Overall optimization and performance analysis of an air conditioning system by adopting series –series couter flow to central water chillers

Under the conditions of high temperature differences and low water flow rates, cooling coil and cooling tower may be affected.. Tube diameter must be as low as 10.08 mm when number of tu

공학박사 학위논문

중앙집중 물냉각기에 직렬-직렬 대향류 방식을 채택한 공기조화시스템의 성능

해석과 최적화

Overall Optimization and Performance Analysis of

an Air Conditioning System by adopting Series-Series

Counter-flow to Central Water Chillers

울산대학교 대학원

기계공학과

Nguyen Minh Phu

Doctor of Philosophy

Overall Optimization and Performance Analysis of

an Air Conditioning System by adopting Series-Series

Counter-flow to Central Water Chillers

The Graduate School

of the University of Ulsan

Department of Mechanical Engineering

Nguyen Minh Phu

Overall Optimization and Performance Analysis of an Air Conditioning System by adopting Series-Series Counter-flow to

Central Water Chillers

Overall Optimization and Performance Analysis of

an Air Conditioning System by adopting Series-Series

Counter-flow to Central Water Chillers

Supervisor: Prof Geun Sik Lee

A Dissertation

Submitted to the Graduate School of the University of Ulsan

In partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

by

Nguyen Minh Phu

Department of Mechanical Engineering

University of Ulsan, Republic of Korea

May, 2012

Nguyen Minh Phu 의 공학박사 학위 논문을 인준함

Overall Optimization and Performance Analysis of

an Air Conditioning System by adopting Series-Series

Counter-flow to Central Water Chillers

This certifies that the dissertation

of Nguyen Minh Phu is approved

Committee Chairman Prof MOO HYUN KIM

Committee Member Prof GEUN SIK LEE

Committee Member Prof SUNG PIL WON

Committee Member Prof MOK IN LEE

Committee Member Prof MOO GEUN KIM

Department of Mechanical Engineering

University of Ulsan, Republic of Korea

May, 2012

ACKNOWLEDGEMENTS

I would like to express my heartfelt gratitude to my advisor, Prof Dr.-Ing Geun Sik Lee, who not only gives me priceless guidance in scientific work but also supports me the financial help for three and half years studying in the University of Ulsan

I would like to thank professors in the committee for their suggestions and comments throughout the research Sincerely thank to University of Ulsan that grants me the scholarship and opportunity for studying in Korea I also express my gratitude to professors and staff members of the Department of Mechanical Engineering for their kind help Special thank to Korea and Korean people for their civilization and friendship

I would like to thank my family members, who encourage and suffer a separation during the period I am away from home Specially thank to all members of the Entire Energy Harmony laboratory who support me a lot in my research work

I’d like to thank the Union of Vietnamese Students at University of Ulsan for spiritual help and consulting abroad living experience, and close friends in Vietnam who always look forward to my returning our motherland

Ulsan, Republic of Korea May, 2012

NGUYEN MINH PHU

-i-CONTENTS

Abstract iii

List of figures vi

List of tables ix

Nomenclature x

Abbreviations xii

Chapter 1 Introduction 1

1.1 Introduction 1

1.2 Problem statement, necessity, objectives and thesis layout 4

Chapter 2 Analysis and design of a water chiller using commercial enhanced tubes 8

2.1 Introduction 8

2.2 Model formulation 9

2.2.1 Heat transfer model 10

2.2.2 Water pressure drop model 14

2.3 Results and discussion 15

2.3.1 Condenser 16

2.3.2 Evaporator 22

2.4 Comparison to commercial software 24

2.5 Summary 29

Chapter 3 Effect of water temperature and water flow rate on wet cooling tower 30

3.1 Introduction 30

3.2 Merkel’s theory and the empirical correlations 31

3.3 Formulation of psychrometric properties of moist air 39

3.4 Solution procedure and validation 41

3.5 Results and discussion 45

3.6 Summary 51

Chapter 4 Experimental and modeling studies of a dehumidifying cooling coil 52

4.1 Introduction 52

4.2 Enthalpy potential method 53

4.3 Experimental set-up 63

4.4 Uncertainty analysis 65

4.5 Results and discussion 66

4.6 Summary 76

Chapter 5 Overall optimization and exergy analysis of the air-conditioning system with series-series counter-flow chillers 77

5.1 Exergy model 77

5.2 Description of the central air conditioning system and solution procedure 79

5.3 Results and discussion 87

5.3.1 Energy analysis 87

5.3.2 Exergy analysis 98

5.4 Summary 100

Chapter 6 Discussion, conclusions, and future work 102

6.1 Discussion and conclusions 102

6.2 Future work 104

References 105

List of publications 110

Appendix 112

I Solution procedures 112

II Matlab codes 114

Nguyen Minh Phu

Department of Mechanical Engineering Graduate School, University of Ulsan

ABSTRACT

When central water chillers in air conditioning are arranged in series-series counter-flow (SSCF), compressor lift of each chiller decreases in comparison with that of water chillers in parallel That means that the compressor power of the chillers in SSCF is lower than that of chillers in parallel However, the water pressure drop of the SSCF chillers increases, i.e increase in power of water pumps, because the water flow rates of SSCF chillers are the flow rates of the whole system This disadvantage will be solved by increasing the temperature difference of water flow through an evaporator and condenser, but the water flow rates will decrease Under the conditions of high temperature differences and low water flow rates, cooling coil and cooling tower may be affected Hence, in this thesis, we consider overall air conditioning system including SSCF water chillers, cooling coil and cooling tower Those components are modeled and simulated in viewpoints of the first and second laws of thermodynamics Model formulations of transfers and pressure drops are performed in the thesis, namely as follows

The water chiller model is based on the logarithmic mean temperature difference (LMTD) method Refrigerant R134a condenses and evaporates on the tube bundles of condenser and evaporator of the chiller; whereas, chilled water and condenser water pass inside tubes The tubes are commercial enhanced tubes so that heat transfer areas can be diminished and the problem can be reached reality Refrigerant pressure drop is neglected But water pressure

drop is considered Results of the water chiller model are verified by the commercial software HTRI Xchanger suite Simulation results show that with larger number of tubes than a specified one, the length of the tube can be short if a tube of small diameter is used It avoids

a design of large number of tube and large tube diameter This is because inner thermal resistance can be lessened with the tube of small diameter This conclusion reduces in capital cost of heat exchanger Tube diameter must be as low as 10.08 mm when number of tubes is more than 630 if the condenser capacity is 3412.4 kW with the common design conditions of cooling water and refrigerant R134a However, tube of small diameter results in high water pressure drop Therefore, an optimization can be carried out by trade-off of capital and operating costs

A cooling tower model is derived by using Merkel’s theory in company with the empirical correlations of transfer and air pressure drop from previous studies The model optimizes power of the cooling tower fan The optimization problem is compared with the previous study that used the optimization package DICOPT (DIscrete and Continuous OPTimizer) A prominent result can be deduced A condition of high temperature of water entering the cooling tower and low water flow does not bring an effective energy consumption of the fan With that condition, the air flow rate can be reduced but the length of cooling tower fill has to

be longer in order to increase the contact time between water of high temperature and air This trade-off leads to maximum power consumption of the fan at a certain value of the entering water temperature That means the water temperature should be higher or lower than this value From this work, the water temperature is 36oC and doesn’t depend on the thermal duty

of the tower Only at a rather high water temperature, potential of heat and mass transfer can

be strengthened and therefore fan power can be lowered

The cooling coil model is based on the enthalpy potential method and sustainable correlations of McQuiston about continuous plate fin under wet and dry environments An experimental apparatus is set up to validate the model and carry out further studies From analysis, it can be deduced that air pressure drop under fully wet and fully dry conditions are well predicted by the correlations of McQuiston However, the correlations have not covered the prediction in partially wet condition Hence, a linear correlation between fully wet and

of the water temperature entering cooling coil, the water temperature leaving cooling tower, and the condenser water flow rate in order to see that an overall optimization is necessary The COP after optimization can be greater up to 26% than that of conventional parallel chillers and the COP reduces as the number of chiller in SSCF increases Optimal parameters corresponding to number of SSCF chillers were shown so that they are can set in reality Exergy analysis was performed with the parameters that make the maximum COP at each number of SSCF chillers Result shows that the exergy efficiency of SSCF chillers system (83%) is higher than that of parallel chillers system (77%) Irreversibilities of the components

in SSCF chillers are lower than those of components in parallel chillers But irreversibilities

of cooling coil and cooling tower in SSCF chillers are slightly higher and lower than those in parallel chillers, respectively

Key words: Air conditioning, Overall optimization, Heat exchanger, Series-series

counter-flow

LIST OF FIGURES

Fig 1.1 Chillers arrangements a) Parallel, b) Series-series counter-flow 2

Fig 1.2 Trends of water temperatures, condensation temperature and evaporation temperature a) Parallel chillers, b) SSCF chillers 3

Fig 1.3 Conceptualization of reduced lift (Groenke and Schwedler, 2002) 4

Fig 1.4 Structure of the present thesis with a central air conditioning system 7

Fig 2.1 Pressure-enthalpy diagram of the considered water chiller 10

Fig 2.2 Notations used in the finned-tube 11

Fig 2.3 Enhanced boiling surface of turbo-B tube (Browne and Bansal, 1999) 12

Fig 2.4 Boiling heat transfer coefficient on Turbo-B tube (Wolverine, Inc.) 14

Fig 2.5 Tube length vs the number of tubes and tube passes 18

Fig 2.6 Reynolds number vs the number of tubes and tube passes 18

Fig 2.7 Water pressure drop vs the number of tubes and tube passes 19

Fig 2.8 Allowable tube side (P t) and shell side (P s) pressure drops (Muralikrishna and Shenoy, 2000) 19

Fig 2.9 Tube length vs the number of tubes and tube inner diameter 21

Fig 2.10 Thermal resistances for four cases 21

Fig 2.11 Reynolds number vs the number of tubes and tube inner diameter 22

Fig 2.12 Water pressure drop vs the number of tubes and tube inner diameter 22

Fig 2.13 Tube length vs the number of tubes and tube passes 23

Fig 2.14 Reynolds number vs the number of tubes and tube passes 24

Fig 2.15 Water pressure drop vs the number of tubes and tube passes 24

Fig 2.16 An interface of HTRI software 26

Fig 2.17 Graphical results from HTRI software a) HTRI condenser, b) HTRI evaporator 28 Fig 3.1 A sketch of cooling tower and its notations 32

Fig 3.2 A differential control volume of a counter-flow cooling tower 33

al., 2010) 35

Fig 3.4 Algorithm for searching the optimal fan power 42

Fig 3.5 Comparison about a) TAC, b) Me and c) K fi to examples in previous study (Serna-González et al., 2010) 44

Fig 3.6 Merkel number against T w,in for all the considered Q 46

Fig 3.7 Dry air flow rate against T w,in and Q 46

Fig 3.8 Cross sectional area of fill against T w,in and Q 47

Fig 3.9 Fill height against T w,in for all the considered Q 48

Fig 3.10 Loss coefficient against T w,in for all the considered Q 49

Fig 3.11 Total pressure drop for all the considered Q 49

Fig 3.12 Fan power against T w,in and Q 50

Fig 4.1 Circular fin in fully dry (a), fully wet (b), and partially wet (c) surface conditions (Pirompugd et al., 2009) 53

Fig 4.2 Tube and wet fin with notations 54

Fig 4.3 Photo and the detailed test coil of the present experimental setup a) Photo of experimental setup, b) Geometry of test coil 64

Fig 4.4 Some devices in the apparatus a) Differential pressure transducers, b) Magnetic flow meter, c) Stirrer motor and d) Data logger with propeller, and temperature and relative humidity sensor 65

Fig 4.5 Theoretical and experimental water pressure drop 67

Fig 4.6 Cooling load components with the inlet water temperature 68

Fig 4.7 The effect of entering water temperature and air face velocity to total heat transfer rate 68

Fig 4.8 The effect of entering water temperature and water flow rate on total heat transfer rate 69

Fig 4.9 The effect of entering water temperature and air face velocity on air pressure drop 70 Fig 4.10 The wet fin with notations 71

Fig 4.11 Air pressure drop under three conditions of the coil surface 74

Fig 4.12 Coil surface at various inlet water temperatures with v a = 4 m/s 75

Fig 4.13 Air pressure drop vs face velocity under fully dry and fully wet conditions 76

Fig 5.1 A schematic diagram of an air conditioning system 79

Fig 5.2 Air conditioning process (a) and its psychrometric chart (b) 81

Fig 5.3 Central air conditioning system with conventionally parallel chillers 82

Fig 5.4 Central air conditioning system with proposed SSCF chillers 83

Fig 5.5 Solution procedure for the system with SSCF chillers 86

Fig 5.6 Power consumption of components against number of chillers a) Full y-axis, b) Limited y-axis 88

Fig 5.7 Variation of the total COP with number of chillers 89

Fig 5.8 Trends of water temperatures, condensation temperature and evaporation temperature with 3 chillers in arrangements a) Parallel chillers (A typical chiller), b) SSCF chillers 89

Fig 5.9 Cooling capacity-dependent configuration with mixed parallel and SSCF arrangements 90

Fig 5.10 Power consumption of components against the water temperature entering coil a) Full y-axis, b) Limited y-axis 91

Fig 5.11 Variation of the total COP with the water temperature entering coil 92

Fig 5.12 Power consumption of components against the water temperature leaving cooling tower a) Full y-axis, b) Limited y-axis 93

Fig 5.13 Variation of the total COP with the water temperature leaving cooling tower 94

Fig 5.14 Power consumption of components against the condenser water flow rate a) Full y-axis, b) Limited y-axis 95

Fig 5.15 Variation of the total COP with the condenser water flow rate 96

Fig 5.16 Qualitative illustration of global maximum COP with 2 independent parameters 97 Fig 5.17 Various COP against number of chillers and parameters which lead to the optimum COP 98

Fig 5.18 Exergy efficiency against number of chillers 99

Fig 5.19 Irreversibility of components in arrangements 100

Fig A1 Solution procedure for investigating cooling coil 112

Fig A2 Solution procedure for the cooling coil subroutine 113

-ix-LIST OF TABLES

Table 2.1 Low fin tubes for condenser Smooth bore N fin=26 fpi,  = 0.33mm 17

Table 2.2 Comparison of this work and HTRI software 27

Table 3.1 Coefficients in Eqs (3.10) and (3.11) 37

Table 4.1 Experimental errors 66

Table 5.1 Exergy loss equations for each system equipment 79 Table 5.2 Range and resolution of the independent parameters for searching optimum COP.97

NOMENCLATURE

A : Area (m2)

b : Ratio of enthalpy to temperature (kJ/kg.K)

(Defined by Eqs (4.2), (4.5), (4.16a) and (4.16b))

c p : Specific heat at constant pressure (kJ/kg.K)

D : Diameter (m)

f : Friction factor (-)

g : Gravity acceleration (m/s2)

G c : Mass velocity based on the minimum free flow area (kg/m2.s)

h : Heat transfer coefficient (kW/m2K)

i : Enthalpy (kJ/kg)

I : Irreversibility (kW)

i fg : Latent heat of vaporization (kJ/kg)

j : The Colburn factor (-)

n chillers : Number of chillers (-)

n t : Total number of tubes (-)

n tp : Number of tube pass (-)

p : Pressure (Pa)

Pr : Prandtl number (-)

Q : Heat transfer rate (kW)

r 1 : Outside radius of tube (m)

Re : Reynolds number (-)

s : Entropy (kJ/kg.K)

S : Fin spacing (m)

T : Temperature (oC or K)

T w1 : The water temperature entering cooling coil (oC)

T w2 : The water temperature leaving cooling coil (oC)

T w3 : The water temperature leaving cooling tower (oC)

T w4 : The water temperature entering cooling tower (oC)

UA : Overall conductance (kW/K)

v : Velocity (m/s)

V w : Volumetric flow rate of water (Lit/min)

W : Power (kW)

X l : Longitudinal tube spacing (m)

X t : Transverse tube spacing (m)

y w : Thickness of water film (m)

ABBREVIATIONS

AHU : Air handling unit

COP : Coefficient of performance

EES : Engineering equation solver

LMTD : Logarithmic mean temperature difference

SHF : Sensible heat factor

SSCF : Series-series counter-flow

to development trend of the world and the human demand, air conditioning systems are being installed popularly Air conditioning systems consume considerable electric power in commercial and residential buildings, especially in tropical countries, more than 50% of total building energy (Lu et al., 2005a) Hence, there are many proposed solutions to save energy and reduce power demand of the air conditioning systems such as cool thermal storage (Fang

et al., 2009; Erek and Dincer, 2008; Zhao et al., 2008; Habeebullah, 2007; Cliche and Lacroix, 2006; Ismail et al., 2003), absorption refrigeration/heat pump system and refrigeration/heat pump system driven by gas engine or gas turbine with a combined cold, heat and power system (Xu and Yang, 2009; Sun, 2008), solar powered air conditioning (Pongtornkulpanich

et al., 2008) or reduction in water consumption of cooling tower (Al-Bassam and Maheshwari, 2011), and so on

In general, central water chillers in an air conditioning system are arranged in parallel as shown in Fig 1.1a Lifts of chillers, i.e the difference between the condensing temperature and the evaporating temperature, are equal as seen in Fig 1.2a Chillers can be also built in series as described in literatures (Wang, 2001 and Petchers, 2003). Fig 1.1b shows another series arrangement where chilled water flows through chiller 1 and chiller 2 in turn;

meanwhile, condenser water flows through chiller 2 and chiller 1 in turn Hence, it can be called series-series counter-flow (SSCF) arrangement In the SSCF arrangement, the lift of each chiller may be reduced in comparison with parallel chillers because the water temperature leaving evaporator of the chiller 1 is higher and the water temperature leaving condenser of the chiller 2 is lower as shown in Fig 1.2b Reduction in the lift leads the reduction of power consumption of compressors of chillers However, pumping power of chilled water pumps and condenser water pumps may be raised in SSCF chillers system because the water flow rate of each condenser and evaporator is the water flow rate of the whole system and thus water pressure drop increased sharply that the pressure is almost proportional to the square of flow rate and the power required is almost proportional to the cube of flow rate Consequently, optimizations and modifications can be imposed to adapt the SSCF chillers to the whole system

Fig 1.1 Chillers arrangements a) Parallel, b) Series-series counter-flow

CondenserEvaporator

CondenserEvaporatorChilled

water

Condenserwater

Chiller 1CondenserEvaporatorChiller 2CondenserEvaporator

Chilledwater

Condenserwater

a)

b)

-3-Fig 1.2 Trends of water temperatures, condensation temperature and evaporation temperature

a) Parallel chillers, b) SSCF chillers

The optimum performance of an air conditioning system with parallel chillers through set points can be found in previous studies (Lu et al., 2005a; Lu et al., 2005b; Lu et al., 2004; and

Ma et al., 2008) For SSCF chillers, Groenke and Schwedler (2002) present results of a system with 2 SSCF chillers where each chiller has two refrigerant circuits Therefore, there are four reductions of the lift as shown in Fig 1.3 The water temperatures entering and leaving SSCF chillers system were fixed in their study, and two condenser water flow rates were considered They prove that a power reduction by 14% is found by using the SSCF arrangement Directional analyses of effects of water flow rate and water temperature on air conditioning system and need of SSCF chillers were reported in study of Eppelheimer (2003)

It was pointed out that high energy efficiency can also be obtained from other the improvement of components of the system such as cooling tower fan and pumps

Fig 1.3 Conceptualization of reduced lift (Groenke and Schwedler, 2002)

To reduce the high water pressure drop of SSCF chillers, the water flow rates should be reduced by increasing water temperature differences The increase in water temperature differences may increase the water temperature entering the cooling tower (Condenser water side) and decrease the water temperature entering the cooling coil (Chilled water side) When the water temperature of the cooling tower is higher and the condenser water flow rate is lower than those in the parallel chillers system, the pumping power of the condenser water loop may be reduced and the fan power of the cooling tower may be also reduced due to high potential of heat and mass transfer between the cold air and hot water For the chilled water side, the pumping power of the chilled water loop may be reduced and also we need to make clear the phenomena occurred in the air side of the cooling coil These judgments should be figured out clearly when chillers are piped in SSCF

1.2 Problem statement, necessity, objectives and thesis layout

Energy consumption of air conditioning systems is a remarkable problem of all investors and managers Hence, improving strategies should be issued continuously and systematically

In this study, we deal with water-cooled central air conditioning system by applying SSCF arrangement for chillers Model formulation and analysis of main components of the system

35.1oC32.9oC31.2oC

Downstream circuit

Upstream circuit

Downstream circuit

Upstream circuit

Downstream circuit

Upstream circuit

Chiller

(1 Circuit)

Chiller module(2 Circuits)

Chiller module(4 Circuits)

-5-are presented in this thesis The main components -5-are water chiller, wet cooling tower and cooling coil Air conditioning schematic, cooling load and outdoor conditions are given previously to limit the scope of the thesis Calculation programs are written by using Matlab R2008a All properties of water, moist air and refrigerant are taken from EES software (Klein, 2003) The set-points of air conditioning system such as water temperatures and water flow rates are assigned as key parameters Most of design parameters are taken from the ASHRAE standard and ARI standard

The objectives of this research are as follows:

 Analyzing the effects of structure of shell-and-tube condenser and evaporator on water pressure drop in order to limit the inherent obstacle of high water pressure drop in SSCF chillers Heat transfer tubes, which are commercial enhanced tubes, are used so that heat transfer areas can be small and the heat exchangers considering a real situation can be designed A water chiller is designed as one in the parallel chillers and SSCF chillers in order to serve the next chapter

 Quantitatively analyze the impact of the high water temperature and the low water flow rate on the performance of a cooling tower

 Cooling coil is modeled in order to investigate transfer characteristics and air pressure drop under different humid conditions with respect to water temperature and water flow rate

 Analyze the effects of the set-points of an air conditioning system and the number of chillers on the performance of the whole system when water chillers are piped in SSCF When the trade-offs of power consumptions have been predicted previously, it is necessary

to carry out an overall optimization

 Analyze exergy to point out the irreversibilities of components in SSCF chillers system

 Perform the energy and exergy analyses of the air conditioning systems with both parallel and SSCF chillers and compare the results

 To obtain reliability, model formulations are validated by one way or another

Judging from the objectives, the dissertation can be organized as follows and organization

of the thesis for next chapters can be seen in Fig 1.4

 Chapter 2 presents a heat transfer model in conjunction with the water pressure drop

of condenser and evaporator using commercial enhanced tubes Advantages and disadvantages of the size of heat transfer surface are analyzed and discussed in this chapter

 Chapter 3 presents the Merkel theory and the empirical correlations from previous studies to predict heat and mass transfer and air pressure drop of an induced draft cooling tower Impact of high water temperature and low water flow on performance of the cooling tower is pointed out in this chapter

 Chapter 4 introduces the enthalpy potential method and sustainable correlations of McQuiston for dehumidifying air coil The coil is studied theoretically and experimentally

so that air pressure drop under different fin conditions (Fully wet, partially wet, and fully dry) is emphasized in this chapter

 Chapter 5 presents energy and exergy analyses of SSCF chillers systems in comparison with those of parallel chillers systems An optimization of the overall air conditioning system with SSCF chillers is presented in order to show that how much energy can be saved when the system is operated at optimum set-points

 Chapter 6 reports results from this study

nth chiller

1st chiller

Pump

Cooling tower Pump

Cooling coil

Chapter 2 Chapter 3

Chapter 4

Chapter 5

C h a p t e r 2

Analysis and design of a water chi ler using

commercial enhanced tubes

2.1 Introduction

As analyzed in the previous chapter, when water chillers are arranged in series-series counter-flow, water pressure drops increase considerably because the water flow rate of each chiller has to be increased Hence, this chapter is to investigate the water pressure drop Design condition in view of low pressure drop under given requirements of refrigeration cycle

is emphasized Commercial enhanced tubes are used in the condensers and the evaporators of the water chiller so that the pressure drop can diminish and the water chiller can be investigated in real situation closely Reviewing previous studies, many researchers paid attention to design, fabrication and operation of the shell and tube heat exchanger by one way

or another Optimization of total cost (Capital cost and operating cost) with respect to baffle spacing was carried out by Khalifeh Soltan et al., (2004) In Soltan’s study, optimal correlations are formulated for the E and J types shell and tube condensers in order to facilitate design calculation A compact formulation based Bell-Delaware method was proposed by Serna and Jimenez (2005) The formulation can be used for either design calculation or optimization of the costs to any of the shell side geometries in industry This kind of problem was also investigated by Ravagnani and Caballero (2007) where the calculated heat exchanger variables are in accordance with the TEMA standards Optimal total cost of condensers using eleven variables was studied by Allen and Gosselin (2008) who consider condensing fluid either in tube or in shell About 134 million possible cases were investigated by using genetic algorithms (GAs) It was also demonstrated usefulness of the GAs with respect to decrease in calculation time Recently, the GAs for optimal design of

2.2 Model formulation

A model for estimation of heat transfer and water pressure drop in water chillers was formulated with the following assumptions

 Fouling problem is neglected

 Refrigerant pressure drop is negligible

 Desuperheat section is carried out in another device, e.g desuperheater Condenser is to condense refrigerant only In fact, from energy saving viewpoint, the desuperheat section can be recovered as a heat source, for example, in study of Tan and Deng (2002)

 The incoming state of compressor is saturated vapor

 The incoming state of expansion valve is saturated liquid

Hence the chiller plant cycle was considered as shown in the pressure-enthalpy diagram of

Fig 2.1 Isentropic efficiency of the compressor was used from the following equation

(Steven Brown et al., 2002):

s

e

p p

where p c and p e are condensation pressure and evaporation pressure, respectively

Fig 2.1 Pressure-enthalpy diagram of the considered water chiller

2.2.1 Heat transfer model

The compressor power can be calculated the following equation

. (2 1)

Comp R

W m i i

where m R is the mass flow rate of refrigerant

Heat transfer equation of condenser (Q Cond. ) and evaporation (Q Evap.) is given by

Q=UA.LMTD

where LMTD is the logarithm mean temperature difference:

, ,

, ,

ln

w in w out sat w in sat w out

2

4

3 pc

pe

r Cond in in t t t in sur out out

Fig 2.2 Notations used in the finned-tube

For an evaporator, enhanced tube, which has special surfaces as shown in Fig 2.3, is used

in this study The fin efficiency is unusual defined for the surfaces Therefore, the overall conductance has the form as (Yang et al., 2008)

.

ln2

r Evap in in t t t in out out

Fig 2.3 Enhanced boiling surface of turbo-B tube (Browne and Bansal, 1999).

The water side heat transfer coefficient can be estimated by using the following Gnielinski’s correlation (Serth, 2007):

2/3 2/3

(Re 1000) Pr

18(1 12.7 / 8(Pr 1)

in

t in w

with A fin is the fin area and N fin is the number of fins per unit length

For a bundle of finned tube, the correction factor of tube rows should be multiplied to Eq (2.2) The correction factor is N r0.08, where N r is number of tube rows (Cavallini et al., 2003) Calculation of fin efficiency can be performed by below equations:

tanh( )

fin

M M

r 

Here, sur and r 2c are the surface efficiency and the correction fin radius, respectively

The boiling heat transfer coefficient on enhanced tube (Turbo-B) can be employed in the following correlation from Wolverine manufacturer for R134a (See more Fig 2.4)

0.23602

350.2706

out out

h  q (Btu/h.ft2.F) (2.3)

where heat flux q out (Btu/h.ft 2 ) = Q/(A out ) Form of Eq (2.3) for other refrigerants is also found

in the study of Browne and Bansal (1999)

2.2.2 Water pressure drop model

The tube side pressure drop of water in a condenser and an evaporator can be composed by the following components:

a) The pressure drop due to fluid friction in tubes is given as follows:

2

2

t w w friction tp

where w is evaluated at the mean water temperature and wall is evaluated at the mean inner

surface temperature of tube And f is the Darcy friction factor For turbulent flow in commercial tubes with Re w3000: 0.

w

f 4137Re For laminar flow, f 64 Re / w

b) The minor losses are computed as follows (Serth, 2007)

2 4

where r 2n tp1.5 for turbulent flow, r 3.25n tp1.5 for laminar flow

c) The pressure drop in nozzles is given by (Serth, 2007)

2 4

2

47.5 10 w n

n

m p

2

41.5 10 w n

n

m p

D



  

  for laminar flow

where D n is the inner diameter of nozzle

Finally, the water pressure drop is sum of all components:

w friction n r

2.3 Results and discussion

In the present work, the following parameters of a chiller were used to investigate water pressure drop:

 Cooling capacity: Q Evap. = 3000 kW

 Condensation temperature: 40o

C

where tube spacing was taken equal to 1.25D out (Kuppan, 2000) Calculation of the shell diameter can be referred to Ref (Thome, 2006) Results for condensers and evaporators are presented in next subsection

2.3.1 Condenser

Several low-fin tubes from High Performance Tube, Inc were used in the condenser calculation They are listed in Table 2.1 The tube is a low-fin tube as shown in Fig 2.2 Nozzle diameter of 16.88 inches was selected for the condenser Figs 2.5~2.7 present the effect of the number of tubes and number of tube passes on the length of a tube, Reynolds number, and pressure drop in water side In these results, a typical tube of No.12 in Table 2.1

was considered At a fixed number of tubes, the tube length decreases with increasing in the number of tube passes because the water velocity in tube raises the number of passes As a result, heat transfer can be accelerated and thus the tube length can reduce As seen in Fig 2.6, Reynolds number increases drastically with the number of passes Positive effects on heat transfer yields negative effects on water pressure drop as shown in Fig 2.7 The pressure drop

is lowest at one tube pass due to the low water velocity and the short journey of water flow When the number of tubes decreases, pressure loss increases because the tube length increases

as seen in Fig 2.5 It can be seen that pressure drop is so high that it may be unacceptable at high number of tube passes and low number of tubes Muralikrishna and Shenoy (2000)

recommend the allowable tube-side and shell-side pressure drop for shell and tube heat exchanger as shown in Fig 2.8 It can be seen that the tube side pressure drop should not

(High Performance Tube, Inc.)

Fig 2.5 Tube length vs the number of tubes and tube passes

Fig 2.6 Reynolds number vs the number of tubes and tube passes

tp = 2 n

tp = 3 n

-19-Fig 2.7 Water pressure drop vs the number of tubes and tube passes.

Fig 2.8 Allowable tube side (p t) and shell side (p s) pressure drops (Muralikrishna and Shenoy, 2000)

Figs 2.9~2.12 show the effect of tube specifications in Table 2.1 on previous qualities at one tube pass Fig 2.9 presents the effect of three typical tubes on the tube length of condenser With a certain tube diameter, the length decreases with the number of tubes as in

Fig 2.5 At a fixed number of tubes, a tube with larger diameter leads to shorter tube length at

small number of tubes On the contrary, at large number of tubes, larger tube diameter leads to longer tube length Tube diameter must be as low as 10.08 mm when number of tubes is more than 630 This can be explained by thermal resistances as shown in Fig 2.10 Fig 2.10 shows the outer wall and inner thermal resistances per unit length in four cases according to the number of tube and the inner diameter of tube

At a small number of tubes (e.g n t=400), outer resistance reduces and inner resistance increases with inner diameter because outer area increases and water velocity decreases, respectively Wall resistance also reduces with the inner diameter Hence, total resistance can

be reduced with D in Therefore, tube with larger diameter leads to tube with shorter length at small number of tubes

At a large number of tubes (e.g n t =900), inner resistance also increases sharply with D in

because the inner resistance increases with not only the D in but also number of tube, as seen in

Fig 2.11 which presents Reynolds number inside tube Meanwhile, outer and wall resistances

decrease slightly with the D in These cause total resistance to increase with the D in Hence, it can be concluded that, at a large number of tubes, tube with larger diameter leads to tube with longer length When a large number of tubes are selected, tube of large diameter can bring the high capital cost due to two reasons as follows

- Large tube diameter leads to large shell diameter And, of course, for the same length, large diameter tube is more expensive than small diameter tube

- Larger tube diameter leads to longer tube length to response the same capacity as pointed out previously A simple example can be shown as follows: for the same 900 tubes (see Fig 2.9) For small tube diameter, the total inner area is  10.083.3 900 (A in D Ln in t), the for large tube diameter, total inner area is  21.133.65900 The ratio

of two calculations is approximately 2.3 The required area for the tube of large diameter is 2.3 times greater than that for the tube of small diameter

Otherwise, from Fig 2.12, we can see that if large tube diameter is used, operating cost is low because water pressure drop is low Trade-off between the increase in capital cost and the decrease in operating cost can lead to an optimization problem in the heat exchanger design and operation with respect to the tube diameter

-21-Fig 2.9 Tube length vs the number of tubes and tube inner diameter.

Fig 2.10 Thermal resistances for four cases

400 21.13 mm

900 10.08 mm

900 21.13 mm