me421lec10p1

7/28/2019 ME421Lec10p1

http://slidepdf.com/reader/full/me421lec10p1 1/18

ME421

Heat Exchanger andSteam Generator Design

Lecture Notes 10 Part 1

Condensation and Evaporation (Boiling)(Condensers and Evaporators)

7/28/2019 ME421Lec10p1


Introduction• Condensation: when saturated vapor contacts a lower-

temperature medium

• Evaporation: when saturated liquid contacts a higher

temperature medium; if this medium is a surface - boiling

• Condenser: a two-phase flow HEX where the heat is

generated from the conversion of vapor into liquid, and the

heat generated is removed from the system by a coolant

• Evaporator: a two-phase flow HEX where the heat is

removed by the conversion of liquid into vapor

• Especially in the refrigeration and air-conditioning industry,evaporators and condensers are widely used

• Other examples are power condensers, boilers, steam

generators, etc

7/28/2019 ME421Lec10p1


Condensation• Film condensation: if the liquid (condensate) wets the

surface

• Droplet condensation: if the liquid does not wet the surface

• Dropwise condensation results in higher HT coefficientsthan filmwise condensation, but is very difficult to sustain

in practice; thus condensers are designed to operate in

filmwise mode.

7/28/2019 ME421Lec10p1


Dropwise

condensation

7/28/2019 ME421Lec10p1


Film Condensation on a Single Horizontal Tube

Laminar Film Condensation

• Local HT coefficient around the tube (Fig. 7.1) as a function of

circumferential angle is

δ is the film thickness and kl is the liquid phase thermal

conductivity

• Average HT coefficient given by Nusselt theory (Eq. 7.2)

subscript l (or f) is for liquid, g (or v) is for gas, ilg is enthalpy of

vaporization (hfg), Tsat is the saturation temperature, Tw is the

wall temperature

• Simple example (7.1) in book

)(

k)(h lφδ=φ

25.0

lwsatl

3lggll

l

m

k)TT(

dgi)(728.0

k

dh

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−µ

ρ−ρρ=

7/28/2019 ME421Lec10p1



Forced Convection Film Condensation

• When vapor moves at a high velocity

– surface shear stress between the vapor and the condensate

– vapor separationbecome important considerations.

• Several correlations are available, see Section 7.3.2, and

the example within• The most conservative approach that satisfies the extremes

of gravity-controlled and shear-controlled condensation is

proposed by Butterworth (Eq. 7.7)

( )( ) 2/12/1

2/1m F47.911416.0

eR~Nu

++=

7/28/2019 ME421Lec10p1



• In the previous correlation

two-phase Reynolds number:l

dueR~g

ν=

wsat

l2g

lglTTT,

Tku

idgF −=∆

∆

µ=

7/28/2019 ME421Lec10p1


Film Condensation in Tube Bundles

continuouslaminar sheet

staggeredconfiguration discretedroplets large vapor velocities

7/28/2019 ME421Lec10p1



Effect of Condensate Inundation

• In the absence of vapor velocity:

– condensate falls by gravity onto lower tubes in the bundle

– condensate thickens around the lower tubes – condensation heat transfer decreases, because the thick condensate

layer acts as an insulator

• Film condensation on a vertical in-line column of N horizontal

tubes using Nusselt idealized theory (Fig. 7.3(a)) gives the

following average coefficient compared to the coefficient for

the first (top) tube

h1 given by Eq. 7.2

4/1

1

N,mN

h

h −=

Fil C d ti i T b B dl

7/28/2019 ME421Lec10p1


Film Condensation in Tube BundlesEffect of Condensate Inundation (continued)

• The local coefficient for the Nth

tube by the Nusselt theory

• Kern's relationship is less conservative

• Eissenberg relation for a staggered bundle (side-drainage

model, Fig. 7.3(b))

• For design purposes, Kern relation is recommended

4/34/3

1

N )1N(Nh

h−−=

6/56/5

1

N6/1

1

N,m)1N(N

h

handN

h

h−−== −

4/1

1

N N42.060.0hh −+=

Fil C d i i T b B dl

7/28/2019 ME421Lec10p1



Effect of Condensate Inundation (continued)

• Example 7.3 compares previous relations, but usesEissenberg for in-line and others for staggered, too

• Staggered arrangement yields a higher HT coefficient

• To prevent inundation, tubes are slightly inclined, which

results in an increase of up to 25% in the HT coefficient


7/28/2019 ME421Lec10p1


Film Condensation in Tube BundlesEffect of Vapor Shear

• For downward and horizontal flow, Fujii et al proposed:

• Mean local steam velocity is ug= g/ρg Am, where Am = wNtL isthe mean flow area in terms of the number of unit cells Nt and

the mean flow width per cell w

600F03.0for F96.0eR

~Nu 5/1

2/1m <<=

m&

L

2

TL

p4/dppw π−=


7/28/2019 ME421Lec10p1


Film Condensation in Tube BundlesCombined Effects of Inundation and Vapor Shear

• Butterworth correlation for the local HT coefficient in the Nth

tube row

where hsh is given by Eq. 7.6 as

• McNaught correlation treats shell-side condensation as two-

phase forced convection:

where hG is

and hsh is given as

( ) [ ]6/56/52/1

2/14L

4sh

2shN )1N(Nhh25.0h5.0h −−×⎥

⎦

⎤⎢⎣

⎡ ++=

2/1lsh eR

~

d

k59.0h =

( )2/12

G

2

shN hhh +=6/56/5

LG )1N(Nhh −−=

Ltt

sh hX

26.1h ⎟⎟ ⎠

⎜⎜⎝

=78.01 ⎞⎛


7/28/2019 ME421Lec10p1


Film Condensation in Tube BundlesCombined Effects of Inundation and Vapor Shear (continued)

• Xtt is the Lockhart-Martinelli parameter

and hL is the liquid phase forced convection heat transfer

coefficient across a bank of tubes, select from Chapter 3 or

elsewhere.

• McNaught correlation is valid for

p/d = 1.25

10≤

G≤

70 kg/m2

s0.025 ≤ x ≤ 0.8 (x: vapor quality)

0.008 ≤ Xtt ≤ 0.8

• See example 7.4

1.0

g

l

5.0

l

g

9.0

ttx

x1X ⎟

⎟ ⎠

⎞⎜⎜⎝

⎛

µµ

⎟⎟ ⎠

⎞⎜⎜⎝

⎛

ρ

ρ⎟ ⎠

⎞⎜⎝

⎛ −=

Condensation inside Tubes (Horizontal)

7/28/2019 ME421Lec10p1


Condensation inside Tubes (Horizontal)• Different flow patterns exist during condensation inside tubes

due to the balance between vapor shear and gravitational

forces

• These flow patterns change the HT coefficients, so local

values must be determined

• To predict flow patterns, define dimensionless mass velocity

– jg* > 1.5, Xtt < 1.0 : mist and annular

– jg* < 0.5, Xtt < 1.0 : wavy and stratified

– jg* < 0.5, Xtt > 1.5 : slug

– jg* > 1.5, Xtt < 1.5 : bubble

• When jg* is low, gravitational forces dominate and stratification

of the condensate will occur

• When jg* is high, interfacial shear forces are large andcondensate flow is annular

( )[ ] 2/1

glg

*

gdg

Gx j

ρ−ρρ=


7/28/2019 ME421Lec10p1



• For laminar flow, stratification occurs and heat transfer

coefficients are too low because heat transfer is negligible inthe stratified region. See p.245 in book for a Nusselt-based

correlation.


7/28/2019 ME421Lec10p1



• In general, turbulent flow models are used.

• In the single-phase region, for example when there issuperheating or subcooling, use proper correlations from

literature (Chapter 3).

• There are numerous correlations for use in the two-phaseregion with different kinds of fluids (refrigerants especially).

• Traviss correlation (Eq. 7.25) is for R-12 and R-22, and

makes use of the liquid Reynolds number (Eq. 7.26) and twoparameters F1 and F2 (Eqs. 7.27-7.30).

• A more recent correlation developed by Cavallini and Zecchin

(Eq. 7.31) is valid for R-11, R-12-, R-21, R-22, R-113, and R-114.


7/28/2019 ME421Lec10p1


Condensation inside Tubes (Horizontal)• The Shah correlation for two-phase (TP) HT coefficient is

valid for a larger group of fluids including water

where

where pr = psat/pcr is the reduced pressure and the liquid-only

HT coefficient hL can be found by Dittus-Boelter equation:

• Shah correlation can be integrated to evaluate the mean HT

coefficient in the whole condensing region, but for a linear variation of quality over a 100% to 0% range,

• See Section 7.5.1 for vertical tube condensation

⎟ ⎠

⎞⎜⎝

⎛ +=

95.0LTPZ

8.31hh

4.0r

8.0

px

x1

Z ⎟ ⎠

⎞⎜⎝

⎛ −=

d

kPr d)x1(G023.0h l

4.0l

8.0

lL ⎟⎟

⎠

⎞⎜⎜⎝

⎛

µ−

=

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ +=

38.0r

Lm,TP

p

09.255.0hh

me421lec10p1

Documents