Ht1 Horizontal And Vertical Condenser Nani 8 Nov 2016 5im18
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Lab Name
Heat Transfer Lab
Course No
CL 312
Experiment Title:
Horizontal and Vertical Condenser
Experiment Number:
HT 1
Department:
Department of Chemical Engineering
Institute:
Indian Institute of Technology Guwahati
Lasted edited date:
Edited by:
Approved by:
1
CONTENTS AIM: ............................................................................................................................................ 3 SPECIFIC .................................................................................................................................... 3 OBJECTIVE: .............................................................................................................................. 3 INTRODUCTION:...................................................................................................................... 3 THEORY..................................................................................................................................... 3 DESCRIPTION ........................................................................................................................... 5 EXPERIMENTAL SETUP ......................................................................................................... 6 EXPERIMENT PROCEDURE:.................................................................................................. 8 EQUIPMENT DATA:................................................................................................................. 8 FORMULAE: .............................................................................................................................. 9 NOMENCLATURE: ................................................................................................................. 11 Error Analysis ........................................................................................................................... 12 PRECAUSTIONS: .................................................................................................................... 13 OBSERVATIONS & SAMPLE CALCULATION: ................................................................. 13 SAMPLE VIVA QUESTIONS: ................................................................................................ 19 REFERENCES .......................................................................................................................... 19
2
AIM: Experimental study on heat transfer efficiency of vertical and horizontal condenser. SPECIFIC OBJECTIVE: Estimate heat transfer rate across the condenser tubes through heat balance
Estimation of overall heat transfer coefficient experimentally for Horizontal and Vertical condenser and compare the results with that of the standard correlation.
Estimate experimental error on overall heat transfer coefficient and propose method to minimize experimental error on estimated overall heat transfer coefficient values
Compare performance both condensers heat transfer efficiency and justify.
INTRODUCTION: When a saturated vapor is brought in with a cooler surface, condensation occurs. Condensation occurs at different rate of heat transfer by either of the two distinct physical mechanism, drop and film wise condensation. The occurrence of drop or film wise condensation depends largely on the characteristics of the condensing vapor and the surface available for condensation. The condensing film coefficient is influenced by the texture of the surface on which the condensation occurs and also by whether the condensing surface is mounted vertically or horizontally. The heat transfer coefficients obtained during film wise condensation are 1/5th to 1/6th of that in drop wise condensation. Most practical cases correspond to mixed condensation. However, due to lack of control in drop wise condensation, calculations are mostly based on film condensation heat transfer coefficients.
THEORY FOR VERTICAL CONDENSER In case of condensation on the surface of a vapor tube, as in vertical condensers, the condensate film flows downwards under the influence of gravity, but is retarded by the viscosity of the condensate film. The flow is normally streamlined and heat flows through the film by conduction only. In vertical tube, about 60% of the vapor condenses in the upper half of the tube. Nusselt has derived a theoretical relation for the determination of film heat transfer coefficient in of physical properties of condensate film, characteristic dimension and the temperature driving force.
3
Assumptions: 1. Both the plate and the vapor are maintained at constant temperatures of Tw and Tsat, respectively, and the temperature across the liquid film varies linearly. 2. Heat transfer across the liquid film is by conduction only. 3. The velocity of the vapor is low (or zero) so that it exerts no drag on the condensate (no viscous shear on the liquid–vapor interface). 4. The flow of the condensate is laminar (Re<30) and the properties of the liquid are constant. 5. The acceleration of the condensate layer is negligible The film coefficient for condensation over a vertical plate of height L is given by – k3 ρ 2 g λ
1/4
ho = 0.943 ( ) L µ ∆T
(1)
VERTICAL & HORIZONTAL CONDENSER Film coefficient for condensation outside of vertical tube is given by: ho D k
= 0.0077 (
k L ∆ T 0.67
) Dλµ
D3 ρ2 g
(
µ
0.56
)
(2)
The physical properties are evaluated at film temperature, Tf, where
Tf = (Th −
3 4
(Th − Tw )) = Th −
3 4
∆T
(3)
FOR HORIZONTAL CONDENSER The value of the condensing coefficient for a given quantity of vapor, on a surface is significantly affected by the position of the condenser. Provide that the condensate film is flowing under laminar flow condition; the average condensing coefficient in case of a horizontal condenser is around three times as great as the vertical coefficient. Nusselt has derived a theoretical relation for the determination of film heat transfer coefficient in of physical properties of condensate film, characteristic dimension and the temperature driving force.
4
The film coefficient for condensation over a horizontal cylinder of outer diameter D o is given byk3 ρ 2 g λ
1/4
ho = 0.729 ( ) D µ ∆T
(4)
Film coefficient for condensation over N number of horizontal tubes of dia. D is given by: 1/4
k3 ρ 2 g λ
hN = 0.729 ( 2/3 ) N µ ∆T D o
(5)
The physical properties are evaluated at film temperature, Tf, where 3
Tf = (Th − ( Th − Tw )) 4
(6)
DESCRIPTION The set up consists of two tube bundle heat exchangers housed in a stainless steel shell, one mount horizontally and the other vertically. Water es through the tubes and steam condenses over the tubes. Steam is supplied to the condenser from a steam generator. The condensate is removed through the steam trap. A valve arrangement allows selecting steam flow into either the vertical or the horizontal condenser. Experiment can be conducted on any one of the condenser at a time. The continuous cooling water supply can also be routed to any of the condensers as required. The heat input by the heater in the steam generator is controlled by the Digital Temperature Controller. Six numbers of temperature sensors are provided to measure the inlet and outlet temperatures of the fluid.
TEMPERATURE SENSORS POSITIONS ARE GIVEN BELOW: T1
= Steam inlet for Horizontal/Vertical Condenser
T2
= Steam outlet for Horizontal Condenser.
T3
= Steam outlet for Vertical Condenser.
T4
= Water inlet for Horizontal Condenser.
T5
= Water outlet for Horizontal Condenser. 5
T6
= Water inlet for Vertical Condenser.
T7
= Water outlet for Vertical Condenser.
EXPERIMENTAL SETUP
Fig. (1) Experimental setup photo
6
Vertical conden ser
4
3
ROTAMETER
STEAM TRAP
WATER IN
Horizontal condenser CONDENSATE 2 WATER OUT
WATER OUT CONDENSATE OUT
1 STEAM IN
STEAM GENERATOR TANK
Fig. (2) Flow diagram for horizontal and vertical condenser 1. Valve 1: steam into apparatus 2. Valve 2: releases steam outside 3. valve 3: release water into horizontal condenser 4. valve 4: release water into vertical condenser 5. valve 5: release steam into horizontal condenser 6. valve 6: release water into vertical condenser
7
EXPERIMENT PROCEDURE: STARTING PROCEDURE: 1.The steam generator is filled with water up to ¾ of its capacity. 2. The digital temperature indicator is set at 110OC. 3. The steam generator valve is closed and time is allowed for steam formation. 4. One of the condensers is connected with cold water supply system. 5. The calibration of the rotameter provided for measurement of water flow rate is checked using a measuring cylinder and stopwatch. 6. When steam is formed, the supply of cold water is started to the condenser at any flow rate fixed by means of the rotameter. 7. The steam supply to the condenser is started and also a stopwatch is started at the same instant. 8. The condensate is collected and measured using a measuring cylinder and stopwatch. 9. The inlet and outlet temperatures of the cold water supply are noted. The temperature of the condensate is also recorded. 10. The above steps as above may be repeated with different flow rates to give another set of readings. 11. The entire process is then to be repeated for the other condenser, to allow comparative study of the results for two types of condensing arrangements. CLOSING PROCEDURE: 12. At the end of the experiment, the power supply to the heater is switched off. Also the mains power supply is switched off. 13. The vent provide on the steam generator is opened slightly to release pressure. 14. The supply of cooling water is disconnected. 15.
After the vapors condense, the condensers and steam generator are to be drained.
EQUIPMENT DATA: Number of tubes Tube length
N: L:
8 500 mm 8
I.D. of tube
di:
9.5 mm
O.D. of tube
D:
12.7 mm
Inside diameter of shell
Ds:
108 mm
Outside diameter of shell
Do:
114 mm
Length of shell
L:
500 mm (approx.)
Condensate Measurement:
Measuring Cylinder & Stopwatch
Water Flow Measurement:
Rota meter, measuring cylinder & Stop Watch.
Temperature sensors:
RTD PT-100 type 7 Nos.
FORMULAE: FOR VERTICAL CONDENSER: 1. The film coefficient for condensation over a vertical plate of height, L, is given by: k3 ρ 2 g λ
1/4
ho = 0.943 ( ) L µ ∆T
(1)
2. Film coefficient for condensation outside of vertical tube is given by: ho Do k
k L ∆ T 0.67
= 0.0077 (
Do λ µ
)
Do 3 ρ2 g
(
µ
0.56
)
(2)
3. The physical properties are evaluated at film temperature, Tf, where
Tf = (Th −
3 4
(Th − Tw )) = Th −
3 4
∆T
(3)
4. The heat balance between the amount of heat given to water by steam and the
9
amount of heat actually taken by the cooling water is obtained from the equation
Q = m (Tco − Tci ) = w𝜆
(4)
5. The overall heat transfer coefficient is calculated from equation:
U = m
(Tco − Tci )
(5)
A ∆Tlm
LMTD = (∆Tlm ) = Here, ∆Ti
∆Ti − ∆To ln (∆Ti /∆To )
= Thi - Tco
And
∆To
= Tho - Tci (for counter flow)
where: Thi
=
Temperature of steam inlet.
Tho
=
Temperature of condensate stream.
Tci
=
Tco
=
Temperature of cold water input. Temperature of cold water output.
FOR HORIZONTAL CONDENSER: 1. Film coefficient for condensation over N number of horizontal tubes of dia., D is calculated from: 1/4
k3 ρ 2 g λ
hN = 0.729 ( 2/3 ) N µ ∆T D o
(6)
2. The physical properties are evaluated at film temperature, Tf, where 3
Tf = (Th − ( Th − Tw )) 4
(7)
10
4. The heat balance between the amount of heat given to water by steam and the amount of heat actually taken by the cooling water is obtained from the equation:
Q = m (Tco − Tci ) = w𝜆
(8)
5. The overall heat transfer coefficient is calculated from equation:
U = m
(Tco − Tci )
(9)
A ∆Tm
LMTD = (∆Tm ) =
∆Ti − ∆To ln (∆Ti /∆To )
Here, ∆Ti
= Thi - Tco
And ∆To
= Tho - Tci (for counter flow)
NOMENCLATURE: 𝞺
=
density of condensate, kg/m3
𝞴
=
latent heat of vaporization of J/gm average temp. of steam & water
µ
=
viscosity of condensate
A
=
heat transfer area
Do
=
OD of tube
g
=
acceleration due to gravity, m/sec2
ho
=
individual heat transfer coefficient, W/m2 0C
k
=
thermal conductivity of condensate at average temperature of steam condensed, W/m0C
L
=
Length of the tubes
m
=
Cooling water rate
N
=
number of tubes
11
Tf
=
average temperature of steam condensate.
Tw
=
wall temp. = temperature of outlet condensed steam.
Th
=
temperature of the condensing vapor.
Thi
=
temperature of steam inlet.
Tho
=
temperature of condensed steam.
Tci
=
temperature of cold water input.
∆Tlm =
log mean temperature difference.
U
=
overall heat transfer coefficient.
w
=
rate of condensation.
ERROR ANALYSIS The error overall heat transfer coefficient is calculated by 1.Relative error: % error = (Uexp – Utheo)/ Uexp
x 100
U theoretical value can be calculated from 1 𝑈𝑜
=
1 ℎ𝑜
𝑑
1 𝑑
+ 𝑑𝑜 ∗ ℎ + 𝑑𝑜 ∗ 𝑖
𝑖
𝑖
𝑥𝑤 𝑘
Where xw is very small and can be neglected 2.Differntial error:
U = m
(Tco − Tci ) A ∆Tlm
LMTD = (∆Tm ) =
dU = m
(∆Tco ) A ∆Tlm
∆Ti −∆To ln (∆Ti /∆To )
+ m
(∆Tci ) A ∆Tlm
+ m
(Tco − Tci ) A ∆Tlm 2
*∂ (∆Tlm ) 12
where ∂ (∆Tlm ) = Differential error =
𝑑𝑈 𝑈
∂∆Ti
∂∆Ti ∂∆Ti + *∆To ln (∆Ti /∆To ) ln (∆Ti /∆To ) (∆To /∆Ti ) ∆To ∆To 2
+
∂∆To
+
∆Ti −∆To
*
× 100
PRECAUTIONS: 1. Check the water level in the steam generator tank before turn on the heater for steam generation. 2. Both condensers cannot be operated at the same time. Either one of them can be operated first 3. Make sure that steam and water valves of the non-running condenser in OFF position 4. Release the steam from steam generator once experiment is over.
OBSERVATIONS & SAMPLE CALCULATION: Given Parameters Number of tubes
N
=
8
Tube length
L
=
500 mm
I. D. of tube
di
=
9.5 mm
O.D. of tube
D
=
12.7 mm
Inside diameter of shell
D0
=
108 mm
FOR VERTICAL CONDENSER S.
Steam
No.
pressure
1
0.4
T1
T3
Cooling water
T6
T7
Rate of condensation
flow rate, LPH
108
44
70
(w)
34.8
85.3
64
13
FOR HORIZONTAL CONDENSER S.
Steam
No.
pressure
1
0.4
T1
T2
Cooling water
T4
T5
Rate of condensation
flow rate, LPH
110.1
60.9
70
(w)
35.7
72.9
93
Sample calculations: Vertical condenser: Film temperature Tf = (Th −
3 4
=(85.3 −
(Th − Tw )) = Th − 3 4
3 4
∆T
(85.3 − 44)) =54.325 oC
Physical properties of condensate film (water) at temp., Tf Thermal conductivity, k = 0.648 W/m-k Density, 𝞺 = 986 kg/m3 Viscosity, µ =0.511x 10-3
Ns/m3
14
Latent heat of steam, 𝞴 =2378 kJ/kg = 4.17 kJ/kg K Temperature drop across condensate film ∆T
= 85.3 – 44 = 41.3 oC
The film coefficient for condensation over a vertical plate of height L is given by – k3 ρ 2 g λ
1/4
= 824.43 w/m2 oC
ho = 0.943 ( ) L µ ∆T
Film coefficient for condensation outside of vertical tube is given by: ho Do k
k L ∆ T 0.67
= 0.0077 (
Do
) λµ
Do 3 ρ2 g
(
µ
0.56
)
= 2418.28
ho = 13746 W/m2 oC The heat balance between the amount of heat given to water by steam and the amount of heat actually taken by the cooling water is obtained from the equation
Q = m (Tco − Tci ) = 70/3600 *4.17*(85.3-34.8) = 4094.7 W
The overall heat transfer coefficient is calculated from equation:
LMTD = (∆Tlm ) = U = m
(Tco − Tci ) A ∆Tlm
∆Ti −∆To ln (∆Ti /∆To )
=
22.8−9.2 ln (22.8/9.2)
=14.98
= 4094.7/0.01995*14.98 =13696.69
U per tube =1712 w/m2 oC
Horizontal condenser: 15
Film temperature Tf = (Th −
3 4
=(72.9 −
(Th − Tw )) = Th − 3 4
3 4
∆T
(72.9 − 60.2)) =63.37 oC
Physical properties of condensate film (water) at temp., Tf Thermal conductivity, k = 0.657 W/m-k Density, 𝞺 = 981.4 kg/m3 Viscosity, µ =0.45x 10-3
Ns/m3
Latent heat of steam, 𝞴 =2354 kJ/kg = 4.18 kJ/kg K Temperature drop across condensate film ∆T
= 72.9 – 60.2 = 12.7 oC
Film coefficient for condensation over N number of horizontal tubes of dia., D is calculated from: 1/4
k3 ρ 2 g λ
= 5111.98 w/m2 oK
hN = 0.729 ( 2/3 ) N µ ∆T D o
The heat balance between the amount of heat given to water by steam and the amount of heat actually taken by the cooling water is obtained from the equation
Q = m (Tco − Tci ) = 70/3600 *4.17*(72.9-35.7) *1000= 3023.53 W
The overall heat transfer coefficient is calculated from equation:
LMTD = (∆Tlm ) =
∆Ti −∆To ln (∆Ti /∆To )
=
37.2−25.2 ln (37.2/25.2)
=30.81
16
U = m
(Tco − Tci )
= 3023.53/0.01995*30.83 =6576.26 w/m2 oK
A ∆Tlm
Error analysis: Vertical condenser: U theoretical value can be calculated from 1 𝑈𝑜
=
1 ℎ𝑜
+
𝑑𝑜 𝑑𝑖
1
1 𝑑𝑜 ℎ 𝑖 𝑑𝑖
∗ +
∗
114
1
𝑥𝑤 𝑘
Where xw is very small and can be neglected
= 13746 + 108 ∗ 124.43 Utheo =1439.04 w/m2 oC Relative error: % error = (Uexp – Utheo)/ Uexp
x 100
= (1712– 1439)/ 1439 x 100 = 18.9 %
Differential error:
∂∆Ti = ∂∆To = 0.1 ∆Ti = 22.8 , ∆To =9.2
∂ (∆Tlm ) =
∂∆Ti
∂∆Ti ∂∆Ti + *∆To ln (∆Ti /∆To ) ln (∆Ti /∆To ) (∆To /∆Ti ) ∆To ∆To 2
+
∂∆To
+
∆Ti −∆To
*
= 0.22+1.274 = 1.494 dU = m
(∆Tco ) A ∆Tlm
+ m
(∆Tci ) A ∆Tlm
+ m
(Tco − Tci ) A ∆Tlm 2
*∂ (∆Tlm )
17
= 27.2 +27.2 +145.14 = 199.54 Differential error =
𝑑𝑈 𝑈
× 100 =
199.54 1712
× 100
= 11.655%
Horizontal condenser: U theoretical value can be calculated from
Utheo =5111.98 w/m2 oC Relative error: % error = (Uexp – Utheo)/ Uexp
x 100
= (6576– 5111)/ 6576 x 100 = 22.6 %
Differential error:
∂∆Ti = ∂∆To = 0.1 ∆Ti = 37.2 , ∆To =25.2
∂ (∆Tlm ) =
∂∆Ti
+
∂∆To
+
∆Ti −∆To
∂∆Ti ∂∆Ti
*
+
ln (∆Ti /∆To ) ln (∆Ti /∆To ) (∆To /∆Ti ) ∆To ∆To 2
*∆To
= 0.5153+0.174 =0.6895 18
dU = m
(∆Tco ) A ∆Tlm
+ m
(∆Tci ) A ∆Tlm
+ m
(Tco − Tci ) A ∆Tlm 2
*∂ (∆Tlm )
= 17.68 +17.68 +146.744 = 182.107 Differential error =
𝑑𝑈 𝑈
× 100 =
182.107 6576.26
× 100
= 2.77%
SAMPLE VIVA QUESTIONS: 1. Why horizontal condenser is more efficient than vertical condenser? 2. In which condenser change in steam temperature is more and why?
REFERENCES 1. Nptel, lesson 22
2. Holman. J.P(2008). Heat Transfer. 9th Ed. ND: McGraw Hill.pp 25-27. 3. McCabe, Smith, Harriott (2005). Unit Operations of Chemical Engineering. 7th Ed. NY: McGraw Hill. Pp 306-307.
19
Heat Transfer Lab
Course No
CL 312
Experiment Title:
Horizontal and Vertical Condenser
Experiment Number:
HT 1
Department:
Department of Chemical Engineering
Institute:
Indian Institute of Technology Guwahati
Lasted edited date:
Edited by:
Approved by:
1
CONTENTS AIM: ............................................................................................................................................ 3 SPECIFIC .................................................................................................................................... 3 OBJECTIVE: .............................................................................................................................. 3 INTRODUCTION:...................................................................................................................... 3 THEORY..................................................................................................................................... 3 DESCRIPTION ........................................................................................................................... 5 EXPERIMENTAL SETUP ......................................................................................................... 6 EXPERIMENT PROCEDURE:.................................................................................................. 8 EQUIPMENT DATA:................................................................................................................. 8 FORMULAE: .............................................................................................................................. 9 NOMENCLATURE: ................................................................................................................. 11 Error Analysis ........................................................................................................................... 12 PRECAUSTIONS: .................................................................................................................... 13 OBSERVATIONS & SAMPLE CALCULATION: ................................................................. 13 SAMPLE VIVA QUESTIONS: ................................................................................................ 19 REFERENCES .......................................................................................................................... 19
2
AIM: Experimental study on heat transfer efficiency of vertical and horizontal condenser. SPECIFIC OBJECTIVE: Estimate heat transfer rate across the condenser tubes through heat balance
Estimation of overall heat transfer coefficient experimentally for Horizontal and Vertical condenser and compare the results with that of the standard correlation.
Estimate experimental error on overall heat transfer coefficient and propose method to minimize experimental error on estimated overall heat transfer coefficient values
Compare performance both condensers heat transfer efficiency and justify.
INTRODUCTION: When a saturated vapor is brought in with a cooler surface, condensation occurs. Condensation occurs at different rate of heat transfer by either of the two distinct physical mechanism, drop and film wise condensation. The occurrence of drop or film wise condensation depends largely on the characteristics of the condensing vapor and the surface available for condensation. The condensing film coefficient is influenced by the texture of the surface on which the condensation occurs and also by whether the condensing surface is mounted vertically or horizontally. The heat transfer coefficients obtained during film wise condensation are 1/5th to 1/6th of that in drop wise condensation. Most practical cases correspond to mixed condensation. However, due to lack of control in drop wise condensation, calculations are mostly based on film condensation heat transfer coefficients.
THEORY FOR VERTICAL CONDENSER In case of condensation on the surface of a vapor tube, as in vertical condensers, the condensate film flows downwards under the influence of gravity, but is retarded by the viscosity of the condensate film. The flow is normally streamlined and heat flows through the film by conduction only. In vertical tube, about 60% of the vapor condenses in the upper half of the tube. Nusselt has derived a theoretical relation for the determination of film heat transfer coefficient in of physical properties of condensate film, characteristic dimension and the temperature driving force.
3
Assumptions: 1. Both the plate and the vapor are maintained at constant temperatures of Tw and Tsat, respectively, and the temperature across the liquid film varies linearly. 2. Heat transfer across the liquid film is by conduction only. 3. The velocity of the vapor is low (or zero) so that it exerts no drag on the condensate (no viscous shear on the liquid–vapor interface). 4. The flow of the condensate is laminar (Re<30) and the properties of the liquid are constant. 5. The acceleration of the condensate layer is negligible The film coefficient for condensation over a vertical plate of height L is given by – k3 ρ 2 g λ
1/4
ho = 0.943 ( ) L µ ∆T
(1)
VERTICAL & HORIZONTAL CONDENSER Film coefficient for condensation outside of vertical tube is given by: ho D k
= 0.0077 (
k L ∆ T 0.67
) Dλµ
D3 ρ2 g
(
µ
0.56
)
(2)
The physical properties are evaluated at film temperature, Tf, where
Tf = (Th −
3 4
(Th − Tw )) = Th −
3 4
∆T
(3)
FOR HORIZONTAL CONDENSER The value of the condensing coefficient for a given quantity of vapor, on a surface is significantly affected by the position of the condenser. Provide that the condensate film is flowing under laminar flow condition; the average condensing coefficient in case of a horizontal condenser is around three times as great as the vertical coefficient. Nusselt has derived a theoretical relation for the determination of film heat transfer coefficient in of physical properties of condensate film, characteristic dimension and the temperature driving force.
4
The film coefficient for condensation over a horizontal cylinder of outer diameter D o is given byk3 ρ 2 g λ
1/4
ho = 0.729 ( ) D µ ∆T
(4)
Film coefficient for condensation over N number of horizontal tubes of dia. D is given by: 1/4
k3 ρ 2 g λ
hN = 0.729 ( 2/3 ) N µ ∆T D o
(5)
The physical properties are evaluated at film temperature, Tf, where 3
Tf = (Th − ( Th − Tw )) 4
(6)
DESCRIPTION The set up consists of two tube bundle heat exchangers housed in a stainless steel shell, one mount horizontally and the other vertically. Water es through the tubes and steam condenses over the tubes. Steam is supplied to the condenser from a steam generator. The condensate is removed through the steam trap. A valve arrangement allows selecting steam flow into either the vertical or the horizontal condenser. Experiment can be conducted on any one of the condenser at a time. The continuous cooling water supply can also be routed to any of the condensers as required. The heat input by the heater in the steam generator is controlled by the Digital Temperature Controller. Six numbers of temperature sensors are provided to measure the inlet and outlet temperatures of the fluid.
TEMPERATURE SENSORS POSITIONS ARE GIVEN BELOW: T1
= Steam inlet for Horizontal/Vertical Condenser
T2
= Steam outlet for Horizontal Condenser.
T3
= Steam outlet for Vertical Condenser.
T4
= Water inlet for Horizontal Condenser.
T5
= Water outlet for Horizontal Condenser. 5
T6
= Water inlet for Vertical Condenser.
T7
= Water outlet for Vertical Condenser.
EXPERIMENTAL SETUP
Fig. (1) Experimental setup photo
6
Vertical conden ser
4
3
ROTAMETER
STEAM TRAP
WATER IN
Horizontal condenser CONDENSATE 2 WATER OUT
WATER OUT CONDENSATE OUT
1 STEAM IN
STEAM GENERATOR TANK
Fig. (2) Flow diagram for horizontal and vertical condenser 1. Valve 1: steam into apparatus 2. Valve 2: releases steam outside 3. valve 3: release water into horizontal condenser 4. valve 4: release water into vertical condenser 5. valve 5: release steam into horizontal condenser 6. valve 6: release water into vertical condenser
7
EXPERIMENT PROCEDURE: STARTING PROCEDURE: 1.The steam generator is filled with water up to ¾ of its capacity. 2. The digital temperature indicator is set at 110OC. 3. The steam generator valve is closed and time is allowed for steam formation. 4. One of the condensers is connected with cold water supply system. 5. The calibration of the rotameter provided for measurement of water flow rate is checked using a measuring cylinder and stopwatch. 6. When steam is formed, the supply of cold water is started to the condenser at any flow rate fixed by means of the rotameter. 7. The steam supply to the condenser is started and also a stopwatch is started at the same instant. 8. The condensate is collected and measured using a measuring cylinder and stopwatch. 9. The inlet and outlet temperatures of the cold water supply are noted. The temperature of the condensate is also recorded. 10. The above steps as above may be repeated with different flow rates to give another set of readings. 11. The entire process is then to be repeated for the other condenser, to allow comparative study of the results for two types of condensing arrangements. CLOSING PROCEDURE: 12. At the end of the experiment, the power supply to the heater is switched off. Also the mains power supply is switched off. 13. The vent provide on the steam generator is opened slightly to release pressure. 14. The supply of cooling water is disconnected. 15.
After the vapors condense, the condensers and steam generator are to be drained.
EQUIPMENT DATA: Number of tubes Tube length
N: L:
8 500 mm 8
I.D. of tube
di:
9.5 mm
O.D. of tube
D:
12.7 mm
Inside diameter of shell
Ds:
108 mm
Outside diameter of shell
Do:
114 mm
Length of shell
L:
500 mm (approx.)
Condensate Measurement:
Measuring Cylinder & Stopwatch
Water Flow Measurement:
Rota meter, measuring cylinder & Stop Watch.
Temperature sensors:
RTD PT-100 type 7 Nos.
FORMULAE: FOR VERTICAL CONDENSER: 1. The film coefficient for condensation over a vertical plate of height, L, is given by: k3 ρ 2 g λ
1/4
ho = 0.943 ( ) L µ ∆T
(1)
2. Film coefficient for condensation outside of vertical tube is given by: ho Do k
k L ∆ T 0.67
= 0.0077 (
Do λ µ
)
Do 3 ρ2 g
(
µ
0.56
)
(2)
3. The physical properties are evaluated at film temperature, Tf, where
Tf = (Th −
3 4
(Th − Tw )) = Th −
3 4
∆T
(3)
4. The heat balance between the amount of heat given to water by steam and the
9
amount of heat actually taken by the cooling water is obtained from the equation
Q = m (Tco − Tci ) = w𝜆
(4)
5. The overall heat transfer coefficient is calculated from equation:
U = m
(Tco − Tci )
(5)
A ∆Tlm
LMTD = (∆Tlm ) = Here, ∆Ti
∆Ti − ∆To ln (∆Ti /∆To )
= Thi - Tco
And
∆To
= Tho - Tci (for counter flow)
where: Thi
=
Temperature of steam inlet.
Tho
=
Temperature of condensate stream.
Tci
=
Tco
=
Temperature of cold water input. Temperature of cold water output.
FOR HORIZONTAL CONDENSER: 1. Film coefficient for condensation over N number of horizontal tubes of dia., D is calculated from: 1/4
k3 ρ 2 g λ
hN = 0.729 ( 2/3 ) N µ ∆T D o
(6)
2. The physical properties are evaluated at film temperature, Tf, where 3
Tf = (Th − ( Th − Tw )) 4
(7)
10
4. The heat balance between the amount of heat given to water by steam and the amount of heat actually taken by the cooling water is obtained from the equation:
Q = m (Tco − Tci ) = w𝜆
(8)
5. The overall heat transfer coefficient is calculated from equation:
U = m
(Tco − Tci )
(9)
A ∆Tm
LMTD = (∆Tm ) =
∆Ti − ∆To ln (∆Ti /∆To )
Here, ∆Ti
= Thi - Tco
And ∆To
= Tho - Tci (for counter flow)
NOMENCLATURE: 𝞺
=
density of condensate, kg/m3
𝞴
=
latent heat of vaporization of J/gm average temp. of steam & water
µ
=
viscosity of condensate
A
=
heat transfer area
Do
=
OD of tube
g
=
acceleration due to gravity, m/sec2
ho
=
individual heat transfer coefficient, W/m2 0C
k
=
thermal conductivity of condensate at average temperature of steam condensed, W/m0C
L
=
Length of the tubes
m
=
Cooling water rate
N
=
number of tubes
11
Tf
=
average temperature of steam condensate.
Tw
=
wall temp. = temperature of outlet condensed steam.
Th
=
temperature of the condensing vapor.
Thi
=
temperature of steam inlet.
Tho
=
temperature of condensed steam.
Tci
=
temperature of cold water input.
∆Tlm =
log mean temperature difference.
U
=
overall heat transfer coefficient.
w
=
rate of condensation.
ERROR ANALYSIS The error overall heat transfer coefficient is calculated by 1.Relative error: % error = (Uexp – Utheo)/ Uexp
x 100
U theoretical value can be calculated from 1 𝑈𝑜
=
1 ℎ𝑜
𝑑
1 𝑑
+ 𝑑𝑜 ∗ ℎ + 𝑑𝑜 ∗ 𝑖
𝑖
𝑖
𝑥𝑤 𝑘
Where xw is very small and can be neglected 2.Differntial error:
U = m
(Tco − Tci ) A ∆Tlm
LMTD = (∆Tm ) =
dU = m
(∆Tco ) A ∆Tlm
∆Ti −∆To ln (∆Ti /∆To )
+ m
(∆Tci ) A ∆Tlm
+ m
(Tco − Tci ) A ∆Tlm 2
*∂ (∆Tlm ) 12
where ∂ (∆Tlm ) = Differential error =
𝑑𝑈 𝑈
∂∆Ti
∂∆Ti ∂∆Ti + *∆To ln (∆Ti /∆To ) ln (∆Ti /∆To ) (∆To /∆Ti ) ∆To ∆To 2
+
∂∆To
+
∆Ti −∆To
*
× 100
PRECAUTIONS: 1. Check the water level in the steam generator tank before turn on the heater for steam generation. 2. Both condensers cannot be operated at the same time. Either one of them can be operated first 3. Make sure that steam and water valves of the non-running condenser in OFF position 4. Release the steam from steam generator once experiment is over.
OBSERVATIONS & SAMPLE CALCULATION: Given Parameters Number of tubes
N
=
8
Tube length
L
=
500 mm
I. D. of tube
di
=
9.5 mm
O.D. of tube
D
=
12.7 mm
Inside diameter of shell
D0
=
108 mm
FOR VERTICAL CONDENSER S.
Steam
No.
pressure
1
0.4
T1
T3
Cooling water
T6
T7
Rate of condensation
flow rate, LPH
108
44
70
(w)
34.8
85.3
64
13
FOR HORIZONTAL CONDENSER S.
Steam
No.
pressure
1
0.4
T1
T2
Cooling water
T4
T5
Rate of condensation
flow rate, LPH
110.1
60.9
70
(w)
35.7
72.9
93
Sample calculations: Vertical condenser: Film temperature Tf = (Th −
3 4
=(85.3 −
(Th − Tw )) = Th − 3 4
3 4
∆T
(85.3 − 44)) =54.325 oC
Physical properties of condensate film (water) at temp., Tf Thermal conductivity, k = 0.648 W/m-k Density, 𝞺 = 986 kg/m3 Viscosity, µ =0.511x 10-3
Ns/m3
14
Latent heat of steam, 𝞴 =2378 kJ/kg = 4.17 kJ/kg K Temperature drop across condensate film ∆T
= 85.3 – 44 = 41.3 oC
The film coefficient for condensation over a vertical plate of height L is given by – k3 ρ 2 g λ
1/4
= 824.43 w/m2 oC
ho = 0.943 ( ) L µ ∆T
Film coefficient for condensation outside of vertical tube is given by: ho Do k
k L ∆ T 0.67
= 0.0077 (
Do
) λµ
Do 3 ρ2 g
(
µ
0.56
)
= 2418.28
ho = 13746 W/m2 oC The heat balance between the amount of heat given to water by steam and the amount of heat actually taken by the cooling water is obtained from the equation
Q = m (Tco − Tci ) = 70/3600 *4.17*(85.3-34.8) = 4094.7 W
The overall heat transfer coefficient is calculated from equation:
LMTD = (∆Tlm ) = U = m
(Tco − Tci ) A ∆Tlm
∆Ti −∆To ln (∆Ti /∆To )
=
22.8−9.2 ln (22.8/9.2)
=14.98
= 4094.7/0.01995*14.98 =13696.69
U per tube =1712 w/m2 oC
Horizontal condenser: 15
Film temperature Tf = (Th −
3 4
=(72.9 −
(Th − Tw )) = Th − 3 4
3 4
∆T
(72.9 − 60.2)) =63.37 oC
Physical properties of condensate film (water) at temp., Tf Thermal conductivity, k = 0.657 W/m-k Density, 𝞺 = 981.4 kg/m3 Viscosity, µ =0.45x 10-3
Ns/m3
Latent heat of steam, 𝞴 =2354 kJ/kg = 4.18 kJ/kg K Temperature drop across condensate film ∆T
= 72.9 – 60.2 = 12.7 oC
Film coefficient for condensation over N number of horizontal tubes of dia., D is calculated from: 1/4
k3 ρ 2 g λ
= 5111.98 w/m2 oK
hN = 0.729 ( 2/3 ) N µ ∆T D o
The heat balance between the amount of heat given to water by steam and the amount of heat actually taken by the cooling water is obtained from the equation
Q = m (Tco − Tci ) = 70/3600 *4.17*(72.9-35.7) *1000= 3023.53 W
The overall heat transfer coefficient is calculated from equation:
LMTD = (∆Tlm ) =
∆Ti −∆To ln (∆Ti /∆To )
=
37.2−25.2 ln (37.2/25.2)
=30.81
16
U = m
(Tco − Tci )
= 3023.53/0.01995*30.83 =6576.26 w/m2 oK
A ∆Tlm
Error analysis: Vertical condenser: U theoretical value can be calculated from 1 𝑈𝑜
=
1 ℎ𝑜
+
𝑑𝑜 𝑑𝑖
1
1 𝑑𝑜 ℎ 𝑖 𝑑𝑖
∗ +
∗
114
1
𝑥𝑤 𝑘
Where xw is very small and can be neglected
= 13746 + 108 ∗ 124.43 Utheo =1439.04 w/m2 oC Relative error: % error = (Uexp – Utheo)/ Uexp
x 100
= (1712– 1439)/ 1439 x 100 = 18.9 %
Differential error:
∂∆Ti = ∂∆To = 0.1 ∆Ti = 22.8 , ∆To =9.2
∂ (∆Tlm ) =
∂∆Ti
∂∆Ti ∂∆Ti + *∆To ln (∆Ti /∆To ) ln (∆Ti /∆To ) (∆To /∆Ti ) ∆To ∆To 2
+
∂∆To
+
∆Ti −∆To
*
= 0.22+1.274 = 1.494 dU = m
(∆Tco ) A ∆Tlm
+ m
(∆Tci ) A ∆Tlm
+ m
(Tco − Tci ) A ∆Tlm 2
*∂ (∆Tlm )
17
= 27.2 +27.2 +145.14 = 199.54 Differential error =
𝑑𝑈 𝑈
× 100 =
199.54 1712
× 100
= 11.655%
Horizontal condenser: U theoretical value can be calculated from
Utheo =5111.98 w/m2 oC Relative error: % error = (Uexp – Utheo)/ Uexp
x 100
= (6576– 5111)/ 6576 x 100 = 22.6 %
Differential error:
∂∆Ti = ∂∆To = 0.1 ∆Ti = 37.2 , ∆To =25.2
∂ (∆Tlm ) =
∂∆Ti
+
∂∆To
+
∆Ti −∆To
∂∆Ti ∂∆Ti
*
+
ln (∆Ti /∆To ) ln (∆Ti /∆To ) (∆To /∆Ti ) ∆To ∆To 2
*∆To
= 0.5153+0.174 =0.6895 18
dU = m
(∆Tco ) A ∆Tlm
+ m
(∆Tci ) A ∆Tlm
+ m
(Tco − Tci ) A ∆Tlm 2
*∂ (∆Tlm )
= 17.68 +17.68 +146.744 = 182.107 Differential error =
𝑑𝑈 𝑈
× 100 =
182.107 6576.26
× 100
= 2.77%
SAMPLE VIVA QUESTIONS: 1. Why horizontal condenser is more efficient than vertical condenser? 2. In which condenser change in steam temperature is more and why?
REFERENCES 1. Nptel, lesson 22
2. Holman. J.P(2008). Heat Transfer. 9th Ed. ND: McGraw Hill.pp 25-27. 3. McCabe, Smith, Harriott (2005). Unit Operations of Chemical Engineering. 7th Ed. NY: McGraw Hill. Pp 306-307.
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