Actual Shell Side Pressure Drop :Bell-Delaware Method

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Five corrections to Cross Flow Pressure Drop…..

Tube Side Calculations

Gr. No. DN di, mm Ret htube, W/m2K

Ntubes Dshell (m) B/Ds

1.

2.

3.

4.

5.

6.

7.

Shell Side Calculations

Gr. No.

Dshell, m Reshell hs, W/m2.K

Uclean

W/m2.KUdirty

W/m2.KLdirty, m Ds/L

0.067–0.2

1.

2.

3.

4.

5.

6.

7.

Hydraulic Analysis for Tube-Side

• The pressure drop encountered by the fluid making Np 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 ttubef

Shell-side pressure drop, Δps

• For a shell-and-tube type heat exchanger with bypass and leakage streams, the total inlet nozzle-to- exit nozzle pressure drop is calculated as the sum of the following three components:

• The combined pressure drop of all the interior cross flow section .

• The pressure drop in the window

• The pressure drop in the entrance and exit sections.

• The total shell-side pressure drop, excluding nozzles, is

•The pressure drop in the nozzles must be calculated separately and added to the total pressure drop.

Friction coefficient for Ideal Cross Flow

2Re33.1

1b

s

b

o

Ti

dP

bf

Where 43

Re14.01 bs

bb

Pressure drop in Ideal Interior Cross Flow

• The pressure drop in an equivalent ideal tube bank in one baffle compartment of central baffle spacing a is calculated from:

where fi is the friction coefficient,Gs is the mass velocity of the shell-side fluid, ρs is the shell-side fluid density, μs is the shell-side fluid viscosity, μs,w is the viscosity of shell-side fluid evaluated at wall surface temperature, and Ntcc is the number of tube rows crossed in one cross flow section.

Pressure drop in the interior cross flow

• By considering the pressure drop in the interior cross flow section (baffle tip to baffle tip), the combined pressure drop of all the interior cross flow section is:

where Nb is the number of baffles,Rl is the leakage correction factor (A and E streams) Rb is the bypass correction factor . Typically, Rb= 0.5 to 0.8, depending on the construction type and number of sealing strips, and Rl = 0.4 to 0.5

The leakage correction factor, Rl

Where

Correction factors for bundle bypass pressure drop, Rb

with the limit of , Rb =1 at rss1/2, &

Cbp=4.5 for laminar flow, Res≤ 100,

Cbp=3.7 for turbulent and transition flow.

The pressure drop in the window

tw

s

m

sw S

m

S

mm

For turbulent flow, Res > 100:

22

42

sin

3602

sin

3604 octlctl

tdsds

stw dNDS

Pressure Drop for Laminar flow through the Window

For laminar flow, Res< 100:

360

4

dsstwo

tww

DNd

SD

Pressure Drop in Window for Res=100

• Comparing the results of laminar and turbulent calculations at the break point of Res=100, it is found that the values are not equal.

• Because they are based on different principles. • In such cases, the larger value should be taken as a

safety factor.

Special Features of Flow Region of the End Zones

• The number of tube rows crossed includes the tube rows in the entry or exit window.

• The leakage streams have not yet developed (entry) or just joined the main stream (outlet) in the end zones, and therefore the leakage correction factor is not applicable.

• The baffle spacing in the end zones may differ from the central spacing, especially for U-tube bundles.

• An end zone correction factor, Rs is therefore used.

• The pressure drop in the two end zones is

Leakage Flow Streams

• There are two different shell side leakage flow streams in a baffled heat exchanger

• Stream A is the leakage stream in the orifice formed by the clearance between the baffle tube hole and the tube wall.

• Stream E is the leakage stream between the baffle edge and shell wall.

Pressure drop correction for unequal baffle spacing at inlet and/or outlet, Rs

n is the slope of the friction factor curve,For laminar flow, (Res < 100); n =1 for turbulent flow, n ≈ 0.2

Pressure Drop Caluculations

Group Ntube ptube pbi pc pw pe pshell

1.

2.

3.

4.

5.

6.

7.

Pumping Power

oilhotp

tubeoilhottube

pmP

oilcrudep

shelloilcrudeshell

pmP

Parametric Study and Thermo-economic Optimization of STHE

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Need for Heat Transfer Area Vs Baffle Spacing

B/Ds

AHT

Normalized pumps power consumption vs dimensionless baffle spacing

B/Ds

Baffle cut can vary between 15% and 45%

of the shell inside diameter.

Thermo-economic Optimization

Objective Function: The total annual cost

HEXDexopT CaEctC 1 Where top is the period of operation per year, cex is the unit cost of the exergy, ED is the exergy destruction, a1 is the capital recovery factor and CHEX is the capital cost of the heat exchanger.

The Exergy Destruction Rate : A Measure of Running Cost

The thermal component of the exergy destruction rate

The pressure component of the exergy destruction rate

The totalexergy destruction rate

pDTDD EEE ,,

Effect of Baffle Spacing on Total Cost