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Numerical simulation of heat transfer enhancement by elastic turbulence in a curvy channel

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Abstract

Although many investigations on elastic turbulence have been conducted in recent years, two major research topics still call for in-depth mechanistic investigations. Specifically, one is heat transfer performance affected by elastic turbulence; the other is so-called high Weissenberg number problem (HWNP) in numerical simulation of viscoelastic fluid flow. Taking these two topics into account simultaneously, the coupled problem becomes heat transfer characteristic of viscoelastic fluid in elastic turbulence at high Weissenberg number (Wi) and very low Reynolds number (Re). In this work, we implement numerical simulations by embedding log-conformation reformulation algorithm into the open-source software OpenFOAM. The heat transfer process of viscoelastic fluid flow in a three-dimensional (3D) curvy channel is simulated over a wide range of Wi. For the first time, significant heat transfer enhancement induced by elastic turbulence in a curvy channel at high Wi was identified numerically. When Wi is above the critical value of O(1), the heat transfer performance is found to be dramatically improved by elastic turbulence and then approaches a saturation. From the transient analysis of flow motions in the axial and cross sections, it can be seen that the flow twists and wiggles in the curvy channel and the field synergy effect of viscoelastic fluid flow becomes more intensive than that of Newtonian fluid flow. These effects give rise to the extremely irregular flow motions in the cross section and consequently lead to heat transfer enhancement.

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Abbreviations

A m :

Area of cross section

A w :

Area of heated wall

B :

Extensional component of velocity gradient

C :

Conformation tensor

c :

Specific heat

D h :

Hydraulic diameter

Fc :

Field synergy number

Gz :

Graetz number

h :

Convective heat transfer coefficient

I :

Unit matrix

k :

Thermal conductivity

L :

Equivalent length of microchannel

\(\dot{m}\) :

Mass flow rate

N :

Anti-symmetric matrix

Nu :

Nusselt number

Pr :

Prandtl number

Po:

Poiseuille number

p :

Pressure

Δp :

Pressure drop of flow

R i :

Inner ring radii of channel

R o :

Outer ring radii of channel

Re :

Reynold number

T :

Temperature

t :

Time

Wi :

Weissenberg number

U m :

Mean velocity in streamwise

U :

Velocity in streamwise

V :

Velocity in vertical direction

W :

Velocity in spanwise

β :

Ratio of solvent viscosity and total viscosity

γ :

Shear rate

Δ :

Difference

η :

Dynamic viscosity

λ :

Relaxation time

Ω :

Anti-symmetric matrixes

ρ :

Destiny

τ :

Stress tensor

υ :

Kinematic viscosity

∇:

Contravariant convected time derivative

+:

Dimensionless parameters

f :

Fluid

p :

Polymer

s :

Solvent

w :

Wall of channel

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Acknowledgements

The authors thank the National Natural Science Foundation of China (51506037, 51606054), Foundation for Innovative Research Groups of the National Natural Science Foundation of China (51421063), the Fundamental Research Funds for the Central Universities (HIT.NSRIF.201667). Zhang also thanks the financial support of China Postdoctoral Science Foundation (2013M541374), Heilongjiang Province Postdoctoral Foundation (LBH-Z15063) and China Postdoctoral International Exchange Program.

Author information

Authors and Affiliations

  1. School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China

    Dong-Yang Li, Hongna Zhang, Jian-Ping Cheng, Xiao-Bin Li & Feng-Chen Li

  2. Institute of Micro/Nanotechnology, Old Dominion University, Norfolk, VA, 23529, USA

    Shizhi Qian

  3. School of Mechanical Engineering, Yeungnam University, Gyeongsan, 712-719, South Korea

    Sang Woo Joo

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  1. Dong-Yang Li
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Correspondence to Hongna Zhang or Xiao-Bin Li.

Additional information

This article is part of the topical collection “2016 International Conference of Microfluidics, Nanofluidics and Lab-on-a-Chip, Dalian, China” guest edited by Chun Yang, Carolyn Ren and Xiangchun Xuan.

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Supplementary material 1 (TXT 0 kb)

Animation 1

Temporal evolution of velocity field in transverse section (x–y plane) at Wi=20 (AVI 11426 kb)

Animation 2

Temporal evolution of velocity field in cross section (y–z plane) of position II at Wi=20 (AVI 9046 kb)

Animation 3

Temporal evolution of temperature distribution in transverse section (x–y plane) at Wi=20 (AVI 10978 kb)

Animation 4

Temporal evolution of velocity and temperature distributions in cross section (y–z plane)of position III at Wi=20 (AVI 34936 kb)

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Li, DY., Zhang, H., Cheng, JP. et al. Numerical simulation of heat transfer enhancement by elastic turbulence in a curvy channel. Microfluid Nanofluid 21, 25 (2017). https://doi.org/10.1007/s10404-017-1859-x

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