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ABSTRACT
Saturated pool film boiling over a flat horizontal surface is investigated numerically for water and refrigerant R134a at near-critical conditions for wall superheats (ΔTSup) of 2 K, 5 K, 8 K, 10 K, 15 K, and 20 K. The flow is considered to be laminar and incompressible. The governing equations are solved using a finite volume method with a collocated grid arrangement. For capturing the interface in two-phase boiling flows, a Coupled Level Set and Volume of Fluid (CLSVOF) with a multidirectional advection algorithm is used. Both single-mode and multimode boiling models are used for the numerical investigation to understand the effect of computational domain sizes on flow and heat transfer characteristics. In the case of water, the evolution of interface morphology shows the formation of a discrete periodic bubble release cycle occurring at lower Jacob numbers, Jav ≤ 10.2(ΔTSup ≤ 8 K), and the generation of jets of stable vapor film columns occurs at higher Jav ≥ 12.7 (ΔTSup ≥ 10 K). In the case of R134a, for all the Jav values considered in this study (0.163 ≤ Jav ≤ 1.63), the formation of a discrete periodic bubble release is observed. The results show that multimode boiling model should be used to understand the flow characteristics better. The magnitude of average Nusselt number obtained from the multimode film boiling model is lower than that of the single-mode film boiling model. The Nusselt numbers obtained from the present numerical studies are also compared with the available semiempirical correlations.
Nomenclature
| Cp,v | = | specific heat of vapor at constant pressure, J/kg · K |
| g | = | acceleration due to gravity, m/s2 |
| hlv | = | latent heat of vaporization, J/kg |
| H(ϕ) | = | smoothed Heaviside function |
| kf | = | thermal conductivity of fluid, W/m · K |
| = | unit normal vector of the interface | |
| P | = | pressure, Pa |
| SI | = | surface area of the interface line segment, m2 |
| Sc | = | surface of line segment bounded by the control volume cell, m3 |
| to | = | time scale, |
| tmax | = | maximum time, s |
| T | = | temperature, K |
| uo | = | velocity scale, uo = (λo/to), m/s |
| VI | = | interfacial velocity, m/s |
| = | position vector of the interface | |
| Nondimensional parameters | = | |
| Jav | = | Jacob number, Cp,vΔTSup /hlv |
| Grv | = | Grashof number, |
| Nu | = | Nusselt number |
| Prv | = | Prandtl number, Cp,vµv/kv |
| α | = | thermal diffusivity, m2/s |
| δ(x) | = | thickness of the vapor film, m |
| κ | = | mean curvature of the interface, 1/m |
| λc | = | critical wavelength, λc = 2πλo, m |
| λd2 | = | two-dimensional most dangerous wavelength, |
| λo | = | capillary length scale, |
| µf | = | dynamic viscosity of the fluid, N · s/m2 |
| ϕ | = | level set distance function, m |
| ρf | = | density of fluid, kg/m3 |
| σ | = | surface tension coefficient, N/m |
| τ | = | nondimensional time, (t/to) |
| ΔTSup | = | wall superheat, (Tw-TSat) |
| Subscripts | = | |
| f | = | fluid phase |
| l | = | liquid |
| I | = | liquid–vapor interface |
| v | = | vapor phase |
| Superscripts | = | |
| n | = | previous time level |
| n + 1 | = | current time level |
Nomenclature
| Cp,v | = | specific heat of vapor at constant pressure, J/kg · K |
| g | = | acceleration due to gravity, m/s2 |
| hlv | = | latent heat of vaporization, J/kg |
| H(ϕ) | = | smoothed Heaviside function |
| kf | = | thermal conductivity of fluid, W/m · K |
| = | unit normal vector of the interface | |
| P | = | pressure, Pa |
| SI | = | surface area of the interface line segment, m2 |
| Sc | = | surface of line segment bounded by the control volume cell, m3 |
| to | = | time scale, |
| tmax | = | maximum time, s |
| T | = | temperature, K |
| uo | = | velocity scale, uo = (λo/to), m/s |
| VI | = | interfacial velocity, m/s |
| = | position vector of the interface | |
| Nondimensional parameters | = | |
| Jav | = | Jacob number, Cp,vΔTSup /hlv |
| Grv | = | Grashof number, |
| Nu | = | Nusselt number |
| Prv | = | Prandtl number, Cp,vµv/kv |
| α | = | thermal diffusivity, m2/s |
| δ(x) | = | thickness of the vapor film, m |
| κ | = | mean curvature of the interface, 1/m |
| λc | = | critical wavelength, λc = 2πλo, m |
| λd2 | = | two-dimensional most dangerous wavelength, |
| λo | = | capillary length scale, |
| µf | = | dynamic viscosity of the fluid, N · s/m2 |
| ϕ | = | level set distance function, m |
| ρf | = | density of fluid, kg/m3 |
| σ | = | surface tension coefficient, N/m |
| τ | = | nondimensional time, (t/to) |
| ΔTSup | = | wall superheat, (Tw-TSat) |
| Subscripts | = | |
| f | = | fluid phase |
| l | = | liquid |
| I | = | liquid–vapor interface |
| v | = | vapor phase |
| Superscripts | = | |
| n | = | previous time level |
| n + 1 | = | current time level |
Acknowledgments
The authors acknowledge the high-performance computing facility provided by the Computer Service Center at IIT Delhi.