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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