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Numerical simulation of superheated vapor bubble rising in stagnant liquid


In present study, the rising of superheated vapor bubble in saturated liquid is simulated using volume of fluid method in OpenFOAM cfd package. The surface tension between vapor–liquid phases is considered using continuous surface force method. In order to reduce spurious current near interface, Lafaurie smoothing filter is applied to improve curvature calculation. Phase change is considered using Tanasawa mass transfer model. The variation of saturation temperature in vapor bubble with local pressure is considered with simplified Clausius–Clapeyron relation. The couple velocity–pressure equation is solved using PISO algorithm. The numerical model is validated with: (1) isothermal bubble rising and (2) one-dimensional horizontal film condensation. Then, the shape and life time history of single superheated vapor bubble are investigated. The present numerical study shows vapor bubble in saturated liquid undergoes boiling and condensation. It indicates bubble life time is nearly linear proportional with bubble size and superheat temperature.

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\(A_{b}\) :

Bubble area (m2)

\(Bo\) :

Bond number (\(\frac{{g(\rho_{L} - \rho_{g} )D_{0}^{2} }}{\sigma }\)) (–)

\(C_{\alpha }\) :

Compression factor (–)

\(C\) :

Specific heat (J/kg K)

\(C_{d}\) :

Drag coefficient (–)

\(D_{eq}\) :

Equivalent diameter (M)

\(D_{0}\) :

Bubble initial diameter (M)


Numerical error

\(\overrightarrow {g}\) :

Gravity acceleration (m/s2)

\(H_{LG}\) :

Latent heat (J/kg)

\(k\) :

Thermal conductivity (W/m K)

\(M\) :

Molar mass (kg/K mol)

\({\dot{\text{m}}}^{\prime\prime\prime}\) :

Condensate mass flow rate per unit volume (kg/m3 s)

\(Mo\) :

Morton number (\(\frac{{g(\rho_{L} - \rho_{g} )\mu_{L}^{4} }}{{\rho_{L}^{2} \sigma^{3} }}\)) (–)

\(P\) :

Pressure (Pa)

\(R\) :

Specific gas constant (\(\frac{{R_{universal} }}{M}\)) (J/kg K)

Re :

Reynolds number (\(\frac{{\rho_{L} U_{t} D_{0} }}{{\mu_{L} }}\)) (–)

\(T\) :

Temperature (K)

\(\overrightarrow {U}\) :

Velocity (m/s)

\(\overrightarrow {{U_{b} }}\) :

Bubble velocity (m/s)

\(\overrightarrow {{U_{c} }}\) :

Compressive velocity (m/s)

\(\overrightarrow {{U_{rel} }}\) :

Relative velocity (m/s)

\(U_{t}\) :

Terminal velocity (m/s)

\(V_{b}\) :

Bubble volume (m3)

\(\alpha\) :

Volume fraction factor (–)

\(\delta_{f}\) :

Film thickness (m)

\(\kappa\) :

Interface curvature (m−1)

\(\mu\) :

Dynamic viscosity (Pa s)

\(\nu\) :

Kinematic viscosity (m2/s)

\(\rho\) :

Density (kg/m3)

\(G\) :

Gas (vapor) phase

\(L\) :

Liquid phase


Saturation condition


Superheated condition


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Correspondence to M. R. Ansari.

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Samkhaniani, N., Ansari, M.R. Numerical simulation of superheated vapor bubble rising in stagnant liquid. Heat Mass Transfer 53, 2885–2899 (2017).

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  • Bubble Size
  • Viscosity Ratio
  • Vapor Bubble
  • Saturated Liquid
  • Bubble Shape