kern method iit - delhi

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Kern Method of

SHELL-AND-TUBE HEAT EXCHANGER Analysis

P V Subbarao

Professor

Mechanical Engineering DepartmentI I T Delhi

Simplified Procedures using Semi-Empirical Correlations.….



Properties Crude Oil Heavy gas oil Density, kg/m3 915 890 Specific heat, kJ/kg K 2.62 3.08 Viscosity, cPoise

0.664/0.563

0.32/0.389

Thermal conductivity,

W/m.K 0.124 0.14



Thermal Analysis for Tube-Side



Number of Tubes

• The flow rate inside the tube is a function of the density of thefluid, 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 p d i2 /4, number of tubes

can be calculated as

2

it t

tubet d u

m N

p

t ct t tube N Aum

where d i 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 oferosion.

• When sand and silt are present, the velocity is kept highenough to prevent settling.



Number of Tubes Vs Reynolds Number



Number of Tubes Vs Heat Transfer Coefficient



Tube-Side Nusselt Number

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

2

322

1

28.3Reln58.1

1Pr 2

7.1207.1

Pr Re2

t

t

t t

tube

f Where

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 < Pr t < 2000 with

10% error.



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

31

Pr Re86.1

L

d Nu it t

tube

is applicable for 0.48 < Pr t < 16700 and (Ret Pr t d i /L)1/3 > 2.

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

i

t t t

d

k Nuh



Thermal Analysis for Shell-Side



Tube Layout

• Triangular pitch (30o layout) is better for heat transfer andsurface area per unit length (greatest tube density.)

• Square pitch (45 & 90 layouts) is needed for mechanicalcleaning.

• Note that the 30°,45° and 60° are staggered, and 90° is in line. • For the identical tube pitch and flow rates, the tube layouts in

decreasing order of shell-side heat transfer coefficient and pressure drop are: 30°,45°,60°, 90°.

• The 90° layout will have the lowest heat transfer coefficientand the lowest pressure drop.

• The square pitch (90° or 45°) is used when jet or mechanicalcleaning is necessary on the shell side.



Tube Layout & Flow Scales

A Real Use of Wetted Perimeter !



Tube Pitch • Tube pitch Pt is chosen so that the pitch ratio is 1.25 < PT/do <

1.5.

• When the tubes are to close to each other (PT/do less than1.25), the header plate (tube sheet) becomes to weak for

proper rolling of the tubes and cause leaky joints.• Tube layout and tube locations are standardized for industrial

heat exchangers.

• However, these are general rules of thumb and can be“violated” for custom heat exchanger designs.



Equivalent Counter Flow : Hydraulic or Equivalent

Diameter

• The equivalent diameter is calculated along (instead of

across) the long axes of the shell and therefore is taken

as four times the net flow area as layout on the tube

sheet (for any pitch layout) divided by the wetted

perimeter.

r erperimeteheattransf De

areaflow-Free Net4



Equivalent diameter for square layout:

O

OT

e

flow

squareed

d P

P

A D

p

p

22

44

4

Equivalent diameter for Triangular layout:

2

84

34

4

2

2

O

O

e

flow

triangular e

d

d P

P

A D

T

p

p



Shell-Side Reynolds Number

Reynolds number for the shell-side is based on theequivalent diameter and the velocity on the cross flow

area at the diameter of the shell:

s

e

s

s s

D Am

Re

s

e s

s

e s s s

DG DU

Re



Shell-Side Flow



Overall Heat Transfer Coefficient for the Heat

Exchanger

The overall heat transfer coefficient for clean surface (U c ) is

given by

Considering the total fouling resistance, the heat transfer

coefficient for fouled surface (U f ) 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



Hydraulic Analysis for Tube-Side

• The pressure drop encountered by the fluid making N p passes through the heat exchanger is a multiple of the

kinetic energy of the flow.

• Therefore, the tube-side pressure drop is calculated by

228.3Reln58.1 t tube f

Properties are evaluated at mean bulk temperature and constants

are adjusted to fit experimental data.

Validity range: 104

< Ret < 5 x 106



Where,

bafflesof Number:b N

velocitymasssideShell: sG

.correction propertyVariable:

14.0

w

b

s

factor frictionsideShell: s f

Shell side Hydraulic Analysis



μb is the viscosity of the shell-side fluid at bulk

temperature, and μw is the viscosity of the tube-side fluid

at wall temperature.

The wall temperature can be calculated as follows:



Pumping Power

oil hot p

tubeoil hot tube

pm P

oil crude p

shell oil crude shell

pm P



Roadmap To Increase Heat Transfer



Roadmap To Increase Heat Transfer • Increase heat transfer coefficent

• Tube Side

– Increase number of tubes

– Decrease tube outside diameter

• Shell Side

– Decrease the baffle spacing

– Decrease baffle cut

• Increase surface area

– Increase tube length

– Increase shell diameter à increased number of tubes

– Employ multiple shells in series or parallel• Increase LMTD correction factor and heat exchanger

effectiveness

– Use counterflow configuration

– Use multiple shell configuration



Roadmap To Reduce Pressure Drop • Tube side

– Decrease number of tube passes

– Increase tube diameter

– Decrease tube length and increase shell diameter and number of

tubes

• Shell side

– Increase the baffle cut

– Increase the baffle spacing

–

Increase tube pitch – Use double or triple segmental baffles



• Study the effect of baffle spacing on size of heat

exchanger.

• Study the effect of baffle spacing on total pumping

power.

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