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Morphological evolution and spreading flow of hollow oil droplet impact on a heated wall

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Abstract

A coupled level set and volume–of–fraction method is applied to investigate hollow oil droplet impacts on heated walls. Results show that given the increase in impact velocity, three evolutionary processes of spreading, transition, and central jet occur after the hollow oil droplet impact on a heated wall. The variation in the spreading length of hollow oil droplets is similar in different evolutionary processes, but the variation in the center height of hollow oil droplets is relatively different. The wall heat flux and the position of the maximum heat flux increase with impact velocity. In addition, the wall temperature influences the flow and heat transfer characteristics of the hollow oil droplet impingement. Considering the viscosity–temperature characteristics of the lubricating oil, the spreading length of the hollow oil droplet increases with the wall temperature, but the central height of the hollow oil droplet is unaffected by the wall surface temperature. The wall heat flux and the position of the maximum heat flux also increase with the impact velocity. Pressure and velocity distribution indicate that the bubble rupture at the central jet originates from the combined effect of inertial force and surface tension. The results of this study provide a basis for an improved understanding of the flow and heat transfer characteristics of hollow oil droplet impact on a heated wall and serve as a theoretical reference for investigating the effect of bubbles on oil–gas lubrication processes.

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Abbreviations

A :

Constant related to lubricant oil

B :

Constant related to lubricant oil

D :

Hollow oil droplet diameter, \(\upmu \)m

\(D_{\mathrm{b}}\) :

Bubble diameter, \(\upmu \)m

\(D_{\mathrm{h}}\) :

Central height, \(\upmu \)m

\(D_{\mathrm{s}}\) :

Spreading diameter, \(\upmu \)m

\({{\varvec{F}}}\) :

Surface tension, N \({\mathrm{m}}^{-1}\)

f :

Spreading factor

\({{\varvec{g}}}\) :

Gravity, \({\mathrm{m}}\,{\mathrm{s}}^{-2}\)

H:

Heaviside function

h :

Central height factor

L:

Height of central jet, mm

\({{\varvec{n}}}\) :

Normal vector

P :

Pressure, Pa

q:

Heat flux, Mw \({\mathrm{m}}^{-2}\)

T :

Degree celsius, \(^{\circ }\hbox {C}\)

\(T_{\mathrm{w}}\) :

Wall temperature, K

t :

Time, \(\upmu \)s

\({{\varvec{U}}}\) :

Velocity vector, m \({\mathrm{s}}^{-1}\)

\(\sigma \) :

Surface tension coefficient

\(\mu \) :

Kinetic viscosity, \(\hbox {Pa s}^{-1}\)

\(\Phi \) :

Level set function

k :

Interface curvature

\(c_{\mathrm{p}}\) :

Specific heat, J kg\(^{-1}\) K\(^{-1}\)

\(\lambda \) :

Thermal conductivity, W \(\mathrm{m}^{-2}\) K\(^{-1}\)

\(\hat{n}_{\mathrm{w}}\) :

Unit vectors normal to the wall

\(\hat{\tau }_{\mathrm{w}}\) :

Unit vectors tangential to the wall

\(\theta _{\mathrm{w}}\) :

Contact angle, \(^\circ \)

*:

Dimensionless

g:

Gas phase

l:

Liquid phase

\(\partial \) :

Partial differential operator

\(\nabla \) :

Del operator

\(\Delta \) :

Difference between two quantities of a variable

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant nos. 51875152, 51875154, 51975005& 51975174), Anhui Natural Science Foundation (Grant nos. 2008085ME148 & 1908085QE195).

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Authors and Affiliations

  1. School of Mechanical Engineering, Anhui University of Technology, Ma’anshan, China

    De-yu Tu, Qing-min Pan, Jian-hong Zhou, Baohong Tong & Guo-tao Zhang

  2. Institute of Tribology, Hefei University of Technology, Hefei, China

    Wei Wang

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Correspondence to Baohong Tong.

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Tu, Dy., Pan, Qm., Zhou, Jh. et al. Morphological evolution and spreading flow of hollow oil droplet impact on a heated wall. Theor. Comput. Fluid Dyn. 35, 209–227 (2021). https://doi.org/10.1007/s00162-020-00557-5

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