AME 60634 Int. Heat Trans. D. B. Go Two-Phase: Overview Two-Phase –two-phase heat transfer describes phenomena where a change of phase (liquid/gas) occurs

AME 60634 Int. Heat Trans.

D. B. Go

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


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Boiling: Overview• Boiling

– associated with transformation of liquid to vapor (phase change) at a solid/liquid interface due 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

surface temperature

saturation temperature of liquid

excess temperature


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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


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Boiling: The Boiling Curve• Boiling Curve

– identifies different regimes during saturated pool boiling

Water at Atmospheric Pressure

free convection

nucleate boiling

transitionboiling

filmboiling

inflection point

Leidenfrost point


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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 and q”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”s increases with increasing ΔTe

• h decreases with increasing ΔTe


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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 conduction and radiation across the vapor blanket• liquid/surface contact is impaired by presence of vapor columns

• q”s decreases with increasing ΔTe until the Leidenfrost 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


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• 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

Boiling: Pool Boiling Correlations

subscripts: l saturated liquid state

v saturated vapor state

correction factor required for surfaces with small characteristic lengths


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Rohsenow Correlation


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• 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


reduced latent heat

Leidenfrost point


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Condensation: Overview

• Condensation– occurs when the surface temperature is 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


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Condensation: Film Condensation

• 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

• Laminar Flow Analysis– assume pure vapor– assume negligible shear stress at liquid/vapor interface

– negligible advection in the film


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Condensation: Film Condensation• Vertical Plate: Laminar Flow Analysis

– film thickness

– flow rate per unit width

– average Nusselt number

– heat transfer rate

– condensation rate

modified latent heat

Jakob number


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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)


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Condensation: Film Condensation• Vertical Plate: Calculation Procedure

– assume a flow regime and use the corresponding equation for to determine Reδ

– if Reδ value is consistent with flow regime assumption, calculate total heat rate and mass flow rate

– if Reδ value is inconsistent with flow regime assumption, iterate on flow regime assumption until it is consistent


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Condensation: Film Condensation• Radial Systems: Single Tubes/Spheres

Tube: C =0.729

Sphere: C=0.826


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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


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Condensation: Dropwise Condensation• Dropwise Condensation

– heat transfer rates ~order of magnitude greater than film condensation– heat transfer coefficients highly dependant on surface properties

Steam on copper with surface coating

Documents

AME 60634 Int. Heat Trans. D. B. Go Two-Phase: Overview Two-Phase –two-phase heat transfer describes phenomena where a change of phase (liquid/gas) occurs