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Studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with right and left helical screw-tape inserts
Experimental Thermal and Fluid Science 32 (2007) 192–197 www.elsevier.com/locate/etfs
Studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with right and left helical screw-tape inserts P. Sivashanmugam *, P.K. Nagarajan Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli 620 015, Tamil Nadu, India Received 28 February 2007; accepted 7 March 2007
Abstract Experimental investigation on heat transfer and friction factor characteristics of circular tube fitted with right-left helical screw inserts of equal length, and unequal length of different twist ratio have been presented. The experimental data obtained were compared with those obtained from plain tube published data. The heat transfer coefficient enhancement for right-left helical screw inserts is higher than that for straight helical twist for a given twist ratio. The effect of right-left helical twist length on heat transfer and friction factor were presented. The empirical relation for Nusselt number, friction relating Reynolds number, twist ratio and right-left distance were formed and found to fit the experimental data within 10% and 20% for Nusselt number and friction factor, respectively. Performance evaluation analysis has been made and the maximum performance ratio of 2.85 and 2.97, respectively were obtained for 300 R and 300 L, and 400 R and 200 L type inserts. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Augmentation; Laminar flow; Right-left helical screw inserts; Twist ratio; Heat transfer
1. Introduction The heat transfer augmentation or intensification is the technique of improving the performance of heat transfer system resulting in reducing the size and cost of the heat exchanger. Heat transfer enhancement technology is being very widely adapted in heat exchanger used for various process applications like refrigeration, automotives, process industry, chemical industry etc. Bergles [1,2] presented a comprehensive survey on heat transfer enhancement by various techniques. Among many techniques investigated for augmentation of heat transfer rates inside circular tubes, tube fitted with full length twisted tape inserts (also
called as swirl flow device) has been shown to be very effective, due to imparting of helical path to the flow. Helical screw-tape swirl flow generators shown in Fig. 1 is a modified form of a twisted tape wound on a single rod gives single way smooth direction of flow like screw motion. In the earlier paper [3] heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with straight helical screw-tape inserts has been reported. The present paper reports the heat transfer and friction factor characteristics of right-left helical screw inserts of equal length, and unequal length of different twist ratio under laminar flow with the water as working fluid.
2. Technical details of helical screw-tape inserts *
Corresponding author. Tel.: +91 431 2501801; fax: +91 431 2500133. E-mail address: [email protected] (P. Sivashanmugam).
0894-1777/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2007.03.005
The geometrical configuration of helical screw-tape inserts is shown in Fig. 1. The helical screw-tape inserts
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197
193
Nomenclature Ai Ao Cp Di Do f fplain ftwist hi k kw L Lt Nu Nuplain Nutwist Q Pr R
inside surface area of test section area, m2 outside surface area of test section area, m2 specific heat at constant pressure, KJ/kg K inside diameter of test section, mm outside diameter of test section, mm friction factor, dimensionless friction factor for plain tube, dimensionless friction factor for twist, dimensionless average convective heat transfer coefficient, W/m2 K thermal conductivity of fluid, W/m K thermal conductivity of the tube wall, W/m K length of the test section, m left twist length, m Nusselt number, dimensionless Nu = hiDi/k Nusselt number for plain tube, dimensionless Nusselt number for twist, dimensionless heat transfer rate, W Prandtl number dimensionless Pr = Cpl/k resistance of the heating element, X (1)
of different twist ratio was made by winding uniformly a strip of 8.5 mm width over a 8 mm rod, and coated with chromium by electroplating to prevent corrosion. The twist ratio ‘Y’ defined as the ratio of length of one full twist (360°) to diameter of the twist is varied from 2.93 to 4.89. The right-left helical inserts were formed by joining 300 mm length of right twist and 300 mm length of left twist alternatively, and joining 400 mm length of right twist and 200 mm length of left twist alternatively as shown in Fig. 1. 3. Experimental set-up and procedure The experimental set-up and procedure for the conduct of experiment is same as that described in earlier paper [3] except that after plain tube run right-left helical twist of equal and unequal length cited above were inserted and experiments were performed. 4. Pressure drop calculation The pressure drop was determined from the differences in the level of manometer fluid. The fully developed friction factor was calculated from the following equation: f ¼ ðDi =LÞðDP =2qu2m Þ
ð1Þ
where DP is the pressure drop over length L. 5. Heat transfer calculation The heat transfer rate in the test section was calculated using [4]
Rt Re Tf Tin Tout Two um Uo V Y
right twist length, m Reynolds number based on internal diameter of the tube, dimensionless average of fluid temperature in the test section, K inlet bulk temperature of fluid, K outlet bulk temperature of fluid, K average wall surface temperature outside test section, K bulk average fluid velocity, m/s over all heat transfer coefficient, W/m2 K voltage output from the Auto-transformer, V twist ratio (length of one full twist (360°) diameter of the twist), dimensionless
Greek symbols q density of fluid, kg/m3 l viscosity of fluid, N s/m2 DP pressure drop of fluid, N/m2
Q ¼ V 2 =R ¼ mC p ðT out T in Þ ¼ U o Ao ðT wo T f Þ
ð2Þ
where 1=ðU o Ao Þ ¼ 1=ðhi Ai Þ þ lnðDo =Di Þ=ð2pk w LÞ
ð3Þ
The internal convective heat transfer coefficient, hi was determined by combining Eqs. (2) and (3). The thermal equilibrium test showed that the heat supplied by electrical winding in the test section was 8– 10% larger than the heat absorbed by the fluid. This was caused by thermal loss from the test section. The average value of heat transfer rate obtained by heat supplied by electrical winding, and heat absorbed by the fluid was taken for internal convective heat transfer coefficient calculation. The Nusselt number was calculated using equation Nu ¼ hi Di =k
ð4Þ
All the fluid thermophysical properties were determined at the average of the inlet and outlet bulk temperatures, Tf. Experimental uncertainty was calculated following Coleman and Steele method [5] and ANSI/ASME standard [6]. The uncertainties associated with the experimental data are calculated on the basis 95% confidence level. The measurement uncertainties used in the method are as follows: bulk fluid temperature and wall temperatures ±0.1 °C, fluid flow rate ±2%, and fluid properties ±2% The uncertainty calculation showed that maximum of ±6%, ±5%, and ±8% for Reynolds number, friction factor and Nusselt number, respectively.
194
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197
Fig. 1. Diagram of right-left helical screw inserts of different twist ratio and equal and unequal length.
6. Results and discussion
10 Plain tube Y=2.93 RL
6.1. Plain tube data
Y=2.93 St.helical
6.2. Effect of twist ratio on heat transfer augmentation Fig. 2 presents variation of Nusselt number with Reynolds number for right-left helical twist with 300 R and 300 L of different twist ratio. Nusselt number for the tube fitted with right-left helical twist is higher than that for plain tube for a given Reynolds number attributing to heat transfer enhancement due to swirl flow. As Reynolds number increases the Nusselt number increases due to increased convection. Also as the twist ratio decreases the Nusselt number increases for a given Reynolds number and reaching a maximum for the twist ratio of 2.89 due to fact that as the twist ratio decrease, the intensity of swirl generated increases with the maximum intensity for the twist ratio 2.89. It is also observed that the Nusselt number for
Friction factor (f)
The data obtained by the experiment for plain tube were compared [3] with Seider and Tate data [7] and the discrepancy was found to be ±11%.
Y=3.91 RL
1
Y=3.91 St.helical Y= 4.89 RL Y=4.89 St.helical 0.1
0.01
0.001 100
1000
10000
Reynolds number (Re) Fig. 2. Friction factor vs Reynolds number for right-left helical insert with 300 R and 300 L and straight helical insert under laminarflow.
right-left twist is more than that for straight helical twist for a given twist ratio. This may be due to reason that
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197
6.3. Effect of twist ratio on friction factor Fig. 3. shows the variation of friction factor vs Reynolds number for the tube fitted with right-left helical twist with 300 R and 300 L. The friction factor for the tube fitted with right-left helical inserts 300 R and 300 L is higher than that for plain tube and decreases with Reynolds number for a given twist ratio. However the friction factor increases with twist ratio for a given Reynolds number and reaching maximum for the twist ratio 2.89. It is also observed from Fig. 3 that the friction factor for right-left twist is more than that for straight twist for a given twist ratio resulting from repeated right-left movement of fluid during course of flow through tube attached with right-left twist.
6.4. Effect of right-left helical twist length on heat transfer augmentation Fig. 4 presents the variation of Nusselt number with Reynolds number for right-left helical twist with 400 R and 200 L of different twist ratio. Nusselt number for tube fitted with right-left helical twist 400 R and 200 L is higher than that for plain tube for a given Reynolds number but lower than that for right-left helical twist with 300 R and 300 L. This is due to fact that the intensity of swirl generated for 300 R and 300 L twist set due to clockwise and anti-clockwise rotation is more than that for 400 R and 200 L twist set. The similar trend was observed for other twist ratio. Fig. 4 also indicate that the Nusselt number for right-left twist is more than that for straight twist for
100
Nusselt number (Nu)
repeated left-right movement of fluid during course of flow through tube attached with left-right twist will enhance the heat transfer by virtue of efficient mixing in the radial direction.
195
10
plain tube Y=2.93 RL Y= 2.93 St.helical Y= 3.91 RL Y=3.91 St.helical Y=4.89 RL Y= 4.89 St.helical
1 100
1000
10000
Reynolds number (Re)
Fig. 4. Nusselt number vs Reynolds number for right-left helical insert with 400 R and 200 L and straight helical insert under laminar flow.
a given twist ratio indicating left-right movement induced by this insert improve the heat transfer rate. 6.5. Effect of right-left helical twist length on friction factor The variation of friction factor vs Reynolds number for the tube fitted with right-left helical twist with 400 R and 200 L is presented in Fig. 5. The friction factor for the tube fitted with right-left helical inserts with 400 R and 200 L is higher than that for the plain tube but lower than that for right-left helical twist with 300 R and 300 L. This is due to fact that the intensity of swirl generated for 300 R and 300 L twist set due to clockwise and anti-clockwise rotation is more than that for 400 R and 200 L twist set. The similar trend was observed for other twist ratio. For this type of twist insert, the friction factor for right-left twist is more than that for straight twist for a given twist ratio resulting from repeated right-left movement of fluid during course of 10
10 Plain tube Y=2.93 RL Y=2.93 St.helical Y=3.91 St.helical Y= 4.89 RL Y=4.89 St. helical 0.1
Friction factor (f)
Friction factor (f)
1
Y=3.91 RL
1
0.1
Plain tube Y=2.91 RL Y=2.91 St.helic al Y=3.91 RL
0.01
0.01
Y=3.91 St.helic al Y=4.89 RL Y=4.89 St. helic al
0.001 100
1000
10000
Reynolds number (Re) Fig. 3. Friction factor vs Reynolds number for right-left helical insert with 300 R and 300 L and straight helical insert under laminar flow.
0.001 100
1000
10000
Reynolds number (Re) Fig. 5. Frictionfactor vs Reynolds number for right-left helical insert with 400 R and 200 L and straight helical insert under laminar flow.
196
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197
flow through tube attached with left-right twist as observed from Fig. 5. The experimental data were fitted by the following empirical equations
f ¼ 739:2ðReÞ
0:608
1:013
ðPrÞðY Þ
ðY Þ
0:386
0:634
0:118
ðRt =Lt Þ
ðRt =Lt Þ
0:234
ð5Þ ð6Þ
The Eqs. (5) and (6) are fitting the experimental data within 10% and 20% for Nusselt number and friction factor, respectively.
ðNutwist =Nuplain Þ ðftwist =fplain Þ
where Nutwist is the Nusselt number for flow in a tube fitted with helical twist insert, Nuplain is plain tube Nusselt number, ftwist is the friction factor for flow in a tube fitted with helical twist insert and fplain is the friction factor for flow in plain tube. Performance evaluation analysis has bee made based on the Eq. (7) to asses the benefits of using left-right inserts. Figs. 6 and 7 presents performance evaluation analysis results for 300 R and 300 L, 400 R and 200 L type inserts, respectively. From Fig. 6 one can observe that for a given Reynolds number the performance ratio is increases with decreasing twist ratio attributing swirl flow generated by helical twist primarily responsible for enhanced performance ratio with the maximum of 2.85 for the twist ratio 2.93. As Reynolds number increases the performance ratio decreases similar to the trend followed in friction factor vs Reynolds number. Fig. 7 indicates that the performance ratio has the maximum value of 2.97 for the twist ratio 3
Performance ratio
2.5
2
1.5
Twist ratio 2.93 Twist ratio 3.91
0 100
1.5 Twist ratio 4.89 1
0 100
ð7Þ
0:1666
Twist ratio 4.89
0.5
2
Twist ratio 3.91
0.5
Performance ratio for constant pumping is defined [8] as
1
2.5
Twist ratio 2.93
6.6. Performance evaluation analysis
Performance ratio ¼
3
Performance ratio
Nu ¼ 0:196ðReÞ
3.5
1000
10000
1000
10000
Reynolds number (Re)
Fig. 7. Performance analysis for right-left helical insert with 400 R and 200 L under laminar flow.
2.93, whereas it has almost similar values for the twist ratio 3.91 and 4.89 for the range of Reynolds number studied indicating the performance of twist of the right-left with twist ratio 3.91 is quite comparable with that of 4.89 for all values of Reynolds number. 7. Conclusions
(i) Experimental investigation of heat transfer and friction factor characteristics of circular tube fitted with right-left helical screw inserts of equal length, and unequal length of different twist ratio have been presented. (ii) The heat transfer coefficient enhancement for rightleft helical screw inserts is higher than that for straight helical twist for a given twist ratio. (iii) The effect of right-left length on heat transfer and friction factor were presented and found that heat transfer enhancement for 300 R and 300 L twist set is higher than that for 400 R and 200 L for all twist ratio. (iv) The empirical correlation for Nusselt number, and friction factor relating Reynolds number, twist ratio and right-left twist distance were formed and found to fit the experimental data within 10% and 20% for Nusselt number and friction factor, respectively. (v) Performance evaluation analysis has been made and the maximum performance ratio of 2.85 and 2.97, respectively were obtained for 300 R and 300 L, and 400 R and 200 L type inserts. References
Reynolds number (Re)
Fig. 6. Performance analysis for right-left helical insert with 300 R and 300 L under laminar flow.
[1] A.E. Bergles, Techniques to augment heat transfer, in: W.M. Rohsenow, J.P. Hartnett, E. Ganie (Eds.), Handbook of Heat Transfer Application, McGraw-Hill, New York, 1985.
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197 [2] A.E. Bergles, Some perspectives on enhanced heat transfer, secondgeneration heat transfer technology, ASME Journal of Heat Transfer 110 (11) (1988) 1082–1096. [3] P. Sivashanmugam, S. Suresh, Experimental studies on heat transfer and friction factor characteristics in laminar flow through a circular tube fitted with helical screw-tape inserts, Journal of Applied Thermal Engineering 26 (2006) 1990–1997. [4] Q. Liau, M.D. Xin, Augmentation of convective heat transfer inside tubes with three-dimensional internal extended surfaces and twisted tape inserts, Chemical Engineering Journal 78 (2000) 95–105.
197
[5] H.W. Coleman, W.G. Steele, Experimental and Uncertainty Analysis for Engineers, Wiley, New York, 1989. [6] ANSI/ASME, Measurement uncertainty, PTC 19,1 – 1985, 1986. [7] E.N. Sieder, G.E. Tate, Industrial and Engineering Chemistry 28 (1936) 1429. [8] H. Usui, Y. Sano, K. Iwashita, A. Isozaki, Enhancement of heat transfer by a combination of internally grooved rough tube and twisted tape, International Chemical Engineering 26 (1) (1996) 97– 104.
Studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with right and left helical screw-tape inserts P. Sivashanmugam *, P.K. Nagarajan Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli 620 015, Tamil Nadu, India Received 28 February 2007; accepted 7 March 2007
Abstract Experimental investigation on heat transfer and friction factor characteristics of circular tube fitted with right-left helical screw inserts of equal length, and unequal length of different twist ratio have been presented. The experimental data obtained were compared with those obtained from plain tube published data. The heat transfer coefficient enhancement for right-left helical screw inserts is higher than that for straight helical twist for a given twist ratio. The effect of right-left helical twist length on heat transfer and friction factor were presented. The empirical relation for Nusselt number, friction relating Reynolds number, twist ratio and right-left distance were formed and found to fit the experimental data within 10% and 20% for Nusselt number and friction factor, respectively. Performance evaluation analysis has been made and the maximum performance ratio of 2.85 and 2.97, respectively were obtained for 300 R and 300 L, and 400 R and 200 L type inserts. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Augmentation; Laminar flow; Right-left helical screw inserts; Twist ratio; Heat transfer
1. Introduction The heat transfer augmentation or intensification is the technique of improving the performance of heat transfer system resulting in reducing the size and cost of the heat exchanger. Heat transfer enhancement technology is being very widely adapted in heat exchanger used for various process applications like refrigeration, automotives, process industry, chemical industry etc. Bergles [1,2] presented a comprehensive survey on heat transfer enhancement by various techniques. Among many techniques investigated for augmentation of heat transfer rates inside circular tubes, tube fitted with full length twisted tape inserts (also
called as swirl flow device) has been shown to be very effective, due to imparting of helical path to the flow. Helical screw-tape swirl flow generators shown in Fig. 1 is a modified form of a twisted tape wound on a single rod gives single way smooth direction of flow like screw motion. In the earlier paper [3] heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with straight helical screw-tape inserts has been reported. The present paper reports the heat transfer and friction factor characteristics of right-left helical screw inserts of equal length, and unequal length of different twist ratio under laminar flow with the water as working fluid.
2. Technical details of helical screw-tape inserts *
Corresponding author. Tel.: +91 431 2501801; fax: +91 431 2500133. E-mail address: [email protected] (P. Sivashanmugam).
0894-1777/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2007.03.005
The geometrical configuration of helical screw-tape inserts is shown in Fig. 1. The helical screw-tape inserts
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197
193
Nomenclature Ai Ao Cp Di Do f fplain ftwist hi k kw L Lt Nu Nuplain Nutwist Q Pr R
inside surface area of test section area, m2 outside surface area of test section area, m2 specific heat at constant pressure, KJ/kg K inside diameter of test section, mm outside diameter of test section, mm friction factor, dimensionless friction factor for plain tube, dimensionless friction factor for twist, dimensionless average convective heat transfer coefficient, W/m2 K thermal conductivity of fluid, W/m K thermal conductivity of the tube wall, W/m K length of the test section, m left twist length, m Nusselt number, dimensionless Nu = hiDi/k Nusselt number for plain tube, dimensionless Nusselt number for twist, dimensionless heat transfer rate, W Prandtl number dimensionless Pr = Cpl/k resistance of the heating element, X (1)
of different twist ratio was made by winding uniformly a strip of 8.5 mm width over a 8 mm rod, and coated with chromium by electroplating to prevent corrosion. The twist ratio ‘Y’ defined as the ratio of length of one full twist (360°) to diameter of the twist is varied from 2.93 to 4.89. The right-left helical inserts were formed by joining 300 mm length of right twist and 300 mm length of left twist alternatively, and joining 400 mm length of right twist and 200 mm length of left twist alternatively as shown in Fig. 1. 3. Experimental set-up and procedure The experimental set-up and procedure for the conduct of experiment is same as that described in earlier paper [3] except that after plain tube run right-left helical twist of equal and unequal length cited above were inserted and experiments were performed. 4. Pressure drop calculation The pressure drop was determined from the differences in the level of manometer fluid. The fully developed friction factor was calculated from the following equation: f ¼ ðDi =LÞðDP =2qu2m Þ
ð1Þ
where DP is the pressure drop over length L. 5. Heat transfer calculation The heat transfer rate in the test section was calculated using [4]
Rt Re Tf Tin Tout Two um Uo V Y
right twist length, m Reynolds number based on internal diameter of the tube, dimensionless average of fluid temperature in the test section, K inlet bulk temperature of fluid, K outlet bulk temperature of fluid, K average wall surface temperature outside test section, K bulk average fluid velocity, m/s over all heat transfer coefficient, W/m2 K voltage output from the Auto-transformer, V twist ratio (length of one full twist (360°) diameter of the twist), dimensionless
Greek symbols q density of fluid, kg/m3 l viscosity of fluid, N s/m2 DP pressure drop of fluid, N/m2
Q ¼ V 2 =R ¼ mC p ðT out T in Þ ¼ U o Ao ðT wo T f Þ
ð2Þ
where 1=ðU o Ao Þ ¼ 1=ðhi Ai Þ þ lnðDo =Di Þ=ð2pk w LÞ
ð3Þ
The internal convective heat transfer coefficient, hi was determined by combining Eqs. (2) and (3). The thermal equilibrium test showed that the heat supplied by electrical winding in the test section was 8– 10% larger than the heat absorbed by the fluid. This was caused by thermal loss from the test section. The average value of heat transfer rate obtained by heat supplied by electrical winding, and heat absorbed by the fluid was taken for internal convective heat transfer coefficient calculation. The Nusselt number was calculated using equation Nu ¼ hi Di =k
ð4Þ
All the fluid thermophysical properties were determined at the average of the inlet and outlet bulk temperatures, Tf. Experimental uncertainty was calculated following Coleman and Steele method [5] and ANSI/ASME standard [6]. The uncertainties associated with the experimental data are calculated on the basis 95% confidence level. The measurement uncertainties used in the method are as follows: bulk fluid temperature and wall temperatures ±0.1 °C, fluid flow rate ±2%, and fluid properties ±2% The uncertainty calculation showed that maximum of ±6%, ±5%, and ±8% for Reynolds number, friction factor and Nusselt number, respectively.
194
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197
Fig. 1. Diagram of right-left helical screw inserts of different twist ratio and equal and unequal length.
6. Results and discussion
10 Plain tube Y=2.93 RL
6.1. Plain tube data
Y=2.93 St.helical
6.2. Effect of twist ratio on heat transfer augmentation Fig. 2 presents variation of Nusselt number with Reynolds number for right-left helical twist with 300 R and 300 L of different twist ratio. Nusselt number for the tube fitted with right-left helical twist is higher than that for plain tube for a given Reynolds number attributing to heat transfer enhancement due to swirl flow. As Reynolds number increases the Nusselt number increases due to increased convection. Also as the twist ratio decreases the Nusselt number increases for a given Reynolds number and reaching a maximum for the twist ratio of 2.89 due to fact that as the twist ratio decrease, the intensity of swirl generated increases with the maximum intensity for the twist ratio 2.89. It is also observed that the Nusselt number for
Friction factor (f)
The data obtained by the experiment for plain tube were compared [3] with Seider and Tate data [7] and the discrepancy was found to be ±11%.
Y=3.91 RL
1
Y=3.91 St.helical Y= 4.89 RL Y=4.89 St.helical 0.1
0.01
0.001 100
1000
10000
Reynolds number (Re) Fig. 2. Friction factor vs Reynolds number for right-left helical insert with 300 R and 300 L and straight helical insert under laminarflow.
right-left twist is more than that for straight helical twist for a given twist ratio. This may be due to reason that
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197
6.3. Effect of twist ratio on friction factor Fig. 3. shows the variation of friction factor vs Reynolds number for the tube fitted with right-left helical twist with 300 R and 300 L. The friction factor for the tube fitted with right-left helical inserts 300 R and 300 L is higher than that for plain tube and decreases with Reynolds number for a given twist ratio. However the friction factor increases with twist ratio for a given Reynolds number and reaching maximum for the twist ratio 2.89. It is also observed from Fig. 3 that the friction factor for right-left twist is more than that for straight twist for a given twist ratio resulting from repeated right-left movement of fluid during course of flow through tube attached with right-left twist.
6.4. Effect of right-left helical twist length on heat transfer augmentation Fig. 4 presents the variation of Nusselt number with Reynolds number for right-left helical twist with 400 R and 200 L of different twist ratio. Nusselt number for tube fitted with right-left helical twist 400 R and 200 L is higher than that for plain tube for a given Reynolds number but lower than that for right-left helical twist with 300 R and 300 L. This is due to fact that the intensity of swirl generated for 300 R and 300 L twist set due to clockwise and anti-clockwise rotation is more than that for 400 R and 200 L twist set. The similar trend was observed for other twist ratio. Fig. 4 also indicate that the Nusselt number for right-left twist is more than that for straight twist for
100
Nusselt number (Nu)
repeated left-right movement of fluid during course of flow through tube attached with left-right twist will enhance the heat transfer by virtue of efficient mixing in the radial direction.
195
10
plain tube Y=2.93 RL Y= 2.93 St.helical Y= 3.91 RL Y=3.91 St.helical Y=4.89 RL Y= 4.89 St.helical
1 100
1000
10000
Reynolds number (Re)
Fig. 4. Nusselt number vs Reynolds number for right-left helical insert with 400 R and 200 L and straight helical insert under laminar flow.
a given twist ratio indicating left-right movement induced by this insert improve the heat transfer rate. 6.5. Effect of right-left helical twist length on friction factor The variation of friction factor vs Reynolds number for the tube fitted with right-left helical twist with 400 R and 200 L is presented in Fig. 5. The friction factor for the tube fitted with right-left helical inserts with 400 R and 200 L is higher than that for the plain tube but lower than that for right-left helical twist with 300 R and 300 L. This is due to fact that the intensity of swirl generated for 300 R and 300 L twist set due to clockwise and anti-clockwise rotation is more than that for 400 R and 200 L twist set. The similar trend was observed for other twist ratio. For this type of twist insert, the friction factor for right-left twist is more than that for straight twist for a given twist ratio resulting from repeated right-left movement of fluid during course of 10
10 Plain tube Y=2.93 RL Y=2.93 St.helical Y=3.91 St.helical Y= 4.89 RL Y=4.89 St. helical 0.1
Friction factor (f)
Friction factor (f)
1
Y=3.91 RL
1
0.1
Plain tube Y=2.91 RL Y=2.91 St.helic al Y=3.91 RL
0.01
0.01
Y=3.91 St.helic al Y=4.89 RL Y=4.89 St. helic al
0.001 100
1000
10000
Reynolds number (Re) Fig. 3. Friction factor vs Reynolds number for right-left helical insert with 300 R and 300 L and straight helical insert under laminar flow.
0.001 100
1000
10000
Reynolds number (Re) Fig. 5. Frictionfactor vs Reynolds number for right-left helical insert with 400 R and 200 L and straight helical insert under laminar flow.
196
P. Sivashanmugam, P.K. Nagarajan / Experimental Thermal and Fluid Science 32 (2007) 192–197
flow through tube attached with left-right twist as observed from Fig. 5. The experimental data were fitted by the following empirical equations
f ¼ 739:2ðReÞ
0:608
1:013
ðPrÞðY Þ
ðY Þ
0:386
0:634
0:118
ðRt =Lt Þ
ðRt =Lt Þ
0:234
ð5Þ ð6Þ
The Eqs. (5) and (6) are fitting the experimental data within 10% and 20% for Nusselt number and friction factor, respectively.
ðNutwist =Nuplain Þ ðftwist =fplain Þ
where Nutwist is the Nusselt number for flow in a tube fitted with helical twist insert, Nuplain is plain tube Nusselt number, ftwist is the friction factor for flow in a tube fitted with helical twist insert and fplain is the friction factor for flow in plain tube. Performance evaluation analysis has bee made based on the Eq. (7) to asses the benefits of using left-right inserts. Figs. 6 and 7 presents performance evaluation analysis results for 300 R and 300 L, 400 R and 200 L type inserts, respectively. From Fig. 6 one can observe that for a given Reynolds number the performance ratio is increases with decreasing twist ratio attributing swirl flow generated by helical twist primarily responsible for enhanced performance ratio with the maximum of 2.85 for the twist ratio 2.93. As Reynolds number increases the performance ratio decreases similar to the trend followed in friction factor vs Reynolds number. Fig. 7 indicates that the performance ratio has the maximum value of 2.97 for the twist ratio 3
Performance ratio
2.5
2
1.5
Twist ratio 2.93 Twist ratio 3.91
0 100
1.5 Twist ratio 4.89 1
0 100
ð7Þ
0:1666
Twist ratio 4.89
0.5
2
Twist ratio 3.91
0.5
Performance ratio for constant pumping is defined [8] as
1
2.5
Twist ratio 2.93
6.6. Performance evaluation analysis
Performance ratio ¼
3
Performance ratio
Nu ¼ 0:196ðReÞ
3.5
1000
10000
1000
10000
Reynolds number (Re)
Fig. 7. Performance analysis for right-left helical insert with 400 R and 200 L under laminar flow.
2.93, whereas it has almost similar values for the twist ratio 3.91 and 4.89 for the range of Reynolds number studied indicating the performance of twist of the right-left with twist ratio 3.91 is quite comparable with that of 4.89 for all values of Reynolds number. 7. Conclusions
(i) Experimental investigation of heat transfer and friction factor characteristics of circular tube fitted with right-left helical screw inserts of equal length, and unequal length of different twist ratio have been presented. (ii) The heat transfer coefficient enhancement for rightleft helical screw inserts is higher than that for straight helical twist for a given twist ratio. (iii) The effect of right-left length on heat transfer and friction factor were presented and found that heat transfer enhancement for 300 R and 300 L twist set is higher than that for 400 R and 200 L for all twist ratio. (iv) The empirical correlation for Nusselt number, and friction factor relating Reynolds number, twist ratio and right-left twist distance were formed and found to fit the experimental data within 10% and 20% for Nusselt number and friction factor, respectively. (v) Performance evaluation analysis has been made and the maximum performance ratio of 2.85 and 2.97, respectively were obtained for 300 R and 300 L, and 400 R and 200 L type inserts. References
Reynolds number (Re)
Fig. 6. Performance analysis for right-left helical insert with 300 R and 300 L under laminar flow.
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