ABSTRACT PATIL, VIKRAM CHANDRAKANT. Efficiency

ABSTRACT

PATIL, VIKRAM CHANDRAKANT. Efficiency Improvement Techniques in Liquid Piston Compressor for Ocean Compressed Air Energy Storage Application. (Under the direction of Dr. Paul I. Ro).

Modern electricity infrastructure needs an efficient large-scale energy storage system to accommodate energy supply from intermittent renewable energy resources. Ocean compressed air energy storage system (OCAES) is a promising large-scale energy storage system. In OCAES, energy is stored in the form of compressed air under the Ocean. This research is aimed at achieving technological advancement of OCAES to attain an efficient large-scale energy storage system.

Energy and exergy analysis of various OCAES configurations is performed first to identify

OCAES configuration with high efficiency. Isothermal OCAES shows significantly higher efficiency over adiabatic and diabatic OCAES with potential to reach a 72% roundtrip efficiency of energy storage. However, attainment of such a high efficiency is conditional on achieving near- isothermal compression and expansion of air. Compression of air using liquid piston is researched to attain efficient near-isothermal compression. Understanding the heat transfer mechanisms during compression is crucial in the design and development of efficient liquid piston compressor.

Therefore, a thorough investigation of heat transfer in liquid piston compressor is performed experimentally. It is observed that convective thermal resistance between air and chamber has significant contribution in total thermal resistance; therefore, heat transfer enhancement techniques to enhance the heat transfer coefficient between gas and chamber can lead to significant improvements in the isothermal efficiency of the liquid piston compressor.

Various heat transfer enhancement techniques are investigated in liquid piston compressor.

First, the heat transfer enhancement using water spray injection is investigated in liquid piston compressor for efficiency improvement. Experiments are performed at various injection pressures of spray with different spray angles at different stroke times of compression. The higher spray injection pressure shows higher improvement in compression efficiency and an optimal spray angle which can create smaller droplets with minimum loss of droplets due to the impact on chamber wall can lead to a marginal improvement in efficiency. Water spray injection is a highly effective technique to achieve near-isothermal compression with an isothermal efficiency up to

95% at a high power density. Moreover, aqueous foam based heat transfer enhancement is investigated in liquid piston compressor. Experiments are performed with the use of aqueous foam generated under different foam generation conditions. The volume of aqueous foam in the chamber, the air flow rate of foam generation, and various foam generator designs are considered in this investigation. A higher volume of aqueous foam in the compression chamber leads to a further increment in isothermal efficiency, however, with higher cyclic variability. Also, experiments highlight the potential of reduction in cyclic variability through the foam generator design. Overall, the use of aqueous foam in the liquid-piston compressor is effective in achieving an isothermal efficiency up to 92%. Additionally, another heat transfer enhancement using metal wire mesh spirals of aluminum and copper materials are investigated in liquid piston compression.

Metal wire meshes have a high thermal conductivity and a large heat surface area and therefore are hypothesized to improve heat transfer from the gas to the liquid inside the liquid piston compressor. Both aluminum and copper meshes are observed to improve isothermal efficiency of compression to 88-90% from the base efficiency of 82-84%.

Lastly, the end-to-end efficiency of liquid piston based OCAES with spray injection, aqueous foam, and metal wire mesh techniques is estimated. Heat transfer enhancement in liquid piston shows significant improvement in end-to-end efficiency of OCAES with spray injection as a highly effective efficiency improvement technique with potential to attain about 60% efficiency of

OCAES from the base 45% efficiency.

Efficiency Improvement Techniques in Liquid Piston Compressor for Ocean Compressed Air Energy Storage Application

by Vikram Chandrakant Patil

A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Mechanical Engineering

Raleigh, North Carolina. 2019

APPROVED BY:

______Dr. Paul I. Ro Dr. Alexei Saveliev Committee Chair

______Dr. Jun Liu Dr. Wenbin Lu

DEDICATION

This dissertation is dedicated to all of my teachers and mentors.

BIOGRAPHY

Vikram Patil was born in Sangli located in the state of Maharashtra in India. He graduated with

Master’s in Mechanical Engineering from Indian Institute of Science, Bangalore, India in June

2013 and with Bachelor of Technology in Mechanical Engineering from Walchand College of

Engineering, Sangli, India in May 2011. He worked as an Assistant Manager in the Research and

Development division of Bajaj Auto Limited in Pune, India from July 2013 to July 2015.

He joined North Carolina State University at Raleigh, USA as a doctoral candidate in the department of Mechanical and Aerospace Engineering in Fall 2015. His research interests are in the field of energy analysis, heat transfer, and energy storage. He is a member of the American

Society of Mechanical Engineering (ASME), American Society of Heating Refrigeration and Air-

Conditioning Engineers (ASHRAE), and Institute of Electrical and Electronics Engineers (IEEE).

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TABLE OF CONTENTS

LIST OF TABLES ...... vii

LIST OF FIGURES ...... viii

CHAPTER 1: Introduction ...... 1

1.1. Compressed Air Energy Storage ...... 3 1.2. Ocean Compressed Air Energy Storage (OCAES) ...... 5 1.3. Research Objectives ...... 6

CHAPTER 2: Energy and Exergy Analysis of OCAES Concepts ...... 7

2.1. Introduction ...... 8 2.2. OCAES Configurations ...... 12 2.2.1. Diabatic OCAES ...... 13 2.2.2. Adiabatic OCAES ...... 14 2.2.3. Isothermal OCAES ...... 16 2.2.4. Liquid Piston based OCAES ...... 17 2.3. Energy and Exergy Analysis ...... 18 2.3.1. Electric Motor and Generator ...... 19 2.3.2. Hydraulic Pump/Motor ...... 20 2.3.3. Compressor ...... 20 2.3.4. Cooler ...... 21 2.3.5. Air Pipelines Connecting Various Components ...... 21 2.3.6. Thermal Energy Storage (TES) ...... 22 2.3.7. Air Storage ...... 22 2.3.8. Heater ...... 23 2.3.9. Expander ...... 23 2. 4. Numerical Simulations...... 24 2.5. Results and Discussion ...... 27 2.5.1. Diabatic OCAES ...... 27 2.5.2. Adiabatic OCAES ...... 28 2.5.3. Isothermal OCAES ...... 30 2.5.4. Liquid Piston based OCAES ...... 31 2.6. Conclusions ...... 34

CHAPTER 3: Heat Transfer in Liquid Piston Compressor ...... 35

3.1. Introduction ...... 37 3.2. Analytical Model ...... 40 3.3. Experiments ...... 45 3.4. Results and Discussion ...... 47 3.4.1. Pressure and Temperature Plots ...... 47 3.4.2. Experiments with different Stroke Time of Compression ...... 50 3.4.3. Rate of Heat Transfer and Compression Work ...... 52 3.4.4. Heat Transfer Coefficient ...... 55 3.4.5. Thermal Resistances ...... 59 3.4.6. Overall Heat Transfer Coefficient ...... 61 3.4.7. Isothermal Efficiency of Compression ...... 62 3.5. Conclusions ...... 64

CHAPTER 4: Spray Injection in Liquid Piston Compressor ...... 65

4.1. Introduction ...... 67 4.2. Experimental Setup ...... 71 4.2.1. Liquid Piston Setup ...... 71 4.2.2. Spray Injection Setup ...... 72 4.2.3. Measurement Devices ...... 75 4.2.4. Range of Experiments ...... 76 4.3. Results and Discussion ...... 77 4.3.1. Pressure and Temperature Plots ...... 77 4.3.2. Effect of Injection Pressure ...... 79 4.3.3. Effect of Spray Nozzle Angle ...... 89 4.3.4. Effect of Stroke Time of Compression ...... 93 4.4. Conclusions ...... 97

CHAPTER 5: Aqueous Foam in Liquid Piston Compressor ...... 100

5.1. Introduction ...... 101 5.2. Conceptual Framework ...... 105 5.2.1. Bubble Dynamics in Aqueous Foams ...... 106 5.2.2. Heat Transfer in Aqueous Foams ...... 109

5.2.3. Isothermal Compression ...... 111 5.3. Experimental Procedure ...... 113 5.3.1. Liquid Piston Compressor Setup ...... 113 5.3.2. Aqueous Foam Generation Setup ...... 114 5.3.3. Experimental Cases ...... 117 5.4. Results and Discussion ...... 118 5.4.1. Bubble Dynamics during Compression ...... 118 5.4.2. Effect of Aqueous Foam Volume ...... 120 5.4.3. Variability with the Use of Aqueous Foam ...... 121 5.4.4. Effect of Air Flow Rate of Aqueous Foam Generation ...... 123 5.4.5. Effect of Foam Generator Designs ...... 126 5.5. Conclusions ...... 131

CHAPTER 6: Metal Wire Mesh Spiral in Liquid Piston Compressor ...... 133

6.1. Introduction ...... 134 6.2. Conceptual Framework ...... 136 6.3. Experimental Setup ...... 139 6.4. Results and Discussion ...... 141 6.4.1. Effect of Metal Wire Mesh Material ...... 141 6.4.2. Effect of Compression Stroke Time ...... 144 6.4.3. Isothermal Compression Efficiency ...... 147 6.5. Conclusions ...... 149

CHAPTER 7: Efficiency Improvement in Liquid-piston based OCAES ...... 150

7.1. Introduction ...... 151 7.2. Efficiency Improvement Techniques ...... 153 7.2.1. Spray Injection ...... 153 7.2.2. Aqueous Foam ...... 154 7.2.3. Metal Wire Mesh ...... 155 7.3. OCAES Efficiency ...... 156 7.4. Conclusions ...... 159

CHAPTER 8: Conclusions ...... 160

LIST OF TABLES

Table 2.1: Stochastic Assignments in Monte Carlo Simulation ...... 25

Table 2.2: Thermodynamic properties and mass flow rates of air at different state points for Diabatic OCAES system (See Figure 1 for state points) ...... 26

Table 2.3: Thermodynamic properties and mass flow rates of air at different state points for Adiabatic OCAES system (See Figure 2 for state points) ...... 26

Table 2.4: Thermodynamic properties and mass flow rates of air at different state points for Isothermal OCAES system (See Figure 3 for state points)...... 26

Table 3.1: Model Parameters of the non-linear regression model for convective heat transfer coefficient during compression with polycarbonate chamber...... 58

Table 4.1: Measurement devices and corresponding accuracies...... 75

Table 4.2: Compression Work and Spray Work for compression at different injection pressures...... 86

Table 5.1: Analysis of Variance (ANOVA) table for efficiencies with foam generator designs...... 129

Table 6.1: Polytropic Index and Isothermal Efficiency of Compression with and without Mesh...... 148

Table 7.1: Polytropic index and isothermal efficiency of compression with spray cooling...... 154

Table 7.2: Polytropic index and isothermal efficiency of compression with aqueous foam. .... 155

Table 7.3: Polytropic index and isothermal efficiency of compression with metal wire mesh..156

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LIST OF FIGURES

Figure 1.1: Energy storage and power output of various energy storage options [10]...... 2

Figure 1.2: Conceptual schematic of compressed air energy storage...... 3

Figure 1.3: Conceptual schematic of Ocean Compressed Air Energy Storage (OCAES) [18]. .... 5

Figure 2.1: Schematic of diabatic OCAES ...... 13

Figure 2.2: Schematic of adiabatic OCAES ...... 15

Figure 2.3: Schematic of isothermal OCAES ...... 16

Figure 2.4: Schematic of a liquid piston based Isothermal OCAES system...... 17

Figure 2.5: Exergy flow in diabatic OCAES ...... 28

Figure 2.6: Exergy flow in adiabatic OCAES ...... 29

Figure 2.7: Exergy flow in isothermal OCAES ...... 30

Figure 2.8: Overall exergy efficiency of different types of OCAES...... 31

Figure 2.9: Experimental setup of liquid piston compressor...... 32

Figure 2.10: Roundtrip efficiency of liquid piston based OCAES for different polytropic indices...... 33

Figure 3.1: Control Volume in Liquid piston compressor ( --- represents control volume) ...... 41

Figure 3.2: Thermal Circuit for liquid piston compressor ...... 42

Figure 3.3: Pressure-Volume plot indicating isothermal and polytropic compression ...... 44

Figure 3.4: Experimental Setup of Liquid piston compressor ...... 46

Figure 3.5: Various Compression chambers used in the study...... 47

Figure 3.6: Pressure over time for 10 continuous compression cycles ...... 49

Figure 3.7: Temperature over time for 10 continuous compression cycles ...... 49

Figure 3.8: Temperature data at various locations during compression ...... 50

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Figure 3.9: Pressure over compression time for various stroke times of compression (With Polycarbonate chamber)...... 51

Figure 3.10: Temperature of air over compression time for various stroke times of compression (With Polycarbonate chamber) ...... 51

Figure 3.11: Temperature of the inner surface of compression chamber over compression time for various stroke times of compression (With Polycarbonate chamber)...... 52

Figure 3.12: Rate of change of internal energy(U), compression work (W) and rate of heat transfer(Q) during compression (With polycarbonate chamber and 5.1 s compression stroke)...... 54

Figure 3.13: Comparison of U, W and Q for different stroke times of compression ...... 55

Figure 3.14: Convective heat transfer coefficient between air and cylinder wall during compression (With polycarbonate chamber and 5.1 s compression stroke)...... 56

Figure 3.15: Comparison of convective heat transfer coefficient between air and cylinder wall for different stroke times of compression (With polycarbonate chamber) ..... 59

Figure 3.16: Contribution of thermal resistances during compression process for different compression chambers...... 60

Figure 3.17: Overall heat transfer coefficient for compression with different compression chambers...... 62

Figure 3.18: Isothermal Efficiency for compression with different compression chambers...... 63

Figure 4.1: A table-top setup of Liquid piston compressor...... 72

Figure 4.2: Spray Injection Setup ...... 73

Figure 4.3: Spray pattern with full cone whirl nozzle...... 74

Figure 4.4: Pressure and Temperature vs time for ten continuous compression cycles without spray...... 77

Figure 4.5: Pressure and Temperature vs time for ten continuous compression cycles with sprays of different injection pressures...... 78

Figure 4.6: Flow rates of the spray with different injection pressure during a single compression cycle...... 80

Figure 4.7: Pressure plots for a single compression cycle with and without spray of different injection pressures. (With 90o spray nozzle and fast level of stroke time)...... 81

Figure 4.8: Temperature plots for a single compression cycle without and with spray of different injection pressures...... 82

Figure 4.9: Pressure volume plots for a compression cycle with spray of different injection pressures in comparison with adiabatic and isothermal plots...... 83

Figure 4.10: Zoomed view of pressure-volume plots of Figure 4.9 near the end of compression...... 84

Figure 4.11: Isothermal efficiency of compression with spray of different injection pressures. .. 88

Figure 4.12: Temperature plots with different spray angles during a single compression cycle. . 90

Figure 4.13: Pressure-volume plots with spray injection of different spray angles during compression. (With 30 psi injection pressure and medium level of stroke time) ... 91

Figure 4.14: Isothermal efficiency with spray injection from different nozzle angles for various injection pressures...... 92

Figure 4.15: Temperature plots with and without spray injection for a compression cycle with different stroke times. (With 30 psi injection pressure and 90° spray angle) . 94

Figure 4.16: Pressure-volume plots with and without spray injection for a compression cycle with different stroke times. (With 30 psi injection pressure and 90° spray angle) .. 95

Figure 4.17: Zoomed view of pressure-volume plots of Figure 4.16 near the end of compression...... 96

Figure 4.18: Isothermal efficiency with and without spray injection at various stroke time of compression for various injection pressures...... 97

Figure 5.1: Foam generation by injecting air through fritted disk [149]...... 105

Figure 5.2: Basic structures of single cell [127]...... 107

Figure 5.3: Experimental Setup of Liquid piston compressor ...... 114

Figure 5.4: Foam Generator designs of 2.5 mm hole diameters with and without tubes...... 115

Figure 5.5: Compression chamber with Aqueous Foam...... 116

Figure 5.6: Aqueous foam bubble dynamics during compression process...... 119

Figure 5.7: Temperature-pressure plot with foam of different volume in the chamber...... 120

Figure 5.8: Isothermal efficiency with foam of different volume in the chamber...... 121

Figure 5.9: Temperature-pressure for multiple cycles using about half of the chamber with foam...... 122 Figure 5.10: Temperature-pressure for multiple cycles using full chamber with foam...... 123

Figure 5.11: Aqueous foam generated using different flow rates of air source...... 124

Figure 5.12: Temperature-pressure plots with aqueous foam generated using different air source flow rate...... 124

Figure 5.13: Isothermal efficiency of compression with the aqueous foam generated by various flow rates of air source...... 125

Figure 5.14: Temperature-pressure plots using foam generator of 2.5 mm holes...... 127

Figure 5.15: Temperature-pressure plots using foam generator of 5 mm holes...... 128

Figure 5.16: Isothermal efficiency with foam generated from different foam generator designs...... 130

Figure 6.1: Conceptual schematic of liquid piston compressor with Metal Wire Mesh...... 137

Figure 6.2: Experimental Setup of Liquid Piston Compressor...... 140

Figure 6.3: Aluminum and Copper metal wire mesh sprials...... 141

Figure 6.4: Pressure during compression process with and without mesh in the chamber...... 142

Figure 6.5: Temperature during compression process with and without mesh in the chamber. 142

Figure 6.6: Temperature-Pressure (Normalized) plots with and without mesh in the chamber. 144

Figure 6.7: Pressure during compression of different stroke times with and without mesh...... 145

Figure 6.8: Temperature during compression of different stroke times with and without mesh...... 146

Figure 6.9: Temperature-pressure (normalized) plots during compression of different stroke times with and without mesh in the chamber...... 147

Figure 7.1: End-to-End Efficiency of OCAES system with various heat transfer enhancement techniques in liquid piston...... 158

CHAPTER 1: Introduction

The electricity sector is one of the major contributors to global warming emissions worldwide.

In the United States, about 29% of global warming emissions come from the electricity sector and most of those emissions originated from fossil fuels like coal and natural gas [1, 2]. Most of the renewable energy sources produce little or no global warming emissions and life cycle emissions

(i.e. emissions from each stage of life- manufacturing, installation, operation, and decommissioning) are minimal for renewable energy resources [3]. Electricity generation from renewable energy sources is desired to reduce energy dependency from fossil fuels and curtain global warming emissions. A comprehensive study by the U.S. Department of Energy’s National

Renewable Energy Laboratory (NREL) shows that the United States can generate most of its electricity from renewable energy by 2050 [4].

Renewable energy sources such as wind, solar, tidal, wave etc. are abundant to supply electricity needs but are intermittent in nature. The intermittency results in variation of energy supply to the electric grid from renewable energy resources. Optimal utilization of renewable energy resources needs energy storage capability to absorb variable electric supply into the electric grid [5]. Energy storage is a dominant factor in the integration of renewable energy sources to the electric grid. Electric energy storage in the electric grid decouples the electricity generation from the load, thus making it easier to regulate supply and demand. Also, it allows distributed storage opportunities for local grids or micro-grids, which could improve energy security [6]. Energy storage capability can reduce power fluctuations and enhance the electric system flexibility to create a robust and reliable modern electricity system [7]. Future energy systems will rely on effective and economical electricity storage of varying performance requirements [8].

Various energy storage technologies are currently engaged in the power applications which include pumped hydro storage, compressed air energy storage, thermal storage, battery storage, flywheel, capacitor-based energy storage, and superconducting magnetic energy storage (SMES)

[9]. Each of these technologies varies in their energy storage and power output capacity for production of a viable energy storage system. A comparison of these technologies with consideration of energy storage capacity, power output, and storage duration is shown in Figure

1.1. Additionally, these technologies differ in various characteristics like their cost, lifetime, cycle efficiency, and environmental impact [10]. Utility-scale energy storage systems are needed for the integration of renewable energy resources in the electric grid [11]. The pumped hydro storage and large compressed air energy storage are key technologies for the large scale energy storage. Pump hydro storage is efficient compared to the compressed air storage systems but pumped hydro is restricted by the availability of suitable geological locations [12].

Figure 1.1: Energy storage and power output of various energy storage options [10].

1.1. Compressed Air Energy Storage

Compressed air energy storage (CAES) system is a reliable large-scale energy storage technology with relatively low specific investment cost [13]. In a CAES system, energy is stored in the form of mechanical energy, or more precisely exergy, of pressured air. A schematic of the

CAES system is shown in Figure 1-2. A typical CAES system consists of the following major components.

a) Electric Motor

b) Air Compressor

c) Compressed Air Storage Reservoir

d) Air Turbine/ Expander

e) Generator

Figure 1.2: Conceptual schematic of compressed air energy storage.

During the storage mode, off peak electricity is used to compress the atmospheric air to high pressure, and compressed air is stored in the high-pressure reservoir. An electric motor consuming electricity drives the compressor to compress air to the high pressure. When electricity demand is high, the stored high pressurized air is expanded through the turbine to generate electricity in the recovery mode. CAES systems can store energy for a significantly long time-frame in terms of weeks or months while having a large-scale energy storage capacity.

Two large-scale CAES plants are in operation, one is in Huntorf, Germany [14] and the other is in McIntosh, Alabama-USA [15]. The CAES plant Huntorf, Germany was the first commercial set up in the 1970s, initially with a 290 MW capacity which was later expanded to 321 MW in

2006. The second commercial CAES plant was built in McIntosh, Alabama in 1991 for a 110 MW capacity. The cycle efficiency of the McIntosh plant is 54% which considerably higher than cycle efficiency of Huntorf plant (42%). This is due to the application of recuperator in McIntosh plant which is completely omitted in the Huntorf plant [16]. For the air storage system, both the plants use underground salt caverns which provide a large storage volume for the high energy storage capacity.

Large-scale compressed air energy storage would become an economical and viable option of energy storage with a high roundtrip efficiency. With the current state of technology in existing

CAES systems, there is still no off-the-shelf machinery available that is suitable for highly efficient

CAES plants. Compressor and expander are the key components of the CAES system in determining roundtrip efficiency. Significant improvement in compressor/expander technology is needed to attain an efficient CAES system. Furthermore, geological restrictions also apply in exploring suitable sites for underground CAES which can be addressed to a certain degree with ocean compressed air energy storage system.

1.2. Ocean Compressed Air Energy Storage (OCAES)

Ocean compressed air energy storage (OCAES) is a promising utility-scale energy storage system [17]. In OCAES, compressed air is stored under the ocean water. A schematic of the

OCAES system is shown in Figure 1.3. In OCAES, energy is stored in the form of compressed air in an underwater storage device. This storage device can be a receiver vessel, vented to sea water, mounted on the seafloor and connected to the compressed air source via pipeline [18].

Alternatively, flexible fabric energy bag architecture can be used for underwater air storage [19].

OCAES uses hydrostatic pressure in the deep ocean in order to store compressed air at a constant high pressure. Due to the constant air pressure in OCAES, significant improvement in the useful isothermal energy of compressed air has been shown over the land-based compressed air energy storage [20]. For energy recovery, compressed air is passed through an expander to generate electricity. Development of an efficient compressor and expander for OCAES application would lead to a highly efficient large-scale energy storage system.

Figure 1.3: Conceptual schematic of Ocean Compressed Air Energy Storage (OCAES) [18].

1.3. Research Objectives

The primary objective of this research is to facilitate technological advancements of Ocean

Compressed Air Energy Storage (OCAES). Development of an efficient OCAES configuration is crucial in this regard. Therefore, energy and exergy analysis of various OCAES concepts is performed first to identify an efficient system configuration and potential of efficiency improvements with the use of advanced technology. As compressor is one of the key components of the OCAES system, development of an efficient compressor is naturally beneficial for efficiency improvement of OCAES system.

Development of an efficient compressor is contingent on the realization of a near-isothermal compression process. Liquid piston compressor can be effectively used to attain a near-isothermal compressor. Understanding of heat transfer characteristics during compression is crucial for the realization of the near-isothermal compressor using liquid piston. Therefore, a thorough investigation of heat transfer in the liquid piston compressor is performed experimentally.

Furthermore, various heat transfer enhancement techniques are explored in liquid piston compressor for efficiency improvement. Specifically, heat transfer enhancement techniques using water spray injection, aqueous foam, and metal wire mesh are studied experimentally in a liquid piston compressor. Isothermal efficiency of the compression process with the use of these techniques is evaluated to identify the potential of these methods in achieving an efficient near- isothermal compression.

Finally, the efficiency of an Isothermal OCAES with the use of various heat transfer enhancement techniques in the liquid piston is evaluated. The potential of liquid piston technology to achieve an efficient OCAES system is explored in this study. Overall, this research aims to develop an efficient compressor for (ocean) compressed air energy storage applications.

CHAPTER 2: Energy and Exergy Analysis of OCAES Concepts

Abstract: Optimal utilization of renewable energy resources need energy storage capability in integration with the electric grid. Ocean compressed air energy storage (OCAES) can provide a promising large-scale energy storage. In OCAES, energy is stored in the form of compressed air under the ocean. Underwater energy storage results in a constant-pressure storage system which has potential to show high efficiency compared to constant-volume energy storage. Various

OCAES concepts viz. - diabatic, adiabatic and isothermal OCAES are possible based on the handling of heat in the system. These OCAES concepts are assessed using energy and exergy analysis in this chapter. The exergy efficiency of individual components, exergy flow and overall efficiencies of diabatic, adiabatic, and isothermal OCAES configurations are presented. Roundtrip efficiency of liquid piston based OCAES is also investigated. Results show that adiabatic OCAES shows improved efficiency over diabatic OCAES by storing thermal exergy in thermal energy storage and isothermal OCAES shows significantly higher efficiency over adiabatic and diabatic

OCAES. Furthermore, liquid piston based OCAES is estimated to show roundtrip efficiency of about 45% and significant efficiency improvement in liquid piston compressor/expander is needed to realize an efficient isothermal OCAES system.

2.1. Introduction

Electricity generation from renewable energy sources plays important role in reducing dependence on fossil fuels and in curtailing greenhouse gas emissions. However, renewable energy sources such as wind, solar, tidal, wave etc. are sporadic in nature. The variability of power from the renewable energy sources makes it hard to integrate with the electric grid [21]. Utility-scale energy storage systems are needed to improve the utilization of renewable energy resources in electric grid [11]. Compressed air energy storage (CAES) system is a reliable large-scale energy storage method with relatively low specific investment cost [13]. In CAES system, intermittent energy is used to compress the atmospheric air to the high pressure and compressed air is stored in the high-pressure reservoir. When electricity demand is high, the stored high pressurized air is expanded through the turbine to generate electricity. Two large-scale CAES plants are in operation, one is in Huntorf, Germany [14] and the other is in McIntosh, Alabama-USA [15]. In both the plants, compressed air is stored in an underground cavern. However, these underground caverns are constant volume air storage reservoirs. In constant volume air storage systems, charging and discharging processes results in pressure variation. These varying conditions can result in low efficiencies of compression and expansion due to deviation from the designed points [22]. This can be avoided by utilizing ocean depth for storage of the compressed air in which high-pressure environment under the water can be effectively used for creating constant pressure storage system

[23]. Such an ocean compressed air storage (OCAES) system can effectively integrate multiple energy sources located offshore with high system efficiency.

Various types OCAES configurations are possible based on the idealized thermodynamic process of compression and expansion of air. These thermodynamic processes are identified based on how heat is handled during compression and expansion processes. The three major types are-

Diabatic OCAES, Adiabatic OCAES, and Isothermal OCAES. These types are discussed in the

next section with more details. Roundtrip efficiency (also called end-to-end efficiency) is an important parameter to assess the efficacy of an energy storage system. As processes in the OCAES system are accompanied by heat and work transfer, it is very difficult to understand the efficiency of an OCAES system using first law of thermodynamics. This is because the first law of thermodynamics deals with heat and work equally. Therefore, roundtrip efficiency based on exergy analysis which is based on the second law of thermodynamics would be beneficial in better understanding the characteristics of the different types of OCAES systems.

Various studies have investigated different types of CAES configurations based on energy and exergy analysis. Kim et al. reviewed the main drawbacks of the existing CAES systems and presented energy and exergy analysis of various innovative CAES concepts [24]. They investigated concepts like adiabatic CAES, isothermal CAES, micro-CAES combined with air-cycle heating and cooling, and constant-pressure CAES combined with pumped hydro storage. Their analysis illustrated that drawbacks of existing CAES systems can be addressed by employing innovative

CAES concepts. Bagdanavicius et al. investigated the potential for using heat generated during compression stage of CAES with a district energy system [25]. Exergy and exergoeconomic analysis of CAES and CAES with thermal storage were performed by them. Their analysis showed that utilization of waste heat increases energy efficiency from 48% for the CAES to almost 86% for CAES with thermal storage. They also observed that highest exergy destruction occurs in the heat exchangers during compression stage.

Different adiabatic CAES configurations were simulated and analyzed by Hartmann et al. [26] using energy balance. Polytropic CAES with one, two and three stages and an isentropic CAES were considered. They observed that high value of 70% efficiency is only achieved for isentropic configuration and efficiency of the polytropic configuration is about 60%. Their analysis also

suggested that developing high-temperature thermal storage (>600 oC) and temperature resistant materials for compressors are key elements in achieving higher efficiency. Grazzini et al. presented a thermodynamic analysis of multistage adiabatic CAES [27]. They proposed a comprehensive set of criteria for the design of adiabatic CAES based on a detailed thermodynamic analysis of the design parameters and influence on system efficiency, with attention to heat transfer devices. An exergy analysis was presented by Tessier et al. on adiabatic CAES system utilizing a cascade of phase change materials for waste heat storage and recovery [28]. Incorporation of phase change materials predicted to show a 15% increased efficiencies of storage and recovery over the current design. An experimental study of CAES system with thermal energy storage by Wang et al. has shown a mere 22.6% roundtrip efficiency [29]. A recent detailed review on CAES has been presented in [30].

The existing CAES plants in Huntorf and McIntosh are of a diabatic type and show roundtrip efficiency of 42% and 54% respectively. The Huntorf plant was primarily designed to provide reserve power and blackstart capability where high efficiency is of minor importance. The

McIntosh plant was designed to perform load shifting on a weekly basis, which requires the cycle efficiency to be as high as possible. The McIntosh plant could achieve considerably higher efficiency over Huntorf plant using a recuperator to reduce exergy loss. The concept of adiabatic

CAES using Thermal Energy Storage (TES) was also considered during development of these plants, however, diabatic CAES is preferred at that time due to technical and economic advantages

[30].

Adiabatic CAES needs a high-temperature TES withstanding the combination of thermal and mechanical stresses which requires special material and complex system engineering. Also, considerable engineering effort is needed to design an electrically driven compressor that operates

at the high outlet temperature essential for adiabatic operation. Recent developments in TES have shown good prospects in achieving adiabatic CAES in practice [31]. An adiabatic CAES is under development under the project name ‘ADELE-ING’ which could show roundtrip efficiency up to

70% [32]. Another approach in achieving high efficiency is through isothermal CAES. Technically, it was very difficult to achieve isothermal operation at high power density. However, recent developments in liquid piston compressor [33] and heat transfer enhancement techniques in the liquid piston [34-36] could result in near-isothermal compression and expansion at high power density. Thermodynamic and economic review of CAES by Rogers et al. [37] indicates that efficiencies of advanced adiabatic CAES and isothermal CAES have been increased by over 30% and energy storage densities have been improved by a factor of 5 using near-surface piping.

A multi-level underwater CAES system integrated with battery pack is proposed by Wang et al [38]. Their thermodynamic analysis shows that round-trip exergy efficiency of the multi-level underwater CAES varies from 62% to 81% in different working mode. Advanced exergy analysis of an underwater CAES by Wang et al. indicates exergy efficiency of 53.6% under real conditions with theoretical maximum exergy efficiency of 84.3% [39]. Clearly, there is a great potential for performance improvement of underwater CAES. A study by Cheung et al. indicates that pipe diameter, turbine, air compressor and air storage depth have the greatest influence on system performance of underwater CAES [40]. Multi-objective optimization of an underwater CAES with objectives of maximizing roundtrip efficiency and operating profit, and minimizing cost rate is performed by Cheung et al. using genetic algorithm [41]. Their analysis indicated roundtrip efficiency of 68.5% and operating profit of $53.5 per cycle for the preferred system designs.

Based on earlier studies on CAES, it can be observed that there could be a significant variation in efficiencies of various OCAES configurations. Comparative analysis of different OCAES

systems would help in understanding these better. Preliminary studies of exergy analysis for various OCAES configurations and end-to-end efficiency of liquid piston based OCAES have been presented earlier in [42, 43]. In this chapter, detailed analysis of various OCAES concepts using energy and exergy analysis is presented. This would help in assessing improvement areas in achieving higher roundtrip efficiency with OCAES.

Investment costs associated with different types of OCAES would also vary as the technology used in these configurations differs considerably. The compressor and expander in the diabatic

OCAES are mature technologies whereas the same in the adiabatic and isothermal OCAES are still in the development stages. Also, the cost of Thermal Energy Storage (TES) used in adiabatic

OCAES differs significantly based on the kind of TES system used. Broadly, there are three types of TES systems- sensible heat TES, latent heat TES and thermo-chemical TES. In general, latent heat TES and thermo-chemical TES are more expensive than sensible heat TES, however, former could be economically viable with a high number of operating cycles [31]. Although the cost of different OCAES configurations might differ significantly, this study only focuses on efficiency aspect without accounting any cost difference. However, an economic assessment of these OCAES configurations would be necessary before investment decisions. This study could provide a framework for an economic assessment of different OCAES by monetizing efficiencies incorporating cost difference.

2.2. OCAES Configurations

OCAES configurations can be broadly distinguished depending on the targeted idealized process of compression and expansion of air. It is decided based on how heat is handled during compression and prior to expansion of the air. Three major OCAES configurations would be -

Diabatic OCAES, Adiabatic OCAES, and Isothermal OCAES. These system configurations are discussed in this section.

2.2.1. Diabatic OCAES

In the diabatic OCAES system, in energy storage mode, air is compressed using conventional compressors and cooled to the surrounding temperature before sending it to the storage system.

Compression process increases the temperature of air due to the heat of compression which is dissipated before sending air to the storage device. This results in loss of thermal energy of compression due to cooling. In energy recovery mode, the air from the storage is heated using fuel and then passed through the expander to generate electricity.

Figure 2.1: Schematic of diabatic OCAES The schematic of Diabatic OCAES is shown in Figure 2.1. Process 1-2 represents compression of atmospheric air using air compressor run using electric motor operating on excess electric energy. The motor efficiency and losses in the compressor would result in loss of energy/exergy during this process. Compressed air from the compressor is then passed through the cooler (process

2-3) before sending it to the underwater air storage system. A significant amount of heat energy

(thermal exergy) is lost in the cooler. Process 3-4 indicates charging and discharging from the air storage system. Mechanical exergy (energy in pressure form) in the high-pressure air is stored in the underground storage. There can be a small amount of loss of energy/exergy due to leakage and pressure drop in the storage system. In process 4-5, high-pressure air is heated using external heat input (thermal exergy) to increase expansion work. The process 5-6 is the expansion process in which mechanical exergy in the form of electrical energy is delivered. However, process 5-6 involves loss of energy/exergy due to inefficiencies in expansion process and also loss of energy/exergy from the exhaust gas.

2.2.2. Adiabatic OCAES

The construction of adiabatic system would require a compressor design delivering higher temperature at the outlet of compression, a reliable TES system to store thermal energy at high temperature and an expander design operating at high inlet air temperature with broad operation range. These components installed and connected with pipelines carrying air with the layout shown in Figure 2.2 would result in the adiabatic OCAES system.

Figure 2.2: Schematic of adiabatic OCAES

It can be seen that cooler and heater in the diabatic OCAES are replaced with thermal energy storage (TES) in the adiabatic OCAES configuration. The diabatic OCAES uses fuel in the heater, therefore, it cannot be considered as a pure storage system and is actually a combination of storage and power plant. This can be overcome in adiabatic OCAES which uses TES to store heat from the compressed air before sending it to the air storage. The stored heat in TES is used to heat the air before passing it to the expander. This eliminates the need for cooler and heater in the adiabatic system as TES works as both. Therefore, thermal energy and thermal exergy losses in the cooler and thermal heat input in the heater of diabatic OCAES are completely eliminated in the adiabatic

OCAES. However, TES involves some energy/exergy losses which result in added inefficiencies in adiabatic OCAES.

2.2.3. Isothermal OCAES

Isothermal OCAES would eliminate the need for fuel and high-temperature thermal energy storage. This can be done by isothermal compression and expansion process which minimizes compression work and maximizes expansion work. Figure 2.3 shows a schematic of isothermal

OCAES system. The compressor in the isothermal-OCAES dissipates heat energy during compression process resulting in the conversion of electrical energy into mechanical exergy form in the compressed air. Ideal isothermal compression does not add any thermal exergy in the compressed air, therefore, loss of exergy is totally avoided. Similarly, in the ideal isothermal expansion, mechanical exergy from the compressed air is completely converted into electrical energy.

Figure 2.3: Schematic of isothermal OCAES

2.2.4. Liquid Piston based OCAES

It is very difficult to achieve isothermal compression and expansion using conventional compressors and expansion devices as conventional compressors and expanders work at high speed with the nearly adiabatic process. Special types of compressors and expanders are required to achieve isothermal OCAES in reality. Liquid piston compressor can be used to achieve near- isothermal compression and expansion operation. In the liquid piston compressor, a column of liquid (usually water) is utilized to compress a gas in the fixed volume chamber. A hydraulic pump is used to generate the flow of the liquid for the liquid pistons. The liquid flow in and out of compression chamber is controlled with valves. As a liquid can conform to an irregular chamber volume, the surface area to volume ratio in the gas chamber can be maximized using a liquid piston. This results in increasing the heat transfer during the gas compression/expansion which facilitates near-isothermal operation [33].

Figure 2.4: Schematic of a liquid piston based Isothermal OCAES system.

A typical liquid piston based isothermal OCAES would have electric motor/generator, hydraulic pump/motor, liquid piston compressor/expander, air cooler/heater, pipelines connecting various components, control valves, and underwater air storage. Figure 2. 4 shows a schematic of a liquid piston based OCAES system. Although liquid piston compression is efficient compared to the existing compressors technologies, the added components like hydraulic pump/motor and hydraulic lines have some inefficiencies which would affect the overall efficiency of OCAES system.

2.3. Energy and Exergy Analysis

Inefficiencies in various components of the OCAES contribute to the loss of energy in the storage system. Energy efficiency of a component is the ratio of energy out from the component to energy into the component. In energy analysis, energy efficiencies of various components in the

OCAES are modeled and used to evaluate the energy efficiency of overall OCAES system.

The exergy transfer to the system can happen by work, heat, and mass transfer. The exergy transfer by heat is given by (2-1).

푇 퐸̇ = ∫ 1 − 0 훿푄̇ (2-1) 푞 푇

where T is temperature, 푄̇ is heat transfer rate and subscript 0 indicates properties at environmental conditions [44].

Exergy transfer by mass flow (푚̇ ) is given by (2-2).

퐸̇푚 = 푚̇ 푒 (2-2)

where specific exergy (e) of an ideal gas is given by (2-3).

푇 푃 푒 = 퐶푝 (푇 − 푇0) − 푇0 [퐶푝 ln ( ) − 푅 ln ( )] (2-3) 푇0 푃0

where 퐶푝 is specific heat at constant pressure, R is the specific gas constant and P is pressure.

The above specific exergy consists of two parts- mechanical exergy and thermal exergy. The mechanical exergy is associated with the system pressure and is the exergy change when the system is brought to the state [T0, P0] from the state [T0, P]. The thermal exergy is associated with the system temperature and is the exergy change when the system is brought to the state [T0, P] from the state [T, P]. Mechanical and thermal exergies are given by (2-4) and (2-5) respectively.

푀 푃 푒 = 푅푇0 ln ( ) (2-4) 푃0

푇 푇 푒 = 퐶푝 (푇 − 푇0 − 푇0 ln ( )) (2-5) 푇0 where superscripts M and T indicate mechanical and thermal parts respectively.

Individual components in the OCAES system can be analyzed based on exergy analysis.

Exergy efficiency of a component is given by (2-6).

− 퐸̇푐표푚 휀푐표푚 = + (2-6) 퐸̇푐표푚

where 휀 denotes exergy efficiency and subscripts indicates component.

Energy efficiency and exergy efficiency of individual components in OCAES are discussed the following subsections.

2.3.1. Electric Motor and Generator

Electric motor/generator has mechanical and electrical losses during its operation. Energy efficiency of electric motor/generator (M/G) is the ratio of power output from M/G to the power input to M/G as calculated using (2-7).

푃푛× 퐿표푎푑 휂푀/퐺 = (2-7) 푃𝑖

As electric motor/generator deals with work transfer (electrical energy and shaft work) only, exergy efficiency of electric motor/generator is its energy efficiency.

2.3.2. Hydraulic Pump/Motor

Energy efficiency of hydraulic pump/motor depends on its displacement, speed of operation and the pressure differential between inlet and outlet. The overall efficiency of a hydraulic pump for a particular power input is given by (2-8).

퐷×푁×∆푝 휂퐻푃 = (2-8) 푃𝑖푛

Exergy efficiency of hydraulic pump/motor is also same as its energy efficiency because it deals only with work transfer.

2.3.3. Compressor

̇ + The exergy transfer to the compressor (퐸퐶 ) is in the form of shaft work from the motor whereas

− exergy transfer from the compressor (퐸̇퐶 ) is due to air mass transfer from the compressor at high pressure and temperature. There are exergy losses in the compressor due to mechanical losses.

Isentropic efficiency [45] and mechanical efficiency of the compressor can be used to evaluate exergy efficiency of compressor.

In case of isothermal OCAES, liquid piston compressor efficiency is defined as the ratio of stored energy to work input. Storage energy is the amount of work extracted from the isothermal expansion of compressed air to the atmospheric pressure. Work input consists of compression work, cooling work and friction work. Atmospheric air compressed to high-pressure results in increasing temperature. This compressed air is cooled to initial temperature to maintain storage pressure [46]. This adds cooling work. In case of liquid pistons, friction work is comparatively small (unless diameter is too small) and can be neglected [33]. Liquid piston compressor efficiency

(ηC) after neglecting viscous friction is given by (2-9).

퐸푆푡표푟푎푔푒 ⏞ 1 ln(푃푟)+ −1 P푟 휂퐶 = 푛−1 (2-9) 푛 −1 −1 푃 −1 1 푟 +푃 푛 −1+(푃 −1)(P 푛 − ) ⏟푛 − 1 푟 푟 r 푃 ⏟ 푟 푊푐표푚푝푟푒푠푠𝑖표푛 푊퐶표표푙𝑖푛푔 where Pr is the pressure ratio (Ratio of storage pressure to the atmospheric pressure) and n is a polytropic index of compression. Storage pressure (hence Pr) depends on the underwater air storage depth and n depends on the magnitude of heat transfer in liquid piston compressor.

2.3.4. Cooler

The compressed air from the compressor contains both mechanical and thermal exergy. In the cooler, the compressed air is cooled to the atmospheric temperature at a constant pressure by dissipating thermal exergy of the compressed air to cooling media. The output compressed air from the cooler would contain only mechanical exergy. Therefore, exergy efficiency of the cooler neglecting pressure losses in the cooler is given by (2-10).

푃푐표 푀 푅푇0ln( ) 푚̇ 푒 푃0 휀푐표 = 푀 푇 = (2-10) 푚̇ (푒 +푒 ) 푃푐표 푇푐표 푅푇0ln( ) + 퐶푝(푇푐표−푇0−푇0ln( )) 푃0 푇0

where 푃푐표 and 푇푐표 are pressure and temperature of compressed air at inlet of the cooler respectively.

2.3.5. Air Pipelines Connecting Various Components

Energy/exergy loss inside the pipeline carrying air is equal to pressure drop times the flow rate.

Pressure drop for steady, fully developed, incompressible flow in the pipe can be calculated using

Darcy –Weisbach equation [47].

2.3.6. Thermal Energy Storage (TES)

In adiabatic OCAES, high-temperature high-pressure compressed air is passed through the

TES to store thermal exergy of compressed air in the TES. This stored thermal energy is used to increase thermal exergy of compressed air before sending it through the expander. The thermal and pressure losses in the TES result in the loss of energy/exergy. The exergy efficiency of TES is given by (2-11).

표푢푡 푃푇퐸푆 푅푇0ln( ) 푃0 휀푇퐸푆 = (2-11) 𝑖푛 𝑖푛 푃푇퐸푆 𝑖푛 푇푇퐸푆 푅푇0ln( ) + 퐶푝(푇 −푇0−푇0ln( )) 푃0 푇퐸푆 푇0

𝑖푛 𝑖푛 표푢푡 where 푃푇퐸푆 and 푇푇퐸푆 are pressure and temperature of compressed air at inlet of the TES. 푃푇퐸푆 and

표푢푡 푇푇퐸푆 are pressure and temperature of compressed air at outlet of the TES respectively.

2.3.7. Air Storage

Leakage and pressure losses in the underwater air storage system result in energy/exergy losses. Leakage per unit volume per unit time can be calculated by measuring pressure drop in an isolated air storage system given by equation (2-12) [48].

휌푠 (∆푃)푆 퐿̇푆 = (2-12) 푡푒 푃푆

where 퐿푆̇ is the leakage rate (kg/hr.m3), ρs is the density of air at storage pressure and temperature, (ΔP)S is the pressure drop in the isolated air storage system in time te and PS is the storage pressure.

The energy/exergy efficiency of an air storage system is given by equation (2-13) [43].

푡0×퐿̇ 푆 휀푆 = 1 − (2-13) 휌푠

where to is the operation time of the OCAES.

2.3.8. Heater

In the diabatic OCAES, external fuel is used to heat the air. The heat (thermal exergy) added in the heater increases exergy of the air. Exergy efficiency of a heater neglecting pressure losses in the heater and considering the constant rate of heat transfer is given by (2-14).

푇 푃 퐶 (푇 −푇 −푇 ln( 퐻)) + 푅푇 ln( 퐻,표푢푡) 푝 퐻 0 0 푇 0 푃 휀 = 0 0 (2-14) 퐻 푇0 푃퐻,𝑖푛 푄푠(1− ) + 푅푇0ln( ) 푇푠 푃0

where 푃퐻,𝑖푛 and 푃퐻,표푢푡 are pressures at inlet and outlet of the heater respectively, 푇퐻 is the temperature of air at heater output, 푇푆 is the temperature of heat source and 푄푆 is the heat transfer per unit mass of air.

2.3.9. Expander

+ The exergy transfer to the expander (퐸̇퐸푥) is by compressed air inlet whereas exergy transfer

− from the expander (퐸̇퐸푥) is in the form of shaft work delivered to the generator. Similar to compressor, exergy efficiency of expander can be calculated using isentropic efficiency [45] and mechanical efficiency of the expander.

In case of isothermal OCAES using a liquid piston, liquid piston expansion efficiency (ηE) for polytropic expansion index n is given by (2-15).

푊퐸푥푝푎푛푠𝑖표푛 ⏞ 푛 − 1 1 푛 푛−1 1−( ) 1 1 푃푟 − ( ) 푛 + 푛−1 푃푟 푃푟 휂퐸 = 1 (2-15) ln(푃푟)+ −1 ⏟ P 푟 퐸푆푡표푟푎푔푒

2. 4. Numerical Simulations

Different types of OCAES systems are modeled based on energy and exergy analysis of individual components in the OCAES system. Storage pressure of 10 bar gauge (100m ocean depth) is considered for analysis. Various components specifications designed for maximum power capacity of 0.5 MW with 2 MWh energy storage were used [49]. Efficiencies of motor/generator and hydraulic pump/motor are considered from the industry standards [24, 50]. Pipelines connecting cooler to air storage and air storage to the heater are considered with 1000m in length,

0.2m in diameter and of 15μm surface roughness [51]. For air storage, the leakage rate of 0.01 kg/hr.m3 [52] and operation time of 8 hours were assumed [53].

Uncertainty analysis is performed using Monte-Carlo Simulations (100000 runs) to estimate mean and confidence interval values of energy efficiency and exergy efficiency. Stochastic assignments considered are given in Table 2.1.

All the simulations were performed considering 1 atm and 20 oC environmental conditions. In all the configurations, single stage compression and single stage expansion were considered.

Adiabatic and isothermal OCAES systems are considered without the use of fuel. In the diabatic configuration, heat source temperature of 1500 oC is considered. The amount of heat transfer from the heat source is evaluated to achieve inlet conditions to expander with 42 bar and 550 oC. These values are referred from HP turbine operating conditions of Huntorf Plant [54]. In adiabatic

OCAES configuration, TES storage temperature of 327 oC is considered [55] and inlet air conditions to the expander of 10 bar and 327 oC are considered. In isothermal OCAES configuration, liquid piston based compression and expansion are considered.

To simplify the thermodynamic model, all the analysis is performed for steady state operation of the system. Also, the kinetic and potential energy of the fluids are assumed to be negligible and

the air is considered as an ideal gas [39]. For these system considerations, the thermodynamic properties and mass flow rate of air at different state points of the system are evaluated. Those are listed in Table 2.2, Table 2.3 and Table 2.4 for diabatic, adiabatic and Isothermal OCAES respectively. Finally, different types of OCAES systems are compared using energy/exergy flow, energy efficiency, and exergy efficiency evaluations.

Table 2.1: Stochastic Assignments in Monte Carlo Simulation

Mean / Max Standard Deviationa Variable Value [μ] or Max/Min value Distribution (%) (%)

εM/G [50] 96 0.5 Normal

εHP/HM [24] 93 1 Normal

ηC,isen 85 2 Normal

ηC,mech 95 1 Normal

푃𝑖푛 − 훥푃 Max= μ, ηP Triangular 푃𝑖푛 Min= μ-0.5

εTES 80 2 Normal Max= μ + 0.5 εS Using (13) Triangular Min= μ - 0.5

εH 95 1 Normal

ηEx,isen 85 1 Normal

ηEx,mech 95 1 Normal aFor Normal distribution

Table 2.2: Thermodynamic properties and mass flow rates of air at different state points for Diabatic OCAES system (See Figure 1 for state points) State Point Pressure (kPa) Temperature (K) Mass flow rate (kg/s) 1 101.3 293 1.33 2 1119.6 633 1.33 3 1114.6 293 1.33 4 1109.6 293 1.32 5 4200.0 823 1.32 6 101.3 364 1.32

Table 2.3: Thermodynamic properties and mass flow rates of air at different state points for Adiabatic OCAES system (See Figure 2 for state points) State Point Pressure (kPa) Temperature (K) Mass flow rate (kg/s) 1 101.3 293 1.33 2 1119.6 633 1.33 3 1114.6 293 1.33 4 1109.6 293 1.32 5 1104.6 600 1.32 6 101.3 354 1.32

Table 2.4: Thermodynamic properties and mass flow rates of air at different state points for Isothermal OCAES system (See Figure 3 for state points) State Point Pressure (kPa) Temperature (K) Mass flow rate (kg/s) 1 101.3 293 2.10 2 1119.6 300 2.10 3 1114.6 293 2.08 4 101.3 286 2.08

2.5. Results and Discussion

Exergy flow in various OCAES configurations is shown in figures 2.5, 2.6, and 2.7 respectively for diabatic, adiabatic, and isothermal OCAES. Each box in these figures represents a component in the OCAES system. The height of the box represents qualitative exergy flow to the component.

The arrows indicate the exergy flow direction and the amount of exergy flow is mentioned on each arrow. The arrows pointing away from the boxes indicates exergy loss to the environment. The exergy efficiencies of the individual components are mentioned in the boxes. The input power of

500kW is considered for the analysis.

2.5.1. Diabatic OCAES

Exergy flow in the diabatic OCAES is shown presented in Figure 2.5. Inefficiencies in electric motor result in exergy loss of 20kW. It is observed that a significant amount of exergy is lost from the cooler to the surrounding. Losses in the pipelines and storage are very small compared to other losses. The addition of heat energy to the heater from the heat source adds exergy to the system.

Although energy input from the heat source to the heater is 443 kW, the exergy value of this heat is only about 370 kW. This addition of exergy in heater compensates the loss of exergy in the cooler to achieve the same level of power output. The expander is the next exergy inefficient component after the cooler in the diabatic system. Inlet air to the expander contains exergy in both thermal and mechanical forms. Irreversibility in expansion process results in exhaust air with a significant amount of thermal exergy, which results in higher exergy loss in the expander. The recuperator is not considered in the current configuration. In recuperative process waste heat from the exhaust of the expander can be used to heat expander inlet air. This would reduce exergy burden from the heat source and hence improve overall exergy efficiency of OCAES system.

The overall exergy efficiency of diabatic OCAES is 55% whereas energy efficiency is 50%.

As diabatic OCAES has fuel input in the heater system, it is not a pure energy storage system but the combination of energy storage and power plant. Therefore, exergy efficiency is a good measure of diabatic OCAES for comparison with other systems.

Figure 2.5: Exergy flow in diabatic OCAES

2.5.2. Adiabatic OCAES

The thermal exergy lost from the cooler in the diabatic OCAES is stored in the adiabatic

OCAES using TES which can improve exergy efficiency of adiabatic OCAES significantly over diabatic OCAES. Figure 2.6 shows exergy flow in adiabatic OCAES. Exergy loss in the cooler of diabatic OCAES can be avoided by use of TES which stores a significant amount of thermal energy. TES supplies heat to the air before the expander thus increasing the exergy potential of air.

With the use of TES, the external heat source is removed in the adiabatic OCAES configuration.

However, inefficiencies in TES account for exergy loss which contribute in reduction energy output. Comparison of diabatic and adiabatic exergy flow reveals that adiabatic CAES gives less exergy output (electric energy) from the generator. This is because the fuel source used in the diabatic OCAES allows the expander to be operated with higher power capacity.

Overall exergy efficiency of adiabatic OCAES is 60% which is 5% higher than that of diabatic

OCAES. This improvement is due to reuse of thermal exergy of the air using TES. Improvement in TES efficiency from current consideration of 80% would further improve the efficiency of adiabatic OCAES. As external fuel is not used in adiabatic OCAES, overall energy efficiency of adiabatic OCAES is same as overall exergy efficiency. Careful observation of exergy losses in adiabatic OCAES shows that losses in compressor and expander are major contributors of inefficiencies in adiabatic OCAES.

Figure 2.6: Exergy flow in adiabatic OCAES

2.5.3. Isothermal OCAES

The need of TES and fuel source is eliminated in the isothermal OCAES. Exergy flow in the isothermal OCAES is shown in Figure 2.7. Liquid piston based compressor and expander requires a hydraulic pump and a hydraulic motor as added components in the isothermal OCAES.

Inefficiencies of these components would contribute to the exergy loss in the system. It can be observed in Figure 2.7 that hydraulic pump/motor show high exergy losses in comparison with losses in other components in Isothermal OCAES. However, the use of liquid piston in conjunction with hydraulic pump and motor has the potential to improve efficiencies of the compressor and expander significantly. This results in a reduction of exergy losses in compressor and expander.

Also, the absence of TES and heater eliminates losses associated with those which helps in improving the overall efficiency of the system. Overall exergy efficiency of the isothermal OCAES is about 70% which is significantly higher than diabatic and adiabatic OCAES.

Figure 2.7: Exergy flow in isothermal OCAES

The overall exergy efficiencies of all the three configurations with 95% confidence interval bounds are shown in Figure 2.8 for comparison. The uncertainties in various assumptions show about 3-4% variation in exergy efficiencies. Clearly, isothermal OCAES is the most efficient and diabatic is the least efficient among three configurations considered based on exergy analysis.

Energy efficiency of diabatic OCAES is about 50% whereas that of adiabatic and isothermal

OCAES is same as their exergy efficiencies. Energy efficiency might not be a reliable comparative parameter as it would undervalue the efficiency of the diabatic system.

Figure 2.8: Overall exergy efficiency of different types of OCAES.

2.5.4. Liquid Piston based OCAES

Although isothermal OCAES shows high exergy efficiency, such a high level of efficiency is contingent upon near-isothermal compression and expansion. Liquid piston compressor is experimentally tested to investigate its effectiveness in achieving near-isothermal compression.

Figure 2.9 shows an experimental setup of liquid piston compressor. The compression chamber

was divided into four parallel copper pipes, each having an inner diameter of 76 mm and length of

760 mm. Two compression chambers were used in the experimental setup to ensure continuous production of compressed air. The compression chambers were enclosed in a plastic cylinder filled with water to maintain the temperature of the outer copper wall a constant. A hydraulic pump was used to alternatively drive water from one compression chamber to the other. The pump delivers a constant flow rate of 10 gpm at a maximum pressure of 13.1 bar gauge (190 psi). A K-type thermocouple of diameter 0.0508 mm (0.002 in) and a pressure sensor were installed at the top of each compression chamber as indicated in Figure 2.9. Experiments were performed with a pressure ratio of 6 and the stroke time of 10 s.

The liquid piston compressor and expansion efficiency can be calculated using the polytropic index of compression and expansion in equations (2-9) and (2-15) respectively. The polytropic index is calculated from the P-T curve (Pressure-Temperature curve) considering P(1-n) Tn =

Constant relation.

Figure 2.9: Experimental setup of liquid piston compressor.

Roundtrip efficiencies of liquid piston based OCAES system with various polytropic indexes of compression/expansion are shown in Figure 2.10. Uncertainty bars represent 95% confidence interval valves. It can be observed that estimated mean value of end-to-end efficiency increases from 24% to 72% with a decrease in the polytropic index of compression from 1.4 (adiabatic process) to 1 (isothermal process). This clearly indicates liquid piston compression and expansion efficiency has a major influence on the end-to-end efficiency. For a polytropic index of 1.14 observed with an experimental liquid piston, a roundtrip efficiency of 45% was shown. Noticeably, this efficiency value is way below efficiency level of isothermal OCAES. However, the liquid piston setup used in the experimental investigation did not involve any heat transfer enhancement mechanism to abate temperature rise. Various designs of liquid pistons leading to a lower polytropic index of compression/expansion would increase compression/expansion efficiency and therefore improve roundtrip efficiency for the OCAES system.

Figure 2.10: Roundtrip efficiency of liquid piston based OCAES for different polytropic indices.

2.6. Conclusions

In pursuit of developing an efficient economical large-scale energy storage, ocean compressed air energy storage can play an important role. Various OCAES concepts are possible namely- diabatic, adiabatic and isothermal OCAES. Energy and exergy analysis of these concepts is performed for OCAES system of the maximum power capacity of 0.5 MW and 2MWh energy storage with storage pressure of 10 bar (100m of ocean depth). Analytical models for energy and exergy analysis of various components in OCAES are presented. The exergy flow, energy efficiency and exergy efficiency of various OCAES concepts are analyzed for comparative assessment.

The analysis shows that energy efficiency of diabatic OCAES is about 50% whereas its exergy efficiency is about 55%. Clearly, energy efficiency undervalues efficiency of diabatic OCAES, therefore, exergy efficiency would be a good measure of efficiency for comparison with other storage concepts. Adiabatic OCAES shows about 5% improvement in exergy efficiency over diabatic OCAES. Isothermal OCAES shows significantly higher efficiency over diabatic and adiabatic OCAES. Analysis of liquid piston based OCAES with the use of experimental liquid piston compressor indicated roundtrip efficiency of 45%. With heat transfer enhancement in the liquid piston, significant improvement in roundtrip efficiency of OCAES is possible. Overall, liquid piston based OCAES with the use of heat transfer enhancement has potential to show significantly higher efficiency than existing compressed air energy storage plants.

CHAPTER 3: Heat Transfer in Liquid Piston Compressor

Abstract: The use of liquid pistons is a promising approach for attaining efficient near- isothermal compression. One of the key factors affecting the efficiency of a liquid piston compressor is heat transfer. Understanding the heat transfer mechanism during compression is crucial for the design and development of an efficient liquid piston compressor. In this chapter, heat transfer in the liquid piston compressor is studied experimentally for air compression. An analytical model is presented based on a thermal resistance circuit. Experiments are performed using compression chambers of different materials for a compression ratio of 2.05-2.35 with various stroke times of compression. It is observed that the rate of heat transfer increases with faster stroke time of compression. However, a faster compression process requires a higher compression work and results in a higher air temperature. The convective heat transfer coefficient of air decreases rapidly as compression proceeds and approaches a steady value towards the end of compression. Thermal resistance analysis for compression with different chamber materials indicates that convective thermal resistance of air has significant contribution in the total thermal resistance. During the initial phase of compression, the high conductivity of the chamber material helps improve the overall heat transfer coefficient; however, it has a marginal effect during the later phase of compression. An isothermal compression efficiency of 84-86% is observed with the liquid piston.

Chapter 3 Nomenclature: a0, a1, a2 Model Constants A Area (m2) 2 Ainner Area of the inner surface of the chamber (m ) Cv Specific heat of air at constant volume (J/kg K) 2 hconv,air Convective heat transfer coefficient of gas (W/m K) hconv,amb Convective heat transfer coefficient of ambient (W/m2 K) 2 hconv,gas Convective heat transfer coefficient of gas (W/m K) 2 hconv,water Convective heat transfer coefficient of gas (W/m K) ksolid Thermal conductivity of the chamber material (W/m K) m Mass of the gas (kg) n Polytropic index of compression process P Pressure (Pa) P0 Pressure at the start of compression (Pa) Pf Pressure at the end of compression (Pa) Pr Compression pressure ratio 푄̇ Rate of heat transfer (J/s) rinner Inner radius of the chamber (m) router Outer radius of the chamber (m) R Gas Constant (J/kg K) Rcond,solid Conductive Thermal Resistance of chamber material (K/W) Rconv,air Convective Thermal Resistance of air (K/W) Rconv,amb Convective Thermal Resistance of ambient (K/W) Rconv,gas Convective Thermal Resistance of gas (K/W) Rconv,water Convective Thermal Resistance of water (K/W) t Time (s) tsolid Thickness of the chamber (m) T Temperature of gas (K) 푇∞ Temperature of ambient (K) 푈̇ Rate of change of internal energy of gas (J/s) 2 Uh Overall heat transfer coefficient (W/m K) V Volume (m3) 3 V0 Volume at the start of compression (m ) 3 Vf Volume at the end of compression (m ) 푊̇푐표푚푝 Compression work (J/s)

Greek Symbols 휂𝑖푠표 Isothermal efficiency of compression

Subscripts 0 At the start of compression conv Convective cond Conductive comp Compression f At the end of compression ∞ Ambient

3.1. Introduction

Compressed air consumes a great share of total energy consumption in the industrial applications. For a typical industrial facility in the USA, approximately 10% of the electricity consumed is for generating compressed air. For some facilities, compressed air accounts for more than 30% of the electricity consumed [56]. Energy costs during the utilization period of the compressor may contribute more than 75% of the overall cost over the life cycle. Improvements in the energy efficiency of compressed air systems can result in energy saving of 20-50% [57].

Another major application of compressors is for the compressed air energy storage. Efficient energy storage systems facilitate effective utilization of intermittent renewable energy sources.

Compressed air energy storage systems have a great potential to serve as large-scale energy storage systems. The compressor and expander are the key components in a compressed air energy storage plant. Development of an efficient compressor and expander would make compressed air energy storage systems economical and competent [58].

The liquid piston concept shows a significant improvement in the efficiency of gas compression and expansion in comparison to the conventional reciprocating compressor. In liquid piston, a column of liquid is used to compress gas in a fixed volume chamber. As liquids conform to irregular volumes, the surface area to volume ratio in the compression chamber can be maximized using a liquid piston. The high surface area to volume ratio helps in attaining a higher rate of heat transfer during gas compression. This results in a compressor with a near-isothermal operation, leading to an efficient compression with minimal compression work [59].

Heat transfer plays an important role in improving the efficiency of compression in the liquid piston. For an isothermal compression, the instantaneous rate of heat transfer should be equal to the instantaneous mechanical power from to the compressor [60]. Piya et al. [61] presented a

numerical modeling of liquid piston gas compression based on thermal-fluids and heat transfer mechanisms. Their results indicated that heat transfer processes actively contribute towards extraction of heat energy from the working gas during compression. Also, their simulation shows that liquid piston compression maintained a lower gas temperature than observed during adiabatic compression. Kermani et al. [62] performed heat transfer analysis of liquid piston compressor for hydrogen applications. They presented a thermodynamic model of liquid piston compressor to investigate the heat transfer phenomenon inside the compression chamber. Increasing the total heat transfer coefficients at the interface and the wall, together with the compression time, played key roles in reducing the hydrogen temperature.

Various heat transfer enhancement techniques have been tried in liquid piston compressor.

Porous media inserts for heat transfer enhancement in liquid piston compressor have been analyzed by Zhang et al. [63] using Computational Fluid Dynamics (CFD) simulations. It was observed that heat exchangers can effectively suppress temperature rise and secondary flows in liquid piston compressor. Further, Yan et al. [64] performed an experimental study using porous media inserts in a liquid piston compressor/expander. Porous media inserts have shown a significant increase in efficiency (up to 18%) at a fixed power and a significant increase in power density (up to 39 folds) at a fixed efficiency. The increase of surface area was the predominant cause of the performance improvement with the use of porous media. Another experimental study of a high pressure (210 bar) liquid piston air compression has shown performance improvement with the use of porous media inserts [65]. The use of porous media could achieve 10x increase in power density at a constant efficiency for the high-pressure air compression. Design analysis of shaped compression chamber using porous media in liquid piston compressor is presented by Zhang et al [66]. It was observed that shaped compression chamber leads to enhanced heat transfer and improvement in

compression efficiency. Highly efficient isothermal air compression and expansion can lead to an efficient large-scale compressed air energy storage system [67]. Various other heat transfer enhancement techniques like trajectory optimization [68], the use of hollow spheres [69] and spray cooling [70] have shown better performance in the liquid piston compressor. Liquid piston compressor with heat transfer enhancement has the potential to develop a highly efficient energy storage system [71].

A review of heat transfer in reciprocating compressors indicates that very little attention was paid to heat transfer modeling and assessment of its effect. This is attributed partly to the lack of consensus about the seriousness of its impact and partly to its complexity [72]. However, there is a good agreement in the literature that heat transfer inside the cylinder is one of the main factors affecting the efficiency of the reciprocating compressors. Recently, Tuhovcak et al. [73] presented a comparative analysis of heat transfer models for the reciprocating compressors. Their analysis indicated that the isentropic efficiency of the compressor is significantly influenced by the type of heat transfer model. They also presented heat transfer analysis in the cylinder of the reciprocating compressor using complex CFD simulations. Results showed a large deviation between integral correlations and numerical model for heat transfer prediction [74]. This illustrates the importance and complexity of heat transfer models in reciprocating compressors.

The optimal design of a liquid piston compressor demands a thorough understanding of the heat transfer process during compression/expansion. However, there are very limited studies investigating heat transfer in liquid piston compressor experimentally. Majority of earlier studies on liquid piston compressor have used heat transfer models for flow through the pipe. However, there exists a considerable difference in fluid flow conditions and heat transfer characteristics between the liquid piston and pipe flow. Also, the validity of a fully developed pipe flow model

for liquid piston compressor has not been confirmed with experimental investigations. In this chapter, heat transfer in the liquid piston compressor is studied experimentally. The rate of heat transfer during the compression process is investigated thoroughly. The effect of stroke time of compression on the rate of heat transfer is studied by experimentally varying stroke time of compression. A detailed analysis of the liquid piston compressor using a thermal resistance circuit is presented. Experiments with compression chambers of different materials are also performed to investigate the influence of the material of compression chamber on heat transfer characteristics.

Finally, the isothermal efficiency of liquid piston compressor is evaluated based on experimental results.

3.2. Analytical Model

A thermodynamic model for liquid piston compressor can be developed by using the first law of thermodynamics. Figure 3.1 shows a representative control volume in liquid piston compressor for thermodynamic modeling. Initially, gas at a lower pressure is filled in the compression chamber. Then, the low-pressure gas in the compressor chamber is compressed using a high- pressure liquid, which provides work for compression. During compression, the volume of the gas decreases as the liquid column moves towards the top end resulting in an increase in the pressure and temperature of the gas. The heat transfer happens from the gas to the surrounding due to the temperature gradient. Finally, when the pressure reaches the desired pressure, the gas is allowed to exit from the compression chamber. The compression of gas can be analyzed as a closed system from the start to the end of the compression process. The first law of thermodynamics applied to the gas in the control volume neglecting changes in kinetic and potential energies gives

푑푇 푈̇ = 푚퐶 = 푄̇ − 푊̇ (3-1) 푣 푑푡 푐표푚푝

where 푈̇ is the rate of change of internal energy, m is mass of the gas, 퐶푣 is the specific heat of the gas at constant volume, T is the temperature of the gas, t is time, 푄̇ is the rate of heat transfer and 푊̇푐표푚푝 is work of compression.

Using heat transfer relation and compression work for a closed system results in

푑푇 푑푉 푚퐶 = 푈 퐴(푇 − 푇) − 푃 (3-2) 푣 푑푡 ℎ ∞ 푑푡

where Uh is the overall heat transfer coefficient, A is the area of heat transfer, 푇∞ is the temperature of the surrounding, P is the pressure of the gas and V is the volume of the gas.

Figure 3.1: Control Volume in Liquid piston compressor ( --- represents control volume)

The heat transfer in liquid piston compressor can be analyzed by using thermal circuits. Figure

3.2-(a) shows a representative thermal circuit for heat transfer from the gas to the surrounding of the liquid piston compressor. The heat transfer from the gas to the surrounding experiences the following resistances.

i) Convective thermal resistance between the gas and the inside surface of compression chamber

given by

1 Rconv,gas = (3-3) hconv,gas Ainner

where hconv,gas is convective heat transfer coefficient between gas and inner surface of the

compression chamber, and Ainner is inner surface area of the compression chamber in contact

with gas. The inner surface area Ainner includes the chamber surface area (top and lateral

surfaces) in contact with gas and the moving liquid piston surface area in contact with gas.

(a) From gas in compression chamber to ambient surrounding

(b) Conductive resistance for cylindrical compression chamber

Figure 3.2: Thermal Circuit for liquid piston compressor (T- Temperature, R- Thermal Resistance) ii) For the cylindrical compression chamber, the conductive resistance of the material consists of

resistance due to the lateral and top surfaces of the cylinder as shown in Figure 3.2-(b). The

total resistance due to conduction can be given by equation (3-4) and resistance from the top

and lateral surfaces of the cylinder are given by equation (3-5) and (3-6) respectively.

1 1 1 = + (3-4) Rcond,solid Rcond,top Rcond,lateral

tsolid Rcond,top = (3-5) ksolid Atop

푟 ln ( 표푢푡푒푟) 푟𝑖푛푛푒푟 Rcond,lateral = (3-6) 2휋 ksolid L

where tsolid is thickness, ksolid is thermal conductivity of the material of compression chamber,

Atop is the top surface area of the cylindrical compression chamber, router is outer radius, rinner

is inner radius and L is length of the compression chamber. iii) Convective thermal resistance between outer surface of compression chamber and ambient

surrounding is

1 Rconv,amb = (3-7) hconv,amb Aouter

where hconv,amb is convective heat transfer coefficient between gas and outer surface of the

compression chamber, and Aouter is the surface area of outer surface of the compression

chamber.

The overall heat transfer coefficient (Uh) in equation (3-2) can be calculated using the total

thermal resistance for the heat transfer from the gas to the surrounding.

1 Rtotal = = Rconv,gas + Rcond,solid + Rconv,amb (3-8) 푈ℎ 퐴

The isothermal process of compression has the least work of compression. However, the actual

compression process is polytropic, which requires a higher work of compression. Figure 3.3 shows

pressure-volume (P-V) plots of a typical compression process with isothermal and polytropic

compression. The polytropic index (n) denote the proximity of compression process towards

isothermal or adiabatic conditions. Polytropic index n=1 denote isothermal conditions whereas

n=k denote adiabatic conditions where k denote specific heat ratio of the gas. The liquid piston

compressor operates under near-isothermal conditions, where n significantly less than k (= 1.4 for

air) is observed in liquid pistons. Therefore, the isothermal process is considered as an ideal

Figure 3.3: Pressure-Volume plot indicating isothermal and polytropic compression process in case of liquid piston compressors, and the actual compression work is compared with the isothermal compression work for efficiency evaluation. The area under the P-V plot gives work of compression. The increase in the temperature demands cooling of air which requires additional cooling work [63]. The total work is the sum of work of compression and cooling work. The isothermal efficiency of compressor (휂𝑖푠표) defined as the ratio of work required for isothermal compression to the actual compression work,

1 푚푅푇0(ln 푃푟−1 + ) 푊𝑖푠표 푃푟 휂 = = 푉 (3-9) 𝑖푠표 푊 푓 푉0 푎푐푡 ∫ (푃−푃0)푑푉+푃0(푃푟−1)(푉푓 − ) 푉0 푃푟

where Pr is compression ratio and subscripts 0 and f indicate properties at initial and final stages of the compression respectively.

The actual compression process can be characterized as the polytropic process by the following relation.

푛 푛 푃푉 = 푃0푉0 (3-10)

where n is a polytropic index of compression which characterizes the heat transfer during the compression process. n=1 represents an isothermal compression whereas n=k represents an adiabatic compression with k as the ratio of specific heats of the gas. Substituting equation (3-10) into equation (3-9) results in equation (3-11) for the isothermal efficiency of compression,

1 ln 푃푟−1 + 휂 = 푃푟 (3-11) 𝑖푠표 푛−1 1 ( ) 1 − 푃푟 푛 − 1 − 푛 1 + 푃푟 푛 −1 + (푃푟−1)( 푃 − ) 푛−1 푟 푃푟

3.3. Experiments

In all the experiments performed in this study, compression of air using water as the liquid piston is studied. The liquid piston compressor setup shown in Figure 3.4 is used for experiments.

A compressor chamber is completely immersed in the water at all times during the compression process. The inlet and outlet valves are installed at the top of the compression chamber. The level of water inside the compression chamber is controlled to achieve the compression process. While the inlet and the outlet valves are closed, the compression of air is achieved with the rise of water level in the compression chamber. The outlet valve is opened when the desired pressure is achieved inside the compression chamber. The suction stroke of the cycle takes place with the drop of the water level while the intake valve stays open to the atmosphere. A reciprocating hydraulic pump is used to supply the water inside the compression chamber. The hydraulic pump is operated through a pneumatic cylinder by controlling the supply of the high-pressure air. A controller is used to control the operation of inlet and outlet valves connected to the compression chamber and supply of air to the pneumatic cylinder. A pressure transducer is installed at the top of the compression chamber to measure the instantaneous pressure of the air during compression. The transient temperature measurements of the air, chamber wall and the surrounding water are performed using fine wire gauge thermocouples having a fast response time. Various

thermocouples are installed as follows to measure the instantaneous temperature at various locations:

i) A K-type thermocouple of 40 gauge diameter is attached to compression chamber wall from inside.

ii) Two K-type thermocouples of 40 gauge diameter (Omega Engineering Part# 5TC-TT-K-

40-72 [75] ) are used to measure the temperature of the air. These thermocouples are positioned axially at 25 mm from the top surface of the compression chamber and approximately 25 mm radially away from the center in opposite directions.

iii) A hermetically sealed T-type thermocouple of 24 gauge diameter (Omega Engineering

Part# HSTC-TT-T-24S-80 [76]) is mounted to measure the temperature of water in the outer cylinder surrounding the compression chamber.

Figure 3.4: Experimental Setup of Liquid piston compressor

Four different compression chambers used for experiments are shown in Figure 3.5. These chambers are selected to cover compression chambers of different diameters, materials, and lengths. Experiments are performed for a compression ratio between 2.05 and 2.35. Various stroke times of compression are also tested with the four compression chambers. A LabVIEW program is used to automate the compression process over a number of continuous cycles. Each experiment is performed for more than 10 compression cycles. All the instantaneous pressure and temperature data during compression cycles are recorded using a data acquisition device through LabVIEW.

(a) Polycarbonate (b) PET (c) Aluminum (d) Copper (D=88mm, L=170mm) (D=100mm, L=150mm) (D=120mm, L=145mm) (D=105mm, L=185mm)

Figure 3.5: Various Compression chambers used in the study.

3.4. Results and Discussion

3.4.1. Pressure and Temperature Plots

The pressure data taken for 10 continuous compression cycles using the polycarbonate chamber with a compression stroke of 6.9 seconds is shown in Figure 3.6. It can be observed that the compression process happens consistently to reach the desired pressure of 237 kPa in each cycle. The temperature data at various locations for corresponding 10 cycles are shown in Figure

3.7. The plot includes the temperature of water, the temperature of the inner surface of the chamber

wall and temperature of the air. The temperature of air has been measured at two locations in the compression chamber as specified in section 3.3, which are labeled as right and left locations for identification. As compression proceeds, the temperature of air increases consistently in all the cycles. Also, for 10 compression cycles, there is not significant cycle-to-cycle variation in the temperature profiles. The temperatures of air measured at both the locations which are 25 mm away from the centerline are approximately the same. This indicates a symmetric temperature profile about the center. For further analysis, the average temperature of both the thermocouples is considered as the temperature of the air. The temperature of the wall (inner surface of the compression chamber) is observed to be increasing very slowly with pressure. The temperature of the water as expected remained constant due to its large volume and high specific heat. Even for continuous compression experiments with higher than 10 continuous compression cycles, the temperature of water remained the same.

Figure 3.8 shows the temperature-pressure plot for a single compression cycle for compression from 101 kPa to 237 kPa. The temperature of air increases rapidly with pressure, while the temperature of the wall increases very slowly with the rise in pressure during the compression process. The Figures 3.6, 3.7, and 3.8 show the results for one sample case (with the Polycarbonate chamber for 6.9 compression stroke) from of a number of cases studied. Similar trends of pressure and temperatures measured at various locations in liquid piston were observed for other chambers with different stroke times.

Figure 3.6: Pressure over time for 10 continuous compression cycles (With Polycarbonate chamber and 6.9 s compression stroke)

Figure 3.7: Temperature over time for 10 continuous compression cycles (With Polycarbonate chamber and 6.9 s compression stroke)

Figure 3.8: Temperature data at various locations during compression (With Polycarbonate chamber and 6.9 s compression stroke)

3.4.2. Experiments with different Stroke Time of Compression

The effect of the stroke time of compression is studied by varying the stroke time from 6.9 seconds to 4.7 seconds. The normalized pressure plots for different stroke times are shown in

Figure 3.9. In all the cases, pressure increases as compression proceeds without any anomaly. The normalized temperature of air over the compression period for this set of experiments is shown in

Figure 3.10. It can be observed that a faster compression results in a higher rate of temperature rise. Similarly, the temperature of the inner surface of the compression chamber (wall) for different stroke times of compression is shown in Figure 3.11. It can be observed that the final temperature of the wall is approximately the same (less than 0.03% change) for different stroke times of compression. A similar effect of stroke time was observed with the other compression chambers.

Figure 3.9: Pressure over compression time for various stroke times of

compression (With Polycarbonate chamber).

Figure 3.10: Temperature of air over compression time for various

stroke times of compression (With Polycarbonate chamber)

Figure 3.11: Temperature of the inner surface of compression chamber over compression time for various stroke times of compression (With Polycarbonate chamber).

3.4.3. Rate of Heat Transfer and Compression Work

Quantitative evaluation of the rate of change of internal energy (푈̇ ), compression work (푊̇ ) and rate of heat transfer (푄̇ ) using instantaneous experimental data was performed for the analysis of heat transfer and work input during compression. Figure 3.12 shows a scatter plot of this data with the polycarbonate chamber and a compression stroke time of 5.1 seconds for 10 compression cycles. It can be seen that 푈̇ and 푄̇ have a higher variance than 푊̇ . This is due to higher cyclic variability with temperature data during compression compared to pressure data and volume flow

푑푇 rate data. The calculation of derivative of temperature ( ) for the data with a small-time step 푑푡

(dt∼0.1 s) further exacerbates the variability. A regression fits with a polynomial of degree 2 are shown in Figure 3.12 to illustrate the mean trend of 푈̇ , 푊̇ and 푄̇ during the compression process.

It can be seen that 푈̇ is always positive. This is an effect of an increase in temperature of air during the compression process. The increase of 푈̇ with pressure indicates a corresponding rise in temperature when pressure rise. The negative value of the rate of heat transfer signify the heat transfer from the gas to the surrounding. The trend of the mean value for the rate of heat transfer indicates that the heat transfer from the gas to surrounding increases slightly with pressure. It can be observed that the compression work consistently increases with pressure. The increase in temperature of air requires more compression work at higher pressure.

Uncertainty quantification of the models for 푈̇ , 푄̇ and 푊̇ are performed to estimate the confidence intervals and prediction intervals. The 95% confidence intervals for all the three regression fitted models (dash-dot lines in Figure 3.12) are observed to be very close to the mean model response (solid lines). The small deviation of confidence intervals about the regression fit denote a high precision of the model in explaining the response variable. Although the scatter plot of 푈̇ , 푊̇ data has a high variability, the smaller confidence intervals for model denote the marginal effect of this variability on regression fits. Furthermore, the 95% prediction intervals (dotted-lines) for 푈̇ , 푄̇ and 푊̇ are also shown in Figure 3.12. These prediction intervals show the 95% prediction region of a new observation and include both the propagated uncertainty in the model and measurement errors. Since the measurement errors for 푈̇ and 푄̇ are higher due to temperature data, the prediction intervals for 푈̇ and 푄̇ show a wider region. The smaller measurement error of pressure data and volume flow rate data result in lower prediction bound for 푊̇ .

Figure 3.12: Rate of change of internal energy(푼̇ ), compression work (푾̇ ) and rate of heat transfer(푸̇ ) during compression (With polycarbonate chamber and 5.1 s compression stroke). Note: The markers represent datapoints, solids lines show regression fits, dash-dot lines indicate 95% confidence intervals and dotted lines denote 95% prediction intervals correpond to each variable.

The regression model fits through the experimental results of different stroke time of compression are evaluated to study the effect of stroke time of compression on heat transfer and compression work. Figure 3.13 shows the regression fits of 푈̇ , 푊̇ and 푄̇ for various stroke time of compression using polycarbonate compression chamber. It can observed that the rate of change of internal energy (푈̇ ) increases with the decrease of stroke time of compression. This is due to the higher temperature of air observed with the faster compression. The compression work (푊̇ ) and the rate of heat transfer (푄)̇ also increase with the shift to a faster compression stroke.

Noticeably, faster compression results in a higher rate of heat transfer but at the expense of higher compression work and higher temperature rise.

Figure 3.13: Comparison of 푼̇ , 푾̇ and 푸̇ for different stroke times of compression (With Polycarbonate chamber).

3.4.4. Heat Transfer Coefficient

The convective heat transfer coefficient between air and the wall of the compression chamber is calculated based on the rate of heat transfer, the surface area of heat transfer, and the temperature difference between the air and the inside surface of the cylinder. Figure 3.14 shows the scatter plot for the instantaneous convective heat transfer coefficient of the air during compression with the polycarbonate chamber and 5.1 second compression stroke for 10 compression cycles. It is observed that the heat transfer coefficient is very high at the beginning of the compression and decreases as compression proceeds to reach a stable value. A high heat transfer coefficient at the

initial phase of compression indicates the presence of thermally developing flow in the initial phase of compression. As compression proceeds, the thickness of the thermal boundary layer increases resulting in a reduction of convective heat transfer coefficient. A stable convective heat transfer coefficient indicates the possibility of a constant thermal boundary layer thickness towards the end of compression. Although the rate of heat transfer does not show significant variation during the compression process, there exists a significant variation in the convective heat transfer coefficient.

The convective heat transfer coefficient of air and area of heat transfer reduce as compression proceeds which should have resulted in the decrease in the rate of heat transfer. However, an increasing temperature difference as compression proceeds helps in achieving a higher rate of heat transfer. Overall, there is a marginal decrease in the rate of heat transfer rate as a result of the interplay between the convective heat transfer coefficient of air, the area of heat transfer, and the temperature difference between air and chamber wall.

Figure 3.14: Convective heat transfer coefficient between air and cylinder wall during compression (With polycarbonate chamber and 5.1 s compression stroke).

The nonlinear regression fit of the functional form given in equation (3-12) is fitted through the scatter plot of the convective heat transfer coefficient of air. The regression fit in Figure 3-14 shows a good fit with a coefficient of determination (R2) of 0.95.

푃 (−푎 ) 2 푃 ℎ = 푎0 + 푎1푃0푒 0 (3-12)

2 where h is the convective heat transfer coefficient in W/m K, P is pressure in Pascal, P0 is atmospheric pressure in Pascal, and a0, a1, and a2 are regression parameters.

Uncertainty propagation in the above model for ‘h’ is performed to evaluate the confidence and prediction regions. The 95% confidence intervals shown in Figure 3.14 indicate that the model response estimate has small confidence bounds. The small bounds of confidence intervals indicate that the regression model given by equation (3-12) is a high precision model for representing the data. The 95% prediction bounds for a new observation are also shown in Figure 3.14. It is observed that prediction intervals are significantly wider compared to the confidence bounds.

Since the prediction bounds indicate the region of a new observation, this account for both the model uncertainty and the measurement errors. Although model uncertainty is low as evidenced in the precise confidence region, the larger measurement error results in wider prediction bounds for a new observation.

Using the model for h given by equation (3-12), the regression fits are performed for the compression with the polycarbonate chamber and different stroke times. Table 3.1 shows the regression parameters and R2 values of the regression fits. All the fits obtained show R2 values higher than 0.93 indicating a good fit of the regression model with the data. Figure 3.15 shows the comparison plots of these regression fits. It is observed that the stable heat transfer coefficient of air near the end of compression increases with a decrease in stroke time of compression.

Compression with a faster stroke time has a higher velocity of the liquid piston which is an

indication of a higher Reynolds number of the flow. In general, the heat transfer coefficient increases with an increase in Reynolds number for fully developed flows. Therefore, a faster compression shows a higher heat transfer coefficient of air towards the end of compression. Also, compression with a higher stroke time reaches a stable heat transfer coefficient earlier (at lower pressure). This is an indication of a smaller thermal entrance length with a higher stroke time of compression. In general, the thermal entrance length decreases with a decrease in Reynolds number. Therefore, a higher compression stroke results in a smaller thermal entrance length and a steeper slope of the heat transfer coefficient model. The parameter a0 in the regression model is a good indicator of the stable value of heat transfer coefficient during the compression. The a0 values in Table 3.1 show that the stable heat transfer coefficient ranges from 8-12 W/m2K in the liquid piston compressor for the polycarbonate chamber significantly lower than heat transfer coefficient during the initial phase of compression.

Table 3.1: Model Parameters of the non-linear regression model for convective heat transfer coefficient during compression with polycarbonate chamber. Stroke Time of a (W/m2 K) a (m/s K) a (-) R2 Compression 0 1 2 6.9 s 8.01 4.40 8.03 0.93 6.2 s 9.21 2.09 7.50 0.94 5.5 s 10.47 1.56 7.26 0.94 5.1 s 10.66 0.84 6.79 0.95 4.9 s 11.06 0.84 6.78 0.95 4.7 s 11.29 0.59 6.48 0.94

Figure 3.15: Comparison of convective heat transfer coefficient between air and cylinder wall for different stroke times of compression (With polycarbonate chamber)

3.4.5. Thermal Resistances

Liquid piston compressor is subjected to convective thermal resistance of air, conductive thermal resistance of solid, and convective thermal resistance of ambient as discussed in section

3.2. The quantitative evaluation of these thermal resistances during compression with different compression chambers and about 4.7 s stroke time of compression is shown in Figure 3.16. For all the chambers, the convective thermal resistance of air increases rapidly with pressure. This is because both the convective heat transfer coefficient of air and area of heat transfer decrease during the compression process.

There exists a noticeable amount of conductive thermal resistance for the polycarbonate and the PET chambers. The conductive resistance increases marginally with pressure. The conductive

Figure 3.16: Contribution of thermal resistances during compression process for different compression chambers. resistance is characteristics of the thermal conductivity of chamber material, diameter of the chamber, thickness of the chamber wall, and height of the chamber in contact with the high-

temperature air. The height of the chamber in contact with air decreases as compression proceeds, which results in an increase in conductive resistance. The low thermal conductivities of polycarbonate and PET (∼0.2 W/mK) result in a significant thermal resistance for the polycarbonate and PET chambers. The thermal conductivities of aluminum and copper are very high (more than 1000 times that of polycarbonate and PET) which result in negligible conductive resistances (less than 0.001 K/W) and therefore is not evident in the plots. The high conductive

material is helpful in reducing conductive thermal resistance. However, the contribution of conductive thermal resistance in the total thermal resistance is fractional in the latter phase of the compression process. Therefore, the use of a highly conductive material may not result in a significant improvement in heat transfer characteristics at high pressure. In the experimental setup, the chamber is completely immersed in water, which acts as the ambient surrounding. It is observed that thermal resistance of water almost remains constant over the compression period for all the chambers. This is expected as the compression chamber was completely immersed in the stationary ambient water which results in a constant heat transfer coefficient.

The overall thermal resistance is a sum of all three resistances. It can be observed that the convective thermal resistance has a significant contribution to the overall thermal resistance.

Therefore, a reduction in convective thermal resistance of air is crucial in achieving a higher rate of heat transfer in the liquid piston compressor.

3.4.6. Overall Heat Transfer Coefficient

The overall heat transfer coefficient during the compression with different compression chambers is shown in Figure 3.17. In general, overall heat transfer coefficient decreases with pressure and reaches a stable value in the latter phase of the compression process. The compression chambers with the high thermal conductivity materials (Aluminum and Copper) show significantly higher overall heat transfer coefficient in the initial phase of compression. As conductive thermal resistance has a significant contribution to the total thermal resistance in the initial phase, the high thermal conductivity material helps in reducing the overall heat transfer coefficient in the initial phase of compression. Towards the end of compression, all the compression chambers reach approximately the same and stable overall heat transfer coefficient of 8-12 W/m2K.

Figure 3.17: Overall heat transfer coefficient for compression with different compression chambers.

3.4.7. Isothermal Efficiency of Compression

The isothermal efficiency of compression with the liquid piston of different chamber materials is shown in Figure 3.18. The uncertainty bars represent a 95% confidence interval. The efficiency values shown for the polycarbonate and the PET chambers are based on a compression ratio of

2.33 while the efficiency values for the aluminum and copper chambers are based on a compression ratio of 2.07. The difference in efficiencies between different compression chambers can be attributed to the variations in overall heat transfer coefficient, compression ratio, diameter, length, and material of compression chamber. The slightly higher stable overall heat transfer coefficient observed with the PET chamber compared to that of the polycarbonate chamber results in a marginally higher isothermal efficiency of compression. A similar effect is observed for compression with the aluminum and the copper chambers. In general, the polytropic index of

compression was between 1.13 - 1.17. This results in an isothermal efficiency of liquid piston compression between 84% - 86%.

Figure 3.18: Isothermal Efficiency for compression with different compression chambers.

Further improvement in isothermal efficiency of compression requires a higher rate of heat transfer during compression. Since the conductive thermal resistance of compression chamber and convective thermal resistance of water have a very small contribution in the total thermal resistance of liquid piston compressor, there is limited scope for improving efficiency by using techniques which reduce these resistances. However, heat transfer enhancement techniques to reduce the convective thermal resistance between the gas and the compression chamber would be helpful to gain significant improvements in isothermal efficiency. Various heat transfer enhancement techniques like the use of porous media inserts [64], spray cooling [77], and use of aqueous foam

[78] have shown varying improvements in the isothermal efficiency of compression. These techniques use a media to help reduce the effective convective thermal resistance between air and compression chamber. Liquid piston compression with such heat transfer enhancement techniques 63

has the potential to achieve a near-isothermal compression with a significantly higher isothermal efficiency than a baseline liquid piston compressor.

3.5. Conclusions

A liquid piston compressor is studied experimentally in order to investigate heat transfer using compression chambers of different materials and various stroke times of compression. It is observed that the rate of heat transfer increases with a faster compression time but at the expense of additional compression work and a higher rise in air temperature. The convective heat transfer coefficient was observed to be high at the initial phase of compression and then decrease to a stable value towards the later phase of compression. Thermal analysis of the liquid piston compressor indicates that there exist three resistances: convective thermal resistance between gas and chamber, conductive thermal resistance of chamber material, and convective thermal resistance between chamber and ambient. Quantitative evaluation of these thermal resistances during the compression process shows that convective thermal resistance of air is significantly higher than the other two, especially in the later part of the compression process. The conductive thermal resistance of the chamber can be reduced significantly using a material of a high thermal conductivity. However, a compression chamber of high thermal conductivity material helps in achieving a higher overall heat transfer coefficient only in the initial phase of compression. The overall heat transfer coefficient of the liquid piston compression stabilizes to a value between 8-12 W/m2K towards the latter part of compression irrespective of the material of compression chamber. For the compression ratio of 2.05-2.35, an isothermal efficiency of 84-86% is observed for compression of air using a liquid piston. Techniques to enhance the heat transfer coefficient between gas and chamber can lead to further improvements in the isothermal efficiency of the liquid piston compressor.

CHAPTER 4: Spray Injection in Liquid Piston Compressor

Abstract: Near-isothermal compression is desired for many compressor applications for high efficiency. Low heat transfer characteristics in conventional compressors is a major bottleneck in attaining a near-isothermal compression. A high rate of heat transfer is possible with an injection of a large number of water droplets using a spray nozzle inside the compression chamber. In this chapter, the effectiveness of spray injection to achieve near-isothermal compression is investigated experimentally in a liquid piston compressor. Experiments are performed with and without spray injection during compression of air using a liquid (water) piston compressor. Parametric investigations are performed by varying injection pressures of spray from 10 psi (69 kPa) to 70psi

(483 kPa), using different spray nozzle angles (60°, 90°, and 120°), and by changing the stroke time of compression. It is observed that water spray injection is highly effective in abating air temperature rise during the compression process. The pressure-volume plots indicate a significant reduction in the compression work and approach near-isothermal compression with spray at higher injection pressures. The isothermal efficiency of compression consistently increases with an increasing injection pressure of spray and reaches up to 95% at the highest injection pressure studied (70 psi). Furthermore, the spray nozzle angle affected the isothermal efficiency marginally with 1-4% improvement in efficiency with the use of a 60° nozzle angle instead of 90° or 120° spray angles at all injection pressures. Also, comparable isothermal efficiency is observed for compression with different stroke times of compression especially at higher injection pressures.

Therefore, spray injection can be a very effective method to attain a high efficiency with a high power density. Overall, with an optimized spray design, water spray injection can achieve a highly efficient near-isothermal compression.

Chapter 4 Nomenclature: A Area (m2) C A constant 2 퐴푑 Surface area of a droplet (m ) 2 퐴푑 Surface area of a droplet (m ) th 2 퐴푑,𝑖 Surface area of i droplet (m ) 2 퐴푑,표 Overall surface area of all the droplets (m ) Cv Specific heat of air at constant volume (J/kg K) ℎ푑 Heat transfer coefficient between a droplet and gas (W/m2 K) th ℎ푑,𝑖 Heat transfer coefficient between i droplet and gas (W/m2 K) k Heat capacity ratio of gas m Mass of the gas (kg) n Polytropic index of compression process N Number of droplets P Pressure (Pa) P0 Pressure at the start of compression (Pa) Pf Pressure at the end of compression (Pa) Pr Compression pressure ratio 푄̇ Rate of heat transfer (J/s) 푞푑̇ Rate of heat transfer to a single droplet (J/s) 푄푑̇ Rate of heat transfer to N droplets (J/s) R Gas Constant (J/kg K) t Time (s) T Temperature of gas (K) 푇∞ Temperature of ambient (K) 푇푑 Surface temperature of a droplet (K) th 푇푑,𝑖 Surface temperature of i droplet (K) 푇푔 Temperature of gas (K) 푈̇ Rate of change of internal energy of gas (J/s) 2 Uh Overall heat transfer coefficient (W/m K) V Volume (m3) 3 V0 Volume at the start of compression (m ) 3 Vf Volume at the end of compression (m ) 푉𝑖푠표 Volume at the end of compression with isothermal process (m3) 푊̇푐표푚푝 Compression work (J/s)

Greek Symbols 휂𝑖푠표 Isothermal efficiency of compression

Subscripts 0 At the start of compression d Droplet g Gas i identification number of the droplet r Ratio iso Isothermal comp Compression

4.1. Introduction

Renewable energy resources play an important role in reducing energy dependency on fossil fuels. Rising energy demands across the world and the devastating effects of global warming have necessitated the use of renewable energy resources to fulfill energy needs. Renewable energy sources such as solar, wind, wave, and tidal energy have significant fluctuations inherent in their power source. This intermittent nature of renewable energy resources makes it harder to effectively use them directly into the electric grid. Large-scale energy storage systems are needed to facilitate effective utilization of renewable energy in the electric grid [79]. Various electrical energy storage methods such as high-power density batteries, fuel cells, hydroelectric storage, and compressed air energy storage (CAES) systems have been explored. Apart from hydroelectric power storage, energy storage is not widely prevalent on a utility grid level [80]. CAES systems can provide a viable alternative to serve as large-scale energy storage systems. Efficient energy storage systems facilitate effective utilization of intermittent renewable energy sources with minimum energy losses. To achieve a commercially viable energy storage system, CAES systems need to be highly efficient along with providing a high power density at the same time [81].

In a typical CAES plant, air is used as an energy storage medium by compressing it using an air compressor and then expanding it at peak time over a gas turbine to generate electricity.

Isothermal CAES is shown to be highly efficient without the need of fuel and thermal energy storage [82]. The compressor and expander are key components in an isothermal CAES and they should operate isothermally to obtain a high roundtrip efficiency [83]. Typically for an isothermal compression/expansion, the process involves a slow pressure change while allowing the heat transfer to maintain a constant temperature during the process. Since in any practical industrial application it is difficult to achieve an isothermal compression and expansion, innovative

techniques to attain a high rate of heat transfer are needed in the compressor/expander to approach a near-isothermal process. Overall, development of a near-isothermal compressor and expander would make CAES systems highly efficient, economical, and competent energy storage [84].

Typical air compressors for industrial applications tend towards an adiabatic process which results in high air temperature at the end of compression. This is because a significant proportion of the compression work is utilized in increasing the internal energy of the gas. Reducing the temperature rise of gas during the compression process decreases the compression work and improves the compression efficiency [85]. Liquid piston gas compression has the potential to obtain significant improvements in the compression efficiency in comparison to conventional reciprocating compressors [86]. In a liquid piston compressor, a column of liquid is used as a moving piston to compress the gas to required pressures for a given chamber volume. Improving the heat transfer characteristics in a liquid piston plays an important role in increasing the efficiency of the liquid piston compressor [87]. It is observed that the heat transfer coefficient in liquid piston compressor is high at the initial phase of compression but reduces to a smaller value towards the later phase of compression. Also, the heat transfer coefficient increases marginally with an increase in the piston velocity [88]. To achieve an isothermal compression the instantaneous compression work should be equal to the instantaneous heat transfer rate. This demands a very high heat transfer rate from the gas to the liquid and surrounding in the liquid piston.

Heat transfer analysis of liquid piston compression for hydrogen applications was studied by

Kermani et al [89]. Their sensitivity analysis suggested that the heat transfer coefficients and compression time were important factors in reducing the hydrogen temperature. Heat transfer enhancement in liquid piston compression can also be achieved by optimizing the trajectories for

the compressor. A 10-40 % increase in power density was observed by optimizing the piston profile while also accounting for the effect of viscous friction [87]. Zhang et al. studied the heat transfer during compression with porous media inserts in a compression chamber [90]. The porous medium allows the gas and liquid to pass through uninterrupted while increasing the surface area available for heat transfer, and thus reducing the temperature rise during the compression process. By improving the heat transfer through porous media inserts the efficiency of the liquid piston compressor increases and shifts the polytropic process towards a near-isothermal condition. An experimental study was conducted by Yan et al. to study the heat transfer enhancement in a liquid piston using porous media inserts and quantify its effects in terms of the power density [91]. They observed that by use of porous media inserts the power density increased by 39 times at 95% efficiency and the efficiency increased by 18% at 100 kW/m3 for the compression process. A

Similar study at high pressure showed a tenfold increase in power density at a constant efficiency during the compression and expansion processes [92]. The major contributing factor for increasing the heat transfer from the liquid piston compressor/expander was the increase in surface area available due to the porous media inserts.

An interesting method of improving heat transfer or reducing the temperature rise of the compressing gas is to inject water droplets during the compression process. For a liquid piston compressor with water as the compressing liquid, water spray injection is miscible while at the same time it utilizes the high specific heat of water to absorb the heat and reduce the temperature of the gas. One dimensional simulations of a liquid piston compression with droplet heat transfer indicate that compression efficiency can be increased from 71% for adiabatic compression up to

98% with spray injection for a tenfold compression ratio [93]. Several researchers have studied droplet dynamics and heat transfer between air and water spray. Experiment and numerical studies

on water spray and ambient air to study evaporative cooling are performed by Sureshkumar et al

[94, 95]. They investigated spray cooling for parallel flow and counter-flow configurations with different nozzle pressures, nozzle diameters, environmental conditions, and air velocities.

Accordingly, they observed that for a given flow-rate, higher injection pressure with a smaller nozzle diameter resulted in a higher temperature drop of air. Since the goal of water spray injection is to minimize the temperature rise, the amount of water injected, and the droplet dynamics are significantly important. Convey et al. described a reciprocating piston compressor using water spray injection to achieve a near-isothermal air compression [96]. They observed a substantial reduction in the air temperature and the compression work by using high mass loading of water.

The injection of spray during compression results in a significant increase in heat transfer out of the system and a significant drop in the temperature of air during the compression process.

Therefore, injection of water spray in liquid piston compressor shows great potential to achieve near-isothermal compression. Furthermore, it is convenient to accommodate water spray injection in liquid piston compressor as the water droplets eventually fall in the liquid piston and there is no need of an extra mechanism to remove water out of the chamber as would be needed in a conventional reciprocating compressor. To the best of our knowledge, water spray injection in liquid piston compressor has not been studied experimentally.

In this chapter, water spray injection is studied experimentally in a liquid piston compressor to investigate its effectiveness to achieve a near-isothermal compression. The injection pressure of spray, nozzle angle of spray, and compression stroke time are varied to examine the effect of these parameters on the compressor performance. The conceptual framework of isothermal compression and spray injection is presented in the next section. Then, details about the experimental setup of the liquid piston with spray injection and a range of experiments performed are presented.

Furthermore, the effects of injection pressure of spray, nozzle angle, and stroke time of compression on temperature, pressure-volume plot, and isothermal efficiency of compression are discussed. Finally, overall conclusions and possible future extensions of this study are stated.

4.2. Experimental Setup

Water spray injection is investigated experimentally in a liquid (water) piston for compression of air. The effectiveness of spray to reduce air temperature rise is assessed from the experimental measurements of pressure, volume, and the temperature of air in the compression chamber.

Detailed descriptions of the liquid piston setup, spray injection setup, measurement accuracies for various measurements devices, and the range of experiments performed are discussed in this section.

4.2.1. Liquid Piston Setup

The experimental setup of the liquid piston compressor used for the experiments is shown in

Figure 4.1. The setup consists of a compression chamber, solenoid valves, intake and exhaust valves, a pneumatic cylinder, a hydraulic pump, controller, Data Acquisition System (DAQ), and measurement instruments. The outer cylinder contains water acting as a surrounding environment for the compression chamber. This helps maintain a constant surrounding temperature and act as a larger heat sink during the compression process compared to air as the surrounding medium. Water from a hydraulic pump drives the liquid piston interface in the compression chamber which compresses the air and is retracted by a coupled pneumatic piston-hydraulic pump for the intake stroke. A cycle consists of a compression stroke followed by the exhaust of high-pressure air and ends with an intake stroke in which atmospheric air fills the chamber to reach the initial conditions.

During the compression process, the liquid column moves in the upward direction and continuously reduces the air volume while increasing the pressure and temperature. Each

Figure 4.1: A table-top setup of Liquid piston compressor. experimental test case is run for about 10-12 continuous cycles to confirm repeatability and evaluate any cyclic variability. The controller actuates the solenoid valves which regulates the intake and exhaust of air at the end of compression. A LabVIEW [97] program was used for the continuous operation of the liquid piston. A polypropylene container was used as the compression chamber with a diameter of 10.96 cm and the height of the initial air volume as 12 cm.

4.2.2. Spray Injection Setup

The liquid piston setup is equipped with an additional flow circuit for injecting water spray inside the compression chamber. A schematic of the spray injection setup is shown in Figure 4.2.

The system consists of pipes, a water pump, a pressure regulator, a flow meter, a spray nozzle, a power source, and a DAQ system. A positive displacement pump set to a maximum pressure of

100 psi (689 kPa) is used to drive the water spray into the chamber. The spray water loop is closed by the water pump with its inlet connected to the bottom of the outer cylinder and its outlet

connected to the spray nozzle in the compression chamber. This ensures that the volume of air at the start of each compression cycle remains the same, and no secondary drain is needed for the additional water from the spray. When the pump is switched on, the spray injection starts in the chamber, and its injection pressure is controlled using a pressure regulator. To measure the flow rate of water flowing through the spray loop, a flowmeter is connected after the pressure regulator.

The flowmeter and pump are powered using a 12 VDC power supply, with the flowmeter readings being recorded by the DAQ. The spray nozzle is mounted on the top surface of the compression chamber and is radially centered to generate a symmetric spray pattern inside the chamber.

Connection to Nozzle

Liquid Piston Power Source Chamber

Pressure Regulator

Flow Meter

Figure 4.2: Spray Injection Setup

Figure 4.3: Spray pattern with full cone whirl nozzle.

The design of the nozzle along with spray angle will affect the droplet dynamics and the resulting heat transfer characteristics. The spray nozzles can be selected based on the type of nozzle

(spray pattern), droplet distribution, spray angle, injection pressure range, and the pipe size. As the compression chamber has a small air volume, a low flow-rate nozzle was selected, with a medium to fine droplet distribution. Therefore, low-flow whirl nozzles of various spray angles with a 0.045 inch (0.1143 cm) diameter from BETE (WL nozzle) were selected. A schematic of the spray pattern for the selected type of nozzle is shown in Figure 4.3. A full cone nozzle shown here was selected as it covers the maximum air volume during the compression process. The pipe size of 1/8 inch was used for the water line connecting to the spray nozzle. The injection pressure of spray was varied from 30psi (207 kPa) to 70psi (483 kPa) using the pressure regulator.

4.2.3. Measurement Devices

Air pressure is measured using a pressure transducer (OMEGA PX309 -100psi) mounted on the top plate of the outside cylinder along with the solenoid valves. The pressure transducer is a stainless-steel transducer which uses a high accuracy silicon sensor. Two thermocouples are placed inside the compression chamber to measure temperature. The thermocouples used are K-type 40- gauge diameter which are placed in radially opposite directions about 1 inch from the center of the spray nozzle and 1/2 inch below the top surface of the compression chamber. To prevent direct injection of spray on to the thermocouples and affect the temperature readings, the thermocouples were protected by a plastic casing. This ensured that the droplets did not directly interact with the thermocouples, however, indirect collisions due to splashing and rebounding water droplets could not be avoided.

For the spray cooling instruments, the injection pressure is controlled using a pressure regulator

(NORGREN R91W-2AK-NLN) and a flowmeter used is OMEGA flr-1012. Using a dial on the pressure regulator, the injection pressure of spray was varied manually for each run. The measurement instruments and their accuracies are listed in Table 4.1. Before starting the experiments, the measurement devices were calibrated repeatedly to maintain measurement accuracy.

Table 4.1: Measurement devices and corresponding accuracies. Measurement Description Accuracy Pressure Electronic Pressure Transducer 0-100psig (0-689 kPa) +/-0.25% Temperature K –Type Thermocouple +/-2.2 °C Volume Location Sensor +/-0.001 inch Flowmeter Electronic Flowmeter 0.5-5 L/min +/- 3%

These measurement instruments are connected to a DAQ system to measure various parameters during the compression and expansion cycles. The DAQ system converts the analog voltage signals from the transducer and thermocouples into digital signals. A controller is used to automate the compression process for multiple cycles. The instantaneous air pressure in the chamber, the air temperature in the chamber, displacement of the pneumatic cylinder, and flow rate of the water in the spray circuit are recorded using a LabVIEW program. Displacement of the pneumatic cylinder is used to calculate the instantaneous air volume as the total volume of water driven by the hydraulic pump into the liquid piston chamber is known (800 mL of water).

4.2.4. Range of Experiments

A parametric study is performed to investigate the effect of water spray on the performance of the liquid piston compression. The parameters studied in the experiments are spray nozzle angle, spray water injection pressure, and stroke time of compression. The spray nozzle angles of 60°,

90°, and 120° are considered. For each spray angle, the stroke time of compression is varied in three levels with stroke time about 3 s (fast), about 4 s (medium) and, around 5 s (slow). The stroke time setting was done manually by adjusting the inlet source pressure of the pneumatic cylinder which dictated the speed of the coupled hydraulic pump system. Also, injection of spray at different injection pressures affects the stroke time marginally. Therefore, the selected three levels of stroke times vary slightly from the set time based on the set inlet source pressure of pneumatic cylinder and the injection pressure of spray. With each spray angle and compression stroke time, the injection pressure is varied between 10-70 psi (69-483 kPa). Initially, the injection pressure was varied only from 30-70 psi (207-483 kPa) for 60° spray angle but it was observed that there was not a significant difference in the temperature and pressure profiles for this injection pressure range. Therefore, the injection pressure range was expanded to 10-70 psi (69-483 kPa) for the 90°

and 120° spray angles. Each compression stroke is performed until 800 mL of water is added into the compression chamber from the liquid piston.

4.3. Results and Discussion

The experimental data for compression with and without spray injection in the liquid piston are analyzed to investigate the effect of injection pressure of spray, spray angle, and compression stroke time on air temperature and the isothermal efficiency of compression.

4.3.1. Pressure and Temperature Plots

First, compression cycles without spray injection are examined. A representative case with a

90° spray angle with a compression stroke time of about 3 s is presented first. The pressure-time and temperature-time plots for ten continuous cycles without spray injection are shown in Figure

4.4. It is observed that the pressure reaches to about 280 kPa in all the cycles, and there is a good

Figure 4.4: Pressure and Temperature vs time for ten continuous compression cycles without spray.

cycle-to-cycle consistency in the pressure data. The temperature plot indicates that the air temperature rises significantly during the compression process. There exists a noticeable cyclic variability in the temperature data mostly due to point measurements of temperature. Also, the thermocouples are installed near the top of the chamber surrounded by a plastic casing which might have influenced the temperature measurement. However, the temperature measurements are useful for a comparative analysis to examine the effect of spray injection on the air temperature.

Similar plots for compression with the spray of different injection pressures are shown in

Figure 4.5. The pressure reached at the end of each compression cycle is between 230 kPa to 280 kPa depending on the injection pressure of spray. For each of the injection pressure, there is consistency in the pressure data during the compression process. The temperature data with 10 psi

Figure 4.5: Pressure and Temperature vs time for ten continuous compression cycles with sprays of different injection pressures.

(69 kPa) spray injection reaches the maximum temperature in each of the compression cycle below

315 K, considerably lower than the maximum temperature reached without spray injection.

Furthermore, at higher injection pressures, the temperature oscillated around 300 K which is significantly lower than the temperature observed without spray. Therefore, spray injection is an effective method of temperature abatement during the compression process. Overall, both the pressure and temperature data showed a good consistency between cycles during the entire operation. The cumulative displacement of the plots with progress in time for different injections pressures occurs due to the minute variation in stroke time of compression.

4.3.2. Effect of Injection Pressure

4.3.2.1. Flow rate

The injection pressure of spray is one of the major influential parameters affecting the spray characteristics such as the flow rate of spray and the droplet size distribution for a given nozzle. In this subsection, experimental results for the variation of injection pressure from 10 psi to 70 psi

(69 kPa - 483 kPa) for a 90° spray angle nozzle are presented. An increase in injection pressure increases the initial flow rate of spray during compression as observed in Figure 4.6. The flow rate of the fluid is determined by the nozzle diameter and effective pressure difference across the nozzle. A higher injection pressure provides a higher pressure difference which results in a higher flow rate for a fixed diameter nozzle. For each of the injection pressure, the flow rates decrease as the compression proceeds. This decrease is due to the backpressure created on the spray nozzle when the chamber air pressure increases as the compression progresses; effectively reducing the pressure differential between the nozzle and compression chamber.

Figure 4.6: Flow rates of the spray with different injection pressure during a single compression cycle.

4.3.2.2. Pressure in compression chamber

The motion of liquid piston from the bottom of the chamber towards the top drives the compression of air. The pressure in the compression chamber for a single compression and intake cycle with and without spray injection are shown in Figure 4.7. The maximum pressure during the compression stroke is observed for the case without any spray injection. On spray injection during compression, the final pressure attained is lower compared to that of no spray. The final pressure reached decreases with an increase in injection pressure, and the compression pressure ratio fell from around 2.9 to between 2.5-2.75 when spray was injected. As pressure and temperature are coupled for a gas in a closed chamber, a lower pressure of gas points towards a lower temperature.

The reduced peak pressure with the higher spray injection pressure implies a temperature reduction.

Figure 4.7: Pressure plots for a single compression cycle with and without spray of different injection pressures. (With 90o spray nozzle and fast level of stroke time).

4.3.2.3. Air temperature during compression

The heat transfer rate of the base liquid piston (no spray) is not sufficient to dissipate heat of compression to the surrounding which results in a significant rise in air temperature during compression as observed in Figure 4.8. A high rate of heat transfer with the spray injection absorbs a significant portion of the heat of compression. This keeps the air temperature close to the initial air temperature throughout the compression process. The large surface area of water droplets contributes to this heat transfer enhancement during the compression process. Additionally, the water droplets have high specific heat and therefore absorb a large amount of heat with a marginal increase in its temperature. This helps maintain a high temperature difference between the air and the droplets to attain a high heat transfer rate.

A higher spray injection pressure results in a lower air temperature towards the end of compression; however, the marginal gain in the temperature abatement reduces as the injection pressure increases. For an injection pressure of up to 40 psi (276 kPa) there is a significant reduction in air temperature at the end of compression, whereas, any further increase in injection pressure above 40 psi (276 kPa) results in only a minute improvement towards temperature abatement. This indicates that the flow rate of spray around 40 psi (276 kPa) injection pressure is good enough to attain a temperature drop close to the initial air temperature, and any further increase in flow rate at higher injection pressures does little to provide further improvement in temperature abatement.

Figure 4.8: Temperature plots for a single compression cycle without and with spray of different injection pressures. (With 90o spray nozzle and fast level of stroke time)

4.3.2.4. Pressure-volume plots

The pressure-volume plot is a useful tool to identify the effectiveness of spray injection to attain a near-isothermal compression. The effect of injection pressure of spray on the pressure- volume plots is shown in Figure 4.9. For comparison, the reference adiabatic and ideal isothermal pressure-volume plots are also presented in the same figure. It is observed that the compression without spray (base liquid piston) shifts the pressure-volume curve marginally towards the isothermal curve while spray injection shifts the pressure-volume curve considerably towards the isothermal conditions. The shift of the curve with an increasing spray injection pressure is easily observable up to 30 psi (207 kPa), while the curves from 40 psi and higher are extremely close to each other due to which they appear indistinguishable.

Figure 4.9: Pressure volume plots for a compression cycle with spray of different injection pressures in comparison with adiabatic and isothermal plots. (With 90o spray nozzle and fast level of stroke time)

Figure 4.10: Zoomed view of pressure-volume plots of Figure 4.9 near the end of compression.

The zoomed-in view shown in Figure 4.10 of the pressure-volume plots shows a perceptible distinction between the various curves. Higher injection pressures shift the curve towards near- isothermal conditions; however, the difference in the curves is not significant for injection pressures of 40 psi (276 kPa) and higher. This indicates that an injection pressure of 40 psi (276 kPa) is good enough to absorb the bulk of heat of compression and any increase in injection pressures has a marginal benefit. Overall, spray at injection pressures of 40 psi (276 kPa) and higher is highly effective in achieving near-isothermal compression.

4.3.2.5. Compression work and spray work

From the pressure-volume plot, the compression work can be calculated as an area under the curve. As spray injection shifts the pressure-volume curve towards an isothermal condition, the compression work reduces significantly compared to the compression without spray. A higher injection pressure of spray leads to a higher reduction in compression work, but this comes at a cost of additional pump work to generate a spray at higher pressures. The compression work and spray work at different injection pressures of spray are summarized in Table 4.2. They are normalized by the product of the initial pressure and volume (P0V0). The normalized compression work reduces with an increase in spray injection pressure. The percentage reduction in compression work with spray injection from the base (no spray) compression case is presented in column (4) of Table 4.2 to evaluate the degree of effectiveness of spray injection. Spray injection at 10 psi (69 kPa) reduces the compression work by about 10%, and a reduction up to 25% can be achieved with spray injection at higher pressures. However, this reduction is accompanied by a higher spray work as shown in columns (5) and (6). For lower injection pressures of spray, the spray work is a small fraction of the compression work, whereas, additional spray work as high as

60% of compression work is needed at higher injection pressures. Comparison of column (4) and column (6) guides whether additional spray work is justifiable to achieve a net reduction in work input. At injection pressures of up to 30 psi (207 kPa), the reduction in compression work is higher than the additional spray work required. However, at injection pressures of 40 psi (276 kPa) and above, additional spray work is higher than the reduction in compression work. This indicates that spray up to 30 psi injection pressures are worthwhile to achieve a net reduction in work when the spray is used as an additional mechanism in the compression system. Furthermore, it can be noted that the highest gain (difference in column 4 and column 6) is achieved with 20 psi injection

pressure. Therefore, the maximum net reduction in work is achieved when the injection pressure is lower than 30 psi (207 kPa).

Table 4.2: Compression Work and Spray Work for compression at different injection pressures.

Injection Normalized1 Reduction in Percentage Normalized1 Spray-Work in Pressure of Compression Compression Reduction in Spray Work2 percentage of 2 Spray Work work with Compression (Standard Error) No Spray spray from No work from No compression (Standard Error) spray Spray (5) work (1) (2) (3) (4) (6)

0.4102 0 No Spray - - 0 (0.0084) (-)

10 psi 0.3683 0.0100 0.0419 10.21% 2.44% (69 kPa) (0.0076) (0.0002)

20 psi 0.3352 0.0340 0.0749 18.27% 8.28% (138 kPa) (0.0065) (0.005)

30 psi 0.3230 0.0655 0.0872 21.26% 15.97% (207 kPa) (0.0053) (0.0006)

40 psi 0.3211 0.1008 0.0890 21.71% 24.58% (276 kPa) (0.0043) (0.0009)

50 psi 0.3139 0.1418 0.0963 23.48% 34.57% (345 kPa) (0.0056) (0.0016)

60 psi 0.3147 0.1878 0.0954 23.27% 45.79% (414 kPa) (0.0044) (0.0029)

70 psi 0.3093 0.2441 0.1009 24.60% 59.51% (483 kPa) (0.0055) (0.0024)

1 2 Notes: Normalized with P0V0, Average of ten cycles and the terms in the brackets denotes standard error.

Potentially, the hydraulic pump can be replaced with a spray injection system to supply the compression work. In such a system, the motion of liquid piston during the compression stroke would be achieved with injection of water from the spray. During the air intake stroke of compression, the liquid needs to be removed from the compression chamber to bring the liquid level to the initial stage. This can be achieved by operating two liquid piston compression systems simultaneously with a phase difference, i.e. during the suction of one liquid piston, compression is performed in another system. In this way, the spray injection system can be effectively used to achieve motion of the liquid piston in both the intake and compression stroke of the compression process. From Table 4.2, it can be observed that spray injection can provide the necessary compression work since the normalized spray work is of the same order as that of the normalized compression work. Further studies into the design of a spray system to match the spray work with the compression work are needed. Such a system would be highly effective because the injection of spray would not account in any additional work requirements.

4.3.2.6. Isothermal efficiency of compression

Isothermal efficiency of compression assesses the effectiveness of a compressor system to achieve a near-isothermal compression. The polytropic index of compression is evaluated by fitting a polytropic process model through the pressure-volume plot to estimate the isothermal efficiency. Figure 4.11 shows the isothermal efficiency of compression for various spray injection pressures. The error bar for each of the cases represent the standard deviation in the efficiency values for ten compression cycles. The base liquid piston without spray injection has an isothermal efficiency around 75%. The efficiency increases consistently with a higher spray injection pressure and approaches close to 95% efficiency. When the compression process shifts towards an isothermal condition, a reduction in the compression work and cooling work is observed. This

results in a significant improvement in the isothermal efficiency. The marginal gain in efficiency at higher injection pressures diminishes with an increase in spray injection pressure. Furthermore, the small error bars indicate that consistent improvement in efficiency is possible with spray injection. Overall, spray injection is effective in achieving an isothermal efficiency up to 95% in a liquid piston compressor.

Figure 4.11: Isothermal efficiency of compression with spray of different injection pressures.

4.3.3. Effect of Spray Nozzle Angle

The droplet characteristics during spray generation are heavily influenced by the injection pressure and the nozzle angle. From the manufacturer’s data on the droplet size distribution of spray, it is noted that increasing the spray angle for a constant injection pressure decreased the mean droplet diameter. Also, the spray angle determines the spread of the droplets in the chamber volume. A smaller spray angle injects the majority of droplets in the middle of the chamber whereas a wider angle injects a large amount of spray on the walls of the chamber. In the current set of experiments, a higher fraction of spray droplets will hit the chamber walls with a 120° spray angle than the 90° and 60° spray angles which may affect heat transfer characteristics of spray. Here, results are presented for the experiments done with spray angles of 60°, 90°, and 120° for a constant injection pressure of 30 psi (207 kPa) and a compression stroke time of about 4s.

4.3.3.1. Air temperature during compression

The effect of the spray angle on temperature abatement is observed from the temperature-time data for various spray angles in Figure 4.12. The three spray angles are equally effective in reducing the air temperature during compression. Since the temperature values are within the accuracy range of the thermocouple, it is difficult to distinguish a clear trend in the temperature plots for different spray angles. However, these temperature plots do suggest that a substantial temperature drop is achieved with spray injection for all the cases. Although the spray angles are different, the flow rates of spray were of a comparable magnitude for these experiments due to the same injection pressure. Theoretically, the spray from 120° nozzle angle should have a higher heat transfer area due to the overall smaller droplets compared to 90° and 60°. However, the similar temperature plots suggest that a similar rate of heat transfer is achieved irrespective of the spray angle.

Figure 4.12: Temperature plots with different spray angles during a single compression cycle. (With 30 psi injection pressure and medium level of stroke time)

4.3.3.2. Pressure-volume plots

Pressure-volume plots with spray injection from different spray angles are shown in Figure

4.13 as a means to further analyze this parameter. Similar pressure-volume curves are observed for a spray with different nozzle angles at the same injection pressure; suggesting that the nozzle angle has only a marginal effect on the heat transfer characteristics due to the spray. The curves for 60° and 90° spray angles appear slightly closer to the isothermal curve than the curve for the120° angle indicating that the 60°- 90° angle range is favorable. With a larger nozzle angle, a higher fraction of droplets impact the walls of the chamber compared to the smaller angles. This causes a reduction in the effective number of droplets available for heat transfer with increasing spray angles.

Therefore, the 120° spray angle appears to be slightly less effective in shifting the compression

process towards an isothermal condition than the 60° and 90° angles. Hence, with the selection of an optimal spray angle, a quantifiable reduction in compression work is possible.

Figure 4.13: Pressure-volume plots with spray injection of different spray angles during compression. (With 30 psi injection pressure and medium level of stroke time)

4.3.3.3. Isothermal efficiency of compression

The isothermal efficiency is calculated for the compression with spray for different nozzle angles using various injection pressures. The isothermal efficiency of compression for all three spray angles (60°, 90°, and 120°) at varied injection pressures of 30 psi (207 kPa), 50 psi (345 kPa), and 70 psi (483 kPa) are shown in Figure 4.14. The error bar for each of the cases represents the standard deviation of ten observations. For any injection pressure, the variation in spray angle marginally affects the isothermal efficiency. Also, a spray angle of 60° is slightly better than a spray angle of 90°, and 120° is the least efficient among all the three angles for any injection

pressure. As discussed earlier, a higher percentage of droplets impact the chamber walls for a larger nozzle angle effectively reducing droplets in contact with the air. This results in the reduction of the net surface area available contributing to a lower heat transfer rate. The reduction in the rate of heat transfer is consistent across all injection pressures, therefore, the isothermal efficiency decreases with an increase in the nozzle angle.

Even though the droplet diameter become finer with the larger spray angle, an overall reduction in the rate of heat transfer is observed with a larger spray angle. This suggests that an optimal spray angle which can generate finer droplets with a minimum loss of droplets is desired for maximum efficiency. Noticeably, in these experiments for different nozzle angles, a 60° nozzle shows around a 1 - 4% improvement in the isothermal efficiency compared to a 120° nozzle irrespective of the spray injection pressure.

Figure 4.14: Isothermal efficiency with spray injection from different nozzle angles for various injection pressures.

4.3.4. Effect of Stroke Time of Compression

An efficient compressor system with a high power density is highly valuable for numerous compressor applications. A high power density demands a small stroke time of compression.

However, the heat transfer characteristics of liquid piston compressor alter with the change in the stroke time of compression. A faster compression (smaller stroke time) provides less time for heat transfer compared to a slower compression (larger stroke time). Thus, a slower compression is favorable to realize a near-isothermal compression though a slow compression results in a low power density. A heat transfer enhancement technique which can attain a near-isothermal compression at a small stroke time is desired to attain a high efficiency coupled with a high power density. The ability of spray injection to achieve near-isothermal compression with a fast compression stroke is investigated in the following sections. Spray injection at various stroke time of compression is examined in three stages (fast, medium, and slow compression).

4.3.4.1. Air temperature during compression

The air temperature with different compression stroke times with and without spray injection is shown in Figure 18. The spray injection for this plot is considered at 30 psi (207 kPa) injection pressure and a 90° spray angle. For compression in the liquid piston without spray injection, the peak air temperature increases with a shift towards faster compression. A longer stroke time provides more time for heat dissipation which results in comparatively lower air temperature.

Spray injection reduces the air temperature significantly for all three stoke times of compression. The fact that the temperatures profiles with spray injection are very similar indicating that spray injection is equally effective at all the studied stroke times for temperature abatement.

Spray injection absorbs a significant portion of the heat of compression and lowers the air temperature significantly. With spray injection, a higher stroke time does not provide significant improvements in heat dissipation as the water droplets absorb the majority of the heat, due to which

the contribution of higher compression stroke time is minimal. Therefore, even with a faster compression process, spray injection is equally effective in maintaining a near-isothermal condition.

Figure 4.15: Temperature plots with and without spray injection for a compression cycle with different stroke times. (With 30 psi injection pressure and 90° spray angle)

4.3.4.2. Pressure-volume plots

Further investigations at different stroke times of compression are performed using pressure- volume plots. For compression without spray injection, the pressure-volume plots in Figure 4.16 indicate that a slower compression shifts the curve slightly towards the isothermal curve.

Therefore, the compression work reduces with an increase in stroke time. However, as a larger stroke time hampers the power density, compression with a smaller stroke time is desired for a high power density. Compression with spray injection balances both of these characteristics. The pressure-volume plots with spray injection are closer to one another and also tend towards the

isothermal curve. This implies a significant reduction in the compression work is possible with spray injection irrespective of the stroke time.

Figure 4.16: Pressure-volume plots with and without spray injection for a compression cycle with different stroke times. (With 30 psi injection pressure and 90° spray angle)

A zoomed-in view of Figure 4.16 towards the end of compression is shown in Figure 4.17. It shows that spray injection with slow compression is marginally closer to the isothermal curve, however, the difference is indistinguishable. This indicates that a faster compression process can be achieved with its compression work comparable to that of a slower compression process.

Therefore, spray injection with a faster compression process is highly effective to achieve an efficient compression process with a high power density.

Figure 4.17: Zoomed view of pressure-volume plots of Figure 4.16 near the end of compression.

4.3.4.3. Isothermal efficiency of compression

The isothermal efficiency with spray injection at different compression stroke times is evaluated for various injection pressures. The isothermal efficiency for the three levels of compression stroke time (fast, medium, and slow compression) at the different injection pressures of 30 psi (207 kPa), 50 psi (345 kPa), and 70 psi (483 kPa) are shown in Figure 4.18. The error bar for each of the cases represents the standard deviation of efficiencies evaluated for ten compression cycles. A base liquid piston case without spray injection displays an isothermal efficiency of around 75% with a faster compression stroke. The efficiency of the base liquid piston can be improved up to 80% with a slower compression process. However, as mentioned in previous sections, this affects the power density of the compressor and is therefore not worthwhile. Spray

injection improves the efficiency significantly for the varied stroke times at given injection pressures. At a lower (30 psi) injection pressure, slowing the compression improves the efficiency marginally. However, at a higher (70 psi) injection pressure, an isothermal efficiency of about 95% is observed irrespective of the level of stroke time. At a higher injection pressure, a faster compression is highly effective in achieving an efficient compression process with a high power density.

Figure 4.18: Isothermal efficiency with and without spray injection at various stroke time of compression for various injection pressures.

4.4. Conclusions

Water spray injection is studied experimentally in a liquid piston compressor for a pressure ratio of about 2.5. Temperature, pressure, and volume of air are measured during the compression process to assess the effectiveness of spray injection. Experiments are designed to include a range of experiments covering various injection pressures of spray, different spray angles, and various

compression stroke times. For each experimental case, at least ten continuous compression cycles are performed. Measurements show cyclic consistency in pressure and temperature data during the compression process with and without spray injection.

The injection of spray is observed to be very effective in reducing the air temperature during the compression process. The temperature abatement increases with an increase in injection pressure of spray from 10 psi (69 kPa) up to 70 psi (483 kPa). With the increase of injection pressure, the flow rate of spray water increases which provides a higher rate of heat transfer and help reduce air temperature significantly. The pressure-volume plots close to isothermal curves are observed with the spray above 30 psi (207 kPa) injection pressures. The spray injection shows up to 25% reduction in compression work from the base liquid piston compression. Reduction in compression work for every additional injection pressure reduces with higher injection pressure.

The spray work also increases with injection pressure, and it’s worthwhile to inject spray with injection pressure less than 30psi to observe a net reduction in work if spray injection is used as an additional system in the compressor. However, if the spray system is used as the main driver for compression work, spray injection could be highly effective at higher injection pressures as well. The isothermal efficiency of compression can be improved significantly with the injection of spray. The improvement in efficiency increases with the increase of spray injection pressure. The injection of spray at 70 psi leads to 19-21% improvement in isothermal efficiency of compression from the base level efficiency of 75% for liquid piston without spray. Overall, water spray injection is highly effective in achieving near-isothermal compression with up to 95% isothermal efficiency.

Furthermore, experiments with different spray angles of nozzles were performed at 60°, 90°, and 120° nozzle angles for different injection pressures. It was observed that 60° nozzle angle is marginally better than 90°, and 120° is least efficient at all the injection pressures of spray. The

wider nozzle angles lead to the loss of water droplets due to the impact of spray on the chamber wall and reduce the effective rate of heat transfer from the spray. An optimal spray angle which can create smaller droplets with minimum loss of droplets due to the impact on chamber wall should be considered for maximum efficiency.

Likewise, the usefulness of spray injection at various stroke times of compression is investigated by varying the speed of compression at 3 levels (fast, medium, and slow compression) at different spray injection pressures. It is observed that slower compression provides only marginal benefit in efficiency at lower injection pressures, and isothermal efficiency of about 95% is observed irrespective of the speed of compression at a high injection pressure (70 psi).

Therefore, spray injection is highly effective to attain efficient compression with a high power density.

Overall, water spray injection is observed to be a highly effective technique to achieve near- isothermal compression in the liquid piston. However, this study is based on experimentation at a relatively low compression pressure ratio, and further investigations are needed to confirm the effectiveness of spray injection at higher compression pressure ratios. Also, contamination of water vapor in the air could be an issue for many compressor applications. The effect of contamination of air on operation and maintenance of compressor system needs to be explored. Further studies on optimizing the spray nozzle design to achieve droplet size distribution and flow rate for maximum heat transfer can provide additional improvement in efficiency.

CHAPTER 5: Aqueous Foam in Liquid Piston Compressor

Abstract: For many compressor applications, high heat transfer rates are desired to achieve the isothermal compression process. A large surface area for heat transfer and a high heat transfer coefficient of aqueous foam can be used in achieving a significantly high heat transfer rate in the compression chamber. In this experimental study, an aqueous foam based heat transfer is investigated in a liquid piston compressor. Experiments are performed with the use of aqueous foam generated under different foam generation conditions. The amount of aqueous foam, the air flow rate for foam generation, and various foam generator designs are considered in this parametric investigation. It was observed that the use of aqueous foam in the compression chamber is highly effective in reducing the temperature of air during the compression process. A higher volume of aqueous foam in the compression chamber leads to a further increment in isothermal efficiency, however, with higher variability. The higher variability in efficiency is due to the higher cyclic variation of the temperature profiles during compression. A compression chamber completely filled with aqueous foam shows a 4-8% improvement in the efficiency for a compression ratio of

2.5. Furthermore, several foam generator designs were tested to see if there is any dependence of cyclic variability of efficiency on foam generator design parameters. The results show some promise on optimizing the design to reduce the variability. Overall, the use of aqueous foam in the liquid-piston compressor used in this experimental study is effective in achieving an isothermal efficiency up to 92% compared to 86% for the no-foam case.

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5.1. Introduction

In a typical compressor application, the energy costs for the compressor operation contribute to a significant share of the overall life-cycle cost. Improvements in the energy efficiency of compressed air systems can result in a significant amount of energy savings [98]. Compressed air energy storage systems have great potential to serve as large-scale energy storage systems.

Compressors and expanders are the key components in compressed air energy storage plants [99].

Development of an efficient compressor would make compressed air energy storage systems viable and economical [100]. Near-isothermal compressors can achieve a high roundtrip efficiency of compressed air energy storage systems [101, 102]. Such efficient compressed air energy storage systems on a broader view facilitate effective utilization of intermittent renewable energy sources.

Isothermal compression results in an efficient compression due to the minimum work input associated with the isothermal process. Recently, the compression of gas using a column of high pressured liquid as a piston (also called liquid piston) has shown better performance in achieving near-isothermal gas compression [103]. The liquid piston can achieve a near-isothermal compression due to a higher heat transfer rate during gas compression. The increased heat transfer is achieved by increasing the surface area to volume ratio in the compression chamber. Clearly, heat transfer plays an important role in achieving near-isothermal compression and thereby, improving the efficiency of compression using the liquid piston [104]. For the isothermal compression, the instantaneous rate of heat transfer should be equal to the instantaneous mechanical power to the compressor [105]. In general, the mechanical power to the compressor is significantly higher than the instantaneous rate of heat transfer. This results in a near-adiabatic process in the compressors. A gradual roadmap from the adiabatic towards isothermal conditions from a thermodynamics and heat transfer point of view is presented in [106]. Convective heat

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transfer coefficient and area of heat transfer should be increased drastically to achieve the near- isothermal compression.

Various methods for improvement in efficiency of liquid piston compressor have been investigated. Pareto optimal compression/expansion trajectory for a liquid piston air compressor/expander that maximizes efficiency for given power has shown improvement in efficiency [107]. Further optimization of compression chamber geometry and liquid flow rate has shown 20 fold improvement in power density for the same efficiency level [108]. Liquid piston with water spray based cooling to augment heat transfer has shown 89% three-stage compression efficiency, substantially higher than the 27% associated with a conventional adiabatic compression at the same pressure ratio [109]. Porous media inserts in the liquid piston increase heat transfer surface area significantly resulting in increased efficiency at a fixed power density or increased power density for a given efficiency. An experimental study with porous media inserts in a liquid piston compression has shown 18% improvement in efficiency at 100kW/m3 power density and a

39-fold increase in power density at 95% efficiency [110]. Clearly, heat transfer in the compression chamber plays important role in improving compression efficiency. Therefore, mechanisms of heat transfer enhancement in the liquid piston will help in achieving near-isothermal compression/expansion process and in-turn efficient compressed air energy storage systems.

Aqueous foam has a large two-phase contact surface which allows its use as a coolant. In comparison to single-phase coolants, aqueous foams provide relatively large heat transfer rate, smaller coolant mass flow rate and low energy consumption in delivering it to the region of heat transfer [111]. Various factors influence heat transfer intensity of aqueous foam flow namely- diameters of foam bubbles, surfactant and its concentration, volumetric void fraction, foam flow velocity, flow direction, foam structure, the geometry of heat exchanger etc. Heat transfer intensity

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and its dependency on flow velocity, volumetric void fraction and flow direction of aqueous foam flow in various heat exchanger geometries has been carried out by Gylys et.al. [112]. Their experimental investigation of the staggered tube bundle heat transfer to the vertical upward and downward aqueous foam flow showed much higher heat transfer intensity (25 to 100 times higher) than that for one-phase airflow under the same flow velocity. Similar results were observed for aqueous foam flow over in-line bundle [113], inclined flat surface [114], vertical flat surface [115] and vertical channel [116].

Tseng et al. [117] experimentally investigated rheology and convective heat transfer of microfoams in horizontal mini-channels. They observed microfoams made of water-surfactant show smaller heat transfer coefficient than single phase water due to reduced specific heat and thermal conductivity of foam. However, specific heat and thermal conductivity of foam are higher than that of air resulting in a higher heat transfer coefficient of foam than that of air. Attia et.al.

[118] analyzed convective heat transfer of aqueous foams under laminar flow in pipes and tube bundle under constant wall heat flux. They explored a wide range of porosity, viscosity, flow rate, heat fluxes, and two different pipe diameters. They proposed that analytical and semi-empirical expressions for single-phase power-law fluids can be extended to two-phase foams by defining the

Reynolds number based on effective viscosity and density of foams. As specific heat and thermal conductivity of the water are higher than that of air, the heat transfer coefficient for aqueous foams is significantly higher than that of air at the same flow conditions. Therefore, the high surface area of heat transfer in combination with a high heat transfer coefficient of aqueous foam results in significantly higher heat transfer rate from aqueous foam.

Introduction of aqueous foam into the liquid piston compressor chamber can enhance heat transfer characteristics and thus improve the efficiency of liquid piston compressor/expander.

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SustainX Inc. has patented such a two-phase heat transfer process in a compressed air storage system and claims the achievement of near-isothermal gas compression and expansion [119].

SustainX reported that foam-based rapid heat exchange has allowed development of a megawatt- scale compressor/expander with isothermal efficiency greater than 95%. End-to-end efficiency analysis on Ocean Compressed Air Energy Storage (OCAES) shows that compressor/expander with 95% isothermal efficiency can lead to OCAES with roundtrip efficiency of about 70% [120].

This level of efficiency is significantly higher than existing CAES plants in Huntorf (Germany) and McIntosh AL (USA) which show the efficiency of 42% and 54% respectively [121]. Also, in large-scale energy storage, an increase in efficiency by a small value leads to tremendous economic benefit and energy savings. These benefits for years of operation of a CAES would lead to a massive amount of economic advantage over the long run. Undoubtedly, the development of an efficient isothermal compressor/expander with the use of aqueous foam would make CAES promising large-scale energy storage.

In this study, aqueous foam based heat transfer is experimentally tested in a liquid piston compressor. The temperature and pressure of air during compression is measured with and without aqueous foam in the compression chamber. Furthermore, the isothermal efficiency of compression is evaluated from the experimental results to estimate the effectiveness of aqueous foam to achieve near-isothermal compression. Conceptual framework about aqueous foam is presented in the next section. The experiment setup, various foam generator designs, and experimental cases are explained in the experimental procedure section. The results and discussion section presents experimental results and analysis. Finally, the major conclusions and limitations of this study are presented.

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5.2. Conceptual Framework Aqueous foams are a dispersion of gas in a liquid, stabilized by surfactant absorbed at the air- liquid interfaces [122]. Foam can be generated by continuously blowing gas into a surfactant solution from the bottom as shown in Figure 5.1. Foams can be classified as wet foams and dry foams based on the liquid content in the foam. When liquid content is high, walls of the cells are thick and none of them are distorted by others resulting in spherical cells. In dry foam, cells are separated by thinner walls and they influence one another resulting in the polyhedral form [123].

The wetness of the foam can be defined in terms of volumetric void fraction (also called porosity) of foam which is the ratio of volume of gas to the total volume of foam [124]. Dry foams have a high volumetric void fraction. There exists a critical volumetric void fraction at which the individual bubbles in the foam take spherical shape splitting region of dry and wet foams. It has been observed that volumetric void fraction of the foam influences heat transfer characteristics. It was observed that the heat transfer rate increases with a decrease in volumetric void fraction [112].

Figure 5.1: Foam generation by injecting air through fritted disk [149].

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Foams can also be classified based on the size of bubbles. Foam with relatively high liquid content and very small dimensions of bubbles are called microfoams. Microfoams are wet foams and possess spherical bubbles. Macrofoams have a very high content of gas (dry foams) and contain polyhedral cell structure. Macrofoams show relatively high heat transfer rate with a low mass flow rate [125]. Therefore, the ratio of heat transfer to coolant density is higher for macrofoams. Volumetric void fraction and size of bubbles are key parameters that influence heat transfer in aqueous foam. However, bubble dynamics in foam changes volumetric void fraction and bubble size distribution of the foam over time. This, in turn, affects the heat transfer behavior of aqueous foam. Therefore, heat transfer in aqueous foam is influenced by complex bubble dynamics which is influenced by various interactive forces active in the foam.

5.2.1. Bubble Dynamics in Aqueous Foams

The main factors that determine bubble dynamics in the foam are drainage of liquid in foam, inter-bubble gas diffusion, and bubble coalescence. Gravity, pressure difference, viscous effects, capillary forces, and film instabilities are driving mechanisms for these factors. The interplay between these mechanisms determines the structure, properties, and stability of foam [126].

5.2.1.1. Liquid drainage

The liquid drainage (also called foam drainage) is a flow of liquid through the interstitial spaces between bubbles. The flow is governed by capillary and gravitational forces. Plateau borders, nodes (vertexes), and films (faces) are basic structures in the foam as shown in Figure 5.2 for a single cell structure [127]. The foam resists to drainage by these three basic dissipative structures.

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Figure 5.2: Basic structures of single cell [127].

Therefore, the draining flow significantly undergoes viscous losses. The foam drainage equation for drainage along the plateau borders is given by equation (5-1) [128].

휕훷 휕 = (훷푞 ) (5-1) 휕푡 휕푧 푃퐵 where 훷 is volumetric void fraction (or porosity), and 푞푃퐵 is the volumetric flux of the liquid phase through plateau border channels at location z and time t given by equation (5-2) [129].

1/2 [1−훷(푧,푡)]2 휌gr2 1.3957휎푟2 휕 훷(푧,푡) 푞 (푧, 푡) = 3.632 × 10−3푐 { + [( ) ]} (5-2) 푃퐵 휈 훷(푧,푡) 휇 훼휇 휕푧 (1−훷(푧,푡))푟2 where ρ is liquid density, g is acceleration due to gravity, μ is the dynamic viscosity of liquid, σ is the surface tension, r is the radius of foam bubble, 푐휈 is a dimensionless velocity coefficient accounts for the mobility of the walls of a plateau border channel, and α is a dimensionless constant representing radius of curvature of plateau border.

Equations (5-1) and (5-2) provide the transient equations for the foam porosity at height z and time t as a function of various foam parameters. These equations evaluate variation in foam porosity over space and time due to liquid drainage.

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5.2.1.2. Inter-bubble gas diffusion

Non-uniform bubble sizes in the foam result in inter-bubble gas diffusion. The slightly higher pressure in the smaller bubbles forces gas to diffuse into the larger bubbles through lamellae resulting in shrinkage of smaller bubbles and growth of larger bubbles. The pressure difference

(ΔP) between gas inside the bubble of radius r and liquid within the foam is given by equation (5-

3) [130].

∞ 1 1 ∫ 푟2퐹(푟,푡)푑푟 ∆푃 = 2휎 ( − ) where 푟 (푡) = 0 (5-3) 푟 푟 푚 ∞ ( ) 푚 ∫0 푟퐹 푟,푡 푑푟 where rm is the mean bubble radius, and F(r, t) is frequency distribution function of radius r at time t.

By conservation of gas moles and using the ideal gas approximation for the gas, equation of radius of the bubble with respect to time is given by equation (4) [130].

푑푟 2퐽휎푅푇 1 1 = ( − ) (5-4) 푑푡 푃푎 푟푚 푟 where J is effective gas permeability, R is a gas constant, T is absolute temperature, and Pa is surrounding pressure. Bubble growth or shrinkage is determined from the difference between r and rm. i.e. if r < rm the bubble shrinks while if r > rm the bubble grows.

Equations (5-3) and (5-4) represent the evolution of bubble size distribution in foam due to inter-bubble gas diffusion mechanism.

5.2.1.3. Bubble coalescence

Bubble coalescence is the process by which two or more bubbles merge to form a single daughter bubble. Coalescence of air bubbles is greatly influenced by the type and concentration of surfactants present in the solution. The coalescence time is often considered as an indication of the stability of the foam. The main factors that determine coalescence time are the surface excess concentration of the surfactant and the repulsive surface forces such as electrostatic double layer,

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hydration and steric forces [131]. The film-drainage models of coalescence time of bubbles in the surfactant solutions is given by equation (5-5) [132].

휇 푟4.06(∆휌g)0.84 푡 = 0.79 (5-5) 푐 휎1.38퐵0.46

-28 where tc is coalescence time, and B=1 x 10 J is a modified Hamaker constant. The equation (5-

5) is for the buoyancy-driven coalescence of a bubble at a flat gas-liquid interface. A liquid film formed between the bubble and the flat surface thins with time by the drainage of liquid. When the thickness of the thin film reaches its critical value, the van der Waals forces cause it to rupture. In general, the average bubble coalescence time of air bubbles in the aqueous foams increases with an increase in surfactant concentration [131].

Clearly, three phenomena namely - liquid drainage, inter-bubble gas diffusion, and bubble coalescence influence volumetric void fraction and bubble size distribution of the aqueous foams.

5.2.2. Heat Transfer in Aqueous Foams

The heat transfer from the hot air to the aqueous foam is given by equation (5-6).

푞 = ℎ 퐴푓 (푇ℎ − 푇푓) (5-6) where q is heat transfer to the aqueous foam, h is heat transfer coefficient, Af is heat transfer area of aqueous foam, and Th and Tf are temperatures of hot air and foam, respectively.

Aqueous foams show significantly higher heat transfer than air because of the following reasons:

i) Aqueous foams show a significantly higher heat transfer coefficient (25-100 times higher) than that of air [112].

ii) Aqueous foams have a very high surface area of heat transfer.

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iii) Aqueous foams have higher specific heat than air. This helps in keeping the temperature of foam (Tf ) lower resulting in higher temperature difference (푇ℎ − 푇푓) which facilitates higher heat transfer.

The dynamic phenomenon in aqueous foam changes the characteristics of the aqueous foam.

(like volumetric void fraction, bubble size distribution). These changes affect thermal properties, and surface area of aqueous foam results in a change of its heat transfer behavior. Therefore, bubble dynamics influence heat transfer with aqueous foam.

Heat transfer coefficient is a key parameter in heat transfer evaluation. The heat transfer coefficient of aqueous foam can be evaluated by extending heat transfer analysis of single phase flow to foams as presented below. Liquid foams flow in a non-Newtonian manner and rheological behavior of foams can be described by the pseudoplastic power law model [133]. Analytical solutions predicting the Nusselt number for single phase power-law fluids can be extended to the foams. A relation between various dimensionless numbers for single phase power-law fluid flow through the circular pipe is given by equation (5-7) [134].

3푛+1 1/3 퐷 푅푒푃푟 1/3 8(5푛+1)(3푛+1) 푁푢 = 1.41 ( ) ( ℎ ) 푎푛푑 푁푢 = (5-7) 푥 4푛 푥 ∞ 31푛2+12푛+1 where 푁푢푥 is Nusselt numer in the entry region, 푁푢∞ is Nusselt number in thermally fully developed region, n is flow behavior index, Re is Reynolds number, Dh is hydraulic diameter, Pr is Prandtl number, and x is length from the entrance.

Recently, Attia et al. [118] showed that heat transfer correlations for single phase power-law fluids can be effectively extended to the foam with Reynolds number based on the effective physical properties of foam whereas, Nusselt and Prandtl numbers should be based on thermal properties of water. Therefore, dimensionless numbers for foam would be

휌푓푈퐷ℎ ℎ퐷ℎ 푐푝,푤 휇푓 푅푒푓 = , 푁푢푓 = , 푃푟푓 = (5-8) 휇푓 푘푤 푘푤

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where subscripts f and w denote foam and water, respectively. The relationship between dimensionless numbers for the foam flow in a circular pipe can be considered as,

1 1 1/3 1/3 − 3푛+1 퐷ℎ푅푒푓푃푟푓 푁푢 = 푎 퐶(휒) 6 (퐶푎 )8 ( ) ( ) (5-9) 푓,푥 푓 4푛 푥 where a is a constant to be determined from experimental data, 퐶(휒) is an empirical function dependent on surfactant mass fraction 휒 in weight percentage, and 퐶푎푓 is capillary number.

The heat transfer coefficient (h) of aqueous foam can be evaluated using the Nusselt number for the foam. It can be observed that the heat transfer coefficient of aqueous foam depends on thermo-physical properties of foam and flow properties through a complex relationship. Overall, the high thermal conductivity of water compared to air leads to a high heat transfer coefficient of foam compared to the air. Moreover, the high surface area of bubbles in the foam provides a high heat transfer area to achieve a high rate of heat transfer.

The complex bubble dynamics and heat transfer mechanisms in the aqueous foam make it challenging to investigate heat transfer with foam of different characteristics. Moreover, the pressure and temperature of the air inside the compression chamber vary during the compression process. Bubble dynamics and heat transfer characteristics of aqueous foam exposed to changing pressure and temperature conditions will add additional complexities to the heat transfer investigation. Therefore, a parametric study by changing foam generation parameters is performed to investigate the usefulness of aqueous foam for temperature abatement during the compression process. The flow rate of air source used to generate foam also affects the bubble size distribution and volumetric void fraction of foam. Additionally, the design characteristics of the foam generation device would influence foam characteristics.

5.2.3. Isothermal Compression

According to the first law of thermodynamics applied to a compressor,

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푑푈 = 푄̇ − 푊̇ (5-10) 푑푡 where U is the internal energy of the gas, 푄̇ is heat transfer rate from the system, and 푊̇ is rate of work done on the system.

푑푈 For isothermal compression, = 0 , which results in 푄̇ = 푊̇ i.e. the rate of heat transfer 푑푡 from the air should be equal to the rate of work input during the compression. In general, |푄̇ | <

|푊̇ | which results in an increase in temperature of air in compression. Isothermal compression demands significantly higher heat transfer rate from the air. Aqueous foam in contact with air in the compression chamber can absorb the heat from the air during the compression process. This would limit the temperature rise of air in compression and hence near-isothermal compression.

The effectiveness of aqueous foam based heat transfer in achieving isothermal compression can be evaluated using isothermal compression efficiency. The compression process can be modeled using the polytropic process relation given by

푛 푛 푃푉 = 푃0푉0 (5-11) where P is Pressure, T is Temperature and n is a polytropic index of compression. A polytropic index of compression (n) can be evaluated by fitting this relation through the experimental pressure and temperature data. The polytropic index equal to 1 indicates isothermal compression whereas polytropic index value equal to k (specific heat ratio) indicates adiabatic compression. The isothermal efficiency of compression for the polytropic process is evaluated using equation (5-12)

[135].

1 ln 푃−1 + 휂 = 푃푟 (5-12) 𝑖푠표 푛−1 1 ( ) 1 − 푃푟 푛 − 1 − 푛 1 + 푃푟 푛 −1 + (푃푟−1)( 푃 − ) 푛−1 푟 푃푟

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5.3. Experimental Procedure 5.3.1. Liquid Piston Compressor Setup

A table-top liquid piston compressor setup shown in Figure 5.3 is used for the experiments. It comprises of a compression chamber, water container, hydraulic pump, solenoid valves, pneumatic cylinder, a pressure transducer, and a thermocouple. The compressor chamber is immersed in a water container. This enhances the heat transfer from the chamber to the surrounding water. The water in the container also provides a large heat sink during the continuous operation of the compressor. The inlet and outlet valves are connected to the chamber on the top. A reciprocating hydraulic pump is used to control the supply of water (liquid piston) inside the compression chamber. The hydraulic pump is operated through a pneumatic cylinder by controlling the supply of a high-pressure air source. A controller is used to control the operation of inlet and outlet valves connected to the compression chamber and supply of air to the pneumatic cylinder.

A stainless-steel pressure transducer which uses a high accuracy silicon sensor (OMEGA

PX309 -100psi) is installed at the top of the compression chamber to measure the instantaneous pressure of the air during the compression process. A K-type thermocouple of 40 gauge diameter was placed in the compression chamber to measure the instantaneous temperature of the air. A

LabVIEW program was used to program the operation of solenoid valves and the motion of liquid piston using the hydraulic pump. Instantaneous pressure and temperature data during compression cycles are recorded using a data acquisition device through the LabVIEW program. The measurement devices were calibrated repeatedly to maintain measurement accuracy.

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Figure 5.3: Experimental Setup of Liquid piston compressor

5.3.2. Aqueous Foam Generation Setup

An aqueous foam generator was designed to create the foam in the compressor chamber. Figure

5.4 shows the model designs of the foam generator used in this study. These designs have a hollow surfactant reservoir for surfactant solution. An equal number of holes with constant diameter were created on the top surface of the foam generator. The foam is generated through the holes by air entering from the air source connector via the surfactant solution. Additional designs with tube extrusion for the holes were also considered. These tube extrusions were hypothesized to create a laminar flow of air for uniform bubble sizes in the foam. Foam generator designs with 2.5 mm and

5 mm hole diameters were considered to investigate the effect of hole diameter of design on the air temperature. These foam generator designs were 3D printed using ABS M30 material.

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(a) Foam Generator design without tubes.

(b) Foam Generator design with tube extrusion.

Figure 5.4: Foam Generator designs of 2.5 mm hole diameters with and without tubes.

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To facilitate visualization of foam during the compression process, a transparent polycarbonate compression chamber was used in the liquid piston experimental setup. The foam generator is attached to the bottom of the compression chamber as shown in Figure 5.5. The air source connected to the foam generator is used to generate foam inside the compression chamber prior to the compression cycle by flowing air through the foam generator. The amount of foam inside the compression chamber can be controlled with the supply of air passed through the foam generator.

The flow rate of the air source can be varied to generate foam of different bubble characteristics.

It was observed that a higher flow rate of air produced foam with overall larger bubble diameters compared to a lower flow rate.

Figure 5.5: Compression chamber with Aqueous Foam.

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5.3.3. Experimental Cases

Compression of air is tested with and without foam in the liquid piston compression for a compression ratio of about 2.5 - 3. All the experiments are performed for the stroke time of compression around 4.2s - 4.5s. A general dishwasher surfactant (DAWN Ultra of P&G) is used to produce a surfactant solution. The foam is generated before the start of the compression cycle by flowing air through the foam generator at atmospheric chamber pressure. No additional foam is generated during the compression process.

In the first set of experiments with the foam, the amount of aqueous foam inside the compression chamber is varied. These experiments are performed to investigate the influence of the volume of aqueous foam in the compression chamber on compression efficiency. Three cases with the aqueous foam filled approximately to 25% of the chamber, 50% of the chamber, and fully filler chamber were tested. The air source flow rate of 1.5 L/min is used to generate aqueous foam in this set of experiments. Next, the flow rate of air source is varied to study the effect of variation in bubble characteristics on the compression efficiency. The flow rates of air source of about 0.4

L/min, 1.5 L/min, and 3 L/min are used to generate the foam of different bubble diameters. A completely filled compression chamber with aqueous foam is tested in this set of experiments.

Experiments are repeated a number of times to confirm the repeatability and to evaluate the variability in the results.

Finally, experiments are performed with four foam generator designs to study the effect of foam generator design on temperature abatement. The compression chamber is fully filled with the aqueous foam in these experiments. Similar conditions are maintained for compression stroke time, the motion of liquid piston, and air source pressure for foam generation in these experiments.

With each design, at least ten compression cycles are performed for uncertainty estimation.

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5.4. Results and Discussion 5.4.1. Bubble Dynamics during Compression

The aqueous foam in the compression chamber is exposed to high-pressure high-temperature conditions during the compression process. The bubbles in the aqueous foam collapse, change their shape and size at high-pressure high-temperature conditions. The mechanisms of liquid drainage, inter-bubble gas diffusion, and bubble coalescence also play an important role in this process.

Figure 5.6 (a)-(f) show the dynamics of aqueous foam during a compression process from the start to the end of compression. At the start of compression, the aqueous foam is filled in the compression chamber. As compression proceeds, the liquid piston moves upwards reducing the volume of chamber resulting in a rise in pressure and temperature. The volume of aqueous foam decreases as the liquid piston moves upwards due to the collapse of bubbles at a higher pressure.

However, these bubbles absorb a significant amount of heat before their collapse and help achieve the temperature drop. The collapse of top layer bubbles of foam exposes the bubbles below it to the hot air. This results in exposure of a large number of bubbles in the foam to absorption of heat from the air. Therefore, the collapse of bubbles helps in achieving a high rate of heat transfer with the use of aqueous foam. The size of bubbles in the foam also decreases during the latter phase of compression. Towards the end of compression (at 4.37s), there is still a small amount of foam left in the chamber which did not collapse. As pressure and temperature at the end of compression are not high enough to collapse these bubbles, the residual foam remains in the compression chamber.

This residual foam reduces the volumetric efficiency of compression. Clearly, the aqueous foam which would fully collapse towards the end of compression should be generated at the start to avoid any residual foam in the compression chamber.

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(a) At time=0s (b) At time=0.9s (c) At time=1.8s

(d) At time=2.7 (e) At time=3.6s (f) At time=4.37s

Figure 5.6: Aqueous foam bubble dynamics during compression process.

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5.4.2. Effect of Aqueous Foam Volume

The aqueous foam of different volume is tested in the compression chamber to study its effect on temperature drop. The aqueous foam was filled with about 25% of chamber volume, 50% chamber volume, and fully filled in these set of experiments. Figure 5.7 shows the temperature- pressure plots observed with these experiments during a compression stroke. It is observed that the temperature of the air inside the compression chamber reduces with the use of aqueous foam especially towards the latter part of the compression process. The higher amount of aqueous foam results in a higher temperature drop. During the initial phase of the compression process, irrespective of the amount of aqueous foam the temperature drop is very small. This can be attributed to the lower air temperature (lower temperature difference) and a lower collapse rate of bubbles in the foam at a lower chamber pressure. The amount of aqueous foam plays an important role in temperature reduction during the latter part of compression. As compression proceeds, the

Figure 5.7: Temperature-pressure plot with foam of different volume in the chamber.

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Figure 5.8: Isothermal efficiency with foam of different volume in the chamber.

higher temperature of the air and a high chamber pressure help in achieving a high rate of heat transfer. This is due to a higher temperature difference and the higher collapse rates of bubbles in the latter part of the compression process.

Figure 8 shows the results of the isothermal efficiency of compression with aqueous foam of different volumes in the chamber. A higher amount of aqueous foam improves the isothermal efficiency of compression. However, the use of a higher amount of aqueous foam increases the variability in isothermal efficiency as well.

5.4.3. Variability with the Use of Aqueous Foam

The temperature drop during the compression process depends on the characteristics of bubbles in the aqueous foam. The aqueous foam generated using similar foam generation conditions may not result in exactly the same bubble characteristics. Any variation in the characteristics of bubbles in the aqueous foam would lead to a different temperature profile during the compression process.

Additionally; liquid drainage, inter-bubble gas diffusions, and bubble coalescence mechanisms

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influence foam bubbles differently with different foam characteristics. This causes variation in the heat transfer characteristics of foam and temperature drop with the use of foam. Figure 9 shows the temperature-pressure plots observed with multiple compression cycles with the aqueous foam filled to about half the chamber volume. Similar plots for aqueous foam filled with the full chamber are shown in Figure 5.10. It can be observed that the use of aqueous foam consistently reduced the air temperature in all the cycles but it is not certain that the same temperature profile would be observed for different cycles. Comparison of Figure 5.10 with Figure 5.9 indicates that the cyclic variability increases with an increase in the amount of aqueous foam in the chamber. The higher amount of aqueous foam has a larger variation in the bubbles characteristics. This results in higher variability in temperature with the use of a higher amount of aqueous foam in the compression chamber.

Figure 5.9: Temperature-pressure for multiple cycles using about half of the chamber with foam.

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Figure 5.10: Temperature-pressure for multiple cycles using full chamber with foam.

5.4.4. Effect of Air Flow Rate of Aqueous Foam Generation

The aqueous foam of different bubble characteristics can be generated by varying the flow rate of the air source used to generate foam. The air flow rates of about 0.4 L/min, 1.5 L/min, and 3.0

L/min are tested for the generation of aqueous foam. Figure 5.11-(a), (b), and (c) show the pictures of aqueous foam generated with these flow rates in the compression chamber. From the visual observation, it is observed that at higher flow rates of air source, foam with larger bubble diameters are generated compared to the foam generated with a lower flow rate of air source. Also, the flow rate of the air source would influence the volumetric void fraction of the foam. The variation in bubble size distribution and volumetric void fraction influence the heat transfer with aqueous foam and, therefore, might affect temperature abatement during the compression process. Figure 5.12 shows the temperature-pressure plots for a compression cycle with aqueous foams generated using different air flow rates. It can be observed that the temperature profiles do not show a significant difference.

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(a) Using 0.4 L/min (b) Using 1.5 L/min (c) Using 3.0 L/min

Figure 5.11: Aqueous foam generated using different flow rates of air source.

Figure 5.12: Temperature-pressure plots with aqueous foam generated using different air source flow rate.

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The isothermal efficiencies of compression with the use of aqueous foam generated using various flow rates are shown in Figure 5.13. All the flow rates show the average isothermal efficiency of compression about 90-92%. However, the aqueous foam generated with the higher flow rates shows higher variability in isothermal efficiency. Again, this is due to the higher cyclic variability in the temperature profile observed with the use of aqueous foam generated by the high flow rate. The larger diameter bubbles generated with the higher flow rates are delicate due to the smaller pressure differential between inside and outside of the bubble. This delicacy affects collapse rate and leads to the high uncertainty with foam generated from a high flow rate. Overall, the use of aqueous foam leads to a 4-8% improvement in isothermal efficiency of compression.

Figure 5.13: Isothermal efficiency of compression with the aqueous foam generated by various flow rates of air source.

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5.4.5. Effect of Foam Generator Designs

Aqueous foam generated with different foam generator designs are compared in this section.

The hole diameter and tube extrusion factors were considered in the experimental design of the foam generator. A total of four designs by combinations of two hole diameters (2.5 mm and 5 mm) and the presence or absence of tube extrusion are considered. Ten runs of compression for each of these designs are considered for analysis.

The temperature-pressure plots during the compression process with foam generator designs

(with and without tubes) of 2.5 mm hole diameters are shown in Figure 5.14. The foam generator without tubes shows a large cyclic variation in temperature-pressure plots. The small holes have a high velocity of air flowing out of the holes which have a higher possibility of creating bubbles of random (non-uniform) sizes. Additionally, foam characteristics are not consistent from cycle to cycle due to the possibility of larger variation in bubble sizes with a higher velocity of air flow.

The addition of tubes helps to reduce variation marginally due to the smooth laminar flow of air generated with tubes. However, there is still significant variation in the temperature-pressure profiles which is due to the variation in bubble dynamics during the compression process.

Furthermore, similar results with foam generator designs of 5 mm hole diameter are shown in

Figure 5.15. The higher hole diameter reduced the variation in temperature-pressure profiles marginally compared to the profiles with 2.5 mm hole diameter. Addition of tubes to the 5 mm holes has an only marginal effect on reducing variation. Although higher diameters and tubes show improvement in reducing variation from the plots, their effect on efficiency needs to be identified quantitatively. As there is a large variation in the compression processes, it is difficult to identify which factors are prominent without considering a variance for the comparison. Therefore, analysis

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of variance is carried out on the isothermal efficiency for each compression cycle in the experimental design.

(a) For Foam generator without tubes

(b) For foam generator with tubes Figure 5.14: Temperature-pressure plots using foam generator of 2.5 mm holes.

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(a) For foam generator without tubes

(b) For foam generator with tubes

Figure 5.15: Temperature-pressure plots using foam generator of 5 mm holes.

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Table 1 shows the analysis of variance (ANOVA) table for isothermal efficiency. The large p- values for interaction and hole diameter factors indicate that these factors are not significant for changing isothermal efficiency. However, the small p-value associated with the ‘presence of tube’ factor indicates that the addition of tubes impacts efficiency significantly. Moreover, the high sum of squares of residuals indicates that there is still significant variation which cannot be explained with the design change. A majority of this variation is due to bubble dynamics and device/measurement uncertainties.

Table 5.1: Analysis of Variance (ANOVA) table for efficiencies with foam generator designs.

Degrees of Sum of Mean Square Factor F-Value P-value Freedom Squares Errors

Hole diameter 1 1.05 1.05 0.71 0.40

Presence of Tube 1 17.01 17.01 11.56 0.002

Interaction

(Hole diameter x Presence 1 0.03 0.03 0.02 0.88

of Tube)

Residuals 36 52.97 1.47

The isothermal efficiencies with the four foam generator designs are summarized in Figure

5.16. The bar chart represents the average value and each error bar represents standard deviation for ten compression cycles. All four designs show average isothermal efficiency higher than 90%.

Addition of tubes to the 2.5 mm hole diameter design reduces the standard deviation for isothermal efficiency from 1.9% to 1.2%. The addition of tubes which is observed as a significant factor

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reduces the average efficiency at both 2.5mm and 5 mm hole diameter designs. Furthermore, the

5 mm hole diameter design shows a comparable average efficiency with significantly smaller standard deviation (0.9%) than 2.5 mm hole diameter design. Clearly, foam generator with a larger hole diameter is effective in reducing variation in isothermal efficiency. Addition of tubes shows a negligible reduction (0.90% to 0.87%) in standard deviation for 5 mm hole diameter design.

Overall, foam generator design parameters are an influential factor for efficiency improvement and uncertainty reduction. Therefore, an optimal design to achieve maximum efficiency with consistent performance would lead to an additional efficiency gain.

Figure 5.16: Isothermal efficiency with foam generated from different foam generator designs.

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5.5. Conclusions

Aqueous foam, due to its a high heat transfer coefficient and high specific heat compared to air along with a high surface area, is hypothesized to reduce air temperature during the compression process. In this study, aqueous foam based heat transfer is experimentally investigated in a liquid piston compressor for temperature abatement. Aqueous foam manifests complex bubble dynamics due to liquid drainage, inter-bubble gas diffusion, and bubble coalescence mechanisms. The bubble dynamics in the foam changes foam characteristics and alter heat transfer behavior of aqueous foam. Additionally, exposure to high-pressure high-temperature conditions in the compression chamber influences bubble dynamics and heat transfer in the foam. It is difficult to control all the complex mechanisms in the aqueous foam, therefore a parametric study by varying parameters which influence aqueous foam generation is considered for this investigation.

The use of aqueous foam in the compression chamber is very effective in reducing the temperature of air during the compression process. The temperature drop increases with an increasing amount of aqueous foam used in the compression chamber. For the compression chamber completely filled with the aqueous foam, a temperature drop of 7-20 K is observed towards the end of compression stroke for a compression ratio of 2.5. A higher amount of aqueous foam in the chamber shows a higher cyclic variability. Furthermore, experiments with the aqueous foam generated using different flow rates of air source show that the higher flow rates of air source resulted in higher variability in isothermal efficiency. Overall, the aqueous foam fully filled in the compression chamber showed a 4-8% improvement in the isothermal efficiency of compression over the base efficiency of about 86% for a liquid piston compressor.

Moreover, four foam generator designs of different hole diameters and with or without tube extrusion are tested. Analysis of variance indicates that the addition of tube is a significant factor whereas hole diameter is not a significant factor in influencing efficiency. Addition of tubes is

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beneficial in reducing variation in efficiency but reduces the efficiency on average. The increasing hole diameter from 2.5 mm to 5 mm reduces variability in cyclic efficiency without significantly affecting efficiency. Overall, all foam generated from all four designs could achieve an isothermal efficiency higher than 90%.

The current study with aqueous foam does not measure any foam characteristics and its effect on the isothermal efficiency of compression. More in-depth scientific investigations would be valuable to study the effect of foam characteristics on temperature abatement and isothermal efficiency of compression. Also, this study only considered macrofoams because of the relatively low-pressure conditions used during compression. Further studies with the use of microfoams and at higher pressure ratios would warrant a greater scalability of the foam-based technique. The accumulation of residual foam over the continuous operation, the high cyclic variability, and presence of water to create a corrosive environment in the chamber are a few challenges for the effective use of aqueous foam in industrial compressors. Also, the effect of different surfactant solutions on the generation, collapse, and heat transfer of aqueous foam can be studied further to evaluate useful surfactant characteristics for optimal utilization of aqueous foam.

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CHAPTER 6: Metal Wire Mesh Spiral in Liquid Piston Compressor

Abstract: Intermittent nature of power from renewable energy resources demands a large scale energy storage system for their optimal utilization. Compressed air energy storage systems have the potential to serve as a long-term large-scale energy storage systems. Efficient compressors are needed to realize a high storage efficiency with compressed air energy storage systems. Liquid piston compressor is highly effective in achieving efficient near-isothermal compression.

Compression efficiency of the liquid piston can be improved with the use of heat transfer enhancement mechanism inside the compression chamber. A high rate of heat transfer can be achieved with the use of metal wire mesh in the liquid piston compressor. In this study, metal wire meshes of aluminum and copper materials in the form of Archimedean spiral are experimentally tested in a liquid (water) piston compressor. Experiments are conducted for the compression of air from the atmospheric pressure to 280-300 kPa pressure at various stroke times of compression.

The peak air temperature is reduced by 26-33K with the use of metal wire mesh inside the liquid piston compressor. Both the materials are observed to be equally effective for temperature abatement. The use of metal wire mesh in liquid piston shifts the compression process towards the near-isothermal conditions. Furthermore, the isothermal efficiency of compression is evaluated to assess the potential for efficiency improvement with this technique. The metal wire mesh was observed to improve the isothermal efficiency of compression to 88-90% from the base efficiency of 82-84%. A 6-7% improvement in efficiency was observed at faster compression strokes signifying efficacy of metal wire mesh to accomplish an efficient compression with a high power density. Further investigations to evaluate the optimal configuration of the metal wire mesh will be useful to achieve additional improvement in compression efficiency.

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6.1. Introduction Power generation from renewable energy resources is intermittent and optimal utilization of renewable energy in the electric grid requires the integration of large-scale energy storage systems with conventional power plants [136]. Compressed air energy storage (CAES) is considered a promising large-scale energy storage system. In CAES, energy is stored in the form of compressed air. Efficient compressors are needed to realize a high storage efficiency of the CAES system [137].

Energy and exergy analysis of CAES systems indicate that compressors operating with the near- isothermal process are highly effective to attain a high storage efficiency of a CAES system [138,

139]. Typical industrial air compressor operates close to the adiabatic process which results in air temperature rise during the compression process. The efficiency of these compressors is very less for energy storage application because a significant portion of compression work is utilized to increase temperature/internal energy which could be lost during storage. The shift of the compression process from adiabatic to isothermal conditions reduces temperature rise and compression work and improves compression efficiency [140].

Liquid piston has shown to be effective in achieving near-isothermal gas compression. In the liquid piston, a column of liquid is used to compress the gas in a compression chamber. The liquid piston enhances heat transfer and eliminates mechanical sliding piston of conventional reciprocating compressors. Likewise, the liquid piston can achieve significant improvements in the compression efficiency in comparison to conventional reciprocating solid-piston [141]. This is accomplished by increasing heat transfer during gas compression to curtail temperature rise. Heat transfer analysis in liquid piston compressor indicates that convective thermal resistance between gas and chamber has a significant contribution to the total thermal resistance [142]. Therefore, a technique to reduce the convective thermal resistance between gas and chamber is needed to achieve heat transfer enhancement in a liquid piston compressor.

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Various heat transfer enhancement techniques have been tested in the liquid piston compressor.

Optimization of trajectories of liquid piston can improve heat transfer to gain in compression efficiency or power density. The optimal trajectory that maximizes power for a given efficiency can result in a 10-40% increase in power density relative to other ad-hoc trajectories [143]. Heat transfer enhancement using porous media inserts have shown to be effective in improving compression efficiency of the liquid piston. The porous media inserts increase heat transfer surface area significantly and therefore show significant heat transfer enhancement during compression.

The efficiency and/or power density of liquid piston compressor increases because of increased heat transfer with porous media inserts. The compression efficiency is increased by 18% at 100 kW/m3 power density and power density is increased by 39 times at 95% efficiency with the use of porous media inserts for a tenfold compression ratio [144]. At high-pressure conditions, porous media inserts resulted in a 13% increase in compression efficiency and 10 times increase in power density [145].

Furthermore, various water-based techniques have been investigated for efficiency improvement in the liquid piston compressor. Droplet heat transfer with spray injection has shown potential to increase compression efficiency from 71% for adiabatic compression to as much as

98% for a tenfold pressure ratio from a simulation study [146]. It was observed that the total surface area of aloft droplets is critical to improving compression efficiency. Experimental investigation with water spray injection in a liquid piston compressor resulted in a 10-20% improvement in efficiency for a compression ratio of 2.5 [147]. Water spray injection reduces air temperature during compression and shifts the compression process towards isothermal conditions. Similar to the water spray injection, the use of aqueous foam in liquid piston is also effective in reducing air temperature. A high surface area of heat transfer and high heat transfer coefficient with aqueous

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foam is useful to absorb the heat of compression. It was observed that 4-8% improvement in compression efficiency is possible with the aqueous foam in the liquid piston for a compression ratio of 2.5 [148]. Overall, a high heat transfer surface area is a key factor to achieve a high rate of heat transfer and to improve compression efficiency in a liquid piston.

Metal wire meshes made up of woven thin metal wires have a high thermal conductivity and a high surface area. A high rate of heat transfer can be achieved with the use of metal wire meshes.

Placement of metal wire mesh in the compression chamber of the liquid piston can be useful to achieve a high rate of heat transfer from the gas to liquid. The low thermal conductivity of air causes high thermal resistance in the liquid piston. Metal wire meshes in the compression chamber in contact with air could reduce effective thermal resistance in the liquid piston and help achieve a high rate of heat transfer.

In this chapter, the use of metal wire meshes in a liquid piston compressor is investigated for improvement in compression efficiency. A thin sheet of metal wire meshes rolled in the

Archimedean spiral shape are placed in the compression chamber during testing. Metal wire meshes of aluminum and copper materials are considered in this study. Compression of air for a compression ratio of about 3 is performed with and without metal wire mesh in liquid (water) piston. Pressure and temperature data measured during compression are used to assess the effectiveness of metal wire mesh in improving compression efficiency.

6.2. Conceptual Framework

In a liquid piston compressor, a finite mass of gas is compressed by reducing the volume of a closed chamber by moving a column of liquid piston. Metal wire mesh will be placed inside the compression chamber in contact with both gas and liquid. A schematic of the liquid piston compression chamber with the metal wire mesh is shown in Figure 6.1. The compression of gas in

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liquid piston can be analyzed as a closed system from the start to the end of the compression process. The first law of thermodynamics applied to the gas in the control volume neglecting changes in kinetic and potential energies gives the following equation.

푑푇 푈̇ = 푚퐶 푔 = 푄̇ − 푊̇ (6-1) 푣 푑푡 푐표푚푝 where 푈̇ is the rate of change of internal energy, m is mass of the gas, 퐶푣 is the specific heat of the gas at constant volume, 푇g is the bulk temperature of gas, t is time, 푄̇ is the total rate of heat transfer and 푊̇푐표푚푝 is work of compression.

Figure 6.1: Conceptual schematic of liquid piston compressor with Metal Wire Mesh.

The total rate of heat transfer consists of heat transfer from gas to surrounding through compression chamber and heat transfer from gas to liquid through the metal wire mesh.

푄̇ = 푄̇푐ℎ푎푚푏푒푟 + 푄̇푚푒푠ℎ (6-2)

The heat transfer through the chamber is given by,

푄̇푐ℎ푎푚푏푒푟 = 푈푐 퐴푐 (푇∞ − 푇푔) (6-3)

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where 푈푐 is the overall heat transfer coefficient between gas and surrounding, 퐴푐 is the surface area of chamber in contact with the surrounding, and 푇∞ is the temperature of the surrounding.

Similarly, heat transfer through the metal wire mesh is given by,

푄̇푚푒푠ℎ = 푈푚퐴푚(푇푚 − 푇푔) (6-4) where 푈푚 is the overall heat transfer coefficient between metal wire mesh and gas, 퐴푚 is the surface area of metal wire mesh in contact with gas, 푇m is the temperature of the metal wire mesh.

Using the above heat transfer relations and relation of compression work for a closed system results in the following model equation for the bulk temperature of gas during the compression process.

푑푇 푑푉 푚퐶 푔 = [푈 퐴 (푇 − 푇 ) + 푈 퐴 (푇 − 푇 )] − 푃 (6-5) 푣 푑푡 푐 푐 ∞ 푐 푚 푚 푚 푔 푑푡 where P is the pressure of the gas and V is the volume of the gas.

Metal wire mesh inside the compression chamber enhances total heat transfer significantly because of a high surface area of metal mesh (퐴푚) and a high transfer coefficient between metal mesh and gas (푈푚). The high conductivity of the metal wire mesh keeps the temperature of the metal wire mesh close to the liquid temperature therefore maintains a high temperature difference.

This helps achieve a high rate of heat transfer during the later phase of compression.

The gas compression can be assessed by considering the polytropic process of compression using the following relationship between pressure and temperature.

푃1−푛 푇푛 = constant (6-6) where n is polytropic index of compression.

The isothermal efficiency of compression is evaluated to assess the efficacy of metal wire mesh in achieving near-isothermal compression. The isothermal efficiency is evaluated using the

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following equation (6-7) which is based on the pressure ratio and polytropic index of compression

[142].

1 푙푛 푃푟−1 + 휂 = 푃푟 (6-7) 𝑖푠표 푛−1 1 ( ) 1 − 푃푟 푛 − 1 − 푛 1 + 푃푟 푛 −1 + (푃푟−1)( 푃 − ) 푛−1 푟 푃푟

6.3. Experimental Setup

A small-scale experimental setup of a liquid piston compressor shown in Figure 6.2 is used in this study. A polycarbonate compression chamber of 88 mm diameter and 170 mm height is installed inside a cylinder. The top of the compression chamber is connected to the inlet and outlet solenoid valves with a pipe. A pressure transducer is mounted at the top to measure instantaneous pressure in the compression chamber. K-type thermocouples are installed inside the compression chamber to measure instantaneous air temperature.

A double acting linear water pump is used to create the motion of the liquid piston. The water pump is operated using a linear pneumatic cylinder. The high-pressure air source is used to operate the pneumatic cylinder which in turn operates the water pump. The outlet of the water pump is connected to the liquid piston cylinder. Linear actuation of water pump using a pneumatic cylinder creates the motion of liquid piston inside the compression chamber. The stroke time of compression can be varied by changing input air pressure to the pneumatic cylinder. The pneumatic cylinder and solenoid valves are operated using by a controller. A data acquisition (DAQ) system is used to measure instantaneous data during the compression process. A LabVIEW program is used to control the operation of the liquid piston and save experimental data to the computer.

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Figure 6.2: Experimental Setup of Liquid Piston Compressor.

A metal wire mesh sheet of width 170 mm and length 322 mm is rolled to form one arm of

Archimedean spiral of 88 mm outer diameter having two turns. The spirals made of aluminum and copper material used for the testing are shown in Figure 6.3. Two bolts on the top and two bolts on the bottom of the spiral are used to keep spiral intact in the desired form. Metal wire mesh of

0.028 inch (0.7112 mm) wire diameter with 8 mesh size per inch is used for both the materials.

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Figure 6.3: Aluminum and Copper metal wire mesh sprials.

6.4. Results and Discussion

Compression experiments are performed with and without metal wire mesh inside the liquid piston compressor for comparative analysis. Instantaneous temperature and pressure data measured during the compression process are used in the analysis. Furthermore, the polytropic index of compression and isothermal compression efficiency are estimated from the pressure- temperature data.

6.4.1. Effect of Metal Wire Mesh Material

Compression experiments without any mesh and with a metal wire mesh of aluminum and copper in the chamber were performed. The pressure data observed during the compression process are shown in Figure 6.4 for about 5 s compression stroke time. The pressure is increased from atmospheric pressure to about 280 kPa during compression. All the three plots follow a similar trend and there is no discrepancy in the pressure with the use of metal wire mesh.

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Figure 6.4: Pressure during compression process with and without mesh in the chamber.

Figure 6.5: Temperature during compression process with and without mesh in the chamber.

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Temperature measurements during compression differ significantly with and without mesh in the chamber as observed in Figure 6.5. The final temperature of about 345K without mesh is reduced to about 320K with the use of mesh. The metal wire mesh is highly effective for temperature abatement in liquid piston compression. Placement of a metal wire mesh spiral in the chamber offers a high rate of heat transfer from the air to liquid to realize a significant temperature drop. Furthermore, the material of metal wire mesh affects the heat transfer characteristics of mesh due to the difference in thermal conductivity of the material. Although thermal conductivity of copper is about twice that of aluminum, similar temperature profiles with both the materials suggest that the thermal conductivity of metal is not a significant factor for a high heat transfer with metal wire mesh. The Archimedean spiral form of the mesh provides a high surface area of heat transfer and spans full chamber volume. The surface areas of both the meshes tested are approximately the same due to the similar spiral form. This indicates that the surface area is a significant factor for temperature abatement.

The initial temperatures for the compression runs differ slightly, however, the compression process can be analyzed with normalized pressure and normalized temperature to eliminate the effect of a small variation in initial conditions. The pressure-temperature plots normalized to the conditions at the start of compression are shown in Figure 6.6. The effect of different initial conditions on temperature-pressure profiles is insignificant and metal wire mesh is highly effective to reduce temperature ratio from about 1.15 to about 1.07 for a compression ratio of about 2.8.

Noticeably, the use of metal wire mesh in liquid piston compressor shifts the compression process towards the isothermal conditions.

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Figure 6.6: Temperature-Pressure (Normalized) plots with and without mesh in the chamber.

6. 4.2. Effect of Compression Stroke Time

Heat transfer enhancement technique to achieve efficient compression at a high power density is always desired. A high power density of compression can be attained with the use of a smaller compression stroke time. Compression with a smaller stroke time is less efficient compared to the larger stroke time. This is because smaller stroke time meaning the faster compression which has less time for heat transfer than slower compression. The effectiveness of metal wire mesh for temperature abatement is tested at different stroke times of compression to evaluate its potential to achieve an efficient compression at a high power density. Compression stroke time of about 5s

(slow), 4s (medium), and 3s (fast) are considered in this study.

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Figure 6.7: Pressure during compression of different stroke times with and without mesh.

The pressure data during compression of different stroke times is shown in Figure 6.7. Mesh cases shown in the figure are for the aluminum wire mesh. The pressure profiles are similar with and without mesh and pressure of about 280-300 kPa is reached at the end of compression at all the stroke times.

Metal wire mesh is effective in reducing air temperature at faster compressions as observed in the temperature plots for different stroke times shown in Figure 6.8. The maximum air temperature for compression without mesh is increased from 344K to 356K with the smaller stoke times. As the metal wire mesh could transfer a significant portion of the heat of compression from air to water, air temperature remained less than 330K with the use of mesh at different stroke times. For the with mesh cases, the air temperature increases marginally with the faster compression. Smaller time with the faster compression affects the total heat transfer with metal mesh as well and therefore impacts temperature abatement.

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Figure 6.8: Temperature during compression of different stroke times with and without mesh.

The normalized pressure-temperature profiles are compared for the compression at different stroke times in Figure 6-9. Faster compression increases the temperature ratio marginally irrespective of the presence of the mesh in the chamber. With the use of mesh, the temperature profiles shift towards isothermal conditions after a pressure ratio of about 1.5. The metal wire mesh flattens the temperature-pressure profile at all the stroke times. Clearly, metal wire mesh is highly effective for lowering the temperature of the gas in the liquid piston at all the stroke times.

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Figure 6.9: Temperature-pressure (normalized) plots during compression of different stroke times with and without mesh in the chamber.

6.4.3. Isothermal Compression Efficiency

The effectiveness of metal wire mesh is estimated in terms of polytropic index and isothermal efficiency of compression. The polytropic index of compression is evaluated by fitting the polytropic process equation through the normalized pressure-temperature profile. Furthermore, isothermal compression efficiency is evaluated using equation (6-7). Table 6.1 presents the polytropic index and isothermal efficiency of compression with and without mesh for various stroke times studied. The polytropic index can be used to assess the compression process relative to isothermal or adiabatic conditions. The polytropic index of 1.4 for air indicates the adiabatic compression whereas polytropic index of 1 denotes the isothermal compression. The polytropic

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index between 1.15-1.18 is observed with the base liquid piston and the use of metal wire mesh significantly decreases polytropic index toward isothermal conditions. Slower compression reduces polytropic index marginally for compression with and without mesh. The metal wire mesh maintains the polytropic index below 1.10 indicating near-isothermal conditions for compression stroke times between 3s-5s. Both aluminum and copper meshes are equally effective in reducing the polytropic index towards near-isothermal conditions.

Table 6.1: Polytropic Index and Isothermal Efficiency of Compression with and without Mesh.

Polytropic Index (n) Isothermal Efficiency (%)

Stroke Time No Mesh Al Mesh Cu Mesh No Mesh Al Mesh Cu Mesh

Slow 1.15 1.08 1.08 83.8 90.0 90.0

Medium 1.18 1.09 1.09 81.5 89.6 89.5

Fast 1.17 1.10 1.09 82.4 88.6 89.4

The isothermal compression efficiency is increased from 82-84% for the base liquid piston to

88-90% with the use of metal wire mesh in the liquid piston. Metal wire mesh shows a significant improvement in efficiency at faster compression strokes. Therefore, metal wire mesh can be used to accomplish an efficient compression with a high power density. The copper material shows a marginal advantage in efficiency over aluminum at a faster compression, however, efficiency values are similar for both the materials at slower compressions. This suggests that the high thermal conductivity of copper is advantageous only during the fast compression and relatively less costly aluminum wire mesh is equally effective at slower compressions.

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6.5. Conclusions

The efficiency of a liquid piston compressor can be improved with the use of heat transfer enhancement inside the compression chamber. Metal wire meshes have a high thermal conductivity and a large heat surface area and therefore hypothesized to improve heat transfer from the gas to the liquid inside the liquid piston compressor. Aluminum and copper wire meshes in the form of Archimedean spiral were tested in a liquid piston during the compression of air from atmospheric pressure to about 280-300 kPa. Furthermore, the stroke time of compression was varied to assess the effectiveness of metal wire mesh at faster compression strokes. It is observed that metal wire mesh is highly effective in temperature abatement during compression at various compression stroke times. A temperature drop of 26-33 K was observed with the use of metal wire mesh. Both aluminum and copper wire meshes were equally effective for temperature abatement.

The large surface area of metal wire mesh is a key factor for heat transfer enhancement. Polytropic index of compression reduced from 1.15-1.18 to 1.08-1.10 with the use of metal wire in the liquid piston. This indicates that the use of metal wire meshes in a liquid piston compressor is useful for shifting the compression process towards near-isothermal conditions. Metal wire mesh improved isothermal compression efficiency by 6-8% from the base liquid piston efficiency of 82-84%.

Overall, the use of metal wire meshes in the liquid piston is highly effective to achieve efficient compression with a high power density. The current study is limited to aluminum and copper meshes with a wire diameter of 0.028 inch wire diameter and 8 mesh per inch mesh size rolled in the form of Archimedean spirals of two turns. Further investigations are needed to assess the usefulness of other materials, wire diameters, mesh sizes, and forms of the spiral to achieve an optimal mesh design for maximum efficiency. Also, the utility of metal wire meshes for compression pressure significantly higher than 300 kPa needs further investigations.

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CHAPTER 7: Efficiency Improvement in Liquid-piston based

OCAES

Abstract: Utilization of intermittent ocean energy resources can be improved by integrating them with an energy storage system. Ocean compressed air energy storage (OCAES) is a promising large-scale energy storage system in the proximity of ocean energy resources. Efficient compressors and expanders are needed to achieve a high roundtrip efficiency of OCAES systems.

In this chapter, the development of an efficient liquid piston compressor is discussed. Heat transfer enhancement techniques such as aqueous foam, spray cooling, and metal wire mesh are tested in a liquid piston compressor to achieve a highly efficient near-isothermal compression. It is observed that all three heat transfer enhancement techniques are highly effective in abating the rise of air temperature during compression and improve the isothermal efficiency of compression. The use of aqueous foam in a liquid piston compressor shows an isothermal efficiency up to 92% whereas spray cooling results in an isothermal efficiency up to 96%. Efficiency analysis of liquid piston based OCAES systems with aqueous foam and spray cooling indicate the potential improvement of 4-14% in roundtrip efficiency of OCAES with the use of aqueous foam and 10-20% improvement with the spray cooling.

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7.1. Introduction

Offshore wind, wave, tidal and gulf-stream are massive ocean renewable energy resources which can support a significant portion of the energy needs of the coastal regions. However, these energy resources are under-utilized due to their sporadic nature. Utility-scale energy storage systems are needed to improve the utilization of such resources in the electric grid. Ocean compressed air energy storage (OCAES) can act as a promising large-scale energy storage system in the proximity of ocean energy resources [1]. In OCAES, the energy is stored in the form of compressed air under the ocean. Underwater energy storage acts as a constant-pressure storage system which has the potential to show a higher efficiency compared to a conventional constant- volume energy storage system. Compressors and expanders are the key components of the OCAES system. Therefore, development of an efficient compressor and expander plays an important role in achieving a high roundtrip efficiency of the OCAES system [2].

Energy and exergy analysis of ocean compressed air energy storage concepts indicated that an isothermal compression and an isothermal expansion are desired for a high roundtrip efficiency of an OCAES system [3]. A liquid piston compressor is a novel compressor concept to achieve a near- isothermal compression process. In a liquid piston compressor, the gas is compressed by the flow of high-pressure liquid in a compression chamber [4]. Due to its low frictional losses and high heat transfer capabilities, the liquid piston can achieve a near-isothermal compression.

Various heat transfer enhancement techniques have been tested in liquid piston compressors for improvement of the compression efficiency. Experimentation with liquid piston trajectories showed that optimal trajectories resulted in up to a 4% efficiency improvement over an ad-hoc constant flow trajectory [5]. Experimental study of heat transfer enhancement using porous media inserts has shown up to 18% improvement in efficiency of a liquid piston compressor at low pressure (10bar) [6]. A similar study at high pressure (210bar) has shown up to 13% improvement

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in efficiency with the use of porous media inserts in liquid piston compression [7]. The high surface area of the porous media inserts is responsible for improving the heat transfer during the compression process and hence increases the efficiency of compression. The high surface area and thermal conductivity of metal wire mesh can provide similar heat transfer enhancement and improve the efficiency of liquid piston significantly. Therefore, metal wire mesh could serve as an economical alternative for porous media inserts.

Water-based heat transfer enhancement techniques could be beneficial for liquid piston compressors since water has good thermal properties and water as the liquid piston media results in a much simpler operation. One such technique is to use spray injection during compression to absorb the heat. A numerical study of droplet heat transfer in a liquid piston compressor indicated that compression efficiency can be increased from 71% for adiabatic compression to as much as

98% with spray injection, for a tenfold pressure [8]. Similarly, the use of aqueous foam has the potential to show a high compression efficiency.

In this chapter, end-to-end efficiency analysis of liquid piston based OCAES with various heat transfer enhancement techniques is presented. Liquid piston compressor with spray injection, aqueous foam, and metal wire mesh techniques are considered in this study. A brief summary of these techniques is presented. The isothermal efficiency and polytropic index of compression are considered as a measure of effectiveness of heat transfer enhancement technique. Furthermore, the end-to-end efficiency of OCAES system is estimated to assess the potential efficiency improvement of the storage system with these techniques.

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7.2. Efficiency Improvement Techniques

Various heat transfer enhancement techniques in liquid piston have been observed to be effective in improving efficiency and power density. Various heat transfer enhancement techniques considered are: spray injection, aqueous foam, and metal wire mesh.

7.2.1. Spray Injection

Investigation of water spray injection in the liquid piston compressor is presented in Chapter

4. It is observed that, in general, injection of spray shifts the polytropic curve towards an isothermal process. With the higher injection pressure of spray, the curves shift further towards the isothermal curve. This indicates that the injection of spray is highly effective in achieving a near-isothermal compression in the liquid piston compressor. The water droplets of the spray absorb heat from the air during the compression process. The large surface area of the droplets help achieve a high rate of heat transfer and therefore, reduce the temperature of air significantly during the compression process. The injection pressure of spray controls the mass flow rate of the spray and droplet size distribution in the spray. In general, a higher injection pressure of spray results in a higher mass flow rate and droplets with a smaller mean diameter. This helps in achieving a larger rate of heat transfer. Therefore, a higher injection pressure of spray results in a higher temperature drop of air and shifts the compression process towards isothermal conditions.

Table 7.1 shows the polytropic index of compression and the isothermal efficiency of compression with spray injection. It is observed that the injection of spray reduces the polytropic index significantly towards near-isothermal conditions. An isothermal efficiency of compression up to 96% can be achieved with spray injection in the liquid piston compressor. The higher injection pressure of spray helps improve the isothermal efficiency of compression, however, the higher injection pressure requires a greater pump work to generate the spray.

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Table 7.1: Polytropic index and isothermal efficiency of compression with spray cooling.

Process Polytropic Index (n) Isothermal Efficiency (%)

No Spray 1.25 77

Spray: 10psi 1.14 85

Spray: 20psi 1.09 90

Spray: 30psi 1.06 93

Spray: 40psi 1.05 94

Spray: 50-70psi 1.04 - 1.03 94 - 96

7.2.2. Aqueous Foam

Experimental investigation of aqueous foam based heat transfer in liquid piston compression experiments is presented in Chapter 5. It is observed that the temperature of the air during the compression process reduces with the use of aqueous foam especially towards the latter part of the cycle. A larger volume of aqueous foam in the compression chamber showed a higher temperature drop during the compression process. Aqueous foam absorbs heat from the hot air during the compression process and hence abates the rise of air temperature. During the initial phase of the compression process, irrespective of the volume of aqueous foam, the temperature drop is very small. The bubbles in the foam start collapsing as the pressure inside the compression chamber increases. This results in the exposure of relatively low-temperature bubbles of the foam to the hot air. The volume of aqueous foam plays an important role in temperature reduction towards the end of compression. As compression proceeds, the higher temperature of the air and higher chamber

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pressure help in achieving a high rate of heat transfer due to the higher collapse rate of bubbles in the latter part of the compression process.

Table 7.2 shows the polytropic index and isothermal efficiency of compression with aqueous foam of different volume inside the compression chamber. It is observed that the polytropic index of compression reduces with the use of aqueous foam into the compression chamber. The isothermal efficiency of compression increases with an increasing volume fraction of aqueous foam inside the chamber.

Table 7.2: Polytropic index and isothermal efficiency of compression with aqueous foam.

Process Polytropic Index (n) Isothermal Efficiency (%)

No Foam 1.13 86%

Foam- 25% of Chamber 1.10 89

Foam- 50% of Chamber 1.09 90

Foam- Full of Chamber 1.09-1.07 90-92

7.2.3. Metal Wire Mesh

Experimental Investigation of metal wire mesh in a liquid piston compressor is presented in chapter 6. It is observed that the installation of metal wire mesh inside the compression chamber reduces the air temperature during the compression process. The high thermal conductivity of wire mesh and the high heat transfer area of mesh help transfer heat from air to liquid during the compression process. Table 7.3 shows the polytropic index and isothermal efficiency of compression with metal wire mesh inside the compression chamber. Metal wire mesh helps reduce

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polytropic index towards isothermal conditions and improve the isothermal efficiency of compression significantly.

Table 7.3: Polytropic index and isothermal efficiency of compression with metal wire mesh.

Process Polytropic Index (n) Isothermal Efficiency (%)

No Mesh 1.15 84

With Aluminum Mesh 1.08 90

With Copper Mesh 1.08 90

7.3. OCAES Efficiency

The end-to-end efficiency of liquid piston based OCAES system with various heat transfer enhancement techniques is evaluated considering modeling of isothermal OCAES shown in

Chapter 2. Storage pressure of 10 bar gauge (100 m of ocean depth) is considered for the analysis and various components specifications designed for maximum power capacity of 0.5 MW with 2

MWh energy storage were used as presented in chapter 2. Polytropic index of compression observed from the experimental results are considered for both compression and expander modeling. For the base liquid piston without any heat transfer enhancement technique, the polytropic index of 1.14 is considered. The polytropic index of 1.05, 1.09, and 1.08 are considered for the spray cooling, aqueous foam, and metal wire mesh respectively. In the ideal Isothermal

OCAES, compression and expansion happen isothermally with a polytropic index of 1. A 95% confidence interval from 100000 Monte Carlo simulations is evaluated for uncertainty estimate.

The end-to-end efficiency estimates of OCAES with various heat transfer enhancement techniques in comparison to the base liquid piston is shown in Figure 7.1. It can be observed that

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estimated end-to-end efficiency is consistently higher with the use of heat transfer enhancement technique over the base liquid piston. The spray injection method has the potential to show about

15% improvement in the OCAES efficiency achieving end-to-end efficiency of about 60%. Water droplets increase heat transfer inside the liquid piston and hence help to curtail the temperature rise in the liquid piston during compression and temperature fall during expansion. The high surface area and high specific heat of the water spray help attain significant heat transfer enhancement and hence improve compression/expansion efficiency of liquid piston.

Similarly, using aqueous foam, a high heat transfer surface area bubbles in foam help absorb the thermal energy from the air during compression. Aqueous foam based heat transfer shows about 7% improvement in roundtrip efficiency. There is potential for additional gain using aqueous foam through optimization of foam configuration for desired pressure conditions. Although spray cooling and porous media improves the efficiency of OCAES significantly, these heat transfer enhancement techniques require other media to be introduced in the liquid piston. This demands special care for continuous reliable heat transfer performance. The change in spray characteristics and aqueous foam characteristics over time due to degradation of components would affect performance and its efficiency benefits.

Furthermore, metal wire mesh in liquid piston can improve OCAES efficiency from about 45% to about 54%. Additional efficiency improvement is possible with the use of spiral of a higher number of turns which would provide higher heat transfer area. However, an additional volume of metal wire mesh would reduce volume for air and affect power density the compressor/expander.

As metal wire mesh does not require any moving fluid power components as opposed spray injection and aqueous foam methods, liquid piston with metal wire mesh is easy to operate and

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maintain. Moreover, the mixing of air and water is minimal with metal wire mesh compared to spray injection and aqueous foam techniques.

Figure 7.1: End-to-End Efficiency of OCAES system with various heat transfer enhancement techniques in liquid piston.

An isothermal liquid piston compressor would define an upper limit for roundtrip efficiency of OCAES, which is about 72% for the given system considerations. This indicates that inefficiencies in the motor/generator, hydraulic pump/motor, pipelines, control valves, and storage result in about 28% of energy loss. End-to-end efficiencies of existing compressed air energy storage (CAES) plants in Huntorf (Germany) and McIntosh AL (USA) are 42% and 54% respectively [14]. Clearly, liquid piston based OCAES with the use of heat transfer enhancement technique in liquid piston can show significantly higher end-to-end efficiency over existing CAES plants.

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7.4. Conclusions

Efficient compressors and expanders are desired to improve the efficiency of OCAES systems.

Heat transfer enhancement in a liquid piston compressor/expander can be effective in achieving a highly efficient near-isothermal compression/expander. Spray injection, aqueous foam, and metal wire mesh based heat transfer enhancement techniques are tested in a liquid piston compressor.

Efficiency analysis of an OCAES system indicates that liquid pistons with spray injection, aqueous foam, and metal wire mesh have the potential to show a significant improvement in the roundtrip efficiency of the energy storage system. Spray injection is highly effective method among the three methods and shows about 14-18% efficiency improvement of liquid piston based OCAES. Such efficient energy storage systems can help facilitate effective utilization of intermittent renewable ocean energy resources.

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CHAPTER 8: Conclusions

Efficient large-scale energy storage is desired for optimal utilization of renewable energy resources. Energy storage in the form of compressed air under the ocean is a promising large-scale energy storage concept. The efficiency of such an ocean compressed air energy storage system

(OCAES) can be improved by developing energy-conversion configuration with minimal energy losses. Three major OCAES configurations based on the handling of heat the system are- diabatic, adiabatic and isothermal. Energy and exergy analysis of these OCAES configurations is performed for comparative assessment. Energy efficiency of diabatic OCAES is about 50% whereas its exergy efficiency is about 55%. Energy efficiency undervalues efficiency of diabatic OCAES, therefore, exergy efficiency would be a good measure of efficiency for comparison with other storage concepts. Adiabatic OCAES shows about 5% improvement in exergy efficiency over diabatic OCAES. Isothermal OCAES shows significantly higher efficiency over diabatic and adiabatic OCAES and show a roundtrip efficiency of about 72%. Although isothermal OCAES is highly efficient compared to other configurations, the realization of such a high efficiency is conditional on achievement of near-isothermal compression and expansion process.

In the pursuit of attaining near-isothermal compression, heat transfer in liquid piston compressor is investigated experimentally during compression of air. Thermal analysis of the liquid piston compressor indicates the thermal circuit can be modeled in terms of three resistances, namely- convective thermal resistance between gas and chamber, conductive thermal resistance of chamber material, and convective thermal resistance between chamber and ambient. Quantitative evaluation of these thermal resistances during the compression process shows that convective thermal resistance of air is significantly higher than the other two, especially in the later part of the

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compression process. This suggests techniques to enhance the heat transfer coefficient between gas and chamber can lead to a significant gain in isothermal efficiency of compression.

Various heat transfer enhancement techniques are studied experimentally in a liquid piston compressor. Heat transfer enhancement using water spray injection, aqueous foam, and metal wire mesh spiral are considered in this investigation. In water spray injection study, experiments are performed to include a range of factors covering various injection pressures of spray, different spray angles, and various compression stroke times. Water spray injection is observed to be very effective in reducing the air temperature during the compression process. The isothermal efficiency of compression can be improved significantly with higher injection pressure. The spray at 70 psi injection pressures leads to 19-21% improvement in isothermal efficiency of compression from the base level efficiency of 75% for liquid piston without spray. Experiments with different spray angels indicate a marginal improvement in isothermal efficiency is possible with the use of an optimal spray angle. Furthermore, spray injection is highly effective in attaining near-isothermal compression at faster compression strokes, which highlights the effectiveness of spray injection to achieve efficient compression with a high power density. Overall, water spray injection is highly effective in achieving near-isothermal compression with up to 95% isothermal efficiency.

Aqueous foam, due to its a high heat transfer coefficient and high specific heat compared to air along with a high surface area, can absorb a significant portion of the heat of compression in the compression chamber. Experiments with aqueous foam in compression chamber show significant temperature abatement during the compression process. The temperature abatement increases with an increasing amount of aqueous foam used in the compression chamber, however with higher cyclic variability. Moreover, experiments with various foam generator designs of different hole diameters indicate that increasing the hole diameter of the foam generator reduces

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cyclic variability without significantly affecting efficiency. Overall, aqueous foam based heat transfer enhancement in a liquid piston compressor is effective in attaining up to 92% isothermal efficiency.

The metal wire mesh spiral is also studied in liquid piston compressor for efficiency improvement. The high thermal conductivity and large heat surface area of metal wire mesh can provide a high rate of heat transfer heat from the gas to the liquid inside the liquid piston compressor. Aluminum and copper wire meshes in the form of Archimedean spiral are tested in a liquid piston during the compression of air. Furthermore, the stroke time of compression was varied to assess the effectiveness of metal wire mesh at faster compression strokes. It is observed that metal wire mesh is highly effective in temperature abatement during compression at various compression stroke times. A temperature drop of 26-33 K was observed with the use of metal wire mesh using both aluminum and copper wire mesh spirals. Metal wire mesh improved isothermal compression efficiency by 6-8% from the base liquid piston efficiency of 82-84%.

Finally, the end-to-end efficiency of liquid piston OCAES system is assessed with various efficiency improvement techniques in the liquid piston. Significant improvement in efficiency of

OCAES system is possible with the use of heat transfer enhancement techniques in liquid piston.

Aqueous foam based heat transfer can achieve about 4-10% improvement whereas metal wire mesh has the potential to show about 6-12% improvement in end-to-end efficiency of OCAES over the base efficiency of about 45%. Spray injection is highly effective efficiency improvement technique with potential to attain about 60% end-to-end efficiency of OCAES. Clearly, liquid piston based Isothermal OCAES configuration with the use of heat transfer enhancement technique in liquid piston has the potential to attain a significantly higher efficiency than existing compressed air energy storage plants.

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