Section 5.4 Shell-And-tube Heat Exchanger_corrected

41

5.1

Shell-and-Tube Heat Exchangers

The most common type of heat exchanger in industrial applications is shell-and-tube heat exchangers. The exchangers exhibit more than 65% of the market share with a variety of design experiences of about 100 years. Shell-and tube heat exchangers provide typically 2 3 the surface area density ranging from 50 to 500 m /m  and are easily cleaned. The design codes and standards are available in the TEMA (1999)-Tubular Exchanger Manufacturers Association. A simple exchanger, which involves one shell and one pass, is shown in Figure 5.18. Tube outlet Shell inlet Tube

Shell sheet

Shell

Baffles Shell outlet

End channel

Tube inlet

Figure 5.18 Schematic of one-shell one-pass (1-1) shell-and-tube heat exchanger.

Baffles In Figure 5.18, baffles are placed within the shell of the heat exchanger firstly to support the tubes, preventing tube vibration and sagging, and secondly to direct the flow to have a higher heat transfer coefficient. The distance between two baffles is baffle spacing .

Multiple Passes Shell-and-tube heat exchangers can have multiple passes, such as 1-1, 1-2, 1-4, 1-6, and 1-8 exchangers, where the first number denotes the number of the shells and the second number denotes the number of passes. An odd number of tube passes is seldom used except the 1-1 exchanger. A 1-2 shell-and-tube heat exchanger is illustrated in Figure 5.19.

42 Tube outlet Shell inlet Tube

Pass partition

Shell

End channel

Baffles Shell outlet Tube inlet

Figure 5.19 Schematic of one-shell two-pass (1-2) shell-and-tube heat exchanger. Lt

B

Ds

Figure 5.20 Dimensions of 1-1 shell-and-tube heat exchanger

Dimensions of Shell-and-Tube Heat Exchanger Some of the following dimensions are pictured in Figure 5.20.  L  = tube length  N t   = number of tube  N  p  = number of pass  D s  = Shell inside diameter  N b  = number of baffle  B  = baffle spacing The baffle spacing is obtained  B =

 Lt   N b

+1

 

(5.128)

43

Shell-Side Tube Layout Figure 5.21 shows a cross section of both a square and triangular pitch layouts. The tube  pitch  P  and the clearance C t   between adjacent tubes are both defined. Equation (5.30) of t  the equivalent diameter is rewritten here for conv enience  De

=

4 Ac  P heated 

 

(5.129)

From Figure 5.21, the equivalent diameter  for the square pitch layout is  De

=

(

2

4  P t 

− π d o 2 4) π d o

 

(5.130a)

From Figure 5.21, the equivalent diameter  for the triangular pitch layout is

  3 P t 2 π d o 2    4  4 − 8         De = π d o

(5.130b)

2

The cross flow area of the shell  Ac  is defined as  Ac

=

 D s C t  B  P T 

 

(5.131)

do

do

di

di

Flow Ct

Ct

Pt

(a)

Pt

(b)

Figure 5.21 (a) Square-pitch layout, (b) triangular-pitch layout. The diameter ratio d r is defined by   d r  =

d o d i

 

(5.132)

Some diameter ratios for nominal pipe sizes are illustrated in Table C.6 in Appendix C. The tube pitch ratio P r is defined by  

44

 P r  =

 P t  d o

 

(5.133)

The tube clearance C t  is obtained from Figure 5.21. C t  =  P t  − d o  

(5.134)

The number of tube  N t   can be predicted in fair approximation with the shell inside diameter D s. 2

 N t  = (CTP )

π   Ds

4

ShadeArea

 

(5.135)

where CTP   is the tube count constant   that accounts for the incomplete coverage of the shell diameter by the tubes, due to necessary clearance between the shell and the outer tube circle and tube omissions due to tube pass lanes for multiple pass design [1]. CTP = 0.93 CTP = 0.9 CTP = 0.85

for one-pass exchanger for two-pass exchanger for three-pass exchanger

ShadeArea = CL ⋅ P t 2  

(5.136)

(5.137)

where CL is the tube layout constant. CL = 1 CL = sin(60°) = 0.866

for square-pitch layout for triangular-pitch layout

(5.138)

Plugging Equation (5.137) into (5.135) gives 2 2 π   CTP    D s CTP   D s    N t  =   2 =   2 2  4   CL    P t  4   CL   P r  d o

π 

Table 5.1 Summary of shell-and-tube heat exchangers Description Equation & 1c p1 (T 1i − T 1o ) q=m Basic Equations & 2 c p 2 (T 2o − T 2i ) q=m Heat transfer areas of the inner and outer surfaces of an inner pipe

= π  ⋅ d i ⋅ N t  ⋅ L  Ao = π  ⋅ d o ⋅ N t  ⋅ L  Ai

(5.139)

(5.140) (5.141) (5.142a) (5.142b)

45

Overall Heat Transfer Coefficient

U o

1  Ao

=

 d o    d  1 1 +   i   + ln

2π kL

hi Ai

(5.143)

ho Ao

Tube side

Reynolds number

 ρ u m d i

=

Re D

µ  2

 Ac

=

π d i

=

& d i m

(5.144)

 Ac µ 

 N t 

(5.144a)

4  N  p 1

Laminar flow (Re < 2300)

=

 Nu D

µ     d  Re Pr   3   = 1.86 i       L    µ  s  

hd i k  f 

0.14

(5.145)

0.48 < Pr < 16,700 0.0044 < (µ  µ  s )  < 9.75 Use Nu D

Turbulent flow (Re > 2300)

=

 Nu D

= 3.66

hd i

=

k  f 

if  Nu D

< 3.66

( f  / 2)(Re D − 1000 ) Pr  12 1 + 12.7( f  / 2 ) (Pr 2 3 − 1)

(5.146)

3000 < Re D < 5 × 10 6 [4] 0.5 ≤ Pr ≤ 2000 Friction factor Shell side Square pitch layout (Figure 5.21)

Triangular pitch layout (Figure 5.21)

−2

 f  = (1.58 ln (Re D ) − 3.28)

 De

=

(

2

4  P t 

− π d o 2 4) π d o

  3 P t 2 π d o 2   4  4 − 8       De = π d o

Cross flow area

Reynolds number

 Ac

=

Re D

(5.147)

(5.148a) (5.148b)

2

(5.149)

 D s C t  B  P t 

=

 ρ u m De µ 

=

& De m  Ac µ 

(5.150)

46

 Nusselt number

 Nu

ho De

=

= 0.36 Re

k  f 

0.55

  µ     Pr   µ     s  

0.14

13

(5.151)

6

2000 2300

f ReD

16 ReD

otherwise

 

(E5.2.26)

The Nusselt number for turbulent or laminar flow is defined using Equations (5.145) and (5.146) with assuming that µ changes moderately with temperature. The convection heat transfer coefficient is then obtained.

) :=

(

 NuD Dh , Lt , ReD, Pr 

 f (ReD)  ⋅   2  

(ReD − 1000)⋅ Pr 

if  ReD > 2300

  0.5    f (ReD)  3 1 + 12.7⋅ ⋅  Pr  − 1    2   2

1

1.86⋅

 Dh⋅ ReD⋅ Pr    

Lt

 

3

otherwise

 

(E5.2.27)

(

)

 Nu1 := NuD di, Lt , Re1 , Pr 1

h 1 :=

 Nu1⋅ k 1 di

 Nu1

= 8.484

 

h 1 = 468.972⋅

(E5.2.28)

W 2

m ⋅ K 

 

(E5.2.29)

Shell side (50% ethylene glycol)

The free-flow area is obtained using Equation (5.131) and the velocity in the shell is also calculated

A c2 :=

v 2 :=

Ds ⋅ Ct⋅ B Pt

mdot2

ρ2⋅ A c2

−4 2

A c2 = 2.581 × 10

m

 

v2

= 1.786

(E5.2.30)

m s

 

(E5.2.31)

53 The velocity of 1.786 m/s in the shell is acceptable because the reasonable range of 1.2 – 2.4 m/s for the similar fluid shows in Table 5.4. The equivalent diameter for a triangular  pitch is given in Equation (5.148b) as

 P 2⋅ t

 De := 4⋅    Re2 :=

3

−

4

π ⋅ do

2

    

8

 π ⋅ do    2  

De

= 2.295⋅ mm  

ρ2⋅ v 2⋅ De

(E5.2.32)

3

Re2 = 5.225 × 10

µ2

 

(E5.2.33)

The Nusselt number is given in Equation (5.152) and the heat transfer coefficient is obtained. 1 0.55

 Nu2 := 0.36⋅ Re2

h 2 :=

⋅ Pr 2

3

 

(E5.2.34)

 Nu2⋅ k 2

4

h 2 = 1.442 × 10

De

⋅

W 2

m ⋅ K 

 

(E5.2.35)

The total heat transfer areas for both fluids are obtained as 2

A i := π ⋅ di⋅ Lt⋅ Nt Ao

A i = 0.403m

:= π ⋅ d o ⋅ Lt⋅ Nt

Ao

 

(E5.2.36)

 

(E5.2.37)

2

= 0.524m ⋅

The overall heat transfer coefficient is calculated using Equation (5.143) with the fouling factors as 1

Uo

Ao

:=

Uo

 do 

1 h1⋅ A i

+

R fi Ai

ln

+

  di  +

2⋅ π ⋅ k w⋅ Lt

R fo Ao

+

= 209.677⋅

W 2

m ⋅ K 

1 h2⋅ A o

 

(E5.2.38)

54 ε -NTU method The heat capacities for both fluids are defined and then the minimum and maximum heat capacities are obtained using the MathCAD built-in functions as C1 := mdot1⋅ c p1

C1

W K 

 

(E5.2.39)

3 W

C2 := mdot2⋅ c p2

(

= 530.61⋅

C2 = 1.716 × 10

)

⋅

K 

(

Cmin := min C1 , C2

)

Cmax := max C1 , C2

 

(E5.2.40)

 

(E5.2.41)

The heat capacity ratio is defined as

Cr :=

Cmin

Cr = 0.309

Cmax

 

(E5.2.42)

The number of transfer unit is defined as

 NTU :=

Uo ⋅ A o

 NTU

Cmin

= 0.207  

(E5.2.43)

The effectiveness for shell-and-tube heat exchanger is give using Equation (5.154) as  NTU1 :=

 NTU  N p

 

(E5.2.44a)

 ε hx := 2⋅ 1 +

 

2

Cr +

1 + Cr 

 2 0.5 1 + exp −NTU ⋅ 1 + C 1 r   ⋅  2 1 − exp −NTU1⋅ 1 + Cr  

   0.5   0.5

−1

ε hx = 0.182 (E5.2.44b)

Using Equation (5.156), the effectiveness is expressed as

ε hx

(

)

(

q

C1⋅ T1i − T1o

q max

Cmin⋅ T1i − T2i

(

C2⋅ T2o

)

(

− T2i)

)

Cmin⋅ T1i − T2i

 

(E5.2.45)

The outlet temperatures are rewritten for comparison with the outlet temperatures.

55 T1i = 120⋅ °C

T2i = 90⋅ °C

T1o := T1i − ε hx⋅

T2o := T2i + ε hx⋅

Cmin C1

⋅ (T1i − T2i)

T1o

= 114.544°C ⋅  

Cmin C2

⋅ (T1i − T2i)

T2o

(E5.2.46)

= 91.687°C ⋅  

(E5.2.47)

The engine oil outlet temperature of 114.544°C is close enough to the requirement of 105°C. The heat transfer rate is obtained

(

)

q := ε hx⋅ Cmin⋅ T1i − T2i

q

= 2.895 ×

3

10 W

 

(E5.2.48)

The pressure drops for both fluids are obtained using Equations (5.158) and (5.161) as

∆P 1 := 4⋅

 f ( Re1) ⋅ Lt di

 

∆P 2 := f ( Re2) ⋅

Ds De

+

 

1

 

2

1 ⋅ N p ⋅

1

2

⋅ ρ1⋅ v1

( N b + 1)⋅ 2 ⋅ ρ2⋅ v22

∆P 1 = 9.325kPa ⋅  

(E5.2.49)

 

(E5.2.50)

∆P 2 = 5.141kPa ⋅

Both the pressure drops calculated are less than the requirement of 10 kPa. The iteration  between Equations (E5.2.9) and (E5.2.46) is terminated. The surface density β   for the engine oil side is obtained using the relationship of the heat transfer area over the volume of the exchanger.

β 1 :=

2

Ao

 π ⋅ D 2  s

 

4

 

β 1 = 679.134⋅

m

3

m

⋅ Lt

 

Summary of the design of the miniature shell-and-tube heat exchanger

Given information T1i = 120⋅ °C

engine oil inlet temperature

T2i = 90⋅ °C

50% ethylene glycol inlet temperature

(E5.2.51)

56

mdot1 = 0.23

kg

mdot2 = 0.47

kg

mass flow rate of engine oil

s

mass flow rate of 50% ethylene glycol

s

− 4 2 K 

R fi = 1.76 × 10

= 3.53 ×

R fo

⋅m ⋅

− 4 2 K 

10

fouling factor of engine oil

W

⋅m ⋅

fouling factor of 50% ethylene glycol

W

Requirements for the exchanger T1o

≤ 115°C

∆P 1 ≤ 10kPa

Engine outlet temperature Pressure drop on both sides

Design obtained  N p

=1

number of passes

Ds

= 50.8⋅ mm

shell inside diameter 

do

= 3.175mm ⋅

tube outer diameter 

d i = 2.442mm ⋅

= 381⋅ mm

tube length

 Nt

= 138

number of tube

Ct

= 0.794mm ⋅

tube clearance

 N b

= 14

= 2 in

Lt

= 15in

tube inner diameter 

Lt

B = 25.4⋅ mm

Ds

baffle spacing

B = 1 in

number of baffle

T1o

= 114.544°C ⋅

engine oil outlet temperature

T2o

= 91.687°C ⋅

50% ethylene glycol outlet temperature

q

= 2.895⋅ kW

heat transfer rate

2

β 1 = 679⋅

m

surface density

3

m

∆P 1 = 9.325kPa ⋅

pressure drop for engine oil

57

∆P 2 = 5.141kPa ⋅

pressure drop for 50% ethylene glycol

The design satisfies the requirements.

Problems (corrected) Shell-and-Tube Heat Exchanger 5.3 A miniature shell-and-tube heat exchanger is designed to cool glycerin with cold water. The glycerin at a flow rate of 0.25 kg/s enters the exchanger at 60°C and leaves at 50°C. The water at a rate of 0.54 kg/s enters at 18°C, which is shown in Figure -3 P5.3. The tube material is Cr alloy (k w = 60.5 W/mK). Fouling factors of 0.253x10 2 -3 2 m K/W for water and 0.335x10 m K/W for glycerin are specified. Route the glycerin through the tubes. The permissible maximum pressure drop on each side is 30 kPa. The volume of the exchanger is required to be minimized. Since the exchanger is custom designed, the tube size may be smaller than NPS 1/8 (DN 6 mm) that is the smallest size in Table C.6 in Appendix C, wherein the tube pitch ratio of 1.25 and the diameter ratio of 1.3 can be applied. Design the shell-and-tube heat exchanger.

Figure P5.3 Shell-and tube heat exchanger