two phase heat transfer

TWO PHASE HEAT TRANSFER

BOILING AND CONDENSATION

CONTENTS

• INTRODUCTION• BOILING MODES• POOL BOILING• FORCED CONVECTION BOILING• CONDENSATION MECHANISMS• FILM CONDENSATION• DROPWISE CONDENSATION

INTRODUCTION

• CONVECTION• LATENT HEAT• BOUYANCY FORCE

Closed loop power cycle

BOILING MODES

• VAPOR BUBBLES DYNAMIC LIQUIDE MOTION NEAR SURFACE HEAT TRANSFER COEFFICIENT

• VAPOR BUBBLESGROWTH & DYNAMIC

1-EXCESS TEMPERATURE

2-NATURE OF THE SURFACE

3-THERMOPHYSICAL PROPERTIES OF THE

FLUID (SURFACE TENTION)

Boiling

Pool Boiling

Forced Convect

ion Boiling

Free Convect

ion

Bubble - Induced

Subcooled BoilingTemperature below saturationBubble condense in liquid

Saturated BoilingTemperature slightly exceeds saturationBubbles are propelled trough liquid by buoyance forceBubbles escape from free surface

POOL BOILING

P

Burnout PointBoiling Crisis

Ts,E>BPT

POOL BOILING CORRELATIONS• NUCLEATE POOL BOILINGROHSENOW CORRELATION (ONLY FORCLEAN SURFACE)

• CRITICAL HEAT FLUXKUTATELADZE & ZUBER CORRELATION (INDEPENDENT OF SURFACE MATERIAL)

• FOR LARGE HORIZONTAL CYLINDERS, SPHERES AND LARGE FINITE HEATED SURFACE C=PI/24

• FOR LARGE HORIZONTAL PLATES C=0.149

• CHF DEPENDS STRONGLY ON PRESSURE

• MINIMUM HEAT FLUXZUBER (FOR LARGE HORIZONTAL PLATE, MODERATE PRESSURE)

FILM WILL COLLAPSE• IF TO COOL SURFACE NUCLEATE BOILING TO BE REESTABLISHED

• FILM POOL BOILING

C= 0.62 horizontal cylinders

C=0.67 spheres h 𝑓𝑔′ =h 𝑓𝑔+0 .8𝐶𝑝 ,𝑣(𝑇 𝑠−𝑇 𝑠𝑎𝑡)

Sensible energy required to maintain temperatures within the vapor blanket above the saturation temperature.

Vapor properties @

Liquid properties @

Total heat transfer coef:

FORCED CONVECTION BOILING• FLOW IS DUE TO BULK MOTION OF THE FLUID

• DEPENDS ON GEOMETRY

I. External flow (over heated places &

cylinders)

II. Internal flow (TWO PHASE FLOW: rapid

changes from liquid to vapor)

EXTERNAL FORCED CONVECTION BOILING > HIGH VELOCITYIF HEAT FLUX PARAMETER < LOW VELOCITY HEAT FLUX PARAMETER=

WEBER NUMBER:

• LIENHARD & EICHHORN

LOW VELOCITY:

HIGH VELOCITY:

TWO PHASE FLOW

FOR 0<<0.8 & CONFIDENTIAL NUMBER==FROUDE NUMBER: STRATIFICATION PARAMETER: = THE SINGLE PHASE CONVECTION COEFFICIENTMEAN VAPOR MASS FRACTION=

=1 for Vertical tubes & horizontal tubes

with Fr≥0.04=2.63 for horizontal tubes with Fr≤0.04

CONDENSATION MECHANISMS

Film condensation

Dropwise condensation Homogenous

condensation

Direct contact condensation

LAMINAR FILM CONDENSATION ON A VERTICAL PLATE

• NUSSELT ASSUMPTION:I. LAMINAR FLOW & CONSTANT PROPERTIESII. PURE VAPOR CONSTANT SATURATED TEMP.III. SHEAR STRESS IS NEGLIGIBLE IV. ADVECTION IS NEGLIGIBLE

FILM THICKNESS

FLOW RATE PER UNIT WIDTH

AVERAGE NUSSELT NUM.

HEAT TRANSFER RATE

CONDENSATION RATE

Modified latent heat

Jakob Num.

TURBULENT FILM CONDENSATION Laminar

wave free(Reδ<30)

Laminar wavy

(30<Reδ<1800)

Turbulent(Reδ>1800)

Modified NUSSELT number for condensation on a vertical plate

FILM CONDENSATION ON RADIAL SYSTEMS

Tube: C =0.729

Sphere: C=0.826

h𝐷 ,𝑁=h𝐷𝑁− 1/4

FILM CONDENSATION IN HORIZONTAL TUBES

• IF VAPOR FLOW RATE IS LOW, CONDENSATION IN BOTH CIRCUMFERENTIAL AND AXIAL DIRECTIONS

• FOR HIGH FLOW RATES, FLOW IS TWO-PHASE ANNULAR FLOW

DROPWISE CONDENSATION• HEAT TRANSFER RATES ~ORDER OF MAGNITUDE GREATER THAN FILM

CONDENSATION• HEAT TRANSFER COEFFICIENTS HIGHLY DEPENDENT ON SURFACE

PROPERTIES

STEAM ON COPPER WITH SURFACE COATING