Design of Condensers/Condensing Zones P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Lowest Shell side Thermal Resistance !!!

Design of Condensers/Condensing Zones

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Lowest Shell side Thermal Resistance !!!

HP CFWH

HP CFWH No. 8

Thermodynamic Layout of HP Closed Feed Water Heater

Desuperheater

Condensing Shell Drain Cooler

HP Turbine

TRAP

Tbi, pbi, Tbsi

Tfi+1Tfi

DS

TTD

Feedwater heater with Drain cooler and Desuperheater

-TTD=Terminal temperature difference

C=Condenser

DC=Drain cooler

DS=Desuperheater

Bled steam

T

L

DCC

Condensate

CDC

Feed Water in

DS

Bleed Steam

Feed Water out

Number of Tubes

• The flow rate inside the tube is a function of the density of the fluid, the velocity of the fluid, cross-sectional flow area of the tube, and the number of tubes.

By using above Eq. and replacing Ac by di2/4, number of tubes

can be calculated as

2itt

tubet du

mN

tctttube NAum

where di is the tube inside diameter.

Tubes in Shell and Tube Hx

• The number and size of tubes in an exchanger depends on the• Fluid flow rates• Available pressure drop.• The number and size of tubes is selected such that the• Tube side velocity for water and similar liquids ranges from 0.9 to 2.4 m/s.• Shell-side velocity from 0.6 to 1.5 m/s.• The lower velocity limit corresponds to limiting the fouling,

and the• upper velocity limit corresponds to limiting the rate of

erosion.• When sand and silt are present, the velocity is kept high

enough to prevent settling.

Tube-Side Nusselt Number

For turbulent flow, the following equation developed by Petukhov-Kirillov is used:

2

322

1

28.3Reln58.1

1Pr2

7.1207.1

PrRe2

t

t

tt

tube

fWhere

f

f

Nu

Properties are evaluated at mean bulk temperature and constants are adjusted to fit experimental data.Validity range: 104 < Ret < 5 x 106 and 0.5 < Prt < 2000 with 10% error.

For laminar flow, the Sieder and Tate correlation is be used.

31

PrRe86.1

L

dNu itt

tube

is applicable for 0.48 < Prt < 16700 and (Ret Prt di/L)1/3 > 2.

The heat transfer coefficient for the tube-side is expressed as follows:

i

ttt d

kNuh

Shell-diameter

2

4 Stubeprot

shell DCTP

ANA

2Ttubepro PCLA

HP Closed Feed Water Heater

Condensate Loading

This can be used to calculate a Reynolds number

Perimeter

condensate of flow Mass

tubes.alfor vertic 0d

mcondensate

tubes.horiontalfor tube

condensate

L

m

filmoncondensati

4Re

General values of condensate loading for horizontal tubes: 0.01 to 0.05 kg/m.s

•Flow is considered laminar if this Reynolds number is less than 1800. •The driving force for condensation is the temperature difference between the cold wall surface and the bulk temperature of the saturated vapor

The viscosity and most other properties used in the condensing correlations are evaluated at the film temperature, a weighted mean of the cold surface (wall) temperature and the (hot) vapor saturation temperature

surfacevapourwallsatdriving TTTTT

4

3

4

3 drivingsatwallsaturationsatfilm

TTTTTT

Onset of Turbulence & Turbulent Film Condensation

• The transition film Reynolds number for the tube bundle is adapted from a vertical plate turbulent transition criterion of 1600 (but also values of 1200, 1800 and 2000 have been proposed).

• Thus, the film will become turbulent on the tube bundle at ReΓ

equal to 1600 and thus when ReΓ > 1600 the following expression should be used.

• The flow is nearly always laminar on single tube because of the short cooling length around the perimeter

Wall Temperatures

• It is often necessary to calculate the wall temperature by an iterative approach.

• The summarized procedure is:

1. Assume a film temperature, Tf 2. Evaluate the fluid properties (viscosity, density, etc.) at

this temperature 3. Use the properties to calculate a condensing heat transfer

coefficient (using the correlations to be presented) 4. Calculate the wall temperature. The relationship will

typically be something like

coolantsat

oo

satwall TT

Ah

UATT

1

1

5. Use the wall temperature to calculate a film temperature

6. Compare the calculated film temperature to that from the initial step. If not equal, reevaluate the properties and repeat.

Laminar Flow Outside Horizontal Tubes

When vapor condenses on the surface of horizontal tubes, the flow is almost always laminar. The flow path is too short for turbulence to develop. Again, there are two forms of the same relationship:

The constant in the second form varies from 0.725 to 0.729. The rippling condition (add 20%) is suggested for condensate Reynolds Numbers greater than 40.

31

2

3

3 Re

51.1

f

vfff

oncondensati

cond

gkh

41

0

3

725.0

dT

ghkh

drivingf

fgvfffcond

Condenser tubes are typically arranged in banks, so that the condensate which falls off one tube will typically fall onto a tube below.

The bottom tubes in a stack thus have thicker liquid films and consequently poorer heat transfer.

The correlation is adjusted by a factor for the number of tubes, becoming for the Nth tube in the stack

4

41

0

3

725.0N

h

dTN

ghkh top

drivingf

fgvfffcond

The heat transfer coefficient on the Nth tube row

• The heat transfer coefficient on the Nth tube row in the bundle h(N) is

43

43

1)1(

)( NN

h

Nh

• Kern (1958) concluded from his practice experience in designing condensers that the Jakob tube row expression was too conservative and that this resulted in condensers that were consistently over-surfaced.

• To improve his thermal designs, he replaced the exponent of (-1/4) in the Nusselt expression with a value of (-1/6) so that corresponding equations become

)1(

)(

h

Nh

N

Condensation on Horizontal Bundles: Prediction of Heat Transfer Coefficient in Nth Tube Row

Falling Film Condensation on Horizontal Tubes

• Falling-film heat exchangers are attractive because they provide good heat transfer performance and low working-fluid inventories.

• The design of falling-film heat exchangers has been largely based on empirical data.

• A thorough understanding of the falling-film flow and heat transfer interactions is important.

• An ability to predict the falling film mode would allow better data correlation and improve the modeling and analysis of heat transfer and fluid flow.

Modes of Condensation on Tube Bundle

The droplet mode

The jet mode The sheet mode

Flow Rate Vs Mode of Falling Film

Condensation on Horizontal Tube Bundles : Flow Map

• Hu and Jacobi (1996) proposed flow mode transition equations with ReΓ versus Ga+ (film Reynolds number vs. the Galileo number) for the following principal flow modes: sheet flow, column flow and droplet flow.

• The mixed mode transition zones of column-sheet and droplet-column were also considered as regimes, bringing the total to five.

• Hence, they presented four flow transition expressions (valid for passing through the transitions in either direction and hence the symbol ⇔):

Range of Validity of Model

Flow Transition Map

Identification Condensation Mode

Final Correlation

Onset of Turbulence & Turbulent Film Condensation

• The transition film Reynolds number for the tube bundle is adapted from a vertical plate turbulent transition criterion of 1600 (but also values of 1200, 1800 and 2000 have been proposed).

• Thus, the film will become turbulent on the tube bundle at ReΓ

equal to 1600 and thus when ReΓ > 1600 the following expression should be used.

Condensation on Horizontal Tube Bundles : Turbulent Flow

• Turbulent flow of the condensate film may be reached in a condenser, which significantly increases heat transfer.

• Comparatively little has been published on turbulent film condensation on tube bundles compared to the information available for laminar films.

• Butterworth (1983) recommends adapting the Labuntsov expression for turbulent film condensation on a horizontal tubes for predicting local turbulent film condensation on the Nth tube row in horizontal tube bundles

h

Overall Heat Transfer Coefficient for the Heat Exchanger

The overall heat transfer coefficient for clean surface (Uc) is given by

Considering the total fouling resistance, the heat transfer coefficient for fouled surface (Uf) can be calculated from the following expression:

Outlet Temperature Calculation and Length of the Heat Exchanger

The outlet temperature for the fluid flowing through the tube is

The surface area of the heat exchanger for the fouled condition is :

and for the clean condition

where the LMTD is always for the counter flow.

The over surface design (OS) can be calculated from :

The length of the heat exchanger is calculated by

Wall Temperatures

• It is often necessary to calculate the wall temperature by an iterative approach.

• The summarized procedure is:

1. Assume a film temperature, Tf 2. Evaluate the fluid properties (viscosity, density, etc.) at

this temperature 3. Use the properties to calculate a condensing heat transfer

coefficient (using the correlations to be presented) 4. Calculate the wall temperature. The relationship will

typically be something like

coolantsat

oo

satwall TT

Ah

UATT

1

1

5. Use the wall temperature to calculate a film temperature

6. Compare the calculated film temperature to that from the initial step. If not equal, reevaluate the properties and repeat.

The heat transfer coefficient on the Nth tube row

• The heat transfer coefficient on the Nth tube row in the bundle h(N) is

43

43

1)1(

)( NN

h

Nh

• Kern (1958) concluded from his practice experience in designing condensers that the Jakob tube row expression was too conservative and that this resulted in condensers that were consistently over-surfaced.

• To improve his thermal designs, he replaced the exponent of (-1/4) in the Nusselt expression with a value of (-1/6) so that corresponding equations become

)1(

)(

h

Nh

N

Condensation on Horizontal Bundles: Prediction of Heat Transfer Coefficient in Nth Tube Row