Condensation Heat Transfer

Dr Vishwas Wadekar

HTFS, Aspen Technology

Filmwise

Condensation

Overview of Four Lectures

• Lecture 1– Condensation - I

• Lecture 2– Condensation - II– Enhancement of heat transfer

• Lecture 3– Pool boiling heat transfer

– Flow patterns– Flow boiling heat transfer

• Lecture 4– Enhancement of boiling

Contents

� Modes of condensation

� Dropwise/filmwise condensation

� Direct/indirect/homogeneous condensation

� Filmwise condensation on

� Flat plate

� Outside/inside a tube

� Other complex effects

� Industrial equipment

Dropwise Filmwise

Condensation

Filmwise Condensation

� Condensed liquid forms a continuous liquid film on the heat transfer surface

� Examples of heat transfer surface can be

� Flat plate (as in the diagram)

� Outside/inside a tube

� Plate of a plate heat exchanger

� Heat transfer coefficient is lower (than dropwise mode) but predictable and stable

� Almost all industrial equipment is designed for this mode of condensation

Dropwise Condensation

� Condensed liquid forms droplets on the

heat transfer surface due to poor wettability

� Very high heat transfer coeff. (50-500 kW/m2K)! However, it can degrade to filmwise values over time

� This mode is promoted by

� Surface coating (e.g. with PTFE)

� Additives in vapour stream

� Still an area of ongoing research to make it work in industrial practice

Homogeneous Condensation

� Small droplets forming as fog

� Increase in pressure can lead to fog formation

� Droplets often too small to separate

� Fog and cloud formation are due to

homogeneous nucleation

� Undesirable in industrial practice

� Loss through venting system

� Possible source of pollution

Direct Contact Condensation

� Subcooled liquid is brought in contact with vapour

� Latent heat raises the temperature of subcooledliquid

� Efficient form of heat exchange

� Sea water desalination

� Power plants

� Emergency core cooling in nuclear reactors

Vapour

Liquid Spray

Vapour

Condensation

In the remaining lecture we now focus on indirect contact filmwise

condensation

Filmwise

Condensation

Resistances to Heat TransferPure vapour

+ non-condensable

vapour vapour+gas

Ti = Tsat

coolant coolantliquid

film

liquid

film

Tg

Ti

pv,b

pv,i

Pure vapour

General Approach to Condensation

� Filmwise condensation is considered

� Various geometries are covered

� Flat plate (vertical and inclined)

� Outside/inside a single tube

� Outside multiple tubes (tube bundle)

� Gravity controlled situations studied in detail

� Further complicating factors such as inundation and vapour shear effects are then examined briefly

General Approach to Condensation

Condensation on Flat Plate

�Nusselt analysed this case in 1916

� Analysis is considered in detail because -

� Milestone in condensation work

� Simplest geometry

� Forms the basis of other geometries

Nusselt Analysis -Assumptions

� Laminar condensate film� Gravitational and viscous forces only� Heat transfer by conduction through the film� Thermodynamic equilibrium at the interface� Uniform -

� Physical properties� Wall temperature

Nusselt Analysis - I

δ

Tsat

Tw

From film analysis

( )η

δρ−ρ=

3

3Wg

Vgl&

We define the mass flow rate per unit width as

( )η

δρ−ρρ=

ρ=Γ

3

3g

W

V glll&

Nusselt Analysis - II

Tsat

Tw

Liquid film flowrate, G, increases with distance, x. If Gc is condensation mass flux then from mass balance Gc = dΓ/ dx

( )dx

dg

dx

dG

gll

c

δδ

η

ρ−ρρ=

Γ= 2

33

dx

As ( )

η

δρ−ρρ=Γ

3

3ggll

Nusselt Analysis - III

Tsat

Tw

Condensation mass flux Gc is related to heat flux, , by (∆hv = latent heat of vaporisation)

( ) cvwsat

l GhTTq ∆=−δ

λ=&

Heat transfer through the film is by conduction. Therefore the heat transfer coefficient will be (λ l / δ)

cvGhq ∆=&cq&

δ

Combining….

( )dx

dgG

gll

c

δδ

η

ρ−ρρ= 2

( ) cvwsat

l GhTT ∆=−δ

λ

Condensation mass flux Gc and heat transfer equation

Condensation mass flux Gc and film flow equation

( )( ) vgll

wsatl

hg

dxTTd

∆ρ−ρρ

−ηλ=δδ3

On integrating…..

Local Coefficient

( )( ) vgll

wsatl

hg

xTT

∆ρ−ρρ

−ηλ=δ

44

….On integrating

δ

xLocal heat transfer coefficient

( )( )

4/13

4

−η

∆ρ−ρρλ=

δ

λ=α

xTT

hg

wsat

vgllll

Average Coefficient On integrating

OR

δ

x = L

( )( )

4/13

0943.0

1

−η

∆ρ−ρρλ=α=α ∫ LTT

hgdx

L wsat

vglllL

( ) η

Γ=

ρ−ρρ

η=

=λ

α= −

4Re;

Re47.1

3/12

3/1

gZ

whereZ

Nu

gll

l

Nusselt Analysis -Assumptions

�Laminar condensate film�Gravitational and viscous forces only�Heat transfer by conduction through the film�Thermodynamic equilibrium at the interface�Uniform -

� Physical properties� Wall temperature

Verification of NusseltAnalysis

� Earlier attempts to experimental verification were not successful because of

� Presence of non-condensible gases

� Presence of dropwise condensation

� Forced convective effects (vapour shear)

� Rippling, splashing and turbulence of the film

� Recent data under “Nusselt conditions” validates the simple Nusselt theory

Extension of Nusselt Analysis

� Condensate subcooling - Bromley (1952); Rohsenov (1956)

� Condensate inertia forces and convection - Sparrow and Gregg (1959a, 1959b)

� Shear stress at the interface - Koh et al (1961); Chen (1961)

� Uniform wall heat flux - Fuji et al (1972)

General Approach to Condensation

Laminar Condensation in Vert. Tubes

( ) 3/13

924.0

Γη

ρ−ρρλ=α

l

glll g

W = πDi

W = πDo

Condensation on Horizontal Tubes

�Gravity controlled condensation on a single horizontal tube is examined

�The analysis is then extended to industrial situation of multiple tubes in a bundle considering inundation effects

Single Horizontal Tube

( )( )

4/13

728.0

−η

∆ρ−ρρλ=α

owsat

vglll

DTT

hg

In alternate form

( )3/1

3/1

2

3

Re523.1−

η

ρ−ρρλ=α l

glll

Inundation Effects

� Indundation - Condensate from upper tubes falls on the lower tubes

� This increases the condensate thickness, decreasing the condensation coefficient

n

N N/1

1

−= αα

n= 4 - Nusselt theory

n= 6 - Kern from experience

Condensation in Horizontal Tube

Gravity controlled Vapour shear case controlled case

Vapour

Film draining under gravity

Liquid pool

Condensation in Horizontal Tube

( )( )

4/13

−η

∆ρ−ρρλβ=α

iwsat

vglll

TopDTT

hg β depends

on the

angle φ

Coefficient for top region where film is

drained:-

Jaster and Kosky (1976) obtained Ψ from void fraction

φ

Average coefficient for the top and bottom region is:-

( )( ) π

φβ=Ψ

−η

∆ρ−ρρλΨ=α ,

4/13

whereDTT

hg

iwsat

vglll

Tube

Vapour Shear Effects

� Vapour shear effects arise from forced convective motion of the vapour

� Vapour shear thins the liquid film, thereby increasing the coefficient

� Onset of laminar to turbulent transition occurs at lower Reynolds number

� Shekriladze and Gomelauri (1966) developed equations for vertical vapour down flow

Industrial EquipmentPure vapour

+ non-condensable

liquid

film

Tg

Ti

pv,b

pv,i

• Drainage of condensate is important. Condensation is almost always carried out in downflow manner

• Provision of a vent for non-condensable gas at proper location is of paramount importance.

vapour+gas

coolantliquid

film

Tg

Ti

pv,b

pv,i

Enhanced Condensation Surfaces

� Special surfaces enhance

condensation by

� Localised thinning of the condensate film using surface tension effects

� (‘Gegorrig surfaces’)

� Easy condensate drainage

� Enhanced condensation tubes are commercially available

� More often these are used as “double enhancement” devices

Cooling wall

Vapour

Condensate

For a Convex Surface…

rpp

satl

σ+=

( )dz

rd

dz

dp /1σ=

• Differentiating with respect to distance along a fin

• For a concave surface ( )dz

rd

dz

dp /1σ−=