A Thesis on EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER

A Thesis on EXPERIMENTAL INVESTIGATION OF HEAT TRANSFER AND FLUID FLOW CHARACTERISTICS IN HEAT EXCHANGER TUBE WITH CIRCULAR PERFORATED DISK INSERTS Submitted by ALOK KUMAR (Roll No. 1351141002) In partial fulfilment of the requirements for the degree of Master of Technology In Energy Engineering Under the supervision of

Dr. Sunil Chamoli Assistant Professor Dept. of Mechanical Engg. DIT University, Dehradun.

Dr. Manoj Kumar Professor Dept. of Mechanical Engg. DIT University, Dehradun.

Department of Mechanical Engineering DIT UNIVERSITY, DEHRADUN, INDIA June, 2015

M. Tech Thesis; June, 2015

DECLARATION

I hereby declare that this submission is my own work towards the Master of Technology degree in Energy Engineering at the DIT University Dehradun, under the supervision of Dr. Sunil Chamoli (Asst. Professor) and Dr. Manoj Kumar (Professor), Department of Mechanical Engineering, DIT University, Dehradun, Uttarakhand. All works refereed have been duly acknowledged in references.

Alok Kumar (M. Tech in Energy Engg.)

...........................................

1351141002

Signature

DIT UNIVERSITY DEHRADUN, UTTARAKHAND

Page ii


DIT UNIVERSITY, DEHRADUN, UTTARAKHAND, INDIA Department of Mechanical Engineering

CERTIFICATE

This is to certify that the thesis entitled “Experimental Investigation of Heat Transfer and Fluid Flow Characteristics of Heat Exchanger Tube with Circular Perforated Disk Inserts” submitted to the DIT University, Dehradun by ALOK KUMAR, Roll No. 1351141002 in partial fulfillment of the requirements for the award of the degree of Master of Technology in Energy Engineering, is a bonafide record of research work carried out by him under my supervision and guidance. The dissertation, which is based on candidate’s own work, has not been stated anywhere else for any degree/diploma.

Day of the month: 15th June 2015.

--------------------------------

-----------------------------------

-----------------------------------

Dr. Sunil Chamoli

Dr. Manoj Kumar

Dr. Manish Mishra

Assistant Professor

Professor

Associate Professor

Dept. of Mechanical Engg.

Dept. of Mechanical Engg.

IIT Roorkee

DIT University, Dehradun.

DIT University, Dehradun.

(External Examiner)


Page iii

M. Tech Thesis; June, 2015 ACKNOWLEDGEMENT

As an author of this thesis, it is my proud privilege to show a deep sense of gratitude and indebtedness towards my thesis supervisors Dr. Sunil Chamoli, Assistant Professor, Department of Mechanical engineering, and Dr. Manoj Kumar, Professor, Department of Mechanical Engineering, DIT University, Dehradun, India, who provided their invaluable guidance and wholehearted cooperation in extending out this work. Their painstaking support, continuous encouragement and exhaustive involvement in the formulation of the manuscript are gratefully praised. I would also thank Professor and Head, Department of Mechanical Engineering, DIT University, Dehradun for providing the necessary facilities whenever required to carry out research. My heartiest thanks to Mr. Rajesh Maithani, Assistant Professor, Department of Mechanical Engg., DIT University, Dehradun, whose support during the work was overbhelhming and encouraging. I convey special thanks to all the staff members of the Mechanical Engineering Department for their time to time moral support and aid during the tenure of work. I also deeply acknowledge the help provided by the staff of Mechanical Engineering Laboratories and Workshop to provide facilities for fabrication and laboratory work. In closing, I am greatly indebted to my parents and kin, for encouragement at the monetary value of their distress.


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ABSTRACT

Heat transfer enhancement by creating turbulence in the physical behavior of fluid flow inside the heat exchanger tube has become a really interesting area for the researchers. The heat exchangers are the most commonly used thermal devices in different thermal and mechanical systems. Hence, many techniques have been investigated on enhancement of heat transfer rate to reduce the size and cost of the involving equipment especially in heat exchangers. Although very significant results has been achieved in the thermal performance of heat exchangers, especially in the range of lower Reynolds number, but still these passive approaches of heat transfer enhancement is not effective for the range of higher Reynolds number. In the present study the effect of perforated circular disk (PCD) turbulators on heat transfer, friction factor and thermal performance of the heat exchanger is evaluated through experimentation. The different parameters used for the experimentation includes, fixed thickness ratio (t/D) of PCD i.e. 0.0075, diameter ratios (d/D= 0.6, 0.7, 0. 8), pitch ratios (l/D= 1,2,3) and perforation Index (PA/TA = 0%, 8%, 16%, 24%). The experiments are conducted in the range of Reynolds number lying between 6,500 to 23,000. The experimentation is carried out in the test section of 1.4 m (L) longer made of galvanized iron with a hydraulic diameter (D) of 68 mm. The test section was heated with constant heat flux of 1000 watt/m2 with the help of a variable voltage transformer and heating coil of equivalent resistance 54 Ω. The data logger is used for temperature measurements, and digital manometer is used for measuring pressure drop across the test section. The flow rate is corrected with the help of gate valve, whose interpretation were selected with the help of u-tube manometer which is situated across the orifice plate. On the basis of observation and result, there is 4 times enhancement in heat transfer in case of PR=1, PI=0% & DR=0. 6, and around 1.47 times enhancement in thermal performance factor in case of PR=1, DR=0. 8 & PI=24% as compared to smooth tube heat exchanger. It was obserbed that for the minimum value of diameter ratio (DR), heat transfer was maximum and as the value of diameter ratio (DR) increases heat transfer rate decrease. Perforation index (PI) played a major role in controlling the friction factor. For maximum value of perforation index (PI) friction factor was minimum hence thermal performance improved to a great extent.


Page v


TABLE OF CONTENT CHAPTER NO.

TOPIC

PAGE NO.

Declaration

ii

Certificate

iii

Acknowledgement

iv

Abstract

v

Nomenclature

ix

List of figures

xi

List of tables

xiv

CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW 1.1

Introduction

1

1.2

Classification of heat exchangers

1

1.2.1

Heat transfer process

2

1.2.2

Geometrical construction

3

1.2.3

Flow arrangement

4

1.3

Applications

5

1.4

Need of heat transfer enhancement in heat exchanger tube

5

1.5

Methods of heat transfer enhancement

7

1.5.1

Active Techniques

7

1.5.2

Passive Techniques

7

1.5.3

Compound Techniques

8

1.6

Literature review

9

1.7

Discussion on literature

15

1.8

Objectives

15

1.9

Summary

15

CHAPTER 2 EXPERIMENTAL INVESTIGATION 2.1

Introduction

16

2.2

Insert geometry and parameters.

17

2.3

Experimental investigation

20


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M. Tech Thesis; June, 2015 2.3.1

Tube section

20

2.3.2

Heating arrangement in test section

21

2.3.3

Insulation of test part

22

2.3.4

Temperature measurements

23

2.3.5

Pressure measurements

24

2.3.6

Flow measurements

25

2.3.7

Level of experimental setup

25

Summary

27

2.4

CHAPTER 3 DATA REDUCTION AND VALIDATION 3.1

Introduction

28

3.2

Mathematical equations for data reduction

28

3.3

Validation test

30

3.4

Summary

32

CHAPTER 4 RESULTS AND DISCUSSION 4.1

Introduction

33

4.2

Heat transfer

33

4.2.1

Effect on heat transfer for diameter ratio 0.6

35

4.2.2


37

4.2.3


39

Friction factor

41

4.3.1

Effect on friction factor for diameter ratio 0.6

42

4.3.2


44

4.3.3


46

Thermal performance factor

48

4.4.1

Effect on thermal performance factor for diameter ratio 0.6

48

4.4.2


49

4.4.3


50

Summary

51

4.3

4.4

4.5

CHAPTER 5 CORRELATION FOR NUSSELT NUMBER, FRICTION FACTOR AND THERMAL PERFORMANCE FACTOR


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M. Tech Thesis; June, 2015 5.1

Introduction

52

5.2

Range of parameters for correlations

52

5.3

Correlation for Nusselt number, friction factor and thermal

53

performance factor 5.3.1

Nusselt number correlation

53

5.3.2

Friction factor correlation

57

5.3.3

Thermal performance factor correlation

63

Summary

68

5.4

CHAPTER 6 CONCLUSIONS

69

APPENDIX 1 UNCERTAINTY ANALYSIS

71

REFERENCES

80


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NOMENCLATURE

Symbol

Title

Ao

Cross section area of orifice

Cd

Coefficient of discharge for orifice meter

CP

Specific heat of air at constant pressure

Unit m2

J/kg K

D

Hydraulic diameter of the pipe

m

d

Internal diameter of insert

m

dh

Diameter of hole for perforation.

h

Convective heat transfer coefficient

W/m2 K

K

Thermal conductivity of air

W/m K

L

Length of the pipe

. m

Mass flow rate of fluid

P

Pressure drop across test section

Pa

Po

Pressure drop across the orifice plate

Pa

Pa

Atmospheric pressure

Pa

Ta

Ambient temperature

K

Ti

Fluid inlet temperature

K

To

Fluid outlet temperature

K



Stefan-Boltzman constant

air

m kg/s

W/m2K4

Density of air

kg/m3



Dynamic viscosity

kg/m s



Thermal performance factor

f

Friction factor

Re l

Reynolds number Spacing between two consecutive insert geometry

Pr

Prandtl number

Nu

Nusselt number

Ta

Total area of circular disk


m2 Page ix

M. Tech Thesis; June, 2015 Tp

Area of perforation

m2

Tw

Local wall temperature

o

Tb

Bulk mean temperature

o

Twm

Wall mean temperature

o

PR

Pitch ratio

DR

Diameter ratio

PI

Perforation index

HE

Heat exchanger


C C C

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LIST OF FIGURES

Figure No.

Title

Page No.

1.1

Direct Contact Type Heat Exchanger

2

1.2

Indirect Type Heat Exchanger

3

1.3

Parallel Flow Type Heat Exchanger

4

1.4

Counter Flow Heat Exchanger

4

1.5

Heat Transfer in Tube Heat Exchanger

6

1.6

Velocity vector of smooth tube flow & stream line in smooth tube

6

1.7

Velocity vector in smooth tube &Velocity vector in tube with

8

turbulators 2.1

Perforated disks with different perforation index and diameter

18

ratios 2.2

Perforated circular disk arrangement with pitch ratio wise

19

2.3

Dimensional details of the insert geometry

20

2.4

Heating element over Aluminium oxide paste and Variac used for

21

providing heat flux 2.5

Insulation

22

2.6

Calibration graph with Calibrating Instrument

23

2.7

Thermocouples connected to a data logger and temperature

24

display 2.8

Digital manometer connected to the test section for pressure drop

24

measurement 2.9

Orifice plate with U tube manometer, gate valve to vary flow rate

25

& Blower 2.10

Leveling of Experimental setup with the help of sprit level

25

2.11

Experimental Setup

26

2.12

Insert placement inside the heat exchanger tube

27

3.1

Validation curve of friction factor (f) and Nusselt number(Nu)

31


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Temperature variation in the test section

33

4.2

Velocity vector contour

34

4.3

Stream line flow in tube with perforated circular disk

34

4.4

Nusselt number (Nu) vs Reynolds number (Re) for DR=0.6

35

4.5

Nusselt number variation with respect to smooth tube HE

36

(Nu/Nus) for DR=0.6 4.6


37

4.7


38



39

4.9


40


Variations in static pressure (Pascal) throughout the test section

41

4.11

Velocity magnitude (m/s)

41

4.12

Friction factor (f) vs Reynolds number (Re) for DR=0.6

42

4.13

Friction factor variation with respect to smooth tube HE (f/fs) for

43

DR=0.6 4.14


44

4.15


45

DR=0.7 4.16


46

4.17


47

DR=0.8 4.18

Thermal performance factor (η) Vs Reynolds number (Re) for

48

DR=0.6 4.19

Thermal performance factor (η) Vs Reynolds number (Re) for

49

DR=0.7 4.20

Thermal performance factor (η) vs Reynolds number (Re) for

50

DR=0.8 5.1

Plot for ln (Nu) Vs ln (Re)


53

Page xii


Plot for ln(Ao) Vs ln(DR)

54

5.3

Plot for ln(Bo) Vs ln(PR)

55

5.4

Plot for ln(Co) Vs ln(PI)

56

5.5

Plot for deviation in error between experimental and predicted

57

value of Nu 5.6

Plot for ln(f) Vs ln(Re)

58

5.7


59

5.8


60

5.9


61

5.10


62

value of f 5.11

Plot for ln(η) Vs ln(Re)

63

5.12


64

5.13


65

5.14


66

5.15


67

value of η


Page xiii


LIST OF TABLES

Table No.

Title

Page No.

1.1

Literature Review

10

2.1

Material with specification

16

2.2

Parameters

17

2.3

Details of tube section

21

3.1

Sample calculation

28

5.1

Parameters used for establishing correlations

52

5.2

Value of coefficient used in correlations

68

A1.1

Value of different parameter for one set of readings

71

A1.2

Maximum possible uncertainty in measurements

79


Page xiv

M. Tech Thesis; June, 2015 CHAPTER – 1 INTRODUCTION AND LITERATURE REVIEW

Whenever it is discussed about any thermo-mechanical systems, heating up is a very common problem in all systems because of friction between its working or moving parts. Hence there is a need to control excessive heating of our systems so that our system could become more efficient in working, or in some systems we need to transport heat from one part of the system to another part or space, like in the air conditioning system, outside warm air comes in contact with cooling coil with air conditioning system and cold air is supplied in indoor conditions and hence cooling of the room takes place. So in the entire scenario, transport of heat from one medium to another or from one part of system to another is a common phenomenon, or simply one can say the exchange of heat. So for proper exchange of heat from one medium to another device like heat exchanger is required. 1.1 Introduction Heat exchanger is a device used for effective transfer of heat from one place to another place. The most common example of heat exchanger can be seen in an automobile engine, which has coolant as circulating fluid flows through the radiator coil carries away the excessive heat of internal combustion engine and keeps the engine cool for its effective working. The heat exchanger is a very significant part of several thermo-mechanical systems and industries, for example, refrigeration system, air conditioning system, solar air heater, solar drier, solar water heater, petrochemical industries, geothermal energy systems, etc. All of these system comprises of the heat exchanger as an important unit for its effective working. On the basis of its working and physical construction heat exchangers can be classified into several types. 1.2 Classification of heat exchanger Since heat exchangers are used in different thermo-mechanical system and industries under different working conditions, according to the need and desire. So there is a proper classification according to its physical arrangement, working, nature of fluid flow and flow arrangements.

DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

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M. Tech Thesis; June, 2015 Some of its important classifications on the basis of its working and physical arrangements are listed below:1.2.1 Heat transfer process: a. Direct contact type: In this heat exchanger, two different fluid interact directly in order to exchanges their heat, and then separated from each other. Its Common applications also comprises of mass transfer along with heat transfer, example is evaporative cooling; applications with only sensible heat transfer are rare. The enthalpy of phase change in these heat exchangers represents a major part of the total energy transfer. The rate of heat transfer generally enhanced by phase change. Direct-contact type heat exchangers has following advantages over indirect contact type:

High heat transfer rates can be achieved,



The heat exchanger construction is relatively inexpensive and simple, and



The fouling problem does not exist, due to the lack of a heat transfer surface in between both the fluids.

However, it has some restriction and it is applicable for only those fluids, whose direct contact between both the fluid streams is permitted. Like as it is shown in Fig. 1.1 that fluid A and fluid B from the two sources mixed together in the heat exchanger and exchanges its heat and get separated further.

Fluid B

Fluid A

Fluid AB

Fig. 1.1 Direct Contact Type Heat Exchanger. b. Indirect contact type: In this type of heat exchanger, one fluid steam remains separated from other fluid streams and the heat transfer takes place through a dividing wall between the two fluid streams. Hence, there is no direct physical contact between the two thermally interacting fluids streams. This type of heat exchangers also comes in the category of surface heat exchanger, since the heat transfer is between two fluids takes place with the help of


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M. Tech Thesis; June, 2015 surface or wall separating them. As it is shown in Fig. 1.2, warm air enters the heat exchanger from one end and leaves after cooling from the other when it indirectly interacts with cool secondary air stream coming from the opposite end.

Fig. 1.2 Indirect Type Heat Exchanger 1.2.2 Geometrical construction: Geometry of heat exchanger plays very important role in its working and application. On the basis of its physical construction heat exchangers may be classified as follows: a. Shell and tube heat exchanger: Shell and tube heat exchangers made of a number of tubes in series arrangement separated by some distance inside a shell. Both shell and tubes are fed with different fluids. One of these tubes or shell contains the fluid that is to be heated or cooled, and the other contains fluid which runs over the primary fluid which is to be heated up or cooled, in order to either provide heat or absorb the heat. A tube bundle which can be made by several types of tubes sets such as plain, longitudinally finned, etc. Shell and tube heat exchangers are normally used for high pressure applications.

b. Plate heat exchanger: Another category of heat exchanger is the plate heat exchanger. It is composed of multiple, thin, slightly separated plates of very large surface areas and fluid flow passages for high temperature transport. This stacked-plate arrangement can be more efficient as compared to shell and tube heat exchanger for a given piece of work. In HVAC systems, large heat exchangers of this type are used. When used in open loops, these plate heat exchanges are mostly of the gasket type in order to allow periodic disassembly,


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M. Tech Thesis; June, 2015 cleaning, and inspection of its efficient and long working. Its maintenance is higher as compared to the tube heat exchangers.

c. Extended surface heat exchanger: It is most commonly used heat exchanger which is mostly seen as extended surface heat exchangers in the form of fins. As it is seen in the automobiles IC engine specially in case of air cooled engines, fins attached to the cylinder head of the engine dissipate the excessive heat of the engine to the surroundings and keeps the engine cool and efficient in its working. It has very low or negligible maintenance cost. 1.2.3 Flow arrangements a. Parallel flow type: In this arrangement [Fig. 1.3], the fluid stream of heated fluid and that of the cold fluid flow is in the same direction. As the direction of fluid flow is the same, hence heat transfer in such an arrangement is minimum.

Fig. 1.3 Parallel flow type heat exchanger.

b. Counter flow type: In this arrangement [Fig. 1.4], the fluid stream of heated fluid and that of the cold fluid flow is in the opposite direction. As the direction of fluid flow is the opposite, hence heat transfer in such an arrangement is maximum.

Fig. 1.4 Counter Flow Heat Exchanger DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

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M. Tech Thesis; June, 2015 c. Cross flow type: In this kind of arrangement, the fluid stream of heated fluid and the direction of the cold fluid flow are perpendicular to each other. As the direction is perpendicular, hence the heat transfer takes place over a large surface area and because of perpendicular flow the rate of heat transfer is very high. This is the most efficient way of cooling or heating in case of heat exchangers. 1.3 Application a. Used widely in the chemical process industries, especially in refineries. b. Used in swimming pool in order to cool or heat water . c. Use for cooling of hydraulic fluid and oil in engines, transmissions and hydraulic power packs. d. Used in geothermal and Thermal power plants. e. Used in space heating. f. Used in petrochemical industries. g. Used in refrigeration and air conditioning systems. h. Used in natural gas processing. i. Used in sewage treatment.

1.4 Need of heat transfer enhancement in tube heat exchanger

As in tube heat exchangers the basis of heat transfer is through tube wall. As the tube wall gets heated by the hot fluid coming in its contact, and releases its heat to the cold fluid which is flowing inside the tube, so there is convective heat transfer between the fluid and tube wall and hence the cold fluid carries away the heat of warm or hot fluid or surface in order to maintain the temperature of thermal system and keeps it thermally stable for its proper and efficient working. As shown in the Fig. 1.5, initial temperature difference (∆t1) of warm fluid (tw1) and cold fluid (tc1) is very large, but as the cold fluid passes through the heat exchanger tube it carries away the heat of hot fluid and at the exit of heat exchanger the temperature difference of hot (t w2) and cold fluid (tc2) i.e. ∆t2 is comparatively lower. So in this way the heat transfer takes place and our thermal systems remains thermally stable while working.


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Fig. 1.5 Heat transfer in Tube Heat Exchanger.

But there is need of heat transfer enhancement in the case of tube heat exchangers as the net heat transfer rate in case of tube heat exchanger is very low. As we can see in the Fig. 1.6, which shows the flow behavior in the form of streamline and vectors, it can be easily seen that there is no deflection in the path of fluid flow as the fluid near the surface of tube heat exchanger remains near the surface and the core fluid remains at their own path throughout the fluid flow. Hence, because of this phenomenon the fluid coming in direct contact of the heat exchanger carries away the heat by direct convection from the tube wall, but the core fluid does not get a chance to take away the heat of the tube wall by direct convection. Thus core fluid receives heat in the form of indirect convection from the other layer of the fluid which is making direct contact with tube wall. And thus the heat transfer is minimized to a very large extent.

Fig. 1.6 (a) Velocity vector of smooth tube flow, (b) Streamline in smooth tube.

So it is very important to develop such a method in which heat transfer rate is maximised and the thermal performance of the tube heat exchangers can be improved. Reserchers are working in the


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M. Tech Thesis; June, 2015 direction of heat transfer enhancement and they are adopting several methods inorder to achieve high heat transfer rate. Some of these important methods are disscussed below.

1.5 Methods of heat transfer enhancement.

As heat exchangers are most commonly used equipment in most of the thermo-mechanical systems, hence it is necessary to develop and install certain energy saving methods in order to improve the working of heat exchanger and reduce its size. In recent years a consistent emphasis has been given in order to develop a method to improve heat transfer rate in the heat exchangers and also to minimise the frictional losses and improve thermal performance. So in order to achieve this several heat transfer augmentation techniques has been adopted. Some of the most important techniques are discussed below. 1.5.1 Active Technique of heat transfer augmentation: [1] In this technique some external power input is introduced for the improvement in heat transfer. This external power may be Surface vibration, electrostatic field, mechanical aids, fluid vibrations, crating pulsation by cam and plunger, static field, suction or injection, etc. But due to complexibility of design of heat exchangers these methods does not show much potential in augmentation of heat transfer. So mostly they are avoided. 1.5.2 Passive Technique of heat transfer augmentation: [2] There is no need of external power input in this technique, as in this technique turbulence promoters are used in the fluid path. This turbulent promoter creates disturbance in the fluid flow and hence because of this there is mixing in the fluid layers. Detachment and reattachment of fluid layer also takes place and because of this there is a significant augmentation in the heat transfer rate. As it can be seen in Fig 1.7, which clearly shows the velocity vector of fluid flow inside the tube heat exchanger with and without turbulence promoters, here we can see that in case of smooth tube the velocity vectors are undisturbed but in case of tube with turbulence promoters the velocity vectors are disturbed in circulating manner. This disturbance causes proper mixing of fluid while its flow, and because of this there is significant improvement in the heat transfer. But due to the disturbance created, energy losses also take place. So it is needed to DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

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M. Tech Thesis; June, 2015 make improvement in this method in order to decrease energy losses and improve thermal performance of heat exchanger. Some of the common turbulence promoters used are following: 

Twisted tape (serrated, broken, single, double, multiple, perforated, delta wing, etc.)



Conical ring (Convergent, divergent, snail entry, with hole, alternative arrangement, etc.)



Coiled wire (Uniformly spaced, randomly spaced, changed cross section, etc.)



Circular ring ( hollow, perforated, combined with twisted tape, etc.)



Surface modification (dimple, protrusion, finned surface, corrugated surface, etc.)

Without turbulence promoter

With turbulence promoter

(a)

(b)

Fig. 1.7 (a) Velocity vector in smooth tube, (b) Velocity vector in tube with turbulators 1.5.3 Compound Technique of heat transfer augmentation:[3] In compound technique combination of both active and passive technique and combination of any two or more techniques is adopted to enhance the heat transfer rate. Some of the commonly used compound techniques are listed below: 

Electromagnetic field with twisted tape insert,



Twisted tape with finned wall surface,



Finned tube subjected to vibration,



Pulsation of air introduced in fluidized bed combustion,



Rough cylinder with vibrations, etc.


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M. Tech Thesis; June, 2015 1.6 Literature Review

On the basis of literature review, it is found that different researchers have used different insert geometry and parameters in order to perform their experimental work. The effect of these insert geometries and their parameters showed different effects on the heat transfer and friction factor. Saal A et al.[4] has used ‘longitudinal interrupted fins’ as geometry with different arrangements like inline, continuous and staggered. It was found that staggered arrangement results in maximum pressure drop. Some of the researchers like Halit Bas et al.[5], M.M.K Bhuiya et al[6] and M.M.K Bhuiya et al[7] used ‘Twisted tape’ as their insert geometry, with different parameters of twist ratio and width ratio. They used single, double and triple twisted tape to investigate the effect on heat transfer and friction factor. It was found that as the value of twist ratio decreases, its significant effect is seen in heat transfer and friction factor, heat transfer increases with a decrease in the value of twist ratio and friction factor also increases, and at minimum twist ratio heat transfer is maximum. Using twisted tape as insert geometry, only core disturbance of the fluid takes place, hence, some researchers like Smith Eiamsa-ard et al[8] used ‘Twisted tape with ring’ as insert geometry with different parameters of twist ratio and pitch ratio. This geometry causes both core disturbance and surface modification of heat exchanger tube. Here also a significant enhancement in heat transfer was observed and was found that as the pitch ratio decreases, augmentation in heat transfer is significantly increased. P. Promvonge[9] and P. Promvonge et al[10] used ‘twisted tape with uniform coiled wire’ insert and ‘twisted tape with conical insert’ respectively. Here also a significant improvement in heat transfer is observed with respect to the smooth tube heat exchanger. Researchers like M.M.K Bhuiya et al[12] and Smith Eiamsa-ard et al[13] used some modified form of twisted tape, they used perforated and serrated twisted tape respectively for their experimental investigation. Effect of perforation was significantly observed in pressure drop in case of perforated twisted tape. Friction factor in perforated and serrated twisted tape were less as compared to normal twisted tape. V. Kongkaitpaiboon et al.[15] used perforated conical ring as insert geometry and here also there was improvemet in the value of heat transfer as compared with the smooth heat exchanger. V. Kongkaitpaiboon et al.[17] used circular ring as their insert geometry with different parameters of pitch ratio and diameter ratio. It was observed that with an increase in the value of pitch ratio , heat transfer enhancement decreases and friction factor also decreases. Maximum DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

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M. Tech Thesis; June, 2015 heat transfer was observed at a minimum value of diameter ratio and maximum thermal performance was observed for the maximum value of diameter ratio and minimum value of pitch ratio. So several insert geometries were used by different researchers in order to investigate the effect of different insert geometry and parameters on heat transfer, friction factor and thermal performance factor. Some of the most effective geometries according to the literature review is mentioned in Table 1.1 with their flow parameter and observation.

Table 1.1 Literature Survey S.No.

Author

Insert geometry &

Observation

Flow Parameters 1.

Saad A et al.[4]

Circular Tube with



Longitudinal

According to result the pressure drop variation is in following order.

Interrupted

Inline < continuous < staggered

Fins

arrangement

Re No. 5000-50,000 2.

Halit Bas et al.[5]

Twisted tape



separated from tube

The

highest

enhancements

wall

heat is

transfer

1.756 times as

compared to plain tube. 

Thermal Performance factor improves upto 1.8 times as compared to plain tube.

Re No. 5132-24989 3.

M.M.K Bhuiya et al

Double twisted tape



[6]

Heat transfer is highest for double counter arrangement twisted tape.

 Re No. 6950-50,050

Thermal Performance factor improves up to 1.34 times as compared to plain tube.


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M. Tech Thesis; June, 2015 4.

M.M.K Bhuiya et al

Triple twisted tape



[7]

Nusselt number improves upto 3.85 time with respect to smooth tube.

Re No. 7200-50,200




5.

Smith Eiamsa-ard et al[8]

Twisted tape with



ring

Heat transfer is 4.47 times the plain tube




Re No. 6000-20,000 6.

P. Promvonge[9]

Twisted tape with



uniform coiled wire

Nusselt umber improves up to 7 times with respect to plain tube.




Re No. 3000-18,000 7

P.

Promvonge

et

al[10]

Twisted tape with



conical tuberators

367 % improvement in heat transfer with respect to plain tube.




Re No. 6000-26,000 8

Smith Eiamsa-ard et al[11]

Double sided delta



wing tape

Thermal Performance factor improves up to 3.6% as compared to plain tube.

Re No. 4000-20,000 9

M.M.K Bhuiya et al[12]

Perforated twisted



tape

can be seen. 


340% improvement in heat transfer

Thermal Performance factor improves Page 11

M. Tech Thesis; June, 2015 up to 59 % as compared to plain tube. Re No. 7200-49,800 10

Smith Eiamsa-ard et Serrated twisted tape  al

[13]

Nusselt number improves up to 72.2% in comparison with the plain tube.



The empirical correlations show only ±5% and ±10% deviation in heat transfer

Re No. 4000-20,000 11

P.

Promvonge

et

al[14]

Conical nozzle with

and

friction

factor

as

compared to experimental values. 

snail

Nusselt number improves by 278% in the context of plain tube for conical nozzle.

 Re No. 8000-18,000

12

V. Kongkaitpaiboon et al.[15]

Perforated conical

While it shows a 316 % improvement for a conical nozzle with snail entry.



ring

185% improvement in heat transfer is found with respect to plain tube.



The thermal performance factor goes up to.92 times as compared to plain tube.

Re No. 4000-20,000 13

Sibel Gunes et al.[16]

Coiled wire of



triangular cross

The maximum thermal enhancement efficiency of 36.5% is seen with

section

respect of plane tube.

Re No. 3500-27,000 14

V. Kongkaitpaiboon

Circular disk

[17]

et al.




195% improvement in heat transfer can be noticed.

Page 12

M. Tech Thesis; June, 2015 


Re No. 4000-20,000 15

C.

Thianpong

et

Twisted ring



al.[18]


Re No. 6000-20,000 16

P.

Promvonge

et Circular ring at some 

al.[19]

angle

4.3

times

improvement

in

heat

transfer.

Re No. 5000-26,000 17

Smith Eiamsa-ard et al.[20]

Short length twisted



tape

Heat transfer augmentation is up to 1.27 times on the plain tube.



The correlations show ±7% deviation for both the heat transfer and friction factor.

Re No. 4000-20,000 18

S.

Eiamsa-ard

et

al.[21]

Non uniform wire



coiled with twisted

Thermal Performance factor improves up to 3.7 %

tape.

as compared to plain

tube.

Re No. 4600-20,000 19

S. al.

Eiamsa-ard [22]

et

V-nozzle



turbulators.

can be noticed. 

Re No. 8000-18,000

270% improvement in heat transfer



Page 13

M. Tech Thesis; June, 2015 20

Shyy Woei Chang et. Al.

Broken twisted tape



[23]

2.4 times improvement in heat transfer can be observed.



Thermal Performance factor improves up to 2.5 times as compared to plain

Re No. 1000-40,000

tube. 21

Pongjet Promvonge et al.[24]

Divergent



convergent nozzel

344% improvement in Nusselt number can be seen



Nusselt number in case of divergent ring is greater than compared to convergent conical ring.

Re No. 8000-18,000 22

P.

Promvonge

al.[25]

et

C-nozel with snail



and free entry

315% augmentation in heat transfer can be noticed.




Re No. 8000-18,000

tube. 23

P. Promvonge[26]

Conical ring CR



CDR DR

333%

augmentation

inn

Nusselt

number is seen, as compared to smooth tube. 

predicted valued can be noticed.

Re No. 6000-26,000 24

K. Nanan et al.[27]

Perforated helical

±10% deviation in experimental and



twisted tape

2.08 times improvement in heat transfer can be observed.




Re No. 6000-20,000 25

Yadav et. al.[28]

Half length twisted

tube. 

Heat transfer coefficient and the

tape

pressure drop were 9–47% and 31–

Re No. 5000-20,000

144% higher than those in the plain tube


Page 14

M. Tech Thesis; June, 2015 1.7 Discussion on literature

On the basis of the above literature review, it was found that plenty of work has been done in order to improve the thermal performance of tube heat exchanger. A lot of work on insert geometries like twisted tape, conical ring, perforated inserts, wire coil, etc. have been completed with significant results. V. Kongkaitpaiboon et al[17] worked on circular ring geometry using geometrical parameter as pitch ratio and diameter ratio in year 2010. Looking at research gap and possible improvement it became very easy to set the objective and determine insert geometry with proper parameters for the experimental purpose. The establishment of experimental setup also became easier as the researchers also explained the methodology and data reduction processes. Objective formulated for the present work is listed below.

1.8 Objectives  To investigate heat transfer and fluid flow characteristics in a circular tube with perforated hollow disk insert.  To investigate the thermal performance factor of the circular tube with perforated hollow disk insert.  To develop statistical correlations for Nusselt number, friction factor and thermal performance factor in terms of flow and geometrical parameters.

1.9 Summary

Hence, in introduction part it is seen that researchers are using different insert geometries in order to improve the thermal performance in heat exchanger tube. Though still thermal performance of heat exchanger needs prime focus for its improvement. According to the literature review still works are being carried out in order to improve the working of this thermal device. It can be said that with the help of different insert geometry, it is possible to improve the performance of heat exchanger significantly and also reduce its size.


Page 15

M. Tech Thesis; June, 2015 CHAPTER – 2 EXPERIMENTAL INVESTIGATION

2.1 INTRODUCTION The experimental setup has been designed and fabricated to achieve the objective mentioned in chapter 1 on the basis of literature review. Measuring instruments were calibrated using standard calibrating machines before installing it on the experimental setup. The material with specification used for the fabrication of experimental setup are listed in Table 2.1 Table 2.1 Material with specification. S.NO

NAME

SPECIFICATION

1.

GI Pipe

68 mm diameter, 6 m length.

2.

GI Flanges

3.

Fasteners

68 mm diameter with internal thread Nuts & bolts (12 mm diameter), and 80 mm length.

4.

Centrifugal Blower with 3 Ø motor.

5.

Variac transformer

6.

Ameter & Volt meter

5.

Heating element

Nicrome wire

6.

Aluminium oxide

Basic / Neutral

7.

Anbond 666 T Plus

High Temperature Binder

8.

Thermocouples

T- Type (Cu-Ni constant)

9.

Orifice plate

10.

U tube manometer

11.

Gate Valve

12.

Glass wool fiber

Insulating tape

13.

Data logger

16 Chanel NI

14.

Computer

15.

Digital Pressure measuring Device

16.

Sprit level


2 HP motor Up to 5 Amp. & 300 Volts supply Digital

35 mm diameter 300 mm 68 mm diameter

With labview setup ------------Page 16

M. Tech Thesis; June, 2015 2.2 Insert Geometry and Parameters. In literature review it is found that V. Kongkaitpaiboon et al

[17]

used circular disk as an insert

geometry with several flow and geometrical parameters. Looking at research gap and the possibility of getting much better results, the parameters of this work has been finalized. In this work slight modification has been made in the geometry and its parameters. Here the emphasis is given on the effect of perforation in the solid disk. Perforated circular disk is used in this work along with solid disk. The parameters used in the experimentation are mentioned in Table 2.2. Table 2.2 Parameters Used S. No

Name of Parameter

Specification

Range

1.

Pitch ratio (PR)

l/D ratio

1-3

2.

Diameter Ratio (DR)

d/D ratio

0.6 - 0.8

3.

Perforation Index (PI)

Pa / Ta ratio

0% - 24%

4.

Thickness Ratio (TR)

t/D ratio

0.0075

5.

Reynolds Number

Flow parameter

6500 - 23,000

Where Ta and Pa are total area and perforated area of Perforated circular disk and value of perforation index is calculated by equation 2.1 where ‘n’ is number of hole used in perforation. PI= (Pa / Ta) =

π 4

n dh 2

(2.1)

π (D−d)2 4

The schematic model of circular disk is shown in Fig. 2.1 and Fig. 2.2 shows PR where n=16.

DR=0.6 PI= 0% pp

DR=0.7 PI= 0% DR=0.6 PI= 0%

DR=0.8 PI= 0% pp

% pp DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 17


DR=0.6 PI= 8%

DR=0.7 PI= 8%

DR=0.8 PI= 8%

pp

pp

pp

DR=0.6 PI= 16%

DR=0.7 PI= 16%

DR=0.8 PI= 16%

pp

pp

pp

DR=0.6 PI= 24%

DR=0.7 PI= 24%

DR=0.8 PI= 24%

pp

pp

pp

Fig. 2.1 Perforated disks with different perforation index and diameter ratios.


Page 18


PR=1

PR=2

PR=3

Fig. 2.2 Perforated circular disk arrangement with different pitch ratio. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 19

M. Tech Thesis; June, 2015 Dimensional details of the perforated circular disk insert is mentioned in schematic diagram, which is shown in Fig.2.3.

Fig. 2.3 Dimensional details of the insert geometry. 2.3 Experimental Investigation In order to construct experimental setup, it was necessary to proceed in a step by step manner with proper deliberation and in accordance with the literature review. Each and every component of the experimental setup were carefully installed for accuracy in measurements. Special emphasis has been given on calibration of measuring instruments in order to minimize the uncertainty in the measurements. Emphasis is also given on the strength of setup frame and leveling of experimental setup in order to avoid any risk of physical failure.

2.3.1 Tube section: Tube section is divided into several important sub sections and in all those sub sections has their specific dimension. Galvanized Iron Pipe is used to construct the different section. The dimension of all the sections is mentioned in Table 2.3.


Page 20

M. Tech Thesis; June, 2015 Table 2.3 Details of tube section S. No.

Section name

Dimension

1.

Calming section

2.5 m

2.

Test Section

1.4 m

3.

Post test section

0.5 m

4.

Pre gate valve section

0.5 m

5.

Post gate valve section

0.5 m

All the segments are united with the help of flanges and fasteners. Calming section is used for fully developed flow to enter the test section. Test section is the main part of the setup and in this part the different inserts were used to carry out the experiments. Orifice plates with U tube manometer are placed in between the post test section and pre gate valve section. The blower is attached to the post gate valve section. 2.3.2 Heating arrangement in the test section Uniform Heat flux is provided to simulate the experimental setup. Uniform heat flux is provided with the help of Nicrome wire as heating elements and Variac transformer. In order to prevent thermocouple which was placed on tube wall, from the electric current, a layer of aluminium oxide paste with anabond was provided on the test section. The heating element was wrapped over the aluminum oxide layer as shown in Fig. 2.4. Constant heat flux of 1000 W/m2 was given in the test section. In Fig 2.4 it can be clearly seen that a layer of aluminium oxide (Al2O3) preventing the flow of electric current over the tube surface and allowing the thermocouple to work efficiently.

Fig. 2.4 Heating element over Aluminium oxide paste and Variac used for providing heat flux. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 21

M. Tech Thesis; June, 2015 2.3.3 Insulation of the test part. Insulation plays an important role in preventing heat losses to the environment. Therefore, special care was given on the insulation part. Insulation was provided with the help of Glasswool fiber tape and Insulating pads. Three layer of glass wool fiber tape were used for insulation purpose. The last two layers of insulation were given with the help of insulating pads. The insulation is clearly depicted in Fig. 2.3.

Fig. 2.5 (a) The aluminum oxide layer with white color along with heating element and the adjacent figure shows insulating layer of glass wool fiber tape.

Fig. 2.5 (b) Insulation with black insulating pad

Fig. 2.5 (c) Three layers of glass wool fiber for the primary layer of insulation. Fig. 2.5 Insulation of test section.


Page 22

M. Tech Thesis; June, 2015 2.3.4 Temperature Measurement T-type (copper-nickel constant) thermocouple was used for taking down the temperature reading with the help of data loggers. Thermocouple was made with T-type thermocouple wire, which was dipped in mercury placed in a conductive medium and constant 20 volt current was supplied with the help of variac transformer. In Fig 2.6 the calibration graphs are shown along with the instrument. This graph shows the variation in temperature measurement with respect to the actual temperature which was given to the calibrating instrument. Total 16 thermocouples were used, out of which 12 was placed on tube wall, 1 at inlet & 3 at the outlet. Thermocouples placed at wall were fixed on the tube wall with the help of m-seal and was placed near the inner surface of the heat exchanger tube. For calibration, the instrument was set on different temperature i.e. 0o, 20o, 40o, 60o, 80o & 100o respectively one by one and thermocouple readings were recorded in order to fine deviation from actual temperature reading. At a time only four thermocouple were calibrated at different temperature. This process was repeated for all the 16 thermocouple. The bar graph in Fig. 2.6 shows the deviation in temperature reading with respect to the actual temperature. Maximum deviation of ±0.23o was recorded.

T1 T6 T11 T16

120

Reading on thermocouples

100

T2 T7 T12

T3 T4 T5 T8 T9 T10 T13 T14 T15

80

60

40

20

0 0

20

40

60

80

100

Calebrating Instruments Reading

Fig. 2.6 Calibration graph with Calibrator.


Page 23

M. Tech Thesis; June, 2015 The temperature readings were recorded with the help of data logger and labview software. All the thermocouples were connected in channels of data logger and the data logger is connected to labview software installed in a computer with the help of a USB cable. As the temperature of fluid changes, the data logger shows transient response and records the temperature in degree Celsius. The measurement of temperature was taken at the steady state condition of the experimentation as in Fig 2.7.

Fig. 2.7 Thermocouples connected to a data logger and temperature reading are on screen. 2.3.5 Pressure measurement Digital manometer is used for measuring the pressure drop across the test section. Taps are provided near the inlet and exit of test section and the taps are connected to rubber tube. These rubber tubes are connected to the digital manometer. Because of the pressure difference across the test section, highly sensitive diaphragm of the digital manometer senses the pressure and displays it on the screen of the instrument. The instrument used is very sensitive and it senses even a very small change in pressure across the test section. Fig. 2.8 shows the photographic view of digital manometer.

Fig. 2.8 Digital manometer connected to the test section for pressure drop measurement. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 24

M. Tech Thesis; June, 2015 2.3.6 Flow Measurement As air is used as the working fluid in this work, therefore blower is used as an air supply medium for the experimental purpose. For the measurement of flow rate orifice plate of diameter 35 mm is used and a U tube manometer is connected across the orifice plate. The flow is controlled with the help of gate valve which is placed near the blower. By varying the flow rate, the Reynolds number is varied and measurement for different flow parameters is taken when it attains steady state condition. Schematic view of flow measuring devices and blower is given in Fig. 2.9. The U-tube manometer contains water as a fluid. When the fluid passes through the orifice plate placed in the tube, it shows deflection in the manometric height. Considering this deflection flow rate is calculated.

Fig. 2.9 Orifice plate with U tube manometer, gate valve to vary flow rate & Blower. 2.3.7 Leveling of the experimental setup For the proper working and good result the leveling of the setup plays an important role. In this case, leveling was done with the help of sprit level instrument at the different sections of the experimental setup as shown in Fig. 2.7. Sprit level was kept parallel to the experimental setup and it was run throughout the length of the setup in order to check its level uniform throughout the setup.

Fig. 2.10 Leveling of experimental setup with the help of sprit level


Page 25


Fig. 2.11 Complete Experimental Setup. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 26


Fig. 2.12 Insert placement inside the heat exchanger tube. 2.4 Summary In this chapter emphasis has been given on design and fabrication of experimental setup for experimentation. Design and fabrication of the setup in appropriate manner is the major aim of this chapter. This chapter includes parameters used for experimentation with their details. Instruments calibration and their working are also discussed along with their pictorial view.


Page 27

M. Tech Thesis; June, 2015 CHAPTER – 3 DATA REDUCTION AND VALIDATION 3.1 Introduction

After recording the experimental data in terms of temperature, pressure and flow rate, the next step is the calculation of parameters. This calculation is done by a sequence of data reduction steps which involves systematic mathematical calculations. In data reduction the results are calculated using mathematical formulae. In this chapter the calculation were done for a set of reading as a sample set. Table 3.1 Sample calculation through the data reduction process.

Ti 14.31

To

Twm

Tb

Cd

28.93333

306.78

294.6217

0.6 0.000962

ρ(air

ρ

(Tfm))

(To))

K (Tfm)

Ao

β

A

D

μ [air (Tfm)]

∆p (Tfm)

0.514

0.299

0.068

1.81736E-05

1006.086

(air H

Δpo

Δp

𝑚

Qu

h

V

0.025814 1.152896 1.124977 0.06 588.0114 525 0.022036 324.207 89.18199 5.396233 Re

Nu(Exp)

Pr

Nu (Corr)

23278

234.9283

0.708312 62.42766

Nu/Nus

f(Exp)

f(Corr)

f / fs

n

3.763208 1.519144 0.025583 59.38121 0.964588

3.2 Mathematical equations used in the data reduction.

The above mentioned data is obtained after mathematical calculation using standard equations. The step by step procedure followed is discussed below. At the steady state condition of the experiment, it is assumed that convective heat transfer by the wall surface of heat exchanger tube is equal to the heat gain by the fluid circulating in the tube. hence the energy balance equation can be written as:


Page 28

M. Tech Thesis; June, 2015 Qair = Qconv.

(3.1)

In equation 3.1, Qair = mCp (To – Ti)

(3.2)

and the convective heat transfer from the heat exchanger wall is given by: Qconv = hA(Twm – Tb)

(3.3)

where Tb is bulk mean temperature of fluid and it is calculated by equation: Tb = (To + Ti) / 2

(3.4)

and Twm = Ʃ Tw/12

(3.5)

In which ‘Tw’ is the local wall temperature at which thermocouple was placed. Thermocouples was placed exactly near the inner wall of the tube and placed on the drilled slot on the tube wall surface. Because of the placing so near to the tube wall, the thermal resistance of the tube wall is neglected and hence the measured ‘Tw’ is assumed as actual wall temperature. ‘Twm’ represents mean wall temperature which was again the average temperature of the total thermocouple placed on the wall surface. The heating surface area, ‘A’ based on the hydraulic diameter ‘D’ of the heat exchanger tube. Mean wall temperature is calculated by averaging all the 12 local wall temperature value obtained from thermocouple reading. It is assumed that temperature distribution is uniform throughout the wall surface. The average heat transfer coefficient, ‘h, and the average Nusselt number, Nu are estimated as follows: h = mCp (To – Ti)/ A(Twm – Tb)

(3.6)

Nu = hD/k

(3.7)

where the mass flow rate is given by equation:

 2. .P o  m  C d  Ao    4  1  

0.5


(3.8)

Page 29

M. Tech Thesis; June, 2015 and velocity is calculated by equation,

V 

m . A

(3.9)

The value of Reynolds number is obtained by standard equation mentioned below: Re = ρVD/ 

(3.10)

and the value of Friction factor is obtained by: f = ΔP/ {(L/D) (ρV2/2)}

(3.11)

In which V is the mean velocity of the tube. All of thermal properties of the tested fluid are determined at the bulk mean temperature of fluid. (To + Ti)/ 2.

(3.12)

Finally the thermal performance factor is calculated by the equation:

𝜂=

𝑁𝑢 /𝑁𝑢 𝑠 (𝑓/𝑓𝑠 )1/3

(3.13)

3.3 Validation test

A thorough check of the instruments and the test set-up was followed by experimentation on conventional smooth pipe. The average values of Nusselt number and friction factor were determined. These values is compared with the values obtained from the standard correlation like Blasius equation for friction factor and Dittus-Boelter equation for Nusselt number in case of smooth tube. The standard equations for Friction factor and Nusselt number is given as: Blasius equation

f s  0.316  Re 0.25

(3.14)

Dittus-Boelter equation

Nu s  0.023 . Re 0.8 . Pr 0.4


(3.15)

Page 30


100

90

Nu correlation Nu experimental + 5%

80

- 5%

Nu

70

60

50

40 10000

15000

20000

25000

30000

35000

40000

Re

0.034

f correlation f experimental

0.032

+ 9%

0.030

f

0.028

0.026

-9%

0.024

0.022

0.020 10000

15000

20000

25000

30000

35000

40000

Re

Fig. 3.1 Validation curve of Friction factor (f) and Nusselt number(Nu)

The graph shown in the above Fig. 3.1 shows the validation of friction factor and Nusselt number as compared to the standard smooth tube equation. Deviation of 5 % is seen in the case of Nusselt number and 9% is noticed in case of friction factor, as compared to plain tube. This shows the accuracy of data obtained from this setup.


Page 31

M. Tech Thesis; June, 2015 3.4 Summary

In this chapter the focus has been given on data reduction using experimental results and mathematical equations. Validation curve is also obtained by comparing standard equations for Nusselt number and Friction factor. It was found that the experimental setup is showing error in permissible range. So experimentation can be continued using setup.


Page 32

M. Tech Thesis; June, 2015 CHAPTER – 4 RESULTS AND DISCUSSION

4.1 Introduction In this chapter discussion on results is focused. The experimentation is carried out using different geometrical and flow parameters; hence it is necessary to discuss the effect of each parameter on heat transfer, friction factor and thermal performance factor of heat exchanger tube. As use of different geometrical parameters shows their independent impact on heat transfer and thermal performance factor, therefore it is necessary to find a geometrical and flow parameters which shows best results for heat transfer and thermal performance factor and at same time it should have less value of friction factor. The effect of each parameter is discussed below.

4.2 Heat transfer Enhancement of heat transfer is the main aim of our experimentation and research. As discussed in chapter 1, in case of smooth tube heat exchangers the amount of heat transfer is very less, as only the outermost fluid lamina receives heat by direct convection from the tube wall and the core fluid receives heat by indirect convection which is very less. So the research is being done in the passive mode of heat transfer enhancement. The effect of heat transfer with respect to different flow parameters and geometrical parameters is discussed below. The discussion has been made on the basis of graphs obtained from the experimental values. In figure 4.1 temperature variation throughout the test section can be seen.

Fig. 4.1 Temperature variation in the test section. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 33

M. Tech Thesis; June, 2015 Due to presence of perforated circular disk as insert geometry in the test section, turbulence is caused in the fluid stream. Due to dominant jet impingement near the perforated circular disk, fluid stream detachment takes place. These fluid streams reattaches as the fluid moved forward and again detaches near the circular disk. This phenomenon takes place throughout the fluid path. Because of this detachment and reattachment of fluid streams, proper mixing of fluid takes place, which helps in heat transfer enhancement. Eddy generation also takes place near the tube surface and inserts geometry. Because of this eddy, vortex flow is developed which too helps in heat transfer enhancement. This dominant disturbance in fluid streams can be seen in Fig. 4.2 and Fig. 4.3. Vortex development near circular disk

Fig. 4.2 Velocity vector contour. Fluid stream detachment and reattachments

Fig. 4.3 Stream line flow in tube with perforated circular disk DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 34

M. Tech Thesis; June, 2015 4.2.1 Effect on heat transfer for diameter ratio (DR ) 0.6

270 240

PI=0%, PR=1 PI=24%, PR=1 PI=16%, PR=2 PI=8%, PR=3



DR=0.6

210

Nu

180 150 120 90 60 8000

12000

16000

20000

24000

Re

Fig. 4.4 Nusselt number (Nu) vs Reynolds number (Re) for DR=0.6

From the graph obtained on the basis of experimentation (Fig 4.4), for Diameter ratio 0.6 the augmentation in heat transfer is very significant. Highest heat transfer is found in case of PR=1 & PI=0%. As in case of PR=1 the insert assembly is densely populated, hence there is a lot of obstruction in the fluid path. When fluid passes from the circular ring, because of the obstruction fluid layer detached from each other and as it moved forward it again reattaches. It is also seen that near the circular ring there is formation of eddy flow and because of that fluid mixing takes place and also there is jet impingement as fluid strikes the insert geometry. Because of these dominant disturbances in the fluid flow, high turbulence is obtained and heat transfer enhances. It is also found that as the PI and PR increases to higher value there is a significant decrease in the heat transfer rate. For PR 1,2 & 3; PI=0% shows the maximum heat transfer as compared to perforation index 8%, 16% & 24%. As perforation index increases heat transfer decreases. The DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 35

M. Tech Thesis; June, 2015 minimum heat transfer is seen in case of PR=3 & PI=24% for the DR=0.6. It is also noticed that as the Reynolds number increases heat transfer also increases and for maximum value of the Reynolds number the heat transfer is maximum in all the insert parameters.

4.9

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

DR=0.6

Nu/Nus

4.2

3.5

2.8

8000

12000

16000

20000

24000

Re

Fig. 4.5 Nusselt number variation with respect to smooth tube (Nu/Nus) for DR=0.6 In view of experimental investigation and graph obtained for Nu/Nus for DR=0.6 as shown in Fig 4.5 it is absorbed that, for the lower value of Reynolds number. i.e. at Re=6,500, heat transfer enhancement as compared to smooth tube (Nu/Nus) is maximum and as the Reynolds number increases the value of Nu/Nus decreases. For PR=1 and PI= 0% , significant improvement in the heat transfer enhancement is noticed i.e. around 4.4 times as compared to smooth tube heat exchanger. As the PI & PR increases to its higher value it shows significant decreases in the rate of heat transfer and hence Nu/Nus also decrease. Minimum Nu/Nus is observed for the insert parameter PR=3 & PI=24% at the higher value of flow parameters i.e. Re=23,000.


Page 36

M. Tech Thesis; June, 2015 4.2.2 Effect on heat transfer for diameter ratio (DR) 0.7 280 PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 DR=0.7 PI=24%, PR=3

240

Nu

200

160

120

80

40 8000

12000

16000

20000

24000

Re


It is observed from the Fig. 4.6 that, for Diameter ratio 0.7 the enhancement in heat transfer is good but in comparison to DR=0.6 it is on the lower side if compared with similar insert geometry. Highest heat transfer in case of PR=1 & PI=0%. As in case of PR=1, circular disk is closely spaced, so the frequency of eddy generation and fluid stream detachment and reattachment increases. This causes proper mixing of fluid stream and hence, there is improvement in the enhancement of heat transfer. There is jet impingement as fluid strikes the insert geometry. Because of these dominant disturbances in the fluid flow, high turbulence is obtained and heat transfer enhances. It is also found that as the PI and PR increases to higher value there is a significant decrease in the heat transfer rate. For PR 1, 2 & 3; PI=0% shows the maximum heat transfer as compared to perforation index 8%, 16% & 24%. As perforation index increases heat transfer decreases. The minimum heat transfer is seen in case of PR=3 & PI=24% for the DR=0.7. It is also noticed that as the Reynolds number increases heat transfer also DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 37

M. Tech Thesis; June, 2015 increases and the maximum value of Reynolds number, i.e. Re=23,000, heat transfer is maximum for all the insert parameters.

4.5 4.2

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 DR=.7 PI=24%, PR=2 PI=24%, PR=3

3.9

Nu/Nus

3.6 3.3 3.0 2.7 2.4 8000

12000

16000

20000

24000

Re

Fig. 4.7 Nusselt number variation with respect to smooth tube (Nu/Nus) for DR=0.7 The experimental observation of Nu/Nus for DR=0.7 as shown in Fig 4.7, it is absorbed that, though the heat transfer is maximum for the higher value of Reynolds number but when it is compared with smooth tube the experimental results are different. For the lower value of Reynolds number, i.e. at Re=6,500, Nu/Nus is maximum and as the Reynolds number increases the value of Nu/Nus decreases. For PR=1 and PI= 0% , the improvement in the amount of heat transfer is maximized and around 4 times improvement in Nusselt number is observed in comparison of smooth tube heat exchanger. As the PI & PR increases to its higher value it shows significant decreases in the amount of heat transfer and hence Nu/Nus also decrease. Minimum Nu/Nus is observed for the insert parameter PR=3 & PI=24% at the higher value of flow parameters i.e. Re=23,000.


Page 38

M. Tech Thesis; June, 2015 4.2.3 Effect on heat transfer for diameter ratio 0.8

220

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

12000

16000

PI=24%, PR=1 DR=0.8 PI=24%, PR=2 PI=24%, PR=3

200 180 160

Nu

140 120 100 80 60 40 8000

20000

24000

Re


From the graph obtained on the basis of experimentation (Fig 4.8), for Diameter ratio 0.8 the augmentation in heat transfer is on the lower side as compared to other diameter ratios. Highest heat transfer (Nu) is found in case of PR=1 & PI=0%. When fluid passes from the circular ring, because of obstruction fluid layer detached from each other and as it moved forward it again reattaches. It is also seen that near the circular ring there is formation of eddy flow and because of which fluid mixing takes place and also there is jet impingement as fluid strikes the insert geometry at 90o. Because of these dominant disturbances in the fluid flow, high turbulence is obtained and heat transfer enhances. It is also found that as the PI and PR increases to higher value there is significant decrease in the heat transfer rate. For PR 1, 2 & 3; PI=0% shows the maximum heat transfer as compared to perforation index 8%, 16% & 24%. As perforation index increases heat transfer decreases. Minimum heat transfer is seen in case of PR=3 & PI=24% for the DR=0.8. It is also noticed that as the Reynolds number increases heat transfer also increases DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 39

M. Tech Thesis; June, 2015 and the maximum value of Reynolds number, heat transfer is maximum for all the insert parameters.

3.9 PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

8000

12000

16000

20000

DR=0.8

3.6

Nu/Nus

3.3

3.0

2.7

2.4

2.1 24000

Re

Fig. 4.9 Nusselt number variation with respect to smooth tube (Nu/Nus) for DR=0.8 Fig. 4.9 shows the enhancement in heat transfer (Nu/Nus) for DR=0.8, on experimentation, it is absorbed that, for the lower value of Reynolds number i.e. at Re=6,500, Nu/Nus is maximum and as Reynolds number increases the value of Nu/Nus decreases. For PR=1 and PI= 0% , the improvement in the amount of heat transfer is maximum and around 3.57 times improvement in Nusselt number is observed in comparison of smooth tube heat exchanger. As the PI & PR increases to its higher value it shows significant decrease in amount of heat transfer and hence Nu/Nus also decreases. Minimum Nu/Nus is observed for the insert parameter PR=3 & PI=24% at the higher value of flow parameters. Here it is also observed that as the value of diameter ratio increases, the rate of heat transfer decreases. This variation is because of decrease in space for the development of eddy flow and fluid stream detachment and reattachment. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 40

M. Tech Thesis; June, 2015 4.3 Friction factor Friction factor (f) plays a dominant role in the efficient working of heat exchangers. For the higher values of friction factor the thermal performance decreases, so it is very necessary to control friction factor in order to improve thermal performance. The friction factor is directly dependent upon the pressure drop across the test section and inversely proportional to the square of fluid velocity. So for the value of higher Reynolds number the friction factor is minimum, but as the Reynolds number decreases the value of friction factor increases as velocity is lower in case of lower Reynolds number. The variation in static pressure is shown in Fig. 4.10. and velocity variation is represented by Fig. 4.11.

Fig. 4.10 Variations in static pressure (Pascal) throughout the test section.

Fig. 4.11 Velocity magnitude (m/s). Due to use of different insert geometry in the heat exchanger for heat transfer improvement, pressure drop also increases because of the disturbance in the fluid flow, which causes an increase in the friction factor and this increment causes loss in the thermal performance of heat exchanger tube to a large extent. Because of this, the main aim should be to improve heat DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 41

M. Tech Thesis; June, 2015 transfer and to control friction factor. For this purpose several geometrical parameters have been tested with respect to a range of flow parameter and different results were absorbed and on the basis of result, graphs are plotted for predicting the performance. The followed graphs predicts the effect of different parameters on the friction factor.

4.3.1 Effect of friction factor for diameter ratio 0.6 It can be easily observed from Fig. 4.12 that, for diameter ratio 0.6 friction factor is maximized for all the insert geometry as compared to higher diameter ratios. In case of diameter ratio 0.6 flow blockage is maximum in the fluid path and because of that friction factor attains maximum value. For the PR=1 and PI=0%, maximum friction factor was observed, of the order 1.85. It is also observed that for lower Reynolds number the friction factor is maximized and as the Reynolds number increases, the value of friction factor decreases as the velocity increases. It is also observed that for 0% perforation index the friction factor is maximum for all the cases. With increase in perforation index, there is decrease in the value of friction factor as the obstruction in fluid flow decreases. 2.4 PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

DR=0.6

f

1.8

1.2

0.6

8000

12000

16000

20000

24000

Re

Fig. 4.12 Friction factor (f) vs Reynolds number (Re) for DR=0.6 DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 42

M. Tech Thesis; June, 2015 Minimum friction factor is observed in case of PI=24% for all the geometrical and flow parameters. Pitch ratio (PR) also played significant role in friction factor value. As the value of PR increases the amount of friction factor decreases and vice-versa for the lower value of PR, i.e. 1, friction factor was found to be maximum for all the geometrical and flow parameters. The minimum value of friction factor observed was around 0.5 for the diameter ratio=0.6 and 24% perforation index.

The trend changes when the friction factor of roughned tube is compared to smooth tube heat exchanger. The friction factor is maximum for higher Reynolds number and minimum for minimum Reynolds number. The trend is same for the geometrical parameters, as it can be observed in Fig. 4.13, maximum friction factor as compared to smooth tube is observed in case of 0% perforation index and PR=1, i.e. around 70 times higher as compared to smooth tube heat exchangers. As the perforation index increases friction factor with respect to smooth tube heat exchangers decreases significantly.

80

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

12000

16000

20000

DR=0.6

f/fs

60

40

20

8000

24000

Re

Fig. 4.13 Friction factor variation with respect to smooth tube (f/fs) for DR=0.6 DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 43

M. Tech Thesis; June, 2015 Further, as the value of pitch ratio increases the effect of friction factor decreases due to decrease in the flow blockage. Minimum f/fs is observed for the PR=3 and PI=24%, i.e. about 14 times as compared to smooth tube for the lower range of Reynolds number i.e. 6,500. Hence the friction factor caused a major obstruction in the thermal performance of heat exchangers. Therefore, it is necessary to overcome the friction factor for getting maximum performance. So work has been focused on using such insert geometries, which provides less resistance in fluid flow.

4.3.2 Effect on friction factor for diameter ratio 0.7

1.35 1.20

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

8000

12000

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

DR=0.7

1.05

f

0.90 0.75 0.60 0.45 0.30

16000

20000

24000

Re

Fig. 4.14 Friction factor (f) vs Reynolds number (Re) for DR=0.7

According to Fig. 4.14 similar variation is observed as it was observed for DR=0.6. It can be said that maximum friction factor was recorded at a minimum value of flow parameter and for PI=0% and PR=1. Friction factor recordes in this case was of order 1.18. As the value of perforation index and pitch ratio increases to higher range there is a significant decrease in the value of DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 44

M. Tech Thesis; June, 2015 friction factor. As compared to the DR=0.6, in this case friction factor is minimum for all the corresponding value of geometrical parameter. While the lowest friction factor is obtained for the PI=24% and PR=3, was of order 0.275 for the higher range of flow parameter.

But when compared to smooth tube heat exchanger, it can be observed from Fig 4.15, maximum friction factor as compared to smooth tube in case of 0% perforation index and PR=1, i.e. around 43 times higher as compared to smooth tube heat exchangers. As the perforation index increases friction factor with respect to smooth tube heat exchanger decreases significantly. A similar effect is observed for the geometrical parameter of pitch ratio also. As the value of pitch ratio increases the amount of friction factor as compared to smooth tube also decreases. Minimum f/fs is observed for the PR=3 and PI=24%, i.e. about 8 times as compared to smooth tube for the lower range of Reynolds number i.e. 6,500.

50

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

DR=0.7

45 40 35

f/fs

30 25 20 15 10 5 8000

12000

16000

20000

24000

Re

Fig. 4.15 Friction factor variation with respect to smooth tube (f/fs) for DR=0.7 DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 45

M. Tech Thesis; June, 2015 This significant decrease in friction factor as compared to DR=0.6 showed chance of improvement in the thermal performance of heat exchanger. Hence, in order to improve the thermal performance, different insert geometry of DR= 0.8 is used for experimentation which is discussed further.

4.3.3 Effect on friction factor for diameter ratio 0.8 0.7

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

DR=0.8

0.6

0.5

f

0.4

0.3

0.2

0.1 8000

12000

16000

20000

24000

Re

Fig. 4.16 Friction factor (f) Vs Reynolds number (Re) for DR=0.8

From Fig 4.16 it is observed that maximum friction factor was seen at a minimum value of the Reynolds number and for PI=0% and PR=1 i.e. around 0.57. As the value of perforation index and pitch ratio increases to higher range there is a significant decrease in the value of friction factor. As compared to the DR=0.6 and DR=0.7, in this case friction factor is minimum for all the corresponding value of geometrical and flow parameter. While the lowest friction factor is obtained for the PI=24% and PR=3 of the order 0.125.


Page 46

M. Tech Thesis; June, 2015 But when compared to smooth tube, as it can be observed in Fig 4.17, maximum friction factor as compared to smooth tube is observed in case of 0% perforation index and PR=1, i.e. around 20 times higher as compared to smooth tube heat exchangers. As the perforation index increases friction factor with respect to smooth tube heat exchanegers decreases significantly. A similar effect is observed for the geometrical parameter of pitch ratio also. As the value of pitch ratio increases the amount of friction factor as compared to smooth tube also decreases. Minimum f/fs is observed for the PR=3 and PI=24%, i.e. about 5.5 times as compared to smooth tube for the lower range of Reynolds number i.e. 6,500. From above discussion, it can be said that, in order to reduce the effect of friction there should be minimum flow blockage. As in case of PI=24%, PR=3 and DR=0.8, flow blockage is minimum whch results in significant decrease in the order of friction factor.

24

21

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

8000

12000

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 DR=0.8 PI=24%, PR=2 PI=24%, PR=3

18

f/fs

15

12

9

6

3 16000

20000

24000

Re

Fig. 4.17 Friction factor variation with respect to smooth tube (f/fs) for DR=0.8


Page 47

M. Tech Thesis; June, 2015 4.4 Thermal performance factor

Thermal performance factor is a very important aspect for the utilization of heat exchanger. As there is tremendous increase found in the value heat transfer and friction factor for different insert geometries, it is very important to use only such geometry in which thermal performance factor is maximum or more than unity. Here the main emphasis has been given on the effect of different insert geometry on the thermal performance factor.

4.4.1 Effect on thermal performance factor for diameter ratio 0.6

PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

DR=0.6

1.2



1.1

1.0

0.9 8000

12000

16000

20000

24000

Re

Fig. 4.18 Thermal performance factor (η) vs Reynolds number (Re) for DR=0.6

According to Fig 4.18 it is observed that maximum thermal performance factor was seen at a minimum value of the Reynolds number and for PI=24% and PR=1 i.e. around 1.17. While the lowest thermal performance factor is obtained for the PI=0% and PR=3 i.e. 0.95 as compared to smooth tube. It is observed that as the PI increases thermal performance also increases, as there DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 48

M. Tech Thesis; June, 2015 is a decrease in friction factor. But when PR increases thermal performance decreases because heat transfer is maximum in case of lower PR.

4.4.2 Effect on thermal performance factor for diameter ratio 0.7 1.3 PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

DR=0.7

1.2



1.1

1.0

0.9 7000

14000

21000

Re

Fig. 4.19 Thermal performance factor (η) vs Reynolds number (Re) for DR=0.7

As shown in graph (Fig. 4.19) plot obtained for DR=0.7 on the basis of experimentation that, the maximum thermal performance factor is at a minimum value of the Reynolds number and for PI=24% and PR=1 i.e. 1.32 times as compared to smooth tube heat exchanger. While the lowest thermal performance factor is obtained for the PI=0% and PR=3 is 1.07as compared to smooth tube. Increase in the value of PI increases thermal performance factor, as there is a significant decrease in friction factor. But when PR increases thermal performance decreases because heat transfer is maximum in case of lower PR. The same trend is seen for the diameter ratio (DR) also, as the thermal performance factor in case of DR=0.7 is more for all the flow and geometrical parameters as compared to DR=0.6. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 49

M. Tech Thesis; June, 2015 4.4.3 Effect on thermal performance factor for diameter ratio 0.8 1.55 PI=0%, PR=1 PI=0%, PR=2 PI=0%, PR=3

1.50

PI=8%, PR=1 PI=8%, PR=2 PI=8%, PR=3

PI=16%, PR=1 PI=16%, PR=2 PI=16%, PR=3

PI=24%, PR=1 PI=24%, PR=2 PI=24%, PR=3

DR=0.8

1.45 1.40



1.35 1.30 1.25 1.20 1.15 4000

8000

12000

16000

20000

24000

Re

Fig. 4.20 Thermal performance factor (η) Vs Reynolds number (Re) for DR=0.8 From Fig 4.20, it can be said that maximum thermal performance factor was seen for PI=24% and PR=1, for lower range of flow parameters. Around 1.47 times improvement was observed as compared to smooth tube heat exchanger. While the lowest thermal performance factor in this case was observed for the PI=0% and PR=3 i.e. 1.20 times as compared to smooth tube heat exchanger, for the higher value of Reynolds number. It is observed that as the PI increases thermal performance also increases, since there is a decrease in friction factor. But when PR increases thermal performance decreases because heat transfer is maximum in case of lower PR. The same trend is seen for the DR also, as thermal performance in case of DR=0.8 is more for all the flow and geometrical parameters as compared to DR=0.7 & 0.6.


Page 50

M. Tech Thesis; June, 2015 4.5 Summary

In this chapter it was observed that the change in geometrical and flow parameter results in the variation of Nusselt number, Friction factor and Thermal performance factor of smooth tube heat exchanger. It was also observed that this method of heat transfer enhancement gives best result at lower values of flow parameters. Still, it is required to focus on the modification of insert geometry, so that it could be equally applicable for the higher range of Reynolds number. The emphasis should always be given on lowering the friction factor value and enhancing the heat transfer.


Page 51

M. Tech Thesis; June, 2015 CHAPTER – 5 CORRELATION FOR NUSSELT NUMBER, FRICTION FACTOR & THERMAL PERFORMANCE FACTOR 5.1 Introduction According to the experimental results obtained for Nusselt number, Friction factor and thermal performance factor with respect to different flow and geometrical parameters of circular perforated disk inserts as discussed in the previous chapter, statistical correlations has been formulated. These correlations are entirely based on the experimental results obtained. As a theoretical solution for fluid flow and heat transfer characteristics of such complex roughness is strenuous and thus the designers have to rely on empirical correlations developed through experiments. Many investigators viz. (Hans et al.[29] [2010], Singh et al.[31] [2011], Sethi et al.[30] [2012], Yadav et al.[32] [2012] etc.) used statistical methods to developed correlations for Nusselt number and friction factor and found that these statistical correlations are capable of predicting the performance of the roughened heat exchanger as the difference in the predicted and experimental values are within acceptable limits. The success of this approach suggests that statistical methods are an effective way to correlate data for rough surfaces. Keeping this in view, experimental data obtained and presented in chapter 4 have been correlated using statistical methods. Sigma plot-12 software has been used as a statistical tool for regression analysis and to develop the correlations for Nusselt number, friction factor and thermal performance factor of the heat exchanger tube with circular perforated disk insert. 5.2 Range of Parameters for Correlation As discussed in chapter 2, “Perforated circular disk” is used as insert geometry with different range of parameters. The parameters used is shown in table 5.1 Table 5.1 parameters used for establishing correlations S. No

Name of Parameter

Specification

Values

1.

Pitch ratio (PR)

l/D ratio

1,2,3

2.

Diameter Ratio (DR)

d/D ratio

0.6, 0.7, 0.8

3.

Perforation Index (PI)

Ta/Pa ratio

8%, 16%, 24%

5.

Reynolds Number

Flow parameter

6500 to 23,000


Page 52

M. Tech Thesis; June, 2015 5.3 Correlations for Nusselt number, friction factor and thermal performance factor It is observed from experimental data that Nusselt number, friction factor and thermal performance factor are strong functions of geometrical and flow parameter. It can be said that Nusselt number, friction factor and thermal performance factor is the function of these parameters and can be written as:  Nu= Nu(Re, DR, PR, PI)  f= f(Re, DR, PR, PI)  η= η(Re, DR, PR, PI)

5.3.1 Nusselt number correlation Nusselt number correlation is formulated with help of experimental value of Nusselt number with respect to different flow and geometrical parameters. Fig. 5.1 shows graph between ln (Nu) Vs ln (Re), and according to the statistical graph and regression coefficient of 1st order quadratic equation the value of Nusselt number is given by equation: 0.7477 Nu= Ao Re

(5.1)

5.6 5.4

Nu= Ao Re

0.7477

5.2

ln Nu

5.0 4.8 4.6 4.4 4.2 4.0 3.8 8.6

8.8

9.0

9.2

9.4

9.6

9.8

10.0

10.2

ln Re

Fig. 5.1 Plot for ln (Nu) Vs ln (Re) DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 53


-2.0

Nu= Bo Re

0.7477

DR

-0.5770

-2.1

-2.2

ln Ao

-2.3

-2.4

-2.5

-2.6

-2.7 -0.5

-0.4

-0.3

-0.2

ln DR Fig. 5.2 Plot for ln (Ao) Vs ln (DR) In the next step for obtaining correlation, graph is plotted between ln (Ao) and geometrical parameter ln (DR) as shown in Fig. 5.2. In this case the value of ln(Ao) is calculated using equation (5.1), and according to equation (5.1) the value of Ao is given by equation: 0.7477 Ao =Nu / Re

(5.2)

And taking log both sides the value of ln Ao is obtained. Similarly the value of ln (DR) is obtained by taking log of all the experimental result of Nusselt number with respect to different diameter ratios. Correlation obtained for ln Ao Vs ln DR is given by equation: 0.7477 -0.5770 Nu= Bo Re DR

(5.3)

In which Bo is regression constant and its value is calculated by regression coefficient with respect to this constant.


Page 54


-2.3

Nu= Co Re

0.7477

DR

-0.5770

PR

-0.1724

-2.4

ln Bo

-2.5

-2.6

-2.7

-2.8 0.0

0.2

0.4

0.6

0.8

1.0

1.2

ln PR Fig. 5.3 Plot for ln (Bo) Vs ln (PR) Further for obtaining correlation, the graph is plotted between regression coefficient ln (Bo) and geometrical parameter ln (PR) as shown in Fig. 5.3. In this case the value of ln (Bo) is calculated using equation (5.3), and according to equation (5.3) the value of Bo is given by the equation:

0.7477 -0.5770 Bo= Nu / Re DR

(5.4)

And taking log both sides the value of ln Bo is obtained. Similarly value of ln (PR) is obtained by taking log of all the experimental results of Nusselt number with respect to different pitch ratios. Correlation obtained for ln Bo Vs ln PR is given by equation: 0.7477 -0.5770 -0.1724 Nu= Co Re DR PR

(5.5)

In which Co is regression constant and its value is calculated by regression coefficient with respect to this constant.


Page 55


-2.2

Nu=0.1467 Re

0.7477

DR

-0.5770

PR

-0.1724

PI

-0.1915

-2.3

ln Co

-2.4

-2.5

-2.6

-2.7 2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

ln PI Fig. 5.4 Plot for ln(Co) Vs ln(PI) Further, graph is plotted between regression coefficient ln (Co) and geometrical parameter ln (PI) as shown in Fig. 5.4. Here in this case the value of ln (Co) is calculated using equation (5.5), and according to equation (5.5) the value of Co is given by equation: 0.7477 -0.5770 -0.1724 Co= Nu / Re DR PR

(5.6)

And taking log both sides the value of ln Co is obtained. Similarly value of ln (PR) is obtained by taking log of all the experimental result of Nusselt number with respect to different pitch ratios. Correlation obtained for ln Co Vs ln PI is given by equation: 0.7477 -0.5770 -0.1724 -0.1915 Nu=Do Re DR PR PI

(5.7)

This is the final correlation obtained for the Nusselt number with respect to its different geometrical and flow parameters.


Page 56


240 220 200 + 5%

Nu experimental

180 160 140

- 5%

120 100 80 60 40 50

100

150

200

Nu predicted Fig. 5.5 Plot for deviation in error between experimental and predicted value of Nu

On the basis of correlation obtained for the Nusselt number with respect to different geometrical parameters of circular perforated disk insert, a different plot as shown in Fig. 5.5, has been developed for showing the percentage error of experimental value with respect to the predicted value of Nusselt number. According to this plot there is around +5 and -5% of error found for the experimental value with respect to the predicted value. This small amount of error is acceptable as there is some losses taking place during the experimentation. So the final equation for the Nusselt number correlation is given by :

0.7477 -0.5770 -0.1724 -0.1915 Nu=0.1467 Re DR PR PI


(5.8)

Page 57

M. Tech Thesis; June, 2015 5.3.2 Friction factor correlation

Friction factor correlation is formulated with the help of experimental value of friction factor with respect to all the flow and geometrical parameters used in the experimentation. Fig. 5.6 shows graph between ln (f) Vs ln (Re), and according to the statistical graph and regression coefficient of 1st order quadratic equation the value of friction factor is given by equation: -0.0916 f = A1 Re

(5.9)

Where A1 is regression coefficient and is used as a constant in equation (5.7). Further for calculation of the regression coefficient another graph is plotted using A1 as constant.

f = A1 Re

-0.0916

ln f

0

-1

-2

8.6

8.8

9.0

9.2

9.4

9.6

9.8

10.0

10.2

ln Re

Fig. 5.6 Plot for ln (f) Vs ln (Re)


Page 58


1.5

f = B1 Re

-0.0916

DR

-4.3858

1.0

ln A1

0.5

0.0

-0.5

-1.0

-1.5 -0.5

-0.4

-0.3

-0.2

ln DR Fig. 5.7 Plot for ln(A1) Vs ln(DR) In the second step for obtaining correlation, graph is plotted between ln (A1) and geometrical parameter ln (DR) as shown in Fig. 5.7. Here in this case the value of ln (A1) is calculated using equation (5.9), and according to equation (5.9) the value of A1 is given by equation: -0.0916 f = A1 Re

(5.10)

And taking log both sides the value of ln A1 is obtained. Similarly value of ln(DR) is obtained by taking loh of all the experimental result of Nusselt number with respect to different diameter ratios. Correlation obtained for lnA1 Vs ln DR is given by equation: -0.0916 -4.3858 f = B1 Re DR

(5.11)

In which B1 is regression constant and its value is calculated by regression coefficient with respect to this constant.


Page 59


-0.8

f = C1 Re

-0.0916

DR

-4.3858

PR

-0.4153

-1.0

-1.2

ln B1

-1.4

-1.6

-1.8

-2.0

-2.2 0.0

0.2

0.4

0.6

0.8

1.0

1.2

ln PR Fig. 5.8 Plot for ln (B1) Vs ln (PR) Further for obtaining correlation, graph is plotted between regression coefficient ln (B1) and geometrical parameter ln (PR) as shown in Fig. 5.8. Here in this case the value of ln(B1) is calculated using equation (5.11), and according to equation (5.33) the value of B1 is given by equation: -0.0916 -4.3858 B1 =f / Re DR

(5.12)

And taking log both sides the value of ln B1 is obtained. Similarly the values of ln (PR) is obtained by taking log of all the experimental results of Friction factor with respect to different pitch ratios. Correlation obtained for ln B1 Vs ln PR is given by equation: -0.0916 -4.3858 -0.4153 f = C1 Re DR PR

(5.13)

In which C1 is regression constant and its value is calculated by regression coefficient with respect to this constant. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 60


-0.6

f = 1.8784 Re

-0.0916

DR

-4.3858

PR

-0.4153

PI

-0.7291

-0.8

ln C1

-1.0

-1.2

-1.4

-1.6

-1.8

-2.0 2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

ln PI Fig. 5.9 Plot for ln (C1) Vs ln (PI) Further for obtaining correlation, graph is plotted between regression coefficient ln (C1) and geometrical parameter ln (PI) as shown in Fig. 5.9. Here in this case the value of ln (C1) is calculated using equation (5.13), and according to equation (5.13) the value of C1 is given by equation: -0.0916 -4.3858 -0.4153 C1 = f / Re DR PR

(5.14)

And taking log both sides the value of ln C1 is obtained. Similarly values of ln (PR) is obtained by taking log of all the experimental results of friction factor with respect to different pitch ratios. Correlation obtained for lnC1 Vs ln PI is given by equation: -0.0916 -4.3858 -0.4153 -0.7291 f = D1 Re DR PR PI

(5.15)

This is the final correlation obtained for the friction factor with respect to its different geometrical and flow parameters. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 61


2.0

f experimental

1.5

+ 9%

1.0

-9%

0.5

0.0

0.5

1.0

1.5

2.0

f predicted Fig. 5.10 Plot for deviation in error between experimental and predicted value of f

On the basis of correlation obtained for the friction factor with respect to all the geometrical and flow parameters of circular perforated disk insert, a graph is plotted as shown in Fig. 5.10, which shows the percentage error of experimental value with respect to the predicted value of friction factor. According to this plot there is around +9 and -9% of error found in the experimental value with respect to the predicted value. This small amount of error is acceptable as there is some frictional losses taking place during the experimental investigation. So the final equation for the friction factor correlation is given by :

-0.0916 -4.3858 -0.4153 -0.7291 f = 1.8784 Re DR PR PI


(5.16)

Page 62

M. Tech Thesis; June, 2015 5.3.3 Thermal performance factor correlation

Thermal performance factor correlation is formulated with the help of experimental value of friction factor and Nusselt number with respect to different flow and geometrical parameters. Fig. 5.6 shows graph between ln (η) Vs ln (Re), and according to the statistical graph and regression coefficient of 1st order quadratic equation the value of friction factor is given by equation: = A2 Re

-0.1027

(5.17)

Where A2 is regression coefficient and is used as a constant in equation (5.17). Further for calculation of the regression coefficient another graph is plotted using A2 as constant.

0.5

-0.1027 = A2 Re 0.4

ln 

0.3

0.2

0.1

0.0

-0.1 8.6

8.8

9.0

9.2

9.4

9.6

9.8

10.0

10.2

ln Re Fig. 5.11 Plot for ln (η) Vs ln (Re) DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 63


1.35

= B2 Re

1.30

-0.1027

DR

0.8849

1.25

ln A2

1.20 1.15 1.10 1.05 1.00 0.95 -0.5

-0.4

-0.3

-0.2

ln DR Fig. 5.12 Plot for ln (A2) Vs ln (DR) Then, for obtaining correlation, graph is plotted between ln (A2) and geometrical parameter ln (DR) as shown in Fig. 5.12. Here in this case the value of ln (A2) is calculated using equation (5.17), and according to equation (5.17) the value of A2 is given by equation: A2=Re

-0.1027

(5.18)

And taking log both sides the value of ln A2 is obtained. Similarly value of ln (DR) is obtained by taking log of all the experimental result of Nusselt number with respect to different diameter ratios. Correlation obtained for lnA2 Vs ln DR is given by equation: -0.1027 0.8849 = B2 Re DR

(5.19)

In which B2 is regression constant and its value is calculated by regression coefficient with respect to this constant. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 64


1.60

= C2 Re

1.58

-0.1027

DR

0.8849

PR

-0.0350

1.56 1.54

ln B2

1.52 1.50 1.48 1.46 1.44 1.42 1.40 1.38 0.0

0.2

0.4

0.6

0.8

1.0

1.2

ln PR Fig. 5.13 Plot for ln(B2) Vs ln(PR) Further for obtaining correlation, graph is plotted between regression coefficient ln (B2) and geometrical parameter ln (PR) as shown in Fig. 5.13. Here in this case the value of ln (B2) is calculated using equation (5.19), and according to equation (5.19) the value of B2 is given by equation: -0.1027 0.8849 B2 = Re DR

(5.20)

And taking log both sides the value of ln B2 is obtained. Similarly value of ln (PR) is obtained by taking log of all the experimental results of Friction factor with respect to different pitch ratios. Correlation obtained for ln B2 Vs ln PR is given by equation: -0.1027 0.8849 -0.0350 = C2 Re DR PR

(5.21)

In which C2 is regression constant and its value is calculated by regression coefficient with respect to this constant. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 65


1.60

= 3.9318 Re

1.58

-0.1027

DR

0.8849

PR

-0.0350

PI

-0.0347

1.56 1.54

ln C2

1.52 1.50 1.48 1.46 1.44 1.42 1.40 2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

ln PI Fig. 5.14 Plot for ln (C2) Vs ln (PI) Further for obtaining correlation, the graph is plotted between regression coefficient ln (C2) and geometrical parameter ln (PI) as shown in Fig. 5.14. Here in this case the value of ln (C2) is calculated using equation (5.21), and according to equation (5.21) the value of C2 is given by equation: -0.1027 0.8849 -0.0350 C2 = Re DR PR

(5.22)

And taking log both sides the value of ln C2 is obtained. Similarly value of ln (PR) is obtained by taking log of all the experimental result of friction factor with respect to different pitch ratios. Correlation obtained for lnC2 Vs ln PI is given by equation: -0.1027 0.8849 -0.0350 -0.0347 = D2 Re DR PR PI

(5.23)

This is the final correlation obtained for the friction factor with respect to its different geometrical and flow parameters.


Page 66


1.6

 experimental

1.4

+8%

1.2 -8%

1.0

0.8 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

predicted Fig. 5.15 Plot for deviation in error between experimental and predicted value of η

On the basis of correlation obtained for the thermal performance factor with respect to different geometrical parameters of perforated circular disk insert, a different plot as shown in Fig. 5.15, has been developed for showing the percentage error of experimental value with respect to the predicted value of thermal performance factor. According to this plot there is around +8 and -8% of error found for the experimental value with respect to the predicted value. This small amount of error is acceptable as there is several losses taking place during the experimental investigation. So the final equation for the friction factor correlation is given by : -0.1027 0.8849 -0.0350 -0.0347 = 3.9318 Re DR PR PI

(5.24)

So, in this way correlations have been developed for the Nusselt number, Friction factor and Thermal performance factor with respect to all the flow and geometrical parameters used in the experiment. The numeric value of all the coefficient used in the correlation of Nusselt number, Friction factor and Thermal performance factor is mentioned in table 5.2. DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 67

M. Tech Thesis; June, 2015 Table 5.2 Value of coefficient used in correlations S. No.

Correlation

Value of Coefficient

1.

Nu

Ao=0.0958, Bo=0.0773, Co=0.08536, Do=0.1467

2.

f

A1=0.7397, B1=0.1735, C1=0.2776, D1=1.8784

3.

η

A2=3.0611, B2=4.1375, C2=4.4026, D2=3.9318

5.4 Summary In this chapter the emphasis has been given to the formulation of correlation and also to find the percentage error between experimental and predicted value using the correlations obtained with the help of regression analysis using SigmaPlot 10.0. Correlation obtained for Nusselt number, Friction factor and Thermal performance factor are given by equation 5.8, 5.16 and 5.24 respectively.


Page 68

M. Tech Thesis; June, 2015 CHAPTER – 6 CONCLUSION On the basis of experimental investigation of heat transfer and fluid flow characteristics of heat exchanger tube with circular perforated disk insert, a significant enhancement is obtained for the heat transfer and thermal performance factor. The experimentation has been carried out for a given range of flow parameter, i.e. for Reynolds number 6,500 to 23,000. Different values of geometrical parameters like pitch ratios, diameter ratios and perforation index has also been used in the experiment. According to the experimental result obtained from the experimentation, following conclusions can be made:  According to the validation test of the experimental setup, error in the value of Nusselt number and Friction factor were ±5% and ±9% respectively. This shows that the error was in the permissible range for conduction experimentation.  For heat transfer, as the value of the Reynolds number increases heat transfer rate also increases and vice-versa. At the maximum value of the Reynolds number, the amount of heat transfer was maximum. When compared to the smooth tube, maximum enhancement in heat transfer was obtained for the lower value of Reynolds number i.e. 6,500 and the geometrical parameter for which maximum heat transfer was obtained was DR=0.6, PR=1 and PI=0%. Enhancement in heat transfer for this case was around 4.5 times as compared to smooth tube heat exchanger.  As DR increases, heat transfer decreases because of only upper layers of fluid which comes in direct contact to heat exchanger tube plays major role in heat transfer. Heat transfer is maximum for the lower value of DR i.e. 0.6. A Similar situation is with PR also. As PR increases, heat transfer decreases and at PR=1 heat transfer is maximum.  For PI in case of 0% perforation, heat transfer is maximum and for the higher value of the perforation index heat transfer decreases significantly.  For Friction factor, similar kind of result is obtained, as the Reynolds number increases the value friction factor decreases and vice-versa. For the higher value of flow parameter friction factor is minimum. As compared to the smooth tube heat exchanger minimum value of friction factor was obtained in the lower range of flow parameter and it was around 4.5 times


Page 69

M. Tech Thesis; June, 2015 higher. This minimum value of friction factor was obtained for the value of geometrical parameter, i.e. DR=0.8, PR=3, PI=24%.  As DR increases, friction factor decreases because of less disturbance in fluid flow takes place. Friction factor is maximum for the lower value of DR i.e. 0.6. A similar situation is with PR also. As PR increases, friction factor decreases and for PR=1 friction factor is maximum.  For PI in case of 0% perforation, friction factor is maximum and for the higher value of perforation index friction factor decreases significantly.  Thermal performance factor was found maximum for the given value of geometrical parameter, i.e. PI=24%, PR=1 and DR=0.8. It was also observed that in the lower range of flow parameter, i.e. for Reynolds number 6,500, Thermal performance factor was maximum and as the value of Reynolds number increases, Thermal performance decreases respectively. Maximum Thermal performance factor obtained was 1.47 times higher as compared to smooth tube heat exchangers.  According to correlation obtained for Nusselt number, friction factor and thermal performance factor with respect to different flow parameters and geometrical parameters, the deviation in the experimental value and predicted value were in permissible range. Deviation in Nusselt number is ±7%, Friction factor is ±12% and Thermal performance factor is ±8% respectively. The correlation of Nusselt number, Friction factor and Thermal performance factor is given by the equations: 

0.7477 -0.5770 -0.1724 -0.1915 Nu=0.1467 Re DR PR PI



-0.0916 -4.3858 -0.4153 -0.7291 f = 1.8784 Re DR PR PI



-0.1027 0.8849 -0.0350 -0.0347 = 3.9318 Re DR PR PI


Page 70

M. Tech Thesis; June, 2015 APPENDIX 1 UNCERTAINTY ANALYSIS As we know that there are several assumptions needed in an experimental investigation. In this study also some of the important assumptions are taken like: 

Heat exchanger is perfectly insulated and there is no heat losses.



Temperature distribution is perfectly uniform.

But in actual cases there are some losses and theses losses cannot be fully controlled. So in order to minimize or calculate our losses we do uncertainty analysis. The losses or error may be because of following reasons: 

Uncertainty in measuring devices.



Uncertainty in heat flux.



Uncertainty in flow measurement.



Uncertainty in insulation.

Hence in order to minimize our error and validate our experiments we calculate maximum possible error for each measurement and compare it with true value. In this work the methodology suggested by Kline and McClintock

[33]

[1953] for estimating uncertainty in

experimental results has been used. Values for different parameters for one set of experimental reading is listed in table A1.1. Table A1.1 Value of different parameter for one set of readings. S. No. Specification

Symbol

Value

1.

Length of test section

L

1400mm

2.

Hydraulic Diameter

D

68mm

3.

Orifice Diameter

Do

35mm

4.

Open area ratio for orifice plate

β

.51

5.

Pressure drop across orifice

ΔPo

140mm

6.

Pressure drop across test section

ΔP

1.94mm


Page 71

M. Tech Thesis; June, 2015 7.

Atmospheric pressure

Patm

101.325 KN/m2

8.

Fluid inlet temperature

Ti

14.32 oC

9.

Fluid exit temperature

To

23.71 oC

10

Bulk mean temperature

Tb

19.02 oC

11

Wall mean temperature

Twm

56.31 oC

Some important relations used in calculations are listed below: Reynolds number Re 

VD 

Heat transfer coefficient h 

m C P To  Ti  AP Twm  T fm 

(A1-2)

hD K

(A1-3)

2.P .D 4. .L.V 2

(A1-4)

Nusselt number Nu 

Friction factor f 

(A1-1)

1. Uncertainty in surface area of test section.

A p  DL 2 2  A p   A p   A p    D     L    L  D    



A p  L  D 2  D  L 2  D  2  L  2        A p  D   L  

A p

0.5



0.5

0.5

0.5

 0.1  2  0.1  2        A p  68   1400   A p 0.5  2.16  10 6   5.102  10 9  Ap

A p



A p Ap



 0.001472


Page 72

M. Tech Thesis; June, 2015 Hence, uncertainty in surface area is 0.147 % 2. uncertainty in area of orifice plate

A0 



d0

2

4 A0 2d 0 2 d 0   d 0 4 2 2  A   0 A0    d 0    d 0  

0.5

1

A0

A0 A0

A0 A0

2 2  d    d    0  d 0     0  d 0     2   2   d 0     2   d 0        d 0 2   4    2  d 0   2  0.1     0.00571  d 0   35 

Hence, uncertainty in the area of orifice plate is 0.571%

3. Uncertainty in the measurement of hydraulic diameter





D 2 4A 4  4  4   D D   4 P D  2

2  2      D   D  D  

D

0.5

2  2      0.1  D    68  

D

   D 1 

0.5

 0.000936

Hence, uncertainty in measurement of hydraulic diameter is 0.09% DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 73


4. Density

0 

Patm RT0

 0 1  Patm RT0  0 P   atm2 T RT 2 2      0   0  0     atm     T0    Patm   T0  

0.5

2 2     Patm  0 RT0  0  1  0 RT0      atm       T0   2  0  RT0 Patm P RT atm   0   

 0  Patm    0  Patm 

2

  T0       T0

  

2

  

0.5

0.5

let Patm  760mmofHg 2 2  0  0.1   0.1          0  760   23.71  

0.5



 0  1.731 10 8   1.778  10 5  0



0.5

 0.004219

Hence, uncertainty in density measurement is 0.42%


Page 74

M. Tech Thesis; June, 2015 5. Mass flow rate  2  P   m  C d Ao  0 4 o   1   m  C d Ao  0

0.5

 P o

0.5

 2   4 1  

  

0.5

Let  2 X  Const.   4 1   Then,

  

0.5

0.5 0.5 m  XCd Ao  0  P o m 0.5 0.5  XAo  0  P o C d m 0.5 0.5  XCd  0  P o A0 m  0.5 0.5  XCd Ao  0.5  0  P o

 0 m  0.5  0.5  XCd Ao  0.5  0  P o  P o

2 2 2 2  m     m   m   m m    C d      0     A0      P o    C d    0   A0    P o  

 C   d m  C d Let

m

2

  0.5 0      0

  A0    P o         A0   P o 2

2

  

2

  

0.5

0.5

 C d     1.5% C  d  P o  140 0.5

2  1.5  2  0.1   2 2        0 . 0021095  0 . 00571      m  140    0.6  100  m  6.25  10  4  4.449  10 6  3.26  10 5  5.102  10 7 m m  0.0257 m

m



 

 

 



0.5

Hence, uncertainty in mass flow rate measurement is 2.57% DIT UNIVERSITY, DEHRADUN, UTTARAKHAND.

Page 75

M. Tech Thesis; June, 2015 6. Uncertainty in the measurement of air velocity in the tube.

V 

m A p 0.5

 m 2    2  A  2     o  p       V  m    o   A p     V 2 2 2 0.5  0.0257  0.004219  0.001472 V V 0.5  0.0006708  0.00001779  0.00000216 V V 0.5  0.0006907  0.0261 V

V





Hence, uncertainty in velocity measurement is 2.61%

7. Uncertainty in the measurement of heat gain.

Qu  m C p To  Ti   m C p T 2 2 Qu  m   C p    (T ) 2      Qu  m   C p   T 

Qu Qu

Qu Qu

Qu Qu

  

0.5

2 2   0.1   0.1   2  0.0257        1005   9.39   



 





0.5

 

 6.7081 10  4  9.9007  10 9  1.13  10  4  7.8380  10  4

0.5



0.5

 0.0277

Hence, uncertainty in the measurement of heat gain is 2.77%


Page 76

M. Tech Thesis; June, 2015 8. Heat transfer coefficient

h

Qu Qu  A p T pm  T fm  A p T fm 

 Q   u h  Qu 

h

  A p       Ap 2

   T fm        T  fm    2

2

   

0.5

2   0.1   2 2   0.0279   0.001472     h   19.02  

h h



 





0.5

 

 7.784  10  4  2.166  10 6  2.764  10 5

h h  8.082  10  4 h

0. 5



0.5

 0.0284

Hence, uncertainty in the measurement of heat transfer coefficient is 2.84%

9. Reynolds number

Re 

VD 

    2  V  2  D  2    2               Re      V   D     

 Re

0.5

0.5

2  0.001  2  0.1  2  0.1  10 7   2         0.000936   5  Re  1.225   8.13   1.983  10    Re  6.66  10 7  1.5129  10  4  8.76  10 7  2.543  10 7 Re 0.5  Re  1.5308  10  4  0.01237 Re

 Re



 





 

 



0.5

Hence, uncertainty in the measurement of Reynolds number is 1.23%


Page 77

M. Tech Thesis; June, 2015 10. Nusselt number

Nu 

hD k

 h  2  D  2  k  2           Nu  h   D   k  

Nu

0.5

0.5

2   0.00001  2 2  0.0284  0.000936     Nu   0.024   Nu  8.0656  10  4  8.76  10 7  1.736  10 7 Nu 0.5 Nu  8.07  10  4  0.02841 Nu

Nu



 



 



0.5



Hence, uncertainty in the measurement of Nusselt number is 2.83%

11. Friction factor

fr 

2 DP  p 4 LV 2

2 2  D 2    2   P  p  L  V       f r                 D      L   V   P  p 

   

2

   

0.5

0.5

2 2 2 2   0.001   0.1   0.1   0.01   2  0.000936           f r   1.225   1400   8.13   1.94   f r  8.76  10 7  6.6638  10 7  1.5129  10  4  2.65  10 5 fr

f r

f r fr



 





 1.7933  10  4

0.5

 

 



0.5

 0.01339

Hence, uncertainty in measurement of friction factor is 1.33%


Page 78


Summary Therefore on the basis of uncertainty analysis, it is found that maximum possible error is in the range of acceptable limits. So losses in the experimentation can be neglected in order to perform experiments. Table A1.2 shows the maximum possible error for each set of readings.

Table A1.2 Maximum possible uncertainty in measurement. S. No.

Specification

% age Uncertainty

1.

Area of test section

0.147

2.

Area of orifice plate

0.571

3.

Hydraulic diameter

0.09

4.

Flow Density

0.42

5.

Mass flow rate

2.57

6.

Velocity of air

2.61

7.

Heat gain

2.77

8.

Heat transfer coefficient

2.84

9.

Reynolds number

1.23

10

Nusselt number

2.83

11

Friction factor

1.33


Page 79

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