Extended abstracts of IWEC2019
The 8th International Workshop of Energy Conversion
August 22-26, 2019, Jiangsu, China

Flow and Heat Transfer Characteristics of Viscoelastic Fluid in a Serpentine Channel
K. Tatsumi,*W. Nagasaka, N. Shinotsuka, R. Kuriyama and K. Nakabe
Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan*corresponding author, E-mail: tatsumi@me.kyoto-u.ac.jp

ABSTRACT
Viscoelastic fluid produces normal stresses in a flow which generate secondary and unsteady flows. These flow canenhance the fluid mixing and heat transfer performances compared with Newtonian fluid flow even under low Reynolds
number conditions. In the present study, measurements and numerical computations on the heat transfer and the flow
characteristics of viscoelastic fluid in a serpentine channel were conducted. The channel curvature changes its direction
periodically in the streamwise direction which generates radial forces and vortices at the curve and produces unsteadyflows at the inflection point. I will introduce the measurement results of the heat transfer characteristics of the channel
walls in the streamwise direction for the fluid flow of polyacrylamide and sucrose water solution. The vortex structure
and unsteady behavior of the flow investigated by the particle image velocimetry, streakline visualization, and pressure
loss measurements will also be shown together with some numerical results. From these works, we found several typesof vortices generated in the flow, with typical ones forming a pair of vortices and single vortices rotating in the clockwise
and counter-clockwise directions. These vortices enhanced the heat transfer at the walls in different forms. Because thevortices relied on normal stresses and significantly affected the enhancement of the local Nusselt number, the vortexstructure, and the Nusselt number distributions showed a good correlation with the Weissenberg number.

Viscoelastic fluid is a non-Newtonian fluid that exhibits elastic properties in addition to viscosity. The
elasticity will produce additional normal stresses in the flow, when shear and shear stress are applied to the fluid.
This force changes the main flow structure, generates secondary flows, and increases the flow instability. The
secondary flow and unsteady flow enhance fluid mixing between the channel core region and wall, and increase thewall heat transfer compared with Newtonian fluid for low Reynolds number flows. Therefore, heat transfer can beenhanced if the normal stress can be effectively controlled by efficiently designing the channel geometry andviscoelasticity of the fluid. On this background, heat transfer characteristics of viscoelastic fluid flow under low
Reynolds number conditions have been investigated keenly in the past for Couette flows, parallel-plates, straightchannels, curved channels, and corrugated channels. Among these, the corrugated channels (or serpentine channels)
provide the curve part in which the normal stress differences of the viscoelastic fluid and the hoop-stresses generatestresses to produce secondary flows effectively in the channel. In addition to this, the inflection point of the curvaturechanges the directions of the stress, streamlines, and vortices which can increase the flow instability and change theflow structure to further enhance the fluid mixing and heat transfer [1-6].
In this study, we investigate the flow and heat transfer characteristics of viscoelastic fluid flow in serpentine
channel under low Reynolds number condition [2,4,6]. We show that the heat transfer enhancement can be achievedby a factor of three compared with Newtonian fluids owing to the generation of strong secondary flow and unsteadyflow. The serpentine channel used in this study had a square cross section of 5 mm on side, and consisted ofsemicircle parts connected periodically in the streamwise direction. The inner and outer radii of the semicircle partwere 5 and 10 mm, respectively. The number of periodic curve units N was 30. Local heat transfer measurements
at the top-bottom and sidewalls of the channel were conducted simultaneously with the flow visualization. PIV andpressure loss measurements were also conducted. We also carried out numerical simulation to understand therelationship between the flow and heat transfer characteristics, and the normal stress distribution generating thevortices. An aqueous solution of 500 ppm polyacrylamide (PAM, molecular weight 1.8×107: Polyscience Inc.), 1
wt% NaCl, and sucrose was used as the viscoelastic fluid. The flow Reynolds number investigated was in the rangeof 0.1-8.8, and for the Weissenberg number it was 8-220.
To demonstrate the revealed characteristics and the performance for heat transfer enhancement, several results will
be shown here. Figure 1 shows the average Nusselt number distribution and the friction factor for the sucrose andviscoelastic fluids in relation to the Weissenberg number. Compared with the sucrose solution case (Newtonian fluid),
Nu shows larger value by a factor of three for Wi > 100. Further, a good correlation is obtained between the values andthe Weissenberg number over solutions of different relaxation times.
Figure 2 shows the representative vortices generated in the channel cross-section for Wi~70. Figure 3 shows thelocal Nusselt number distribution in the streamwise direction measured at the top-bottom walls and sidewalls. The Nusselt

20

PAM(64)
PAM(60)PAM(57)
NewtonianNum

15

10

50
10100

WiFig. 1 Average Nusselt number in relation
to Weissenberg number.

Fig. 2 Velocity vectors of the pair of vortices
and the single vortex.

30

Top wallBottom wall
Sucrose (numerical)

25

Nux

20
15
10
50

Nux

20
15
10500152025

30 0x /Lp
30
Outer wall
25
Inner wall
Sucrose(Numerical)
20
1510505 10 15 20 25 30 0x /Lp

551010151520202530 0x /Lp30252015105025 30 0x /Lp

551010151520202530 0x /Lp
30252015105025 30 0x /Lp

Local Nusselt number: Nux

2510Local Nusselt number: Nux

305Local Nusselt number: Nux

051015202530x /Lp

51015202530x /Lp(a) Wi = 729(b) Wi=2945(c) Wi = 5085(d) Wi = 100150
Figure 3 Local Nusselt number distribution in the streamwise direction for the top-bottom walls and sidewalls inrelation to the Weissenberg number.
number varies with channel walls, streamwise locations, and Wi. This was mainly attributed to the structure of the vortices
generated in the cannel. As shown in Fig. 2, the vortices appeared in the forms of a pair of vortices, and single vortex
with clockwise and anti-clockwise rotation. In small Wi conditions, the stress is relatively small and the vortex forms asingle vortex with the rotation direction depending on the position of the main flow (high velocity region) in the crosssection. As the Wi increases, the increase of the stress makes the vortex formation more stable resulting in the generationof the pair of vortices. The single vortex increase the heat transfer at the top and bottom walls, and the pair of vortices
increase the heat transfer at the outer wall of the curved channel as shown in Fig. 2.
The results and discussion on the effects of the normal stresses on the flow instability, the relationship between thelocal heat transfer and vortex structure, and the correlation between the non-dimensional variable of flow and heat transferwill be introduced in my talk.

ACKNOWLEDGMENTS
This work was supported by JSPS KAKENHI Grant Numbers 24360080 and 18H01381.

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microchannel”, Journal of Physics Conference Series, Vol. 318, 092020.
[3] Poole, R.J., et al., 2013, “Viscoelastic secondary flows in serpentine channels”, J. Non-Newtonian Fluid Mech., Vol. 201, 10-.
[4] Tatsumi, K., et al., 2014, “A numerical and experimental study on flow and heat transfer characteristics of viscoelastic fluid ina serpentine channel”, Proc. of the 15th International Heat Transfer Conference IHTC15-9615, 1-.
[5] Li, D.-Y., et al., 2017, “Efficient heat transfer enhancement by elastic turbulence with polymer solution in a curved
microchannel”, Microfluid Nanofluid, 21-.
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