Two-Phase: Overview

1. Two-Phase: Overview • Two-Phase • two-phase heat transfer describes phenomena where a change of phase (liquid/gas) occurs during and/or due to the heat transfer process • two-phase heat transfer generally considers processes that occur at a solid/fluid interface and are therefore a sub-field of convection • because of the change of phase, the latent heat (hfg)of the fluid must be considered • the surface tension (σ) is another parameter that plays an important role • Boiling • heat transfer process where a liquid undergoes a phase change into a vapor (gas) • Condensation • heat transfer process where a vapor (gas) liquid undergoes a phase change into a liquid

2. Boiling: Overview surface temperature saturation temperature of liquid excess temperature • Boiling • associated with transformation of liquid to vapor (phase change) at a solid/liquid interfacedue to convection heat transfer from the solid • agitation of the fluid by buoyant vapor bubbles provides for large convection coefficients large heat fluxes at low-to-moderate surface-to-fluid temperature differences • Modified Newton’s Law of Cooling

3. Boiling: Overview • Flow Cases • Pool Boiling • liquid motion is due to natural convection and bubble-induced mixing • Forced Convection Boiling (Flow Boiling/2-Phase Flow) • liquid motion is induced by external means and there is also bubble-induced mixing • Temperature Cases • Saturated Boiling • liquid temperature is slightly higher than saturation temperature • Subcooled Boiling • liquid temperature is less than saturation temperature

4. Boiling: The Boiling Curve inflection point transition boiling film boiling nucleate boiling free convection Leidenfrost point Water at Atmospheric Pressure • Boiling Curve • identifies different regimes during saturated pool boiling

5. Boiling: Boiling Curve • Free Convection Boiling (ΔTe < 5 °C) • little vapor formation • liquid motion is primarily due to buoyancy effects • Nucleate Boiling (5 °C < ΔTe < 30 °C) • onset of nucleate boiling ΔTe ~ 5 °C (ONB) • isolated vapor bubbles (5 °C < ΔTe< 10 °C) • liquid motion is strongly influenced by nucleation of bubbles on surface • h andq”s increase sharply with increasing ΔTe • heat transfer is primarily due to contact of liquid with the surface (single-phase conduction)and not to vaporization • jets and columns(10 °C < ΔTe < 30 °C) • increasing number of nucleation sites causes bubble interactions and coalescence into jets and slugs • liquid/surface contact is impaired by presence of vapor columns • q”sincreases with increasing ΔTe • hdecreases with increasing ΔTe

6. Boiling: Boiling Curve • Nucleate Boiling (5 °C < ΔTe < 30 °C) • critical heat flux (CHF) (ΔTe ~ 30 °C) • maximum attainable heat flux in nucleate boiling • water at atmospheric pressure • CHF ~ MW/m2 • hmax~ 10000 W/m2-K • Transition (30 °C < ΔTe< 120 °C) & Film Boiling (ΔTe > 120 °C) • heat transfer is by conductionand radiationacross the vapor blanket • liquid/surface contact is impaired by presence of vapor columns • q”sdecreases with increasing ΔTeuntil theLeidenfrost point corresponding to the minimum heat flux for film boiling and then proceeds to increase • a reduction in the surface heat flux below the minimum heat flux results in a abrupt reduction in surface temperature to the nucleate boiling regime • Heat flux controlled heating: burnout potential • if the heat flux at the surface is controlled it can potentially increase beyond the CHF • this causes the surface to be blanketed by vapor and the surface temperature can spontaneously achieve a value that potentially exceeds its melting point (ΔTe > 1000 °C) • if the surface survives the temperature shock, conditions are characterized as film boiling

7. Boiling: Pool Boiling Correlations subscripts: l saturated liquid state vsaturated vapor state • correction factor required for surfaces with small characteristic lengths • Due to complexity of fluid mechanics and phase-change thermodynamics, boiling heat transfer correlations are empirical • Rohsenow Correlation: Nucleate Boiling • note: can be as much as 100% inaccurate! • Critical Heat Flux

8. Boiling: Pool Boiling Correlations Rohsenow Correlation

9. Boiling: Pool Boiling Correlations Leidenfrost point reduced latent heat • Minimum Heat Flux • Film Boiling • correlation for spheres & cylinders • total average heat transfer coefficient due to cumulative & coupled effects of convection (due to boiling) and radiation across the vapor layer

10. Condensation: Overview • Condensation • occurs when the surface temperatureis less than the saturation temperature of an adjoining vapor • heat is transferred from vapor the surface to the surface • Film Condensation • entire surface is covered by the condensate which flows continuously from the surface and presents a thermal resistance to heat transfer from the vapor to the surface • typically due to clean, uncontaminated surfaces • can be reduced by using short vertical surfaces & horizontal cylinders • Dropwise Condensation • surface is covered by drops ranging from a micron to large agglomerations • thermal resistance is lower than that of film condensation • surface coatings may inhibit wetting and stimulate dropwise condensation

11. Condensation: Film Condensation • Laminar Flow Analysis • assume pure vapor • assume negligible shear stress at liquid/vapor interface • negligible advection in the film • Vertical Plate • thickness and flow rate of condensate increase with increasing x • generally, the vapor is superheated (Tv,∞>Tsat) and may be part of a mixture that contains noncondensibles • a shear stress at the liquid/vapor interface induces a velocity gradient in the vapor as well as the liquid

12. Condensation: Film Condensation modified latent heat Jakob number • Vertical Plate: Laminar Flow Analysis • film thickness • flow rate per unit width • average Nusselt number • heat transfer rate • condensation rate

13. Condensation: Film Condensation • Vertical Plate: Turbulence • transition may occur in the film and three flow regimes may be delineated • wave-free laminar region (Reδ<30) • wavy laminar region (30<Reδ<1800) • turbulent region (Reδ>1800)

14. Condensation: Film Condensation • Vertical Plate: Calculation Procedure • assume a flow regime and use the corresponding equation for to determine Reδ • if Reδvalue is consistent with flow regime assumption, calculate total heat rate and mass flow rate • if Reδvalue is inconsistent with flow regime assumption, iterate on flow regime assumption until it is consistent

15. Condensation: Film Condensation Tube: C =0.729 Sphere: C=0.826 • Radial Systems: Single Tubes/Spheres

16. Condensation: Film Condensation • Radial Systems: Vapor Flow in a Horizontal Tube • if vapor flow rate is low, condensation in both circumferential and axial directions • for high flow rates, flow is two-phase annular flow

17. Condensation: Dropwise Condensation Steam on copper with surface coating • Dropwise Condensation • heat transfer rates ~order of magnitude greater than film condensation • heat transfer coefficients highly dependant on surface properties