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CFD modelling of most probable bubble nucleation rate from binary mixture with estimation of components’ mole fraction in critical cluster

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Abstract

The employment of different mathematical models to address specifically for the bubble nucleation rates of water vapour and dissolved air molecules is essential as the physics for them to form bubble nuclei is different. The available methods to calculate bubble nucleation rate in binary mixture such as density functional theory are complicated to be coupled along with computational fluid dynamics (CFD) approach. In addition, effect of dissolved gas concentration was neglected in most study for the prediction of bubble nucleation rates. The most probable bubble nucleation rate for the water vapour and dissolved air mixture in a 2D quasi-stable flow across a cavitating nozzle in current work was estimated via the statistical mean of all possible bubble nucleation rates of the mixture (different mole fractions of water vapour and dissolved air) and the corresponding number of molecules in critical cluster. Theoretically, the bubble nucleation rate is greatly dependent on components’ mole fraction in a critical cluster. Hence, the dissolved gas concentration effect was included in current work. Besides, the possible bubble nucleation rates were predicted based on the calculated number of molecules required to form a critical cluster. The estimation of components’ mole fraction in critical cluster for water vapour and dissolved air mixture was obtained by coupling the enhanced classical nucleation theory and CFD approach. In addition, the distribution of bubble nuclei of water vapour and dissolved air mixture could be predicted via the utilisation of population balance model.

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Abbreviations

C :

Correction factor

D :

Rate of molecules striking on a surface area of the cluster (molecules/m2s)

f L :

Lost degree of freedom during the dissolution process

G(V):

Growth rate of bubble number density (number/m3s)

ΔH vap :

Enthalpies for the evaporation of the solution

ΔH f :

Enthalpies for the freezing of the solution

J :

Bubble nucleation rate (nuclei/m3s)

k B :

Boltzmann’s constant (J/K)

k :

Specified number of moments

Li:

Abscissas

m k :

kth moment of number density function

m :

Mass of molecule (kg)

n c :

Number of molecules

N:

Number density of the liquid (molecules/m3)

n(V,t):

Bubble number density distribution per unit volume (V) for a given time (t)

P :

Pressure (Pa)

P i :

Pressure to saturate the dissolved gas in the liquid

Q :

Order of quadrature approximation

r :

Radius (m)

R :

Gas constant (J/K mol)

x :

Mole fraction of dissolved gas molecules in the solution

T :

Liquid temperature (K)

T f :

Melting temperature of the solution (K)

v :

Volume of a molecules (m)

wi:

Weights

Z f :

Zeldovich nonequilibrium factor

β′ :

Accommodation coefficient of molecules to the cluster

ξ :

Fraction of vapour or gas molecules in the critical cluster

η :

Weight factor of the vapour and dissolved gas molecules for the formation of critical cluster

λ :

Rate of number of gas molecules participated in the formation of critical cluster per unit volume (molecules/m 3 s)

ρ :

Density (kg/m3)

g :

Gas

H2O:

Water

l :

Liquid water

v :

Vapour

gv :

Vapour and Gas

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Authors and Affiliations

  1. Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750, Tronoh, Perak, Malaysia

    Ban Zhen Hong, Lau Kok Keong & Azmi Mohd Shariff

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  1. Ban Zhen Hong
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  2. Lau Kok Keong
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Correspondence to Lau Kok Keong.

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Communicated by Andreas Öchsner.

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Hong, B.Z., Keong, L.K. & Shariff, A.M. CFD modelling of most probable bubble nucleation rate from binary mixture with estimation of components’ mole fraction in critical cluster. Continuum Mech. Thermodyn. 28, 655–668 (2016). https://doi.org/10.1007/s00161-014-0398-x

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