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Lattice Boltzmann Study on Influence of Gravitational Acceleration on Pool Nucleate Boiling Heat Transfer

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Abstract

Under both normal gravity and microgravity conditions, pool boiling is an efficient mode of heat transfer which has been widely applied in practice. Studying the influence of gravitational acceleration on boiling heat transfer is not only of academic significance, but also helpful for the design of space equipment related to boiling. With the development of computer technology, numerical method has been a new reliable way to investigate the boiling heat transfer under different gravities. Pseudopotential lattice Boltzmann (i.e., LB) model is one of the most popular multiphase LB models, in which the phase interface could be formed, disappeared and migrated naturally. In this paper, the Multi-Relaxation-Time (i.e., MRT) pseudopotential LB model coupled with phase-change model was applied to simulate the pool boiling heat transfer under different gravitational accelerations and wall superheats. Pool boiling curves under different gravities were obtained. It’s found that: 1) the pool boiling heat transfer coefficient at a given wall superheat decreases with a decrease in gravity; 2) the wall superheat, as well as heat flux, at the CHF (i.e., critical heat flux) point and ONB (i.e., onset of the nucleate boiling) decrease gradually with a decrease in gravity. In addition, based on the numerical results, a new gravity scaling model was proposed to predict the influence of gravitational acceleration on the nucleate boiling heat transfer under different wall superheats. Finally, the new gravity scaling model was proved to be capable of predicting the heat flux during the nucleate boiling under different wall superheats and gravities.

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Abbreviations

a,b,R,ω :

parameters in EOS

T sat :

saturation temperature

c v :

specific heat at constant volume

T w :

temperature of the heated surface

e α :

lattice velocity vector

u :

fluid velocity

f α, f :

distribution function for density

v :

real fluid velocity

F :

external force

v 0 :

characteristic velocity

F α’:

forcing term in the velocity space

w α :

weighting coefficient

F ads :

fluid-solid interaction force

x :

position

F g :

buoyancy force

F m :

intermolecular interaction force

g :

gravitational acceleration

G :

interaction strength

θ w :

contact angle

G w :

a parameter to tune the contact angle

∆t :

time step

h fg :

latent heat of vaporization

∆T :

wall superheat

ρ :

density

Ja :

Jacob number

σ :

parameter to tune the mechanical stability

l 0 :

characteristic length

L x :

width of computational domain

L y :

height of computational domain

M :

orthogonal transformation matrix

p :

pressure

p c :

critical pressure

p EOS :

prescribed non-ideal equation of state

R b :

liquid radius

s(x):

switch function

S :

forcing term in the moment space

τ :

relaxation time

χ :

thermal diffusion coefficient

ν :

kinematic coefficient of viscosity

γ :

surface tension

P :

pressure tensor

Λ :

diagonal matrix of relaxation time

Π :

viscous stress tensor

κ :

parameter to tune the surface tension

μ :

dynamic coefficient of viscosity

λ :

thermal conductivity

ψ :

pseudopotential

Q loc(x, t):

local heat flux on the heated surface

Q s(t):

space- averaged heat flux

Q :

time- and space- averaged heat flux

t :

time

t 0 :

characteristic time

T :

temperature

T c :

critical temperature

*:

dimensionless properties

α :

lattice direction

c :

critical properties

L, V :

liquid, vapor

x, y :

direction

eq :

equilibrium properties

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Acknowledgements

This work was supported financially by the joint fund between the Chinese Academy of Sciences (CAS) and National Natural Science Foundation of China (NSFC) under the Grant of U1738105.

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Authors and Affiliations

  1. State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Yuan Feng, Huixiong Li, Kaikai Guo & Xianliang Lei

  2. CAS Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Jianfu Zhao

  3. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Jianfu Zhao

Authors
  1. Yuan Feng
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  2. Huixiong Li
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  3. Jianfu Zhao
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  4. Kaikai Guo
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  5. Xianliang Lei
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Correspondence to Huixiong Li or Jianfu Zhao.

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Highlights

1) Simulations of pool boiling processes at different gravity levels were performed.

2) Wall superheat and heat flux at ONB decreased with a decrease in gravity.

3) Wall superheat at CHF point and CHF decreased with a decrease in gravity.

4) A new scaling model for the nucleate boiling heat transfer was proposed.

Appendix: the determination of surface tension and contact angle.

Appendix: the determination of surface tension and contact angle.

In the two-dimensional simulations, according to the Laplace equation of capillary, the relationship between the pressure difference across the interface of a droplet Δp and the radius of this droplet satisfies Eq. (A-1).

$$ \Delta p=\frac{\upgamma}{R_b} $$
(A-1)

where γ is the surface tension. It can be seen from Eq. (A-1) that the pressure difference across the interface of the droplet is proportional to the inverse of droplet radius, and the proportionality coefficient equals to the surface tension.

To determine the surface tension in our simulations, the static droplets with different radii are simulated. In the simulations, a 120 × 120 computational domain is adopted and the periodic boundary condition is utilized at all of the boundaries. The static droplet is located at the center of the computational domain. All of the parameters in Peng-Robinson EOS, Eqs. (6), (10) and (19), and the physical parameters of fluid are chosen as those in Chapter 3. The fluid-solid interaction force and the buoyancy force are ignored. Figure 13 represents the influence of droplet radii on the pressure difference across the phase interface. As shown in Fig. 13, our numerical results could be fitted with a straight line that goes through the origin point with a slope of 0.0748. According to the Laplace equation of capillary, the surface tension could be determined as γ = 0.0748.

Fig. 13
figure 13

The influence of droplet radii on the pressure difference

Full size image

In order to determine the wettability of the heated surface in our simulations, the equilibrium shape of a droplet on the horizontal wall is simulated and the static contact angle is measured. In this simulation, a 300 × 100 computational domain is adopted. The periodic boundary condition is adopted at the left and right boundaries, while the non-slip boundary condition is utilized at the top and bottom boundaries. The parameters in P-R EOS, Eqs. (6), (10), (11) and (19) and the physical parameters of fluid are chosen as those in Chapter 3. The gravitational acceleration is set to be 0, so the buoyancy force is ignored. Initially, a droplet with a radius of Rb = 30 is located at (150, 20). The simulation is carried out for 10,000 time steps to ensure that the equilibrium state has been reached. As shown in Fig. 14, the static contact angle is measured to be 27.3°.

Fig. 14
figure 14

The equilibrium shape of a droplet on the horizontal wall

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Feng, Y., Li, H., Zhao, J. et al. Lattice Boltzmann Study on Influence of Gravitational Acceleration on Pool Nucleate Boiling Heat Transfer. Microgravity Sci. Technol. 33, 21 (2021). https://doi.org/10.1007/s12217-020-09864-2

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