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ABSTRACT
The effects of subcooled flow boiling of nanofluids (Al2O3/water and Cu/water) through a vertical heated pipe are investigated numerically considering a number real flow factors such as uneven particle distributions and particle deposition on the wall surface. The results from the Eulerian–Eulerian two-phase model (liquid/nanofluid–gas) and those of the Eulerian–Lagrangian three-phase model (liquid–gas particles) are compared in detail. For the heat transfer coefficient prediction, the latter model gives about 6% error, whereas the Eulerian–Eulerian model gives about 12% error when it is compared with Chen’s correlation. The uneven distribution of nanoparticles concentrations, i.e., lower near the tube wall and higher at the pipe center, is well predicted by the Eulerian–Lagrangian model. On top that, for the first time, the changes on heating surface wettability induced by nanoparticles deposition is included via user define functions.
Nomenclature
| a | = | acceleration (m/s2) |
| aif | = | interfacial area concentration (m−1) |
| Ab | = | bubble area (m2) |
| Aq | = | quenching area of heat transfer (m2) |
| Bo | = | boiling number |
| CC | = | Cunningham correction |
| CD | = | drag coefficient |
| CL | = | lift coefficient |
| Cp | = | specific heat capacity at constant pressure (J/kg K) |
| db | = | bubble mean diameter (m) |
| ddb | = | bubble departure diameter (m) |
| dp | = | nanoparticle diameter (m) |
| Dbd | = | bubble departure diameter (m) |
| f | = | bubble departure frequency (Hz) |
| f | = | drag friction factor |
| FB | = | Brownian force (N) |
| Fd | = | drag force (N) |
| FL | = | lift force (N) |
| Flg | = | action of interfacial forces from vapor on liquid (N) |
| Flg | = | action of interfacial forces from liquid on vapor (N) |
| FLub | = | Lubrication force (N) |
| FT | = | thermophoretic force (N) |
| Fturb | = | turbulent dispersion force (N) |
| Fvm | = | virtual mass force (N) |
| G | = | mass flux (kg/m2 s) |
| g | = | gravitational acceleration (m/s2) |
| h | = | heat transfer coefficient (w/m2k) |
| hfg | = | latent heat of vaporization (J/kg) |
| hp | = | fluid–particle heat transfer coefficient (w/m2k) |
| H | = | enthalpy (J/kg) |
| Ja | = | Jakob number |
| k | = | thermal conductivity (W/m K) |
| k | = | turbulent kinetic energy (m2/s2) |
| kB | = | Boltzmann constant |
| Kn | = | Knudsen number |
| kt | = | turbulent conductivity (W/m K) |
| mp | = | mass of a single nanoparticle (kg) |
| Na | = | active nucleation site density (m2) |
| Nu | = | Nusselt number, Nu = hD/k |
| p | = | static pressure (N/m2) |
| Pr | = | Prandtl number |
| Prt | = | turbulent Prandtl number |
| Q | = | interphase heat transfer (w/m2) |
| = | heat flux (w/m2) | |
| qc | = | heat transfer due to forced convection (W/m2) |
| qe | = | heat transfer due to evaporation (W/m2) |
| = | quenching heat transfer (W/m2) | |
| Re | = | Reynolds number, |
| Se | = | sink/source term of energy equation |
| Sm | = | sink/source term of momentum equation |
| Sk, Sε | = | sink/source term of k − ε equation |
| St | = | Stanton number |
| T | = | temperature (K) |
| Tsat | = | saturated temperature (K) |
| Tsub | = | subcooled temperature (K) |
| Tsup | = | superheat temperature (K) |
| Tw | = | wall temperature (K) |
| V | = | velocity (m/s) |
| X | = | flow quality |
| Greek symbols | = | |
| αg, αl | = | vapor or liquid volume fraction |
| σ | = | surface tension (M/m) |
| ϵ | = | dissipation rate of turbulence kinetic energy (m2/s3) |
| μ | = | dynamic viscosity (kg/m s) |
| μb | = | bubble induced viscosity (kg/ms) |
| μt | = | turbulent viscosity (kg/m s) |
| ρ | = | density (kg/m3) |
| Γlg | = | interfacial mass transfer from vapor to liquid (kg/m3s) |
| Γgl | = | interfacial mass transfer from liquid to vapor (kg/m3s) |
| λ | = | molecular mean free path |
| θ | = | droplet or vapor bubble contact angle |
| φ | = | particle volume fraction |
| τ | = | shear stress (N/m2) |
| δ V | = | cell volume (m3) |
| Subscripts | = | |
| b | = | bulk |
| bf | = | base fluid |
| e/eff | = | effective |
| f | = | fluid |
| FC | = | forced convection |
| g | = | vapor |
| l | = | liquid |
| NB | = | nucleate boiling |
| NP | = | nanoparticle |
| p | = | particle phase |
| l | = | liquid phase |
| t | = | turbulent |
Nomenclature
| a | = | acceleration (m/s2) |
| aif | = | interfacial area concentration (m−1) |
| Ab | = | bubble area (m2) |
| Aq | = | quenching area of heat transfer (m2) |
| Bo | = | boiling number |
| CC | = | Cunningham correction |
| CD | = | drag coefficient |
| CL | = | lift coefficient |
| Cp | = | specific heat capacity at constant pressure (J/kg K) |
| db | = | bubble mean diameter (m) |
| ddb | = | bubble departure diameter (m) |
| dp | = | nanoparticle diameter (m) |
| Dbd | = | bubble departure diameter (m) |
| f | = | bubble departure frequency (Hz) |
| f | = | drag friction factor |
| FB | = | Brownian force (N) |
| Fd | = | drag force (N) |
| FL | = | lift force (N) |
| Flg | = | action of interfacial forces from vapor on liquid (N) |
| Flg | = | action of interfacial forces from liquid on vapor (N) |
| FLub | = | Lubrication force (N) |
| FT | = | thermophoretic force (N) |
| Fturb | = | turbulent dispersion force (N) |
| Fvm | = | virtual mass force (N) |
| G | = | mass flux (kg/m2 s) |
| g | = | gravitational acceleration (m/s2) |
| h | = | heat transfer coefficient (w/m2k) |
| hfg | = | latent heat of vaporization (J/kg) |
| hp | = | fluid–particle heat transfer coefficient (w/m2k) |
| H | = | enthalpy (J/kg) |
| Ja | = | Jakob number |
| k | = | thermal conductivity (W/m K) |
| k | = | turbulent kinetic energy (m2/s2) |
| kB | = | Boltzmann constant |
| Kn | = | Knudsen number |
| kt | = | turbulent conductivity (W/m K) |
| mp | = | mass of a single nanoparticle (kg) |
| Na | = | active nucleation site density (m2) |
| Nu | = | Nusselt number, Nu = hD/k |
| p | = | static pressure (N/m2) |
| Pr | = | Prandtl number |
| Prt | = | turbulent Prandtl number |
| Q | = | interphase heat transfer (w/m2) |
| = | heat flux (w/m2) | |
| qc | = | heat transfer due to forced convection (W/m2) |
| qe | = | heat transfer due to evaporation (W/m2) |
| = | quenching heat transfer (W/m2) | |
| Re | = | Reynolds number, |
| Se | = | sink/source term of energy equation |
| Sm | = | sink/source term of momentum equation |
| Sk, Sε | = | sink/source term of k − ε equation |
| St | = | Stanton number |
| T | = | temperature (K) |
| Tsat | = | saturated temperature (K) |
| Tsub | = | subcooled temperature (K) |
| Tsup | = | superheat temperature (K) |
| Tw | = | wall temperature (K) |
| V | = | velocity (m/s) |
| X | = | flow quality |
| Greek symbols | = | |
| αg, αl | = | vapor or liquid volume fraction |
| σ | = | surface tension (M/m) |
| ϵ | = | dissipation rate of turbulence kinetic energy (m2/s3) |
| μ | = | dynamic viscosity (kg/m s) |
| μb | = | bubble induced viscosity (kg/ms) |
| μt | = | turbulent viscosity (kg/m s) |
| ρ | = | density (kg/m3) |
| Γlg | = | interfacial mass transfer from vapor to liquid (kg/m3s) |
| Γgl | = | interfacial mass transfer from liquid to vapor (kg/m3s) |
| λ | = | molecular mean free path |
| θ | = | droplet or vapor bubble contact angle |
| φ | = | particle volume fraction |
| τ | = | shear stress (N/m2) |
| δ V | = | cell volume (m3) |
| Subscripts | = | |
| b | = | bulk |
| bf | = | base fluid |
| e/eff | = | effective |
| f | = | fluid |
| FC | = | forced convection |
| g | = | vapor |
| l | = | liquid |
| NB | = | nucleate boiling |
| NP | = | nanoparticle |
| p | = | particle phase |
| l | = | liquid phase |
| t | = | turbulent |