tube with angle of attack of 25 degree shows a higher heat transfer capacity than that of oval tubes but considering the pressure drops the overall performance of oval tube is better than the circular ones. Suppose, oval tubes with 15 degree angle of attack gives h=42.5 for pressure drop of 29 Pa (h/p= 1.465) at Re=850. On the other hand, circular tubes with 15 degree angle of attack gives h=50 for pressure drop of 40 Pa (h/p= 1.25) at Re=850.
Reynolds number,Re
500 600 700 800
heat transfer coefficient, h(Wm-2 k-1 )
25 30 35 40 45 50
55 Circular tube(=15o) Circular tube(=25o) Oval(
Oval(=25o)
(a)
60
Reynolds number, Re
500 600 700 800
Pressure drop,dP(Pa)
10 20 30 40 50 60
70 Circular( Circular( Oval( Oval(
Figure 56- Effect of Angle of attack on (a) heat transfer coefficient and (b) pressure drop with Reynolds number for 7VGs.
Variation of Heat Flux per Unit Pressure Drop with Reynolds Number
Reynolds number, Re
500 600 700 800
Q/dP
20 25 30 35 40 45
Circular Oval
(b)
61 Figure 57- Heat flux per unit pressure drop with Reynolds number at 7VGs for 15º angle of
attack
Figure 57 shows the variation of performance parameter (heat flux per unit pressure drop) with Reynolds number. It is investigated that increasing Reynolds number decreases the parameter for both circular and oval tubes. Oval tubes shows a higher value of 40 than that of circular which shows a value near 34.At the same time, considering pressure drop, the performance factor actually decreases with the increment of Reynolds number.
Friction Factor for Different Number of Vortex Generators
As Reynolds number increases, friction factor gradually decreases for all the stated cases.
Higher Reynolds number implies lower viscous force, thereby lower shear stress and hence lower friction factor.
Reynolds number , Re
500 600 700 800
fr ict io n fact or, f
0.04 0.06 0.08 0.10
0.12
Baseline1VG3VGs 7VGs
Figure 58- Friction factor at various Reynolds number for different number of vortex generators at 15ºangle of attack
62 Area goodness Factor for Different Number of Vortex Generators
Reynolds number, Re
500 600 700 800
j/f
0.15 0.20 0.25
1VG3VGs 7VGs
Figure 59- Area goodness factor at various Reynolds number for different number of vortex generators.
The overall performance of the fin-and-tube heat exchangers with different tube arrangements are evaluated using the criterion of the area goodness factor j / f as depicted in Figure 59. For the Reynolds number ranging from 500 to 850, for the case of 1-RWP (Rectangular Winglet Pair), the increment of j/ f ratio is 27% over 7RWP case. The same causes the increment of the j / f ratio 15% over the 3RWP case. It is interesting to note that the influence of the tube arrangement on the overall performance becomes progressively small with the increasing number of the RWPs. From the viewpoint of “area goodness,”
the1RWP and 3 RWP case will require a smaller frontal area than the other cases and would be more efficient in compact heat exchanger design.
63