Development of a Combined Thermal Management and Power Generation System Using a Multi-Mode Rankine Cycle

DEVELOPMENT OF A COMBINED THERMAL MANAGEMENT AND POWER GENERATION SYSTEM USING A MULTI-MODE RANKINE CYCLE

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering

By:

NATHANIEL M. PAYNE B.S., Ohio Northern University, 2019

2021 Wright State University

Cleared for Public Release by AFRL Public Affairs on June 2, 2021

Case Number: 2021-0296

The views expressed in this article are those of the author and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government.

WRIGHT STATE UNIVERSITY GRADUATE SCHOOL April 27, 2021

I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Nathaniel M. Payne ENTITLED Development of a Combined Thermal Management and Power Generation using a Multi-Mode Rankine Cycle BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Mechanical Engineering. ______Dr. Mitch Wolff, Ph.D. Thesis Director

______Dr. Raghu Srinivasan, Ph.D., P.E. Chair, Mechanical & Materials Engineering Committee on Final Examination:

______Dr. Rory Roberts, Ph.D.

______Dr. José Camberos, Ph.D.

______Levi Elston, M.S.

______Barry Milligan, Ph.D. Vice Provost for Academic Affairs Dean of the Graduate School

ABSTRACT

Payne, Nathaniel M. M.S.M.E., Department of Mechanical and Materials Engineering, Wright State University, 2021. Development of a Combined Thermal Management and Power Generation System using a Multi-Mode Rankine Cycle.

Two sub-systems that present a significant challenge in the development of high- performance air vehicle exceeding speeds of Mach 5 are the power generation and thermal management sub-systems. The air friction experienced at high speeds, particularly around the engine, generates large thermal loads that need to be managed. In addition, traditional jet engines do not operate at speeds greater than Mach 3, therefore eliminating the possibility of a rotating power generator. A multi-mode water-based Rankine cycle is an innovative method to address both of these constraints of generating power and providing cooling. Implementing a Rankine cycle-based system allows for the waste heat from the vehicle to be used to meet the onboard power requirements. This application of a Rankine cycle differs from standard power plant applications because the transient system dynamics become important due to rapid changes in thermal loads and electrical power requirements.

Both an experimental and computational investigation is presented. An experimental steady state energy balance was used to determine a 5.1% and 11.5% thermal and Second

Law efficiency, respectively. Transient testing showed an increase in power generation of

283% in 30.5 seconds when starting from idle, with a steady state power generation of 230

W. In addition to the power generation, the experimental system removed 10.7 kW from the hot oil loop which emulates a typical aircraft cooling fluid. Experimental results were

used in the development of dynamic computational models using OpenModelica, an open- source modeling tool. Deviation between model and experimental results was within 5% for component models and 3.5% when analyzing the system energy balance. Testing of the vehicle level model included steady state, transient, and simulated mission, which was used to characterize performance and develop the system controls. During transient testing, the system controls demonstrated the ability to meet both the cooling and power requirements of the system through rapid response times and minimal temperature overshoot (2.72%).

The development and testing of this model provides an opportunity for scaling and optimization of a combined power and thermal management system across a wide range of vehicle sizes and operating conditions.

TABLE OF CONTENTS

1. Introduction ...... 1

1.1 Problem Overview ...... 1 1.2 Approach ...... 2 1.3 Thesis Organization ...... 2 2. Background ...... 4

2.1 Motivation and Historical use of Thermal management Systems in Aircraft ...... 4 2.1.1 Early Use of Aircraft Thermal Management Systems ...... 4 2.1.2 Thermal Management Needs ...... 5 2.1.3 Materials ...... 6 2.2 Thermal Management Systems ...... 8 2.2.1 Passive Thermal Management Systems ...... 9 2.2.2 Regenerative Thermal Management Systems ...... 10 2.2.3 Film Cooling ...... 21 2.3 Power generation ...... 24 2.4 Modeling ...... 26 2.4.1 OpenModelica ...... 26 2.4.2 Evaporator Modeling ...... 27 3. Methodology ...... 30

3.1 Innovative Solution ...... 30 3.1.1 Rankine Cycle Review ...... 30 3.1.2 Implementation for Aircraft Thermal Management Applications ...... 31 3.1.3 Multi-Mode Rankine Cycle ...... 33 3.2 Experimental System ...... 34 3.2.1 System Description ...... 34 3.2.2 System Data Acquisition System ...... 37

3.3 Experimental System Operation Conditions ...... 38 3.4 Steady State Testing ...... 39 3.5 Transient Testing ...... 40 4. Model Development...... 44

4.1 HPTMS Package Development ...... 44 4.2 Heat Exchangers ...... 46 4.2.1 Moving Boundary Method ...... 46 4.2.2 Heat Exchanger Configurations ...... 53 4.2.3 Transient Effects ...... 57 4.3 Turbine ...... 58 4.4 Fluid Models ...... 62 4.5 Pump ...... 63 4.6 Open-Source Models Used ...... 64 4.7 Solver Overview ...... 65 4.8 SHEEV Model ...... 65 4.9 Vehicle Level Model ...... 66 4.10 Vehicle Model Operating Conditions ...... 70 5. Results ...... 75

5.1 Experimental Results ...... 75 5.1.1 Steady State ...... 75 5.1.2 Transient ...... 79 5.2 Component Model Validation ...... 84 5.2.1 Evaporator Model Comparison ...... 85 5.2.2 Liquid-Liquid Heat Exchanger Model Comparison ...... 88 5.3 SHEEV Model Comparison ...... 93 5.4 Vehicle System Model ...... 94 5.4.1 Quasi-Steady State Parametric Study ...... 95 5.4.2 Transient Model Control ...... 105

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5.4.2 Simulated Mission Capabilities ...... 112 6. Conclusion ...... 119

Appendix A ...... 122

Appendix B ...... 123

References ...... 137

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LIST OF FIGURES Figure 1: Schematic of a scramjet engine with typical distribution of heat flux [3] ...... 6

Figure 2: Yield strength and maximum service temperature of common materials used in aircraft [5] ...... 8

Figure 3: Concepts of passive TMS for aerospace vehicles [5] ...... 9

Figure 4: Cooling channel structures within a scramjet engine [8] ...... 11

Figure 5: Recooling cycle for a scramjet engine with a single turbine [10] ...... 13

Figure 6: T-S diagram for recooling cycles with multiple expansion processes to increase the total available heat sink of the system [11] ...... 14

Figure 7: Recuperation effectiveness (left) and specific thrust (right) across a range of

Mach numbers for a regenerative cooling system (RC) and recooling cycle (RCC) [10] 15

Figure 8: Total heat sink (top) and heat sink due to cracking (bottom) of JP-7 fuel [12] 18

Figure 9: Regenerative cooling system for a scramjet engine utilizing cracked hydrocarbon fuel [13] ...... 20

Figure 10: Diagram showing a film cooling slot and the resulting interaction with the freestream gas (left) [8] Schematic of film cooling configuration on a vane in a turbine engine (right) [14] ...... 22

Figure 11: Normalized temperature profile for film cooling within boundary layer [14] 23

Figure 12: Comparison of hot-gas-side wall temperature between regenerative cooling and combine regenerative and film cooling [15] ...... 24

Figure 13: Heat exchanger with two-phase and vapor regions for a FCV (top) and MB

(bottom) models [20] ...... 28

Figure 14: Schematic showing basic components of a Rankine cycle (left) and temperature-entropy diagram showing the four processes of an ideal Rankine cycle

(right) [22]...... 31

Figure 15: Rankine cycle thermal management system utilizing fuel as the cooling medium...... 32

Figure 16: Flow path schematic of experimental system...... 35

Figure 17: Hierarchical structure of the models included in the HPTMS Modelica package ...... 45

Figure 18: Pressure-enthalpy diagram demonstrating the thermodynamic boundaries that are utilized in a moving boundary heat exchanger...... 47

Figure 19: Control volume diagram of a moving boundary scheme for a concentric pipe, counterflow evaporator ...... 48

Figure 20: Arrangement of nodes for a parallel flow evaporator ...... 54

Figure 21: Arrangement of nodes for a counter flow evaporator ...... 55

Figure 22: Arrangement of nodes for a parallel flow condenser ...... 56

Figure 23: Arrangement of nodes for a counter flow condenser ...... 56

Figure 24: Schematic of heat transfer processes within a heat exchanger ...... 57

Figure 25: Use of transfer functions for the dynamic heat exchanger models (counterflow evaporator shown) ...... 58

Figure 26: Overview of scroll expander model operation ...... 59

Figure 27: An enthalpy-entropy diagram showing the difference in power generation between an actual and an isentropic process [26]...... 60

Figure 28: Object oriented view of full system model in OpenModelica ...... 66

Figure 29: Aircraft level system model of a combined power and thermal management system ...... 67

Figure 30: View of cooling channel model found within the vehicle level cooling system model with time dependent wall temperatures...... 68

Figure 31: Simplified cooling channel model using a defined heat flow rate...... 69

Figure 32: Diverting valve used for switching between open and closed operation developed using the MSL...... 70

Figure 33: Logical flowchart for the controller model for the diverting valve position. .. 73

Figure 34: Logical flowchart for the controller for the water flowrate...... 74

Figure 35: Experimental schematic including labels that identify the sensor locations. .. 76

Figure 36: Power generation responses to step change increases in the water flowrate ... 80

Figure 37: Distribution of time constants from experimental results for step changes in flowrate...... 82

Figure 38: Power generation responses as the scroll expander returns to idle...... 83

Figure 39: Oil exit temperature from the evaporator response to a step increase in flow with an inlet temperature of 230°C ...... 84

Figure 40: Experimental results for heat loss within the evaporator for fixed oil inlet conditions ...... 86

Figure 41: Comparison between water ΔT from experimental and model results ...... 87

Figure 42: Comparison between oil ΔT from experimental and model results ...... 87

Figure 43: Percent error of model ΔT for both the oil and water sides of the evaporator 88

Figure 44: Experimental results for heat loss within the oil cooler for fixed inlet conditions ...... 89

Figure 45: Comparison of cooling water ΔT from the experiment and model...... 90

Figure 46: Comparison between oil ΔT from experimental and model results ...... 91

Figure 47: Percent error of model ΔT for both the oil and water sides of the oil cooler .. 92

Figure 48: Regenerative cooling system used to provide baseline system cooling capacities...... 95

Figure 49: Fuel temperatures at exit of channel A (left) and channel B (right) for the regenerative cooling system...... 96

Figure 50: Percent decrease in the fuel temperature at the exit of channel B for open system for 0.005 (a), 0.01 (b), 0.015 (c), 0.02 (d), 0.025 (e), 0.03 (f), and 0.04 kg/s (g). 99

Figure 51: Total heat transfer for open system in the evaporator for water flowrates of

0.005 (a), 0.01 (b), 0.015 (c), 0.02 (d), 0.025 (e), 0.03 (f), and 0.04 kg/s (g)...... 101

Figure 52: Percent increase in total cooling capacity for open system when compared to a regenerative system for 0.005 (a), 0.01 (b), 0.015 (c), 0.02 (d), 0.025 (e), 0.03 (f), and

0.04 kg/s (g)...... 103

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Figure 53: Percent decrease in the fuel temperature at the exit of channel B for closed system for 0.005 (left) and 0.01 (right) ...... 104

Figure 54: Percent increase in total cooling capacity for closed system when compared to a regenerative system for 0.005 (left) and 0.01 (right)...... 105

Figure 55: Fuel flowrate change from acceleration to cruise in an aircraft...... 106

Figure 56: Expected change in maximum fuel temperature during transition from closed to open cycles following step change...... 107

Figure 57: Prescribed water mass flowrate for the system (top) and the controller values used to determine the prescribed mass flowrate (bottom) ...... 108

Figure 58: Diverting valve position following step change decrease in the fuel flowrate.

...... 110

Figure 59: Fuel temperature response for a step change decrease in fuel flowrate...... 111

Figure 60: Net power production during change from acceleration to cruise conditions112

Figure 61: Prescribed fuel flowrate (top) and heat flux (bottom) for the simulated mission...... 114

Figure 62: Water flowrate for the simulated vehicle mission...... 115

Figure 63: Diverting valve position for t the simulated vehicle mission...... 116

Figure 64: Maximum fuel temperature for the simulated vehicle mission...... 117

Figure 65: System net power through the duration of the changing conditions of the generic mission...... 118

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LIST OF TABLES

Table 1: Matrix outlining conditions used for steady state testing and the randomized testing order………………………………………………………………...…………... 40

Table 2: Representative values of the overall heat transfer coefficients in heat exchangers [25]………………………………………………………………..………50

Table 3: Matrix outlining vehicle depended operating conditions used in quasi-steady state parametric study………………………………………………………………….71

Table 4: System energy balance for both the oil and water portions of the system…..76

Table 5: Steady-state power generation and average time constant for each step change response………………………………………………………………………………..81

Table 6: Comparison of experimental and model steady state values for processes on the water side of system………………………………………………………………..94

Table 7: Comparison of experimental and model steady state values for processes on the oil side of system…………………………………………………………………..94

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Acronyms and Symbols

FCV = Finite Control Volume MB = Moving Boundary MSL = Modelica Standard Library NACA = The National Advisory Committee for Aeronautics NTU = Number of transfer units ORC = Organic Rankine Cycle RC = Regenerative Cooling RCC = Recooling Cycle SHEEV = Subscale High-speed Energy Extraction Validator TEG = Thermoelectric Generator TMS = Thermal Management System ΔP = Pressure difference ΔT = Temperature difference ε = Emissivity ε = Heat exchanger effectiveness η = Film effectiveness parameter

휂 = Carnot efficiency

휂 = Isentropic efficiency

휂 = Mechanical efficiency

휂 = Second Law efficiency θ = Normalized temperature profile

휌 = Density at edge of boundary layer

σ = Stefan-Boltzmann constant ω = Rotational velocity c = capacity ratio C = Heat capacity rate

퐶 = Local heating coefficient haw = Adiabatic wall enthalpy hin = Inlet enthalpy hls = Enthalpy of condensation hout = Outlet enthalpy hvs = Enthalpy of evaporation hw = Wall enthalpy L = Total heat exchanger length

L2p = Length of two-phase control volume

Lsc = Length of subcooled control volume

Lsh = Length of superheated control volume 푚̇ = Mass flow rate

푞̇ = Convective heat transfer

푞̇ = Radiative heat transfer

푞̇ = Local aerodynamic heating

푄̇ = Maximum heat transfer

푄̇ = Heat transfer in two-phase region

푄̇ = Heat transfer in subcooled region

푄̇ = Heat transfer in superheated region R = Recuperative effectiveness ST = Specific thrust

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T = Temperature

Taw = Adiabatic wall temperature

Tc = Coolant temperature

Tw = Wall temperature

T∞ = Freestream temperature U = Overall heat transfer coeficient

푢 = Velocity at edge of bound 푊̇ = Power generation

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ACKNOWLEDGEMENTS

Partial support for this project was supplied by the Dayton Area Graduate Studies

Institute. The U.S. Government is authorized to reproduce and distribute reprints for

Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of Air Force Research Laboratory or the U.S. Government.

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1. Introduction

1.1 Problem Overview

A notable trend in the development of the next generation of aircraft is a drastic increase in vehicle speed. These extreme speeds, which often exceed Mach 5, present several distinct and complex design challenges. This thesis addresses a potential solution to two of these challenges: thermal management and power generation. Traditionally, these are separate subsystems operating independently; however, a combined thermal management and power generation system is advantageous in this application. Intuitively, a notable advantage of a combined system is a reduction of size and weight. Although the reduction in weight and volume adds value to the design, the most notable reason for a combined system is the ability to take advantage of the aircraft’s waste heat. This combination is important to next generation aircraft where the tightly integrated subsystems place a premium on space needed for each subsystem in addition to the weight. High temperatures experienced by the vehicle provide a large amount of thermal energy available to power a thermodynamic cycle, producing electrical power for the vehicle. As part of a thermodynamic cycle’s operation, thermal energy is pulled away from critical areas which reduces the temperature and provides a means of cooling the aircraft.

1.2 Approach

The Air Force Research Lab (AFRL) has begun research to study potential solutions in order to meet the thermal management and power requirements of high-speed aircraft. One potential solution is the use of a Rankine cycle system. In this system, water is pumped through a heat exchanger, leading to boiling and superheating of the water and removal of heat from the secondary working fluid. The superheated steam then undergoes an expansion process, producing power, prior to rejecting its waste heat and condensing.

Current research involves experimental testing at AFRL to study the steady state and transient behavior of a Rankine system. The experimental results will be used to validate a physics-based model being developed in parallel to the experiments.

The modeling effort consists of three distinct phases: toolset development, experimental system modeling, and vehicle level modeling. Initial modeling efforts consisted of developing the individual component models that would be used in later stages of the project. These efforts resulted in a Modelica toolset that can be used in future modeling efforts in addition to modeling of the experimental and vehicle systems. Once developed, the models were then used with experimental data to improve the component models. This increased the confidence in the component models prior to their use in the vehicle level model.

1.3 Thesis Organization

The thesis is divided into six sections. Section II provides an overview of the challenges associated with high-speed flight, aircraft thermal management and power generation systems, and the Modelica language. Section III discusses the experimental

system developed at AFRL, the operating conditions, and the design of method used for the experimental testing. In Section IV, an overview is given of the model development portion of the thesis. A description of each of the component models developed is provided, followed by an overview of the experimental and vehicle level models. Both experimental and model results are presented in Section V. A summary of the discoveries, conclusions drawn from the results, and future work are outlined in Section VI.

2. Background

2.1 Motivation and Historical use of Thermal management Systems in Aircraft

A major limiting factor in the development and operation of high-speed aircraft is extreme aerodynamic heating. This is a challenge that has been addressed in previous aerospace vehicles such as those that arose from the space program of the mid to late-20th century. The thermal management systems (TMS) developed for these vehicles alone will not meet the needs of high-speed aircraft of the future. These legacy aerospace vehicles only experienced extreme speeds during reentry, and therefore were able to employ the use of passive TMS. A major challenge arises in developing a TMS which can protect the aircraft during a flight with sustained high-speeds where extreme heating occurs. This technical challenge has led to an increased interest in developing active TMS to enable sustained high-speed flight.

2.1.1 Early Use of Aircraft Thermal Management Systems

The development and design of high-speed aircraft became an area of great interest in the early and mid-20th century. A driving force behind this was in part due to the space program and the technical challenges presented by the design of vehicles that would be able to sustain the speeds and temperatures associated with reentry into the atmosphere.

The National Advisory Committee for Aeronautics (NACA) began investigating technical issues associated with space flight in the early 1950s. Four major areas of technical interest

included: materials and structures capable of withstanding the temperatures experienced during reentry; aerodynamics at extreme speeds, the vehicle’s stability and control systems, and pilots operating in the space environment [1]. The North American X-15 was developed as a joint program between the United States Air Force, Navy, NACA, and the private sector to develop a test vehicle to address these design challenges. Reaching a top speed of Mach 6.7, the lessons learned from the X-15 contributed to future programs ranging from Gemini to the Space Shuttle. This aircraft is the first practical application of any form of thermal management system on an aircraft.

2.1.2 Thermal Management Needs

The high rates of heat transfer to the surfaces of high-speed aircraft dominate their thermal management needs. An extreme example of this aerodynamic heating is demonstrated by the flow behind the shock of the Apollo during reentry, which reached temperatures of 11,000 K at speeds of Mach 36. Similarly, the National Aerospace Plane, which was ultimately cancelled, expected temperatures in excess of 1,800 K along the leading edges for speeds of Mach 8 [2]. These extreme temperatures lead to large rates of heat transfer between the freestream gas and the aircraft’s surface via convective heating, qc, (1) and radiative heat transfer, qr, (2).

푞̇ = 휌푢퐶(ℎ − ℎ) (1)

푞̇ = 휀휎푇 (2)

In addition, heat from the aircraft’s engine increases the overall thermal demand of the aircraft. At extreme speeds, scramjets are used as a propulsion system instead of turbine engines. Scramjet engines, having no moving parts, rely on the compression of the freestream air by using the inlet. Air is then slowed inside of the engine, increasing the air’s temperature, pressure, and density. Temperatures peak within the combustor, resulting in high heat transfer rates into the aircraft from the engine which can easily exceed rates as high as 2000 Btu/ft2-sec [3]. The distribution of the heat flux along the length of a scramjet shown in Figure 1 highlight the high cooling demand within the combustor. Heat resulting as a waste product from the aircraft’s engine presents an additional challenge for thermal management.

Figure 1: Schematic of a scramjet engine with typical distribution of heat flux [3]

2.1.3 Materials

For high-speed vehicles, heat fluxes resulting from aerodynamic heating and the aircraft’s engine influence the entire design of the aircraft, particularly in the selection of

materials. Figure 2 outlines the variations in the yield strength with maximum service temperatures of common materials used in aircraft structures. Selection of the materials for high temperature regions such as the combustor, leading edges, or other stagnation points is imperative to design feasibility. Many of the high temperatures on the aircraft will exceed the operating limits of common materials used in aerospace applications such as aluminum, titanium, and lightweight composites. Examples of the impact of aerodynamic heating is observed in several vehicles. Reaching speeds of Mach 3, the SR-71 is designed to withstand aerodynamic heating, which is evident in the materials selected. Temperatures on the surface of the aircraft exceeded 500°F and as a result, the SR-71 was designed with titanium as its structural material due to its higher operational temperature [4]. Dangers associated with aerodynamic heating are illustrated in the X-7 program from the 1950s, which reached speeds above Mach 4.3. Constructed of stainless steel and nickel alloys, the

X-7 had better temperature resistance than the SR-71. However, the aircraft suffered from structural failure due to the high temperatures during flight. As a result of the trend of increased operating temperatures, Figure 2 shows that for practical operation of high-speed aircraft, either the development of new materials or the implimentation of TMS is necessary.

Figure 2: Yield strength and maximum service temperature of common materials

used in aircraft [5]

2.2 Thermal Management Systems

Aircraft thermal management systems are classified into different categories based upon their operation: active and passive. The first classification are passive thermal management systems, also referred to as thermal protection systems, which do not rely on a cooling medium. Instead, these systems rely on the material properties of the aircraft to protect critical subsystems from high temperatures. Active thermal management systems rely on a cooling medium to remove heat from high temperature regions. This is accomplished with either internal flows, such as regenerative cooling systems, or external flows like film cooling. Each of these classifications have variations that can be used depending upon the region of the aircraft or the application. It is expected that future high-

speed aircraft will rely on a combination of these types of thermal management systems to meet the high cooling demand.

2.2.1 Passive Thermal Management Systems

Passive TMS are characterized by the lack of a working fluid used in the removal of heat. As the simplest form of TMS, passive systems rely on the heat being either radiated away from the aircraft’s surface, absorbed by a heat sink, such as the structure [6]. Passive

TMS is the type of system utilized in the X-15 as well as many of the aircraft developed later in the space program. Passive systems (Fig. 3) include but are not limited to: heat sinks, insulative materials, and ablative materials [5].

Figure 3: Concepts of passive TMS for aerospace vehicles [5]

The heat sink style TMS absorbs and stores the thermal energy, typically within the structural material. For passive TMS to be effective, the material used as a heat sink must have both high thermal conductivity and high heat capacity. This method requires a sufficiently large mass to store the heat throughout the aircraft’s mission profile, creating an issue of excessive weight as flight durations increase.

Insulative TMS use materials with low thermal conductance like ceramic insulation. As this insulative material reaches high temperatures, much of the heat flux is radiated away from the vehicle’s surface as portrayed in Figure 3. The remaining heat flux that dissipates into the vehicle’s structure avoids reaching critical temperatures. These insulative materials generally have low fracture toughness and are unsuitable for leading edges or other areas of high thermal and mechanical stress [5]. This presents a problem for implementation in aircraft which would experience high temperature regions due to stagnation points along the leading edge.

Ablative heat shields have been used for over half of a century to protect aircraft from high temperatures. Most notably, these systems have been used by NASA, from the

Mercury missions to the Space Shuttle [7]. Ablative heat shields protect the aircraft by dissipating the heat as the outer layer of the heat shield is burned away. Additionally, the reaction products from the heat shield provide an insulative layer of protection for the aircraft. Ablative heat shields are consumptive in nature, burning away throughout flight, and the heat shields must be replaced after each use. This makes the use of ablative heat shields rather costly in reusable aircraft.

2.2.2 Regenerative Thermal Management Systems

In some applications, the use of passive TMS is not practical because of an extreme heat flux. If only passive means are used in these cases, the thermal protection layer would become thick. This increased thickness would add unnecessary weight to the aircraft. To increase the cooling capacity of a TMS, active systems are used. An active TMS is characterized by the use of a cooling medium to reduce the temperature in regions of high heat flux. Examples of active TMS include regenerative, film, and transpiration cooling.

The concept of regenerative cooling is characterized by heat transfer through means of internally forced convection, as the cooling medium passes though cooling channels.

Figure 4 shows cooling channels for a regenerative cooling thermal management system for a scramjet engine. Regenerative cooling systems are frequently considered for scramjet cooling applications; however, the principle can be extended to any high temperature regions of the vehicle. Heat flux from the engine is transferred into the cooling medium as it passes through the cooling channels. The engine’s fuel is typically selected to be used as the cooling medium, reducing the weight of the aircraft by eliminating the need for a secondary coolant. Fuel passes through cooling channels in the engine or other high temperature portions of the aircraft, increasing in temperature as it absorbs the thermal energy. After serving as the cooling medium, the high temperature fuel is then burned in the combustor.

Figure 4: Cooling channel structures within a scramjet engine [8]

Regenerative cooling systems are sometimes limited in their ability to meet the cooling requirements for the entire vehicle. This could be a result of the limited heat sink available in the fuel. To increase the convective cooling capacity, the fuel flowrate would need to be increased. An increased flowrate for cooling purposes would exceed the needs of the engine and the excess fuel would be abandoned [9]. For regenerative cooling to be a viable option for an aircraft TMS, the heat sink available must be increased. One method of increasing the heat sink is the recooling cycle such as the application shown in Figure

5. Recooling cycles utilize the fuel as a heat sink repeatedly, thereby increasing the cooling capacity of the system [10]. In the recooling cycle, the fuel passes through a portion of the cooling channel, absorbing thermal energy from the engine. This high temperature fuel is then expanded through a turbine prior to flowing through the rest of the cooling channel.

Utilizing the turbine decreases the enthalpy of the fuel, thereby increasing the available heat sink for the second portion of the cooling channel. A secondary benefit of the turbine is the production of power through the expansion work of the fuel. Figure 5 shows a flow schematic of a recooling cycle that employs a single turbine.

Figure 5: Recooling cycle for a scramjet engine with a single turbine [10]

Recooling cycles offer an increased cooling capacity as the turbine allows the fuel to be used repeatedly without exceeding the upper temperature limit of the fuel. The T-S diagram for a recooling cycle with secondary cooling, the process in Figure 5, is shown in

Figure 6 (a). More heat can be absorbed by the fuel as the number of expansion processes increase. This is exemplified in Figure 6 (d) which shows continuous secondary cooling as the number of expansion processes approaches infinity. The key limitation of a recooling cycle is that the increase in cooling is limited by the enthalpy decrease caused by the turbine. Similar methods using an evaporative process could result in large increases in cooling capacity.

Figure 6: T-S diagram for recooling cycles with multiple expansion processes to

increase the total available heat sink of the system [11]

For both a standard regenerative cooling and a recooling cycle system, the fuel enters the combustor of the engine after it is used to remove waste heat. The cooling system selected for the scramjet has a direct effect on the enthalpy of the fuel entering the combustor, and by extension engine performance. Qin et al. performed a coupled heat transfer and flow model analysis for a hydrogen fueled scramjet, utilizing both regenerative and recooling cycle systems. System performance is evaluated using the specific thrust,

ST, as well as the recuperative effectiveness, R. The recuperative effectiveness is defined

as the ratio of the heat reinjecting by the fuel to the fuel heat value. The regenerative cooling system presented a higher recuperative effectiveness but approaches a limit as the fuel reaches its maximum temperature. This indicates that the heat sink available becomes insufficient above approximately Mach 8 for the regenerative system modeled here.

However, the recooling cycle system shows an increased effectiveness across the entire range. When observing the specific thrust of the scramjet for each system, the recooling cycle showed a slightly lower value across its range.

Figure 7: Recuperation effectiveness (left) and specific thrust (right) across a range of Mach numbers for a regenerative cooling system (RC) and recooling cycle (RCC)

[10]

To improve the performance of active TMS, the available heat sink must be maximized. For a hydrocarbon fuel, the heat sink available can be classified as either physical or chemical [11]. Thus far, the only method of increasing the heat sink is through increasing the physical heat sink. The physical heat sink is the direct result of the heating the fuel, leading to raising the fuel’s temperature. For recooling cycles, the expansion work

process is used to decrease the temperature of the fuel for further cooling. In doing so, the physical heat sink is increased. A fuel’s chemical heat sink is comprised of the endothermic

(heat absorbing) reactions that occur. Thermal and catalytic cracking (process in which the heavier hydrocarbon molecules are broken into lighter molecules) can be used to achieve an increased chemical heat sink, as these reactions are endothermic. Depending upon the operating conditions of the system, such as flowrate and residence time within the cooling channel, these processes begin at approximately 1000◦F. However, the operational temperature is limited by a process referred to as coking. This is where the carbon that results as a byproduct of the cracking process accumulates. To prevent accelerated coking and carbon build up within a system, the operational temperature is generally limited to approximately 1300◦F.

Work done by Huang et al., investigated the potential chemical heat sink properties of the common fuels JP-7, JP-8+100, and JP-10 [12]. Testing was conducted for each of the fuels in a single tube reactor rig, which represented flow within a single passage heat exchanger. From these tests, the total heat sink, comprised of both physical and chemical, were obtained as well as the resulting coke deposits. Experimental results studying the total and chemical heat sinks for the JP-7 fuel across its range of operating temperatures is shown in Figure 8. For a peak fuel temperature of 1334◦F the total heat sink is 1468

Btu/lbm. Of the fuels studied, JP-7 had the highest overall heat sink available. At this same temperature, the chemical heat sink of the JP-7 fuel was 462 Btu/lbm. These experimental results show that the chemical heat sink for the JP-7 fuel comprises 31.5% of the total heat sink. For both chemical and total heat sink, an increase occurs in the heat sink available as the temperature of the fuel increases. However, for the chemical heat sink shown on the

bottom of Figure 8 a limit exists above 1300◦F, coinciding with the temperature at which the rate of coking increases. In addition to the heat sink measurements, the coke deposits that resulted were examined. These results concluded that JP-8+100 has a lower rate of coke formation than JP-7. This is an important design consideration, as the buildup of carbon deposits would hinder the performance and possibly damage the TMS or engine.

Figure 8: Total heat sink (top) and heat sink due to cracking (bottom) of JP-7 fuel

[12]

Utilizing the aircraft’s fuel in regenerative cooling applications initially appears advantageous and practical due to the elimination of a secondary cooling medium on the aircraft. This is especially important for next generation aircraft where the tightly integrated subsystems place a premium on space and weight. A secondary benefit of using the fuel as a coolant arises when a hydrocarbon fuel is chosen, due to the chemical heat sink available.

Making use of the chemical heat sink through thermal cracking appears promising for use in TMS applications.

Benefits may exist in the performance of the TMS by making use of these methods concurrently to increase the total heat sink available. Li et al. conducted a study which used a regenerative cooling system with thermally cracked fuel for aircraft power generation

[13]. As the fuel flows through the cooling channel, removing heat from the engine, sufficient temperatures are reached to cause thermal cracking of the fuel. Exiting the cooling channel, the cracked fuel enters the turbine where expansion occurs, producing electrical power, prior to the fuel entering the engine. The purpose of this study was to investigate the proposed solution of using an expansion cycle with a cracked hydrocarbon fuel to produce power. In this study, there was a significant improvement in power generation using the cracked fuel when compared to the uncracked fuel.

Figure 9: Regenerative cooling system for a scramjet engine utilizing cracked

hydrocarbon fuel [13]

The work done by Li et al. uses thermally cracked fuel for power generation applications rather than as a TMS. Expansion work done by the turbine in this study is used primarily as a means of power generation rather than as a means of increasing cooling capacity, as with recooling cycles. The similarities between the power generation scheme in Figure 9 and the recooling cycle shown in Figure 5 are evident by comparison of the system diagrams. Elements of increasing the physical heat sink through expansion work as well as the chemical heat sink through thermal cracking are present within this study.

However concerns in coke deposits within the fuel system arise when thermal cracking occurs. Though this work is focused on power generation, it combines methods of increasing cooling capacity in a TMS. Utilizing multiple thermal management concepts in parallel can be used to increase the cooling capacity of a TMS to meet the cooling needs of an aircraft.

2.2.3 Film Cooling

As previously discussed, active thermal management systems rely on a cooling medium to mitigate the extreme heat transfer rates within regions of an aircraft. For regenerative cooling systems, this is achieved by the cooling medium passing through cooling channels, removing heat through convective heat transfer. Film cooling is another form of active TMS, which utilizes a coolant to reduce temperatures in regions of high heat flux. However, the operating principle for film cooling differs from that of regenerative cooling systems. In a film cooling system, a coolant released from openings on the surface of the body is injected into the boundary layer as shown in Figure 10. The presence of the coolant within the boundary layer lowers the rate of convective heat transfer between the surface and the hot freestream gas.

This method of thermal management has been in use for decades with applications including gas turbine engines. Film cooling of turbine blades has improved engine efficiency as well as a decrease in fuel consumption. Figure 10 illustrates a cut away view of a turbine blade with film cooling capabilities. In a gas engine, cooling air is bled from the compressor, where it then flows to the internal portion of the blade. From there, the cooling air is bled through openings in the blade’s surface, where it then forms a cooling film within the boundary layer. This simplistic and effective operating principle makes film cooling an attractive TMS option to apply to aerospace vehicle design.

Figure 10: Diagram showing a film cooling slot and the resulting interaction with

the freestream gas (left) [8] Schematic of film cooling configuration on a vane in a

turbine engine (right) [14]

Film cooling operates by decreasing the convective heat transfer rate between the freestream gas and the surface of the body. Injecting the cooling medium into the flow reduces the temperature within the boundary layer. Convective heat transfer is reduced because of this reduction in temperature. The expression for convective heat transfer due to aerodynamic heating, Eqn 1, can be rewritten assuming constant specific heats resulting in Eqn. 3. The temperature gradient is the driving potential for aerodynamic heating.

Reductions can be made to the heat transfer by reducing this temperature gradient and, in the case of film cooling, this is done by reducing the adiabatic wall temperature, Taw.

푞̇ = 휌푢퐶푐(푇 − 푇) (3)

The benefits of film cooling and the potential for reducing the heat transfer rates are demonstrated by observing the temperature profile within the boundary layer.

Temperature within the boundary layer is represented by the normalized temperature

profile, θ, given in Eqn. 4, where T is the local temperature and TC denotes the temperature of the coolant injected into the boundary layer [14].

푇 − 푇 휃 = (4) 푇 − 푇

The temperature profile within a boundary layer in which film cooling occurs is shown in Figure 11, in terms of the normalized temperature, θ. Decreased temperatures are seen throughout the boundary layer, with the greatest reductions in temperature near x=0.

A rapid increase in temperature is seen as the flow progresses downstream, with the temperature near the surface remaining lower. Despite this behavior, there is still a notable reduction within the boundary layer when compared to the temperature of the freestream flow.

Figure 11: Normalized temperature profile for film cooling within boundary layer

[14]

There is current interest in film cooling using hydrocarbon fuels in scramjet engines. In a paper published by Zuo et al., a study was conducted using a combination of regenerative and film cooling with hydrocarbon fuel in a scramjet engine. Much like the regenerative cooling systems discussed previously, the fuel would flow through cooling

channels in the engine. During the regenerative cooling process, the fuel undergoes thermal cracking. From there, a portion of the fuel is used to cool the engine wall as film coolant, while the remaining fuel is burned in the engine. A 1-D model of a scramjet using the combined cooling processes was developed and validated to measure its performance. The combined cooling system outperforms the regenerative cooling system, without the use of additional fuel. The resulting decrease in wall temperature is depicted in Figure 12, where fuel is injected into the boundary layer at x=0.3 and x=1.14. A notable decrease in temperature is achieved through the combined cooling system with a maximum reduction in wall temperature of 60 K.

Figure 12: Comparison of hot-gas-side wall temperature between regenerative

cooling and combine regenerative and film cooling [15]

2.3 Power generation

The power requirements of auxiliary systems such as fuel pumps, environmental control systems, flight actuation, and radars on modern aircraft require electrical power.

The high velocities of high-performance aircraft present a challenge for on board electrical

power in addition to the thermal management challenges. Traditional aircraft use a gas turbine engine coupled to a generator via a gearbox to produce the necessary power.

However, traditional gas turbine engines do not operate at speeds greater than Mach 3 [16].

Above Mach 3, ramjets and scramjets are likely propulsion systems. Unlike turbine engines, ramjets and scramjets have no rotating parts which can be used for power extraction.

Waste heat recovery for power generation onboard air vehicles has been investigated. The waste heat caused by aerodynamic heating and within the combustor may enable a waste heat recovery system. Li and Wang investigated the use of an integrated thermoelectric generator (TEG) for power generation in a scramjet and completed an exergy analysis on the waste heat driving the TEG [17]. The TEGs were used in conjunction with a regenerative cooling system. A second law efficiency of 22% was obtained, producing 62 kW of electrical power. So, waste heat utilization from the scramjet combustor using a TEG is possible, but ideally a more efficient method is needed.

Regenerative cooling systems are also a feasible source of electrical power for the aircraft. As previously discussed, power can be extracted from the expansion process of the cycles. These systems are attractive because they are a combined system that can be used for both power generation and thermal management. Combining of subsystems can be valuable for saving space and weight in the highly integrated designs of the next generation of aircraft.

2.4 Modeling

The development of a dynamic system model is necessary for understanding the behavior of the system during transient operation, including behavior during start-up, shut- down, and rapid changes in the demands on the system. To develop system controls, an analysis of dynamic behavior is required. The dynamic behavior of the system is described by the governing partial differential equations, including mechanical, electrical, fluid, and thermal aspects. As a result, any modeling language used must be capable of handling these complex, interdisciplinary systems. Several programming languages are available that are capable of modeling transient behavior of complex systems. Modelica, specifically the

OpenModelica software suite, is used for this research.

2.4.1 OpenModelica

Modelica is a specialized, object-oriented modeling language designed for use in the simulation of complex, multi-domain systems [18]. The standard Modelica library contains components for modeling mechanical, electrical, electronic, hydraulic, thermal, control, and power systems. A key advantage of the Modelica language is that in addition to the standard libraries, commercial and open-source libraries can be imported and used to expand the modeling capabilities.

There are currently several compilers available that utilize the Modelica language.

A commercially available package commonly used is Dymola, which contains a simple to use interface and a robust solver. Many of the commercial and 3rd party, open-source libraries are compatible with the Dymola software. Another software available based on

the Modelica language is OpenModelica. Unlike Dymola, OpenModelica is a free, open- source software and is used for this research.

Modelica is a language intended for the modeling of multi-component systems. One key advantage of the Modelica language is the numerous open-source and commercial libraries in addition to the standard libraries within Modelica. The Fluid and Thermal package within the Modelica standard library serves as the framework for the TMS simulation. The Fluids package contains components that model zero- and one- dimensional thermo-fluid components [19]. Tools contained within the Thermal package will aid in the modeling of heat transfer within the system model. Additionally, the

Modelica Media library contained in the MSL is used to provide the fluid properties as the component equations are decoupled from the equations to compute the fluid properties.

2.4.2 Evaporator Modeling

The basic heat exchanger models in the MSL were not created to accommodate liquid-vapor phase change in the working fluid. This limitation is due to the heat exchanger model employing the Dynamic Pipe model found in the Modelica Fluids library. The

Dynamic Pipes model is unable to model 2-phase flow because it employs the pressure and temperature to obtain fluid properties. This leads to a behavior where the fluid reaches but does not exceed the saturation temperature. For a heat exchanger model to be capable of handling two-phase flow, pressure and enthalpy need to be used to obtain fluid properties.

Developing a dynamic heat exchanger model capable of handling the phase change of a fluid is critical to the modeling of the proposed system. Much of the modeling efforts found in literature can be classified as either finite control volume (FCV) or moving

boundary (MB) heat exchanger models [20]. FCV models discretize the length of the heat exchanger into fixed volume regions where the phase and fluid properties are assumed constant within each volume. Accuracy of this model is dependent upon the number of volumes used. Conversely, the MB model is divided into the number of fluid phases that are present within the heat exchanger [21].

Figure 13: Heat exchanger with two-phase and vapor regions for a FCV (top) and

MB (bottom) models [20]

The difference between the two models is exemplified in Figure 13 where a heat exchanger with two-phase fluid at the inlet and vapor at the exit is depicted. The FCV volume requires adequate volumes specified by the user to be accurate, while only two are required for the MB model. The conservation laws are applied to each control volume in the same manner for both models. As a result, the FCV model requires more computational time. Desideri et al, developed both a FCV and MB model in the Modelica language for an organic Rankine cycle (ORC) application and compared the results of each model with experimental data. Their work concluded that for small scale ORC applications, a minimum of 20 nodes are required for the FCV model to be accurate, leading to a computational time three orders of magnitude larger than the MB model. Additionally, comparable levels of robustness are achieved for each model for the given application, despite most literature citing the FCV model as being more robust. From their work it appears that the MB model heat exchanger is best suited for the given modeling application.

3. Methodology

3.1 Innovative Solution

An innovative solution to meet both the thermal management and power generation requirements in an aircraft is the Rankine cycle TMS. This approach is similar to the recooling cycles discussed previously, where an expansion process is used to increase the cooling capacity of the fuel. However, rather than the fuel undergoing an expansion process, a secondary fluid – water – is used. This allows for a secondary increase in heat sink available due to the phase change of the water. The following sections provide an overview of the operating principles of a Rankine cycle and its implementation in an aircraft TMS application.

3.1.1 Rankine Cycle Review

The Rankine cycle is the idealized thermodynamic cycle used to predict performance of steam turbine systems. This cycle and the four processes involved are outlined by the temperature-entropy diagram in Figure 14. Descriptions for these processes are as follows:

 12: Pressure of fluid is increased by the pump.

 23: Heat added to fluid, causes phase change and superheating.

 34: Fluid expands through a turbine, power extracted.

 41: Waste heat rejected, and fluid condenses.

Figure 14: Schematic showing basic components of a Rankine cycle (left) and temperature-entropy diagram showing the four processes of an ideal Rankine cycle

(right) [22].

The Rankine cycle is a strong candidate for use in a regenerative cooling system for an aircraft. A major advantage results from the phase change that occurs during process

23 inside the evaporator. This phase change requires a significant amount of thermal energy to occur, increasing the total amount that can be removed from the aircraft. Figure

14 demonstrates this point, showing a large increase in energy is required for the fluid to cross the vapor dome, during which the temperature of the fluid does not change. For this reason, two-phase systems are of strong interest for cooling applications.

3.1.2 Implementation for Aircraft Thermal Management Applications

The concept of using a Rankine cycle for waste heat recovery is something that has been studied and implemented previously. Like many aircraft TMS methods, the fuel is

proposed as the cooling medium. Prior to being used by the engine, the fuel passes through cooling channels in high temperature regions, such as avionics bays or the full authority digital engine controller (FADEC), removing heat. The cooling capacity of the of the fuel can be increased through the implementation of a Rankine cycle as shown in Figure 15.

Heat is removed from the fuel by the condenser, thereby increasing the total heat removed from the fuel while remaining below the fuel’s coking limit. On-board power generation is an additional benefit to the increased cooling capacity resulting from implementing a

Rankine cycle TMS.

Figure 15: Rankine cycle thermal management system utilizing fuel as the cooling

medium.

When adapted to an aviation TMS, the transient effects of the Rankine cycle become more important. The system will always be under transient operation because of loads and boundary conditions that vary with time. These loads on the TMS are driven by the mission of the vehicle. During acceleration, the vehicle will experience high temperatures. The high temperatures are due to both the engine producing a large amount

of waste heat and the effects of aerodynamic heating as the vehicle reaches high Mach numbers. The TMS will need to exhibit a fast system response to handle the increased vehicle temperatures. Additionally, to meet increases in demand for onboard electrical power, the system will need to be capable of rapidly increasing the power generated.

3.1.3 Multi-Mode Rankine Cycle

The rejection of waste heat from the Rankine cycle provides a unique challenge regarding the weight of the vehicle. There are two system configurations that dictate how the waste heat is rejected from the system: closed and open system. Both systems are described by Figure 15 where the key difference is in the flow path of the working fluid as shown by the diverting valve between the turbine and the condenser. The closed system configuration is used during portions of the mission where the thermal load on the vehicle is within the enthalpy/flowrate bounds of the heat sink (fuel). During the closed configuration, the waste heat from the Rankine cycle is rejected to the fuel before the fuel is burned in the engine. This manageable thermal load during closed cycle operation allows the fuel to be used as a heat sink for the condenser while remaining within an acceptable temperature range.

During the cruise portion of the mission, the fuel flowrate will be substantially decreased. This decrease in flowrate means that the fuel can no longer be used as a heat sink without exceeding the enthalpy bounds of the fuel. This eliminates the heat sink for the condenser portion of the Rankine cycle used in the closed configuration. To accommodate this, the steam is exhausted prior to the condenser, eliminating the need for a heat sink on the vehicle. This system can be used within the same vehicle, and the

configuration is adjusted depending upon the conditions of the mission. By operating as both an open and closed Rankine cycle, the aircraft TMS is a Multi-Mode Rankine cycle.

3.2 Experimental System

An experimental system based on the multi-mode Rankine cycle outlined above has been constructed at Wright-Patterson Air Force Base. This system, referred to as the

Sub-Scale High-speed Energy Extraction Validator (SHEEV), is being used to study the multi-mode Rankine cycle for thermal management applications. Focus is placed on studying the transient system dynamics observed during system tests.

3.2.1 System Description

SHEEV, shown in Figure 16, maintains the same operating principles as the multi- mode Rankine cycle system previously outlined. However, there are some differences in the operation and layout of SHEEV for practical purposes of a lab scale system. The most notable difference between the systems is the change from an open loop fuel system to a closed loop hot oil system. In Figure 15, the fuel is heated in cooling channels and then burned in the combustor, resulting in cool fuel continuously entering the system from the tank. However, this system is adapted to operate on a closed loop oil system. Heat is introduced to the system as the oil (Therminol-XP) is heated by a pair of resistance heaters.

Then following the evaporator, the oil is cooled by a chilled water system to bring the temperature of the oil to within the safe operating limits of the pump. Implementing a closed loop for the oil system allows a consistent temperature to enter the evaporator.

Figure 16: Flow path schematic of experimental system

An additional change that should be noted is the heat sink used by the condenser, during closed loop operation. For aircraft cooling applications, the fuel would be used for cooling within the condenser. However, utilizing a closed loop oil system makes this inconvenient. Instead, a chilled water system is used to provide cooling to the condenser in addition to the oil cooler.

The power extraction device is an important component. It is critical in the system efficiency, power output, and transient operation of the Rankine cycle. The use of a scroll expander was selected based on the expected operating pressures and being generally more tolerant to lower quality steam than turbines. A scroll expander manufactured by

AirSquared (model E15H022A-SH) is used. This model is rated for a nominal output of 1 kW of electrical power with a volumetric ratio of 3.5 [23]. Recommended working fluids include air, carbon dioxide, natural gas, and most refrigerants. Most applications that

employ the use of scroll expanders in lab scale applications used refrigerants as the working fluid. Rather than using refrigerants, steam is selected as the working fluid for the cycle.

Steam was selected as the working fluid because during the open configuration, the steam will be vented to the atmosphere after exiting the turbine. Using steam rather than a refrigerant eliminates environmental concerns associated with this venting. Unfortunately, the use of steam presents challenges as a working fluid within a scroll expander, particularly due to the start-up procedure when compared to other fluids. Adhering to the supplier recommended operating conditions and monitoring the bearing life will enable steam to be used as a working fluid.

An eddy current brake is used to measure the power output of the scroll expander.

The eddy current brake is composed of a series of coils mounted freely on the output shaft of the scroll expander, as well as a moment arm. As electrical current passes through the coils, the resulting electromagnetic field applies a torque to the shaft. This torque is measured using a strain gauge attached to the moment arm. Using the measured torque and rotational speed of the shaft, the mechanical power output for the scroll expander is determined.

For aircraft thermal management, the fuel serves as the heat transfer mechanism between high temperature regions and the Rankine cycle. High temperature regions of the aircraft transfer thermal energy into the TMS. For the experimental system, the thermal energy is introduced into the system through a pair of 15 kW resistance heaters placed in series.

Thermal energy in the experimental system is transferred from the oil to the steam through a counterflow, concentric pipe heat exchanger. This heat exchanger serves as the evaporator/boiler within the Rankine cycle and is a critical component in driving the efficiency of the system and total power generation. The heat exchanger used is manufactured by Exergy Heat Transfer Solutions (Model No. AS-00528). The heat exchanger is constructed from 316 stainless steel and has a heat transfer area of 0.23m2 between the inner and outer pipes per heat exchanger. For the experimental system, the oil passes through the outer pipe and the water passes through the inner pipe of the heat exchanger.

The heat exchanger is critical when considering the system dynamics during rapidly changing thermal loads. In both the experimental system and an aircraft TMS, the heat exchanger must be capable of handling rapid changes in temperatures and flowrates on both sides of the system. Improper flow conditions within the heat exchanger may result in the steam losing the energy (superheated state) necessary to produce power. The presence of two-phase or liquid/vapor water within the scroll expander will also likely damage internal components. The heat exchanger model, developed as outlined in the modeling section, will be valuable in optimizing flow conditions for improved system response and performance. Therefore, an essential aspect of this project is the development of an accurate heat exchanger model.

3.2.2 System Data Acquisition System

Data acquisition for the experimental system enables real time measurement of system conditions ranging from fluid properties, flowrates, and power production. All

instrumentation and system controls communicate using a LabView VI program developed for this system. Pressure transducers and thermocouples are placed throughout the system, including at key locations. Power production for the scroll expander is measured using an eddy current brake. This consists of a series of electrical coils around the rotating shaft of the scroll expander and a moment arm with a strain gauge. The power is then determined using the torque on the moment arm and the rotational speed of the scroll expander.

3.3 Experimental System Operation Conditions

It is important to define the range of operating conditions that can serve as a starting point for steady state testing of the SHEEV. Major user controlled operating conditions include the water and oil flowrates as well as the set point temperature for the oil heaters.

Secondary operating conditions that can be controlled include the scroll expander rotational speed, position of the back-pressure valve, and oil return temperature. Initial system tests indicated the upper bound is dictated by the scroll expander and the lower bound by the evaporator, consisting of a series of concentric pipe heat exchangers. From the heat transfer rates determined from the calorimetry of the oil side of the evaporator, a maximum volumetric flowrate for the water was estimated to be of approximately 0.34 LPM. Steady state testing confirmed this estimation when a maximum flowrate of 0.325 LPM was observed. Exceeding this maximum flowrate results in two-phase fluid at the exit of the evaporator, when superheated steam is required for the safe operation of the scroll expander. The minimum operating flowrate for the scroll expander is determined by the minimum pressure ratio, which was observed to be approximately 2.7 corresponding to a flowrate of 0.25 LPM. These operating bounds define the upper and lower limits for the operating conditions of the system.

3.4 Steady State Testing

SHEEV will be utilized to conduct three classifications of experiments: steady- state, transient, and simulated missions. The first series of experiments following initial tests of the system were used to collect steady-state results. These experiments consisted of operating the system under the same operating conditions for extended periods of time at various points within the system’s operating range. A system energy balance was obtained from the steady-state results, which provided valuable insight into the operation and troubleshooting of the system. Major discrepancies in the energy balance were used to identify errors in the data acquisition system for SHEEV. Results from this stage in testing provided data for the tuning of the individual components of the system model.

Two variables that are changed in the steady state testing include: water flowrate and scroll expander speed. Initial testing is used to determine the minimum and maximum water flowrates for the system, and the same is done for the scroll expander speed at the given flowrate. Operating conditions for the steady state runs are illustrated in Table 1.

Table 8: Matrix outlining conditions used for steady state testing and the

randomized testing order.

Water Flowrate (LPM)

Scroll Expander 0.250 0.275 0.300 0.325 Speed (RPM)

1500 6 12 2 3

1750 7 1 2 15

2000 x 9 14 11

2250 x x 8 3

2500 x x 10 13

3.5 Transient Testing

The transient system response to changing operating conditions is critical, as these will vary drastically throughout the mission. A key condition that will change is the heat transfer into the TMS. As the aircraft accelerates, the fuel demand from the propulsion system is much higher. This elevated flowrate allows for a higher rate of convective heat

transfer through the cooling channels, resulting in a lower heat load on the TMS. As the aircraft enters the cruise phase of the mission, the fuel rate decreases, placing more of the thermal management demands on the TMS.

The second major operating condition that will change in the mission is the power generation requirements for the aircraft. Sharp increases in the power draw from auxiliary electrical systems will occur when these systems are used by the aircraft. Meeting these large swings in power demand will require the system to be able to rapidly respond by increasing electrical power.

For thermal and power control for the SHEEV, the flowrate of the water within the

Rankine cycle is used. The oil loop portion of the system has a slow response and will be held at a fixed flowrate and temperature set point. This is consistent with the aircraft under steady cruise conditions. As the aircraft enters cruise conditions, the fuel flowrate and temperature will reach steady state. This will also be the leg of the mission with the greatest thermal load on the TMS. To observe the response due to an increase in the thermal management needs, the water flowrate will undergo a step change increase. With a fixed flowrate and inlet temperature on the oil side of the heat exchanger, the dependent variable monitored during that step change will be the exit temperature of the oil. Finally, the total heat extracted from the oil is observed as a response to the step change.

Electrical power extracted by the scroll expander is dependent upon several operating parameters. The fluid flowrate and enthalpy entering the scroll expander are significant drivers of power extraction. Of these two variables, the flowrate is the most convenient operating condition to control. Eqn. 5 shows how changes to the flow rate

effects the power. However, this increase is limited by the capacity of the heat exchanger.

If the flowrate is increased, the temperature exiting the heat exchanger will decrease, resulting in lower enthalpy fluid entering the scroll. For a given set of operating conditions, there exists a flowrate that optimizes the power generation of the system.

푊̇ = 푚̇ (ℎ − ℎ) (5)

The power generation of the scroll expander is also dependent upon the operational set point. A PID controller is used to control the rotational speed of the scroll expander by adjusting the load on the eddy current brake. As with all rotating machinery, the efficiency and power generation are closely coupled to the rotational speeds.

Understanding the system dynamics and transient response to changes is required to properly tune the system model. These transient responses are obtained through experimental testing. The testing procedure for observing the response of the heat transfer rate and power generation will consist of a step change increase in the water flowrate, while still maintaining superheated conditions at the scroll inlet and exit. This will emulate the time varying power production and thermal management requirements of the system. The water side of the experimental system will initially be operating at a low flowrate. During this initial idle phase, the scroll expander will be operating at a slow rotational speed, producing a small amount of electrical power. By idling the scroll expander, an improved system response is obtained compared to a cold start. From idle a step change increase in the water flowrate occurs, indicating the transition from idling to increased demand for power and thermal management requirements. Transient response of the scroll expander

power and heat transfer within the evaporator will be used to accurately capture the system time constants.

4. Model Development

4.1 HPTMS Package Development

The flexibility of the Modelica language allows for the creation of models that are compatible with the existing libraries. Several models were developed to meet the specific needs of the system modeling effort including heat exchangers, turbomachinery, and fluid models. These models make up the HPTMS Modelica package which provides a toolset to the user for modeling thermal-fluid systems (Figure 17). The models outlined in the following sections provide the framework for modeling of the experimental system, vehicle thermal management systems, and future work.

Figure 17: Hierarchical structure of the models included in the HPTMS Modelica

package

4.2 Heat Exchangers

The restrictions previously discussed limit the ability of the heat exchanger models found in the MSL to be used in cases where phase change occurs due to using pressure and temperature to define fluid properties. This leads to issues modeling two phase flow where pressure and enthalpy are the dependent variables needed to define the fluid properties. To accurately model an evaporator or condenser, multiple control volumes are required because of the large changes in fluid properties between the subcooled, two-phase, and superheated regions. Two viable options for model structure are finite volume and moving boundary evaporators which are outlined previously in 2.4.2 Evaporator Modeling. A moving boundary model is selected because it is structurally simpler and less computationally expensive when compared to the finite volume model while maintaining similar levels of accuracy according to the studies referenced in 2.4.2 Evaporator Modeling.

4.2.1 Moving Boundary Method

Moving boundary evaporators make use of thermodynamic bounds for determining the size of the control volume rather than defining fixed sizes for the control volumes. This principle is visualized using the pressure-enthalpy diagram in Figure 18. The first case that is considered is an evaporator, where subcooled water enters the heat exchanger and superheated steam is desired at the exit. For a given evaporator, only the pressure is needed to define the saturation conditions: enthalpy of condensation, hls, and enthalpy of evaporation, hvs.

Figure 18: Pressure-enthalpy diagram demonstrating the thermodynamic

boundaries that are utilized in a moving boundary heat exchanger.

The three control volumes for the parallel flow evaporator are shown in Figure 19.

This configuration will serve as the generic example to demonstrate the principle of a moving boundary evaporator. By rearranging the control volumes within the model, this principle can be adapted to meet any needs that may be encountered during the modeling effort.

Figure 19: Control volume diagram of a moving boundary scheme for a concentric

pipe, counterflow evaporator

Figure 18 demonstrates that there is a certain amount of energy required to increase the enthalpy from the inlet enthalpy, ℎ, to the enthalpy of condensation, hls. The critical heat transfer for the subcooled control volume, 푄̇, is dependent upon the inlet conditions and the mass flowrate of the water. The critical heat transfer is determined using Eqn. 6.

푄̇ = 푚̇ (ℎ − ℎ) (6)

The critical heat transfer found above is assumed to be independent of the geometry and the conditions of the oil control volume. This assumption allows the length of the control volume to be determined using the effectiveness-NTU method. Using this method, the maximum heat transfer for the control volume is found using Eqn. 7. The effectiveness,

ε, is then found as the ratio of the critical, subcooled heat transfer found previously in Eqn.

6 to the maximum heat transfer.

푄̇, = 푚̇ 퐶,푇, − 푇, (7)

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

Previously, the critical heat transfer was independent of the geometry. However, the relationship between the effectiveness, ε, and the number of transfer units, NTU, is dependent upon the geometry of the heat exchange. In the case being considered, the heat exchanger is parallel flow, so the expression provided in Eqn. 8 relates ε to NTU [24].

1 − exp (−NTU(1 + 푐) 휀 = (8) 1 + 푐

where 퐶, 푐 = 퐶,

From the value for NTU found in Eqn. 8, sufficient information is now known to determine the control volume length. The definition of NTU given in Eqn. 9 provides a relation between the overall heat transfer coefficient, the heat transfer area, and the

minimum heat capacity rate. To close the system of equations and determine the control volume length, the overall heat transfer coefficient, U, must be defined. The overall heat transfer coefficient encompasses both the conductive and convective heat transfer within the heat exchanger and is dependent upon the two fluids within the heat exchanger. As a result of the phase change, the overall heat transfer coefficient varies between each control volume. Table 9 provides an expected range of values for the heat transfer coefficient depending upon the fluids. These values are used as initial bounds for the coefficient selected within the model, prior to fine tuning based upon experimental results.

Table 9: Representative values of the overall heat transfer coefficients in heat

exchangers [25]

Closing the system of equations for the water side of the subcooled control volume, the heat transfer area is found in Eqn. 9. The diameter of the pipe is known, so the length can be determined using Eqn. 10.

푈퐴 NTU = (9) 퐶,

퐴 퐿 = (10) 휋퐷

Exit conditions for the oil side of the control volume are the only remaining unknowns. The heat removed from the oil is calculated using the system energy balance in

Eqn. 11, which includes the critical heat transfer found previously, and a loss term which is derived from experimental results.

푄̇, = 푄̇, + 푄̇, (11)

where 푄̇, = 푚̇ ℎ, − ℎ,

Following the subcooled control volume, the two-phase region is considered. In this control volume the heat transfer is dictated by fixed enthalpy differences in the same manner as the subcooled control volume. The critical heat transfer for the two-phase control volume is visualized in Figure 18 as the energy required to cross the vapor dome.

Using Eqn. 12, the critical heat transfer is determined using the enthalpy of condensation, hls, and the enthalpy of evaporation, hvs.

푄̇ = 푚̇ (ℎ − ℎ) (12)

Using the effectiveness-NTU method, the length of the two-phase control volume is found. After determining the control volume length, the energy balance for the two-phase control volume is then used to determine the exit conditions of the oil (Eqn. 13).

푄̇, = 푄̇, + 푄̇, (13)

where 푄̇, = 푚̇ ℎ, − ℎ,

For the previous two control volumes, the heat transfer was dictated by fixed enthalpy values and from this, the required heat transfer area was determined. The superheated control volume differs in that the control volume side is fixed and depends upon the total heat exchanger length. Using the control volume lengths found previously,

Eqn. 14 is used to determine the size of the superheated control volume.

퐿 = 퐿 − 퐿 − 퐿 (14)

Again, the effectiveness-NTU method is used for the superheated control volume.

However, rather than an effectiveness being known and the area being the dependent variable, the area is given and the relations are used to find the effectiveness for the control volume. Using the effectiveness and the maximum heat transfer, the energy balance for the control volume (Eqn. 15) can be used to determine exit conditions for both the steam and oil.

푄̇, = 푄̇, + 푄̇, (15)

where 푄̇, = 푚̇ ℎ, − ℎ,

푄̇, = 푚̇ ℎ, − ℎ,

4.2.2 Heat Exchanger Configurations

Outlined in the previous section is the application of the effectiveness-NTU method for a moving boundary, two-phase heat exchanger. Within the experimental system model, three distinct heat exchanger models are present: counterflow evaporator, parallel flow condenser, and parallel flow oil chiller. In the cases of the evaporator and condenser, phase change occurs on the water side of the heat exchanger, so the moving boundary model is used. However, no phase change occurs within the oil chiller so only a single control volume is required.

The flow within the heat exchangers is treated as quasi-one dimensional and is discretized into control volumes depending on the fluid phase. For the number of control volumes present, n, there are n + 1 nodes within the model. The arrangement of these nodes allows for adaptation to the type of heat exchanger required by the model. In the previous section, a parallel flow evaporator is described. The arrangement of the nodes along the 1-

D length are shown in Figure 20. Nodes A are designated as the inlet for both the oil and water and D is the outlet node. Within the model, these nodes are the Fluid Port interfaces that transfer the fluid state information in and out of the model. The expressions used within

the model are implemented in the manner described in the previous section, however they are written in terms of the nodes. The nodal forms of the model equations are outlined in

Appendix B.

Figure 20: Arrangement of nodes for a parallel flow evaporator

In the case of a counterflow evaporator, the nodal arrangement for the oil side is reversed. This arrangement is shown in Figure 21. Changes to the governing equations are required because of the counterflow configuration, mostly effecting how 푄̇ is determined and the relationship between ε and NTU. The equations used for the counterflow evaporator model are outlined in Appendix B.

Figure 21: Arrangement of nodes for a counter flow evaporator

In addition to modeling of evaporators, the behavior of condensers can be captured using a moving boundary scheme. The arrangement of the nodes for parallel and counterflow is unchanged. The key difference falls in the order of the control volumes within the water side. For a condenser, the inlet is superheated steam, and the exit is subcooled liquid. This change is reflected in the diagram given in Figure 22 and Figure 23.

Because of the difference in inlet conditions, slight changes are required for the governing equations within the model. The equations used within each of these models are outlined in Appendix B.

Figure 22: Arrangement of nodes for a parallel flow condenser

Figure 23: Arrangement of nodes for a counter flow condenser

The remaining heat exchanger configuration to be discussed is the fluid-fluid heat exchanger. Unlike the previous heat exchanger models discussed, no phase change occurs.

Because each side of the heat exchanger is single phase, only one control volume is required, which simplifies the model.

4.2.3 Transient Effects

The moving boundary heat exchangers developed in the previous section are suitable to many applications and provide accurate steady state results. These models, however, are limited in providing accurate transient heat transfer responses and are therefore listed in the sub-package StaticHX.

Figure 24: Schematic of heat transfer processes within a heat exchanger

When studying the governing physics of a heat exchanger, a thermal lag is introduced by the conduction process within the material dividing the two fluids. This process is demonstrated in the schematic given in Figure 24. Rather than trying to capture the transient physics of the conduction and convection processes within the model, a transfer function is used. The static models are used as the base for the dynamic models, shown in Figure 25, where the heat transfer rates for each control volume are related using

a transfer function. Additionally, the mass flow rates incorporate a transfer function to better handle step changes in the incoming flowrate. The base, static model is used with the TransferFunction model found within the MSL.

Figure 25: Use of transfer functions for the dynamic heat exchanger models

(counterflow evaporator shown)

The transfer functions used within the models will be derived from time constants obtained during transient testing of the SHEEV.

4.3 Turbine

Modeling the scroll expander is important to providing an accurate estimation of the power generation potential of the system. For modeling purposes and future applications, the scroll expander is modelled as a generic turbine with user defined

performance maps. The operational flowchart for the turbine model is outlined below in

Figure 26. This model utilizes the isentropic efficiency to determine both power production and exit conditions. A turbine’s isentropic efficiency, as well as the mechanical efficiency, and pressure ratio are dependent upon the operating conditions. Steady-state results are used to develop look-up tables to provide an accurate model.

Figure 26: Overview of scroll expander model operation

An isentropic process occurs when the process is adiabatic and reversible, meaning there is no frictional or heat losses. In an isentropic turbine, with defined inlet and exit pressures, the entropy at the inlet and exit conditions are the same. For an actual turbine, the system is irreversible, and losses are present, causing entropy generation. This increase in entropy changes the enthalpy at the exit for a given pressure. The enthalpy-entropy diagram in Figure 27 shows this change in exit enthalpy, resulting in a decreased power when compared to the isentropic process. A turbine’s difference between the isentropic and actual power is defined by the isentropic efficiency given in Eqn. (16.

Figure 27: An enthalpy-entropy diagram showing the difference in power

generation between an actual and an isentropic process [26].

ℎ − ℎ 휂 = (16) ℎ, −ℎ

As mentioned previously, there are several variables within the model that are dependent upon the operating conditions of the turbine. System dependent variables include the isentropic efficiency, mechanical efficiency, and pressure ratio, shown in Eqns.

17, 18, and 19 respectively. These variables were shown to be dependent upon the water mass flowrate and the rotational speed of the scroll expander. Modelica’s built in function for lookup tables was utilized to incorporate experimental results for these variables.

휂 = 푓(푚̇ , 휔) (17)

휂 = 푓(푚̇ , 휔) (18)

푃푅 = 푓(푚̇ , 휔) (19)

When generating performance maps for compressors and turbines, this is typically done in a controlled environment at standard pressure and temperature. It is expected that the system will be operating outside of this range at much higher ambient temperatures. To account for these changes, correction factors are applied to the mass flow rate and rotational speed [27]. These expressions are provided in Eqns. 20 and 21. These corrected values are then used as the inputs for the performance map lookup tables.

푇 (20) 푇 푚̇ = 푚̇ 푃 푃

휔 휔 = (21) 푇 푇

The inlet conditions are given in the model from the port interface, defining inlet enthalpy, pressure, entropy, and mass flow. Utilizing the lookup table, the pressure ratio is used to define the inlet and exit pressure shown in Eqn. 22.

Δ푃 = 푃(1 + 푃푅) (22)

where 푃 푃푅 = 푃

The isentropic enthalpy at the exit is then defined using the exit pressure and the inlet enthalpy. Using the lookup tables, both efficiency values are given, closing the system of equations when solving for the turbine power generation.

ℎ − ℎ = 휂ℎ − ℎ, (23)

푊̇ = 푚̇ 휂(ℎ − ℎ) (24)

4.4 Fluid Models

A basic concept used within the Modelica Fluids library is the use of replaceable media models. By using a replaceable media model, the mass and energy balance equations are decoupled from the media model equations. Many of these models will use media models from the Media library found in the MSL. One such model, StandardWater, is used throughout the system model outlined in this thesis for water side models. However, there is not a model that is suited for use in modeling the heat transfer fluid used in SHEEV,

TherminolXP.

A media model was developed for TherminolXP using the framework provided by the Incompressible package found within the Modelica Media library. This framework assumes that pressure has a negligible effect on the density of the fluid, resulting in the fluid properties being solely dependent upon the temperature. Tables used by the model to

find fluid properties including density, specific heat capacity, thermal conductivity, viscosity, and vapor pressure are provided in Appendix A. These tables are derived from manufacturer provided data.

Using the same methodology, as was used in developing the TherminolXP media model, several media models are included in the HPTMS package. The most notable of these it the JP-7 media model used as the fuel in the aircraft system model. JP-7 is an endothermic fuel, so the specific heat as a function of temperature is not linear. For this media model, the specific heat is determined from results given by Huang, Sobel, and

Spadaccini [12]. Kerosene is selected to serve as a surrogate for the remaining fuel properties.

4.5 Pump

For both the experimental and vehicle level systems, pumps are required for both the heat transfer fluid and the water. A simple pump model with a defined mass flow rate was developed for use within these models. The differential pressure across the pump, ΔP, is determined by the downstream head loss and sets the outlet pressure of the pump (Eqn.

25).

푃 = 푃 + ∆푃 (25)

Power required by the pump can be determined using the differential pressure and the mass flowrate, using Eqn. 26. This assumes that the pump is isentropic, which provides a simple estimation of the pumping power required despite neglecting losses.

푚̇ 푊̇ = ∆푃 (26) 휌

4.6 Open-Source Models Used

Many of the major components of the full system model were developed specifically for the application of this model. The remainder of the models used are available in the MSL, mostly from the Fluid and Media libraries. For the water loop portion of the model, the replaceable media model that is used is StandardWater, found within the

Media library. This model calculates the media properties for water in the liquid, gas, two- phase regions according the IAPWS/IF97 standard [28]. Using the model, the fluid properties can be defined by pairs of independent variables in three ways: pressure and enthalpy, pressure and temperature, and density and temperature. For this application, pressure and enthalpy is the most practical, particularly because phase changes occur.

Several important components used within the system model are the boundaries, mass flow sources, tanks, and pipes, which are found within the Fluids library. For many applications in the model, a pump is used. However, in some cases, such as the cooling water system and particularly during model development, an ideal mass flow source is preferable for simplicity. For the tanks within the system model, the OpenTank is selected for use. This model represents a tank that is under ambient pressure. The OpenTank model allows for the user to define the number of ports as well as their size and position on the tank. Two pipe models are available: StaticPipe and DynamicPipe. The key difference between the models is that the DynamicPipe models the storage of mass and energy and

StaticPipe does not [28]. The StaticPipe model is used in the system to capture the pressure

losses due to pipe runs. The DynamicPipe model is used in cases where heat transfer occurs in only a single fluid, such as the oil heaters.

4.7 Solver Overview

When a model is simulated within OpenModelica, the Modelica model is transformed into an ODE representation in order to perform a simulation using numerical integration methods [29]. The default solver for OpenModelica is DASSL which is an implicit, higher order, multi-step solver. This solver has been used with no notable issues throughout model development. OpenModelica also supports several explicit solvers, including a 1st order Euler method. This solver incorporates a user defined fixed step size.

The Euler method was selected for use in most of the model simulation. A time step of

0.005 seconds was selected with a convergence tolerance of 10-6.

4.8 SHEEV Model

The various models in the HPTMS package outlined previously serve as the building blocks for the system level models. First, a Modelica model for the experimental system is developed (shown in Figure 28) and follows the same basic layout as SHEEV given previously in Figure 16. From the heat exchanger portion of HPTMS, the counterflow evaporator, parallel condenser, and the fluid-fluid heat exchanger models are implemented. Other models include the pump and turbine model from the same package, utilizing the performance maps obtained from experimental results.

Figure 28: Object oriented view of full system model in OpenModelica

For simplification of the modeling results, some changes are made between the physical system and the model. Most notably is the omission of the oil heaters in the model.

A prescribed mass flow source with a fixed temperature is selected to minimize any transient effects caused by the oil heaters and tank. For similar reasons, the same approach is used in the modeling of the chilled water system for both the oil chiller and the condenser.

4.9 Vehicle Level Model

Research on both the SHEEV and the development of a system level model are part of an overall effort to develop an accurate model representing a Rankine cycle TMS in an aircraft. This model, shown in Figure 29, follows the same basic operating principles as the SHEEV model, but notable changes are present.

Figure 29: Aircraft level system model of a combined power and thermal

management system

The most notable difference is the cooling channel architecture present within the model. Two cooling channel structures are developed and provided in HPTMS: fixed wall temperatures and fixed heat flow rate. The first cooling channel model is provided in Figure

30 which relies on the MSL. This approach provides more detailed results; however, a significant amount of information must be known about the cooling channel geometry.

Figure 30: View of cooling channel model found within the vehicle level cooling

system model with time dependent wall temperatures.

A simpler cooling channel approach is selected for use which relies only on a defined heat flow rate. This eliminates the need for any information regarding the cooling channel geometry. The object-oriented view of this model is given in Figure 31 and it contains two simple sub-models.

Figure 31: Simplified cooling channel model using a defined heat flow rate. These sub-models calculate the exit conditions for the primary and secondary cooling channel using the energy balance expression given in Eqn. 27. Additionally, two temperatures are defined as outputs of the model and are to be used in the system controls.

푄̇ = 푚̇ (ℎ − ℎ) 27

An integral part of the system’s controls is operating between open and closed configurations. This is achieved through the diverting valve model shown in Figure 32.

Models used in this include the StaticPipe and ValveLinear, both found in the Fluids package of the MSL. The input term, u, determines the valve position which ranges from

0-1, where 1 indicates a fully open valve and 0 indicates fully closed.

Figure 32: Diverting valve used for switching between open and closed operation developed using the MSL.

4.10 Vehicle Model Operating Conditions

Selection of the operating conditions for the vehicle model requires careful consideration to properly understand the system performance. To simplify the model, only two vehicle dependent operating conditions are selected as inputs: fuel flowrate and cooling demand. The value of these inputs will vary throughout the flight of a vehicle.

When considering the flowrate of the fuel, the greatest demand will occur during when the aircraft is accelerating, but it will be significantly lower during cruise. Flowrates of 1.75 –

2.25 kg/s are considered for acceleration and 0.5 - 0.75 kg/s for cruise. These will determine the upper and lower bounds of the fuel flowrates used in the model.

When determining the bounds for the cooling demand on the system, many factors were considered. Aerodynamic heating, combustor temperatures, and portion of vehicle being cooled greatly affect the cooling demand of the aircraft. To simplify the model, a fixed value for the total cooling demand on the system is defined, ranging from 0.5 – 2

MW. This will be divided equally between the primary and secondary cooling channels in

Figure 31. Knowing the bounds of the vehicle operating conditions, a simple, two factor

design of experiments can be outlined. The conditions given in Table 10 are repeated for water side operating conditions, as necessary.

Table 10: Matrix outlining vehicle depended operating conditions used in quasi- steady state parametric study.

Total Heating Rates (MW) Fuel Flow(kg/s) 0.5 0.625 0.75 0.875 1 1.5 2 0.5 x x x x x x x Cruise 0.75 x x x x x x x Mid 1.25 x x x x x x x 1.75 x x x x x x x Accel 2.25 x x x x x x x

The secondary level of inputs determines the operation of the water side of the system. First, the water flowrate range will be determined by the capacity of both the heat exchanger and the condenser. Secondly, the position of the diverting value determines how much heat is being rejected into the fuel. The parametric study outlined in the next section is used to determine these conditions.

4.11 Vehicle Model System Controls

Transient operation of the system presents a major challenge resulting from both the large range of operating conditions and the system’s dual purpose of thermal management and power generation. During a given generic mission profile for the aircraft, the power generation is driving the controls, and at other times the cooling needs are. For the control of the system, there are two control signals: valve position and water flowrate.

The control variables that are chosen include the maximum temperature of the fuel (at the inlet to the combustor) and the power required by the fuel pump. Additionally, a third control variable is chosen, 푄̇, which is determined from the condenser model (Eqn 28) and ensures the limits of the condenser are not exceeded. Therefore subcooled liquid is

always present at the exit. The logic for determining the diverting valve position and water flowrate is as follows.

(28) 푄̇ = 퐶푇, − 푇,

The first portion of the controller logic is the determination of a closed or open system through the diverting valve positions (Figure 33). A maximum allowable temperature was defined at 1000 K and was chosen to limit the rate of coke deposition [12].

Additionally, the control variable for maintaining condenser performance is defined as

푄̇ = 0. By defining this limit, it ensures that the valve position is selected in a way that maximizes the cooling capacity of the condenser. PID controllers are used for both the temperature and condenser limits to determine the valve position. The controller then compares and selects the smaller of the values.

Figure 33: Logical flowchart for the controller model for the diverting valve position.

The second portion of the controller logic is used to determine the mass flowrate of the water (Figure 34). This handles both the thermal management and power demands of the system. Power generation goals include producing power to meet the demands of the fuel pump. The power generation need is determined in the pump model outlined in Section

4.5. A PID controller is used to determine the water flowrate for the turbine to produce enough power for the system. Similarly, a second PID controller is used to determine the water flowrate needed to meet the cooling demands. The maximum of these two flowrates is used for the water pump.

Figure 34: Logical flowchart for the controller for the water flowrate.

The controller logic provides a reliable and generic framework for the control of a combined power and thermal management system. The method balances both needs of the system through a conservative approach by determining which is greater. One result is portions of the mission where either excess cooling, or electrical power generation occurs.

These situations demonstrate the challenge with developing efficient controls for a combined system under transient operation.

5. Results

5.1 Experimental Results

Experimental testing and analysis provide valuable insight into the operation of a lab-scale Rankine cycle system. Both steady state and transient testing is used to characterize the system’s operation under its full range of operating conditions. Steady state results proved vital to troubleshooting and optimizing the operating conditions of the experimental system. Transient results provided important transient characteristics to be utilized in future modeling work.

5.1.1 Steady State

The analysis of the steady state results consists of investigating the system energy balance. Therefore, the system efficiencies, heat transfer rates, and losses can be identified.

Furthermore, identifying the change in energy for each process within the system creates a convenient, simple way of quantifying the operation of a large complex system. This method allows for a simpler method of comparing the experimental results to the system model.

Locations within the system (1 – 4) for both the oil and water sides of the systems are identified and labeled in Figure 35. These locations coincide with pressure transducers and thermocouples used to collect experimental data. This allows for an accurate representation of the energy change for each process.

Figure 35: Experimental schematic including labels that identify the sensor locations.

During testing, the system reaches steady state for the each of the given operating conditions outlined in Table 1. Energy values obtained for specific conditions are presented in Table 11. The convention is positive values indicate energy entering the fluid and negative values indicate energy leaving the fluid.

Table 11: System energy balance for both the oil and water portions of the system.

Oil Water Location Process Calorimetry (kW) Location Process Calorimetry (kW) 1 - 2 Heater 30.9 1 - 2A Evaporator 13.1 2 - 3 Evaporator -13.2 2A - 2B Line -0.1 3 - 4 Chiller -16.8 2B - 3 Scroll Expander -0.67 4 - 1 Tank -0.8 Energy Out Scroll Expander -0.25 3 - 4 Condenser -12.1 4 - 1 Tank -0.23

As closed loop systems, both the oil and water follow a similar thermodynamic cycle of heat addition and removal. The change in energy for each process is determined through the change in the fluid enthalpy and the mass flowrate. Only one point of heat

addition is present for each fluid: heaters for the oil and the evaporator for the water.

Observing the oil system first, of the 30.9 kW introduced by the heaters, 13.2 kW of the energy is removed by the water within the evaporator. The rest of the energy is lost either within the chiller or the tank. The thermal efficiency of the oil system is defined as the ratio of useful energy extracted to the energy added, so an efficiency of 42.7% is achieved. This efficiency drives the total amount of energy available to the water and is dependent upon the system’s geometry and operating conditions.

It is important to note the energy values for both fluids within the evaporator. Only minor losses are measured within the evaporator, indicating efficient heat transfer between the fluids (0.1 kW of losses). Additional losses recorded in the system occur between the exit of the evaporator and the inlet of the scroll expander. These losses can be attributed to heat transfer between the fluid pipes and the surrounding air. There are two energy values that are important when analyzing the energy change within the scroll expander. The first, the actual change in the enthalpy of the fluid across the scroll expander, and the second is the net power measured by the eddy current brake. Isentropic and mechanical efficiencies of the scroll expander are 73% and 37% respectively. A majority of the total heat absorbed by the fluid within the evaporator is later rejected by within the condenser, indicating a low overall system efficiency.

To understand the system performance, several efficiencies are determined. The maximum thermal efficiency of a reversible power cycle is the Carnot efficiency (Eqn. 29)

[30]. Temperatures 푇 and 푇 are the cold and hot reservoirs that the system is operating between. For the experimental system, these are the cooling water within the evaporator

and the hot oil with respective temperatures of 15°C and 245°C. These conditions result in a Carnot (maximum) efficiency of 44.4%.

푇 휂 = 1 − (29) 푇

Determining the thermal efficiency of the system quantifies the system’s ability to convert thermal energy into useful work. The energy values from Table 12 for the evaporator and the scroll expander, result in a thermal efficiency of 5.1%.

The relationship between the thermal efficiency and the Carnot efficiency can be analyzed using the Second Law efficiency. Using the definition of the Carnot efficiency as the maximum obtainable system efficiency, the Second Law efficiency measures the system’s departure from the reversible limit (Eqn. 30) [31]. The Carnot and thermal efficiency found previously lead to a Second Law efficiency of 11.5%. Understanding the performance of the system in terms of the Second Law efficiency helps determine the maximum achievable performance.

푊̇ 휂 = 푊̇

휂 or (30) 휂 = 휂

Several factors contribute to the system efficiency including thermodynamics, mechanical and heat losses. From a thermodynamic perspective, one method of increasing the potential system efficiency is to increase the heat available. An increase in heat available would

improve the pressures and flowrates that the system could operate at while maintaining superheated steam. Secondly, the system efficiency is limited by the scroll expander.

Optimizing the operating conditions to maximize the efficiency of the scroll expander will improve the overall system efficiency.

5.1.2 Transient

The primary control for the power generation of the system is the water flowrate.

To observe the response to a change in the power generation demand, the flowrate undergoes a step change increase. These responses are shown in Figure 36 for four different steps. In all cases, the system is initially operating at idle conditions, Figure 36. For idle conditions, the minimum water flowrate needed for scroll expander operation and the scroll spinning freely at a low speed with no load. Small variations in the scroll expander speed and power generation at idle are shown. At time t=0, a signal is sent to the pump motor to increase the flowrate of the water. The responses shown in Figure 36 are for a 50, 67, 84, and 100% increase in flowrate. Oil operating conditions for each case are a fixed oil flowrate and inlet temperature of 230°C in the evaporator.

450 450 400 400 350 350 300 300 250 250 200 200

Power (W) Power 150 (W) Power 150 100 100 50 50 0 0 0 50 100 150 200 250 0 50 100 150 200 250 Time (s) Time (s)

50% 67%

450 450 400 400 350 350 300 300 250 250 200 200

Power (W) Power 150 (W) Power 150 100 100 50 50 0 0 0 50 100 150 200 250 0 50 100 150 200 250 Time (s) Time (s)

84% 100%

Figure 36: Power generation responses to step change increases in the water flowrate

All cases show a notable increase in the power generation following the flowrate increase. Following the step change at time t = 0, a slight lag occurs in the response followed by a rapid increase in power generation. Overshoot occurs in the response for the larger step changes (67, 84, and 100%) and increases with the step change size (Table 12).

This can be attributed to the parameters used in the PID controller. An observable trend in the system response is a decreased response time as the step size increases. Table 12

provides the time constant for the responses in Figure 36. A significant decrease occurs between the 50% and 100% steps with a 25.5% decrease in the time constant between these two cases.

Table 12: Steady-state power generation and average time constant for each step change response

Step Change Size Steady-State Time Constant Percent Power (W) Overshoot 50% 135 18.4 0 67% 185 14.8 65 84% 193 14.6 60 100% 238 13.7 72

This trend is further shown in Figure 37, which provides the time constants obtained across multiple repeat tests for each step change size. Some variance is seen across the experimental data, however, a general decrease in the time constant is shown as the step size increases. This behavior indicates that in order to reduce the system response time, a larger nominal flowrate is desired. Besides decreasing response time, higher flowrates were capable of producing more electrical power. The time constant distribution in Figure 37 for the step increase in flow also shows the time constants for a step increase of 120% (not included in the responses in Figure 36). Experimental results for a 120% increase in flow at the same operating conditions showed an increased response time. Despite an increased response time, this higher flowrate yields a higher power than the other step changes. This trade-off between system response time and power generation presents an opportunity for future optimization of system operating conditions.

Following the initial overshoot of the power response, the oscillations decrease, and the system begins to approach steady-state conditions for the increased flowrate. A

secondary response is observed as the system reaches steady state, showing a slight increase in power. This is attributed to the response of the evaporator which is significantly slower than the scroll expander response. Following the step change in flowrate, a slow increase in the heat transfer into the steam from the oil inside the evaporator occurs, increasing the steam’s temperature at the exit. The delayed increase of power can be attributed to the response of the heat exchanger which, when compared to the scroll expander, is significantly slower. This increase in the working fluid’s enthalpy results in a secondary increase in power generation over time.

Figure 37: Distribution of time constants from experimental results for step changes in flowrate.

Responses shown and discussed previously correspond to an increased demand for electrical power in the system. Beginning from idle, the flowrate is increased to meet these power demands. In the case where the water flowrate decreases, the response as the system returns to idle becomes pertinent. Time constants derived from experimental results are shown in Figure 37. Unlike the step change increase results, the time constant is constant across the step changes with a slight decrease for the 100% step change. Power generation as the system returns to idle for each case is shown in Figure 38. The power generation at

idle is similar to Figure 36. Consistency in the time constants shown in Figure 37 manifest in a decreased response time for the larger step changes.

300 300

250 250

200 200

150 150

Power (W) Power 100 (W) Power 100

50 50

0 0 0 20 40 60 80 0 20 40 60 80 Time (s) Time (s)

50% 67%

300 300

250 250

200 200

150 150

Power (W) Power 100 (W) Power 100

50 50

0 0 0 20 40 60 80 0 20 40 60 80 Time (s) Time (s)

84% 100%

Figure 38: Power generation responses as the scroll expander returns to idle.

The experimental system is a proof of concept for a combined power generation and thermal management system. In addition to the power generation responses shown previously, the thermal response is also of interest. For the experimental system, the oil emulates the aircraft’s fuel which is cooled within the evaporator of the TMS. The

experimental response of the oil exit temperature is given in Figure 39. These responses are to the same step increases in flowrate as in the power generation responses. For all responses, the oil is entering the evaporators at 230°C for the duration of the run.

240 240 230 230 220 220 210 210 200 200 190 190 180 180

Oil Temperature (⁰C) Temperature Oil (⁰C) Temperature Oil 170 170 160 160 150 0 50 100 150 200 250 0 100 200 300 400 Time (s) Time (s)

50 67 Inlet Temperature 84 100 Inlet Temperature

Figure 39: Oil exit temperature from the evaporator response to a step increase in flow with an inlet temperature of 230°C

Results in Figure 39 show a lower exit temperature is achieve for the larger step changes. This indicates a higher heat transfer occurring at higher flowrates on the water side of the evaporator. These results show a maximum of 11.3 kW being removed from the oil, by comparison, the oil heaters are adding 30 kW of heat into the system. The increases in heat removed from the oil is significant compared to approximately 4 kW during system idle.

5.2 Component Model Validation

A critical reason for the steady state and transient testing is to gather information for the validation and tuning of component models in Modelica. Tuning of component models individually rather than the whole system model simplifies the process and allows

a quantification of the error within the individual component models. Furthermore, it builds confidence in the component models themselves which can be used in applications outside the system models outlined in the thesis. The component model results are provided in the following sections.

5.2.1 Evaporator Model Comparison

A significant portion of the modelling effort was devoted to the development of two-phase heat exchanger models. The experimental results were compared to the counterflow heat exchanger model developed. This model relies on a user defined heat loss parameter, determined from experimental testing. For testing, the oil flowrate and inlet temperature are fixed, however the water flowrate is varied. The mean and standard deviation values of the heat loss obtained from steady state testing are presented in Figure

40. Mean values for each flowrate are selected for use within the model.

1.8

1.6

1.4

1.2

1 Heat Loss (W)

0.8

0.6

0.4 4 4.5 5 5.5 -3 Water Mass Flow Rate (kg/s) 10 Figure 40: Experimental results for heat loss within the evaporator for fixed oil inlet conditions A test model is developed for the evaporator model and is placed under the same flow conditions as experimental testing. The comparison of temperature differences on both the water and oil side of the heat exchanger are provided in Figure 41 and Figure 42 respectively. For the given tuning parameters, the model slightly over predicts the ΔT of the water across the entire operating range, which stays relatively constant across the whole range of flowrates tested. Conversely, the oil ΔT is slightly under-predicted across most of the operating range tested. However, the linear increase in ΔT for the oil experimentally also occurs in the model predictions.

Figure 41: Comparison between water ΔT from experimental and model results

Figure 42: Comparison between oil ΔT from experimental and model results

Model error for both the oil and water is presented in Figure 43. Percent error is determined based on the difference between the mean experimental and model value. In all cases, the percent deviation between the model and experimental results is within +/- 5% and, the variation of the error of ΔT for the water is notably smaller than the oil.

Figure 43: Percent error of model ΔT for both the oil and water sides of the evaporator

5.2.2 Liquid-Liquid Heat Exchanger Model Comparison

A comparison was made between experimental and modeling results for a single phase, liquid-liquid heat exchanger. Experimental results obtained from the oil chiller within the SHEEV was used for this comparison. Heat loss as a function of the water flowrate is presented in Figure 44. For the liquid-liquid heat exchanger modeling, the oil

and chiller water flowrates are held constant, however the inlet oil temperature changes to reflect the changes in the system water flowrate.

Figure 44: Experimental results for heat loss within the oil cooler for fixed inlet conditions

Having obtained the heat loss for each condition, the heat transfer coefficient, U, is the main tuning parameter within the component model. This parameter is adjusted to best match the experimental results. A comparison of the temperature difference for the cooling water across the heat exchanger is provided in Figure 45. The overall value of the temperature change is within an acceptable amount of error across the four conditions examined.

Figure 45: Comparison of cooling water ΔT from the experiment and model.

The oil temperature difference is tuned and compared in the same manner as the cooling water. A comparison between experimental and model results given in Figure 46 show the temperature difference obtained by the model to be similar in value to experimental results. Discrepancies between the model and the experimental results can be attributed to both variations in experimental data and the use of one set of model tuning parameters across the range of operating conditions

Figure 46: Comparison between oil ΔT from experimental and model results

Observing the model results for the oil and cooling water, these values are of similar magnitude and follow similar trends to the experimental results. In order to quantify discrepancies between the model and experimental results, the percent difference between the values is determined. The percent error for both the oil and water temperature difference is presented in Figure 47. Across the range of operating conditions tested, the percent error stays below 4% for both fluids, which for the purposes of this model is deemed acceptable.

Figure 47: Percent error of model ΔT for both the oil and water sides of the oil cooler

For both heat exchanger models presented, there are several sources of error that are considered. The first is error attributed to the experimental results, which can be addressed through further testing. Reduction in experimental result error would consist of increasing the size of the data set used to obtain the mean ΔT values. Secondly, error can be attributed to the heat exchanger models. The first source of error which effects the evaporator is the modeling scheme used for two-phase flow. A MB modeling scheme was selected for these applications based on the literature, however future work in developing

FCV heat exchangers may increase the model accuracy. Additionally, the effectiveness –

NTU method was applied to the heat exchanger modeling. This method was selected because it simplified the use of the MB modelling scheme rather than relying upon convection and conduction relations.

5.3 SHEEV Model Comparison

An analysis of the SHEEV’s system energy balance provided a method of characterizing the operation of the system. A system energy balance approach is used to quantify, analyze, and validate the system model developed within Modelica. The component model comparison to experimental results allowed for the tuning of heat transfer coefficients, determination of efficiencies, and incorporation of losses. Many of the component models were developed with the intent to incorporate empirical results to better reflect the experimental results that would be obtained.

First, the energy balance of the water side of the system is analyzed (presented in

Table 13). For each of the processes within the experimental system, the change in energy is presented as determined by pressure and temperature measurements of the fluid.

However, some simplifications exist in the model and are not reflected. Most notably, the line losses from process 2A - 2B are not included. Energy change within each process as determined by the model is presented in Table 13 as well. For the four processes being modeled, the values of the change in energy aligns quite well with the experimental results.

This observation is confirmed when considering the percent error between the model and the experimental results. The largest of these errors results from the total change in energy across the scroll expander. This large discrepancy between the model and experiment is partially attributable the exclusion of process 2A – 2B from the model.

Table 13: Comparison of experimental and model steady state values for processes on the water side of system.

Calorimetry Percent Location Process Model (kW) (kW) Error 1 - 2A Evaporator 13.1 13.22 -0.949 2A - 2B Line -0.10 0 N/A Scroll 2B - 3 -0.67 -0.7084 -5.73 Expander Energy Scroll -0.25 -0.2540 -1.60 Out Expander 3 - 4 Condenser -12.1 -11.71 3.18 4 - 1 Tank 0 0 0

Similarly, the energy balance of the oil side of the system and the model comparison is presented in Table 14. It is important to note that because the model uses a defined temperature mass flow source rather than a heater model, the energy absorbed by the fluid in the heater is not included. The largest discrepancy resulting from the comparison of the oil side of the system results from the liquid-liquid heat exchanger model from the oil chiller.

Table 14: Comparison of experimental and model steady state values for processes on the oil side of system.

Calorimetry Location Process Model (kW) Percent Error (kW) 1 - 2 Heater 30.9 N/A N/A 2 - 3 Evaporator -13.2 -13.01751 1.38 3 - 4 Chiller -16.8 -16.67 0.83 4 - 1 Tank -0.8 N/A N/A

5.4 Vehicle System Model

The driving force behind the experimental testing and system modeling was to build confidence in the component models and the ability to develop a system level model.

Testing and analysis of the vehicle system model first consisted of a quasi-steady state

parametric study to define the range of operating conditions that the system would operate.

Analysis of these results aided in the development of system controls and defining the conditions of transient and mission level testing. Transient and mission level model testing was then utilized to tune system controls and to demonstrate the model’s dynamic capabilities.

5.4.1 Quasi-Steady State Parametric Study

Much of the cooling capacity of the proposed aircraft TMS is dependent upon the aircraft’s fuel. The system schematic in Figure 15 contains a cooling channel which the fuel passes through prior and after the evaporator. The heat load on the system is divided evenly between the two cooling channels. For a baseline comparison of the fuel cooling capacity without the Rankine cycle, a simple regenerative cooling system model is developed following the schematic given in Figure 48. Rather than a single cooling channel, the model is composed of two separate cooling channels in series to provide a better representation of a baseline for the Rankine cycle TMS.

Figure 48: Regenerative cooling system used to provide baseline system cooling capacities.

Using the regenerative system model, the fuel temperatures at the exit of each cooling channel are recorded under the operating conditions outlined in Table 10. Fuel temperature values obtained by the model are presented in Figure 49: Fuel temperatures at exit of channel A (left) and channel B (right) for the regenerative cooling system. Two trends can be noted in both plots: an increase in temperature with increased cooling demand, and a decrease in temperature with increased flowrate. Both trends are intuitive when observing the heat equation used in Eqn. 27. It is important to note the discontinuities for the cases of 0.5 and 0.75 kg/s. These trends do not continue past 0.875 and 1.0 MW respectively, due to the fuel exceeding the temperature limit of 1200 K imposed by the model. This trend demonstrates the need to implement a TMS to increase the cooling capacity of the fuel for cruise conditions.

Figure 49: Fuel temperatures at exit of channel A (left) and channel B (right) for the regenerative cooling system. Building upon the simple regenerative cooling system, the next simplest implementation of a TMS is the open configuration. The same vehicle operating conditions are used from Table 10. A water flowrate of 0.005 kg/s is selected initially and increased

until the evaporator limit is exceeded. The water flowrates used were: 0.005, 0.01, 0.015,

0.02, 0.025, 0.03, and 0.04 kg/s.

The open configuration consists of two important measures of performance: percent decrease in fuel temperature and percent increase in cooling capacity. Because the open configuration does not use the condenser, there is no change in the temperature at the exit of channel A. Only the change in the temperature for channel B is considered, and the percent decrease is shown in Figure 50. As the water flowrate increases, the fuel temperature overall decreases. However, across all water flowrate conditions, this decrease in temperature is minimized as the fuel flowrate and cooling demand increase.

1.4 2.4 0.5 kg/s 0.5 kg/s 0.75 kg/s 2.2 0.75 kg/s 1.2 1.25 kg/s 1.25 kg/s 1.75 kg/s 2 1.75 kg/s 2.25 kg/s 2.25 kg/s 1.8 1 1.6

0.8 1.4

1.2 0.6 1

0.4 0.8

0.6

0.2 0.4 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW) Cooling demand (MW)

(a) (b)

4 5 0.5 kg/s 0.5 kg/s 0.75 kg/s 4.5 0.75 kg/s 3.5 1.25 kg/s 1.25 kg/s 1.75 kg/s 1.75 kg/s 2.25 kg/s 4 2.25 kg/s 3

3.5 2.5 3 2 2.5

1.5 2

1 1.5

0.5 1 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW) Cooling demand (MW)

7 0.5 kg/s 0.75 kg/s 6 1.25 kg/s 1.75 kg/s 2.25 kg/s

3 Percentdecrease in fuel temp 2

1 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW)

(e) (f)

(g)

Figure 50: Percent decrease in the fuel temperature at the exit of channel B for open system for 0.005 (a), 0.01 (b), 0.015 (c), 0.02 (d), 0.025 (e), 0.03 (f), and 0.04 kg/s (g).

In this configuration, the condenser is bypassed so all heat removed from the fuel by the evaporator is a net increase in the system cooling capacity. This results in a substantially higher overall heat removal when compared to the closed system operation.

Heat transfer within the evaporator is shown in Figure 51. Similar results to the temperature comparisons given previously in Figure 50, where there is greater cooling capacity as the water flowrate increases is shown. A similar trend when comparing the heat transfer under different fuel flowrates is found. In Figure 51 (f), a minimum heat transfer of 113 kW occurs at the highest fuel flowrate, while a maximum heat transfer of

155 kW occurs at the minimum fuel flowrate. This behavior indicates the increased reliance on the cooling provided by the evaporator during cruise conditions.

Q Q e e 19 37

18.5 36

35 18

34 17.5 33 17 32 0.5 kg/s 0.5 kg/s 0.75 kg/s 16.5 0.75 kg/s 31 1.25 kg/s

EvaporatorHeat Transfer (kW) 1.25 kg/s EvaporatorHeat Transfer (kW) 1.75 kg/s 1.75 kg/s 2.25 kg/s 16 2.25 kg/s 30

15.5 29 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW) Cooling demand (MW)

(a) (b)

Q e 76

62 0.5 kg/s

EvaporatorHeat Transfer (kW) 0.75 kg/s 60 1.25 kg/s 1.75 kg/s 58 2.25 kg/s

56 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW)

€ (d)

100

EvaporatorHeat Transfer (kW)

(e) (f)

Q e 155

150

145

140

135

130

125 0.5 kg/s 0.75 kg/s

EvaporatorHeat Transfer (kW) 120 1.25 kg/s 1.75 kg/s 115 2.25 kg/s

110 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW)

(g)

Figure 51: Total heat transfer for open system in the evaporator for water flowrates of 0.005 (a), 0.01 (b), 0.015 (c), 0.02 (d), 0.025 (e), 0.03 (f), and 0.04 kg/s (g).

The heat transfer values given in Figure 51 increase with the cooling demand placed on the system. This is intuitive when considering the increased heat that is delivered by the fuel to the evaporator. To better quantify this heat transfer, the percent increase in cooling when compared to the regenerative system is calculated, Figure 52.

When considering the percent increase in cooling, the highest water flowrates still offer the highest improvements in performance of 27%. However, unlike the results shown

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previously in Figure 51, the percent increase in cooling decreases dramatically for all conditions as the cooling demand increases. This behavior indicates that as the cooling demand placed on the system increases, much of the cooling will be provided by the fuel, no matter the water flowrate.

1.4 0.5 kg/s 0.75 kg/s 1.2 1.25 kg/s 1.75 kg/s 2.25 kg/s

0.8

0.6

0.4

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW)

(a) (b)

14 0.5 kg/s 0.75 kg/s 12 1.25 kg/s 1.75 kg/s 2.25 kg/s

2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW)

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18 22 0.5 kg/s 0.5 kg/s 0.75 kg/s 20 0.75 kg/s 16 1.25 kg/s 1.25 kg/s 1.75 kg/s 18 1.75 kg/s 2.25 kg/s 2.25 kg/s 14 16

12 14

10 12

10 8 8

6 6

4 4 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Cooling demand (MW) Cooling demand (MW)

(e) (f) Percentincrease in total cooling

(g)

Figure 52: Percent increase in total cooling capacity for open system when compared to a regenerative system for 0.005 (a), 0.01 (b), 0.015 (c), 0.02 (d), 0.025 (e), 0.03 (f), and 0.04 kg/s (g). The final system configuration the must be considered is the closed Rankine cycle.

This is the case in which the condenser is utilized, and waste heat is rejected to the fuel.

Because the condenser is used, the cooling capacity is decreased when compared to the open system, however the closed system must be used to extend duration of the water available to the system.

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0.24 0.45 1.25 kg/s 1.25 kg/s 0.22 1.75 kg/s 1.75 kg/s 2.25 kg/s 0.4 2.25 kg/s

0.2

0.35 0.18

0.16 0.3

0.14 0.25

0.12

0.2 0.1

0.08 0.15 0.4 0.6 0.8 1 1.2 1.4 1.6 0.4 0.6 0.8 1 1.2 1.4 1.6 Cooling demand (MW) Cooling demand (MW)

Figure 53: Percent decrease in the fuel temperature at the exit of channel B for

closed system for 0.005 (left) and 0.01 (right)

The percent decrease in the final fuel temperature is observed for the closed configuration in Figure 53. Similar to the open configuration, the final temperature decreases as the water flowrate increases. However, when compared to the open system the decrease in temperature is less for the same conditions. Additionally, the increase in total cooling is obtained for the closed system when compared to a regenerative system

(Figure 54). This is notable lower than the open system as a result of the heat that is rejected by the condenser into the fuel, lowering the overall cooling increase.

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0.9 1.8 1.25 kg/s 1.25 kg/s 1.75 kg/s 1.75 kg/s 0.8 2.25 kg/s 1.6 2.25 kg/s

0.7 1.4

0.6 1.2

0.5 1

0.4 0.8

0.3 0.6 0.4 0.6 0.8 1 1.2 1.4 1.6 0.4 0.6 0.8 1 1.2 1.4 1.6 Cooling demand (MW) Cooling demand (MW)

Figure 54: Percent increase in total cooling capacity for closed system when

compared to a regenerative system for 0.005 (left) and 0.01 (right).

5.4.2 Transient Model Control

To demonstrate the capability of both the model’s transient behavior and the system’s controller, a change of operating conditions is applied to the model. A change in fuel flowrate simulating a transition from acceleration to cruise conditions is implemented.

The prescribed fuel flowrate, Figure 55, experiences a drastic decrease over a short period of time.

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Figure 55: Fuel flowrate change from acceleration to cruise in an aircraft.

Several changes are expected to result from the change in fuel flowrate. As shown previously through the parametric study, the cooling capacity of the fuel alone decreases with the flowrate. In order to meet the cooling demand following this step change, both the water flowrate must increase as well as the flow must be diverted past the condenser. This transition drives the system from closed to open, and based on the given operating conditions, an expected fuel temperature can be predicted from the parametric study.

Similarly, the pumping power demands of the system are a time dependent factor of the system operation. During the acceleration phase when a high flowrate is needed, the power demands are drastically higher than during cruise conditions. The competing factors of power and cooling demand lead to a system that is driven by power demand during acceleration and cooling needs during cruise.

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Figure 56: Expected change in maximum fuel temperature during transition from closed to open cycles following step change.

Provided below is the water flowrate response to the change in flowrate. The plot given on the top in Figure 57 provides the prescribed mass flowrate determined by the controller over time. During acceleration conditions, the flowrate is steady until the step change occurs. Following the step change a decrease happens until an inflection point at approximately t = 13 sec, at which point the water flowrate increased towards a steady state value. The plot on the bottom of Figure 57 provides insight into the reason for this inflection dictated by the controller. During acceleration conditions, the water flowrate is driven by the power demand of the system. However, during the transition from acceleration to cruise, the power demand decreases shortly before the cooling demand increases. The inflection point that occurs is the result of this delayed transition in the water flowrate requirements of the system.

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Figure 57: Prescribed water mass flowrate for the system (top) and the controller values used to determine the prescribed mass flowrate (bottom)

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Also of interest is the difference in the two flowrate values as dictated by the cooling needs. The raw signal provided by the controller results in a step change increase in the water flowrate when the maximum fuel temperature exceeds the set point temperature. Using this raw signal would result in a discontinuity in the mass flowrate in the system, leading to errors within the Modelica solver. To address this issue, a second order transfer function is used to smooth the cooling flowrate response.

The second controller used in the cooling of the system is the diverting valve position. Like the water flowrate response, the diverting valve position changes to bypass the condenser when the fuel temperature exceed the set point. By doing so, this eliminates the waste heat within the condenser being rejected into the fuel. The valve response shown in Figure 58 features a rapid change in valve position following the increase in fuel temperature. These specific operating conditions are at the extremes of the operating conditions of the system, leading to the valve being fully open or closed.

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Figure 58: Diverting valve position following step change decrease in the fuel flowrate.

As the model transitions from acceleration to cruise conditions, the maximum temperature of the fuel is expected to increase dramatically. It is important for the control system to ensure the fuel stays within an acceptable temperature range by minimizing both the response time and the overshoot. The temperature response of the maximum fuel temperature using the control system previously outlined is given in Figure 59. A rapid increase in temperature occurs following the step change in flowrate and for the current

PID controller settings, minimal overshoot is achieved. A percent overshoot for the fuel temperature of 2.72% is achieved with a maximum fuel temperature of 1007 K, with a set point of 1000 K used by the controller.

110

Figure 59: Fuel temperature response for a step change decrease in fuel flowrate.

The decrease in fuel flowrate leads to a decreased power demand for the system as it transitions to cruise. However, the cooling demand at cruise requires an increased water flowrate, leading to a surplus of power generation. This behavior is outlined in the net power production (difference between power produced by turbine and power required by fuel pump) of the system, Figure 60. Leading up to the step change, the net power of the system is near zero which indicates that the turbine is producing the fuel pump demands.

As the system reaches steady state, the turbine produces more power than is required for the fuel pump, leading to an excess in power generation, available for use by other systems or storage in batteries.

111

Figure 60: Net power production during change from acceleration to cruise conditions

Observing a step change in the system’s fuel flowrate demonstrates the ability of the system to capture time dependent variables as well as the operation of the system controls. Throughout the duration of the step change, the system power requirements were met or exceeded, the maximum temperature set point was maintained at steady state, with minimal overshoot of the set point temperature.

5.4.2 Simulated Mission Capabilities

One of the greatest benefits of developing a dynamic system model within

Modelica is the ability to model behavior through the duration of an aircraft’s mission. A generic profile was selected to demonstrate both the system’s dynamic modeling capability and the range of operating conditions possible. For generic profile, both the fuel flowrate and heat flux are intended to represent three phases: take-off, acceleration, and cruise. The values used for the fuel flowrate and heat flux in the generic mission are provided in Figure

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61. From start to time t = 10, is the take-off phase of the mission, consisting of a lower heat flux value and a moderate fuel flowrate. The acceleration phase follows take-off and lasts until t = 30, during which both the fuel flowrate and heat flux increase to the maximum values. Lastly during the cruise phase the fuel flowrate decreases dramatically while maintaining a constant heat flux.

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2.4

2.2

1.8

1.6

1.4

1.2

0.8

0.6 0 10 20 30 40 50 60 Time (s)

Figure 61: Prescribed fuel flowrate (top) and heat flux (bottom) for the simulated mission.

The response provided in Figure 62 indicates that system power demands are driving the water flowrate during both take-off and acceleration. An increase in water

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flowrate following t = 10, corresponding to the increased power demand from the fuel pump is evident. Similar to the step change previously observed, the water flowrate increases to meet cooling demand as the vehicle transitions from acceleration to cruise conditions.

Figure 62: Water flowrate for the simulated vehicle mission.

The valve position controller operates uniquely for each of the three phases of the simulated mission, which is evident by controller flowchart provided in Figure 33. During the take-off phase leading up to t = 10, the valve is partially close. This is a result of the logic within the controller used to prevent two-phase fluid from exiting the condenser.

During the acceleration phase, the valve must be fully open to ensure sufficient cooling of the fuel within the evaporator. Lastly, during the cruise conditions, the valve is fully closed because the fuel temperature is approaching the upper limit.

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Figure 63: Diverting valve position for t the simulated vehicle mission. Observing the fuel temperature throughout the duration of the simulated mission in

Figure 64, the temperature increases for each of these phases. The first increase between the take-off and acceleration phases results from the increase in heat flux within the cooling channel model. The second increase as the vehicle enters cruise conditions is caused by the decrease in the fuel flowrate, driving the valve and water flowrate to adjust for the system cooling needs.

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Figure 64: Maximum fuel temperature for the simulated vehicle mission.

As previously noted, the water flowrate increases following the increased pumping power demand at t = 10. The system power response, Figure 65, shows no discontinuities or variations in net power because of this. This response behavior is desirable because it minimizes the risk of insufficient power as the fuel flowrate ramps up to acceleration conditions. In the same manner as the step change observed previously, the net power increases following the transition from acceleration to cruise.

117

Figure 65: System net power through the duration of the changing conditions of the generic mission.

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6. Conclusion

Both experimental testing and numerical modeling has been used to develop a

Rankine cycle-based system to meet the thermal management and power generation needs of next generation aircraft. Experimental results consisting of both steady state and transient testing provided insight into the operation of a lab-scale Rankine cycle. Steady state analysis shows a system efficiency (5.1% thermal and 11.5% Second Law efficiency).

Analysis of transient results provide time constants for both heat transfer and power generation that can be utilized in future modeling efforts.

Much of the modeling effort focused on the development of a component model library suited to the modeling of the Rankine cycle and phase change systems. These component models included an array of heat exchange models including evaporators, condensers, and single-phase heat exchangers. Comparison of the heat exchanger component models to experimental results yielded deviations within 5% when observing the ΔT of the working fluids. Using the component models from the HPTMS library, system level models were developed for both the SHEEV and a vehicle system. A steady state energy balance comparison between the model and experimental results provided a convenient comparison of the system behavior. When translating the SHEEV model performance to the vehicle model, key components include the evaporator and the water loop portions of the system. Deviation within +/- 3.5% of the experimental results was

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achieved for these portions of the model, building confidence in the accuracy when translated to the vehicle level model.

Development of the vehicle level model included three phases: quasi-steady state parametric study, transient testing, and simulated generic missions. Each of these phases serve a distinct purpose in the model development and testing. The quasi-parametric study provides a system level performance map and a comparison of the cooling performance to a regenerative cooling system under the same conditions. Results from the study aided in defining the operating conditions used in the transient and simulated mission testing.

Transient testing of the vehicle model allowed for development and tuning of system controls able to meet both cooling and power demands of the system. The control system proved to be capable of meeting the system needs as the operating conditions of the system changed over time. Transient testing where one operating condition was changed lead to modeling of generic vehicle missions where multiple operating conditions were changed in a time dependent manner.

To advance the research regarding the development of this system, there are several paths that are recommended. First, continued testing and analysis of the operation of the experimental system is imperative for use in component model development, tuning, and verification. Increasing the sample size of data for steady state and transient analysis will minimize errors and discrepancies in the results. This will increase the quality of the model parameters such as heat transfer coefficients and time constants.

Secondly, continued component model development and refinement should be an area of focus. The lack of open-source models suitable to this application which are

120

compatible with OpenModelica drove the decision to develop the HPTMS package and the component models within it. The next phase of the modelling effort should continue to focus on the further development of the component models, particularly the heat exchangers. A MB model using effectiveness-NTU heat transfer correlations was used.

Future work should investigate the FCV method for modeling of two-phase heat exchangers to determine if this modeling scheme is better suited. Additionally, other heat transfer relations should be considered as well. The effectiveness-NTU method was selected for ease of tuning, extension to future modelling of various heat exchanger geometry, and stability issues in arising from the use of other heat transfer relations.

Modeling of phase change within heat exchangers is a complex research topic and further development of these models within OpenModelica would add significant value.

The previous recommended paths for future research are with the intent of improving the accuracy of experimental and model results. Many opportunities for future work are currently available using the system models as developed. A range of operating conditions (ie. heat flux and fuel flowrate) can be selected to observe the system response.

Different fuel models can be developed and used to study how the system behavior changes with fuel type. Sizing studies can be conducted in order to estimate size and weight of the system needed to meet the needs of various vehicles. All of these opportunities for future work were factors motivating the development of a vehicle level model for a Rankine cycle system.

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Appendix A

TherminolXP Media Model Tables Temperature Density (kg/m3) Specific Heat Capacity Thermal Conductivity (K) 20 878 1.82 0.1155 30 872 1.86 0.1148 40 866 1.91 0.1141 50 859 1.96 0.1133 60 853 2.00 0.1125 70 847 2.05 0.1118 80 840 2.10 0.1109 90 834 2.14 0.1101 100 827 2.18 0.1093 110 821 2.23 0.1084 120 814 2.27 0.1075 130 808 2.31 0.1065 140 801 2.36 0.1056 150 795 2.40 0.1046 160 788 2.44 0.1036 170 782 2.48 0.1025 180 775 2.52 0.1015 190 768 2.56 0.1004 200 731 2.60 0.0993 210 755 2.63 0.0982 220 748 2.67 0.0970 230 741 2.71 0.0959 240 734 2.75 0.0947 250 727 2.78 0.0934 260 720 2.82 0.0922 270 712 2.85 0.0909 280 705 2.89 0.0896 290 698 2.92 0.0883 300 690 2.95 0.0869 310 682 2.99 0.0856 320 675 3.02 0.0842 330 667 3.05 0.0828

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Appendix B

Parallel Flow Evaporator

Subcooled Control Volume

푄̇ = 푚̇ ℎ −ℎ,

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 + 푐) 휀 = 1 + 푐 where 퐶 푐 = , 퐶,

123

푈퐴 NTU = 퐶,

퐴 퐿 = 휋퐷

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

Two-Phase Control Volume

푄̇ = 푚̇ (ℎ −ℎ)

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 + 푐) 휀 = 1 + 푐 where 퐶 푐 = , 퐶,

푈퐴 NTU = 퐶,

124

퐴 퐿 = 휋퐷

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

Superheated Control Volume

퐿 = 퐿 − 퐿 − 퐿

퐴 = 퐿 휋퐷

푈퐴 NTU = 퐶,

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 + 푐) 휀 = 1 + 푐 where 퐶 푐 = , 퐶,

125

푄̇, = 휀 푄̇,

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

푄̇, = 푚̇ ℎ, − ℎ

Counter Flow Evaporator

Subcooled Control Volume

푄̇ = 푚̇ ℎ −ℎ,

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

126

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 − 푐) 휀 = 1 − 푐 exp (−NTU(1 − 푐) where 퐶 푐 = , 퐶,

푈퐴 NTU = 퐶,

퐴 퐿 = 휋퐷

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

Two-Phase Control Volume

푄̇ = 푚̇ (ℎ −ℎ)

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

127

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 − 푐) 휀 = 1 − 푐 exp (−NTU(1 − 푐) where 퐶 푐 = , 퐶,

푈퐴 NTU = 퐶,

퐴 퐿 = 휋퐷

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

Superheated Control Volume

퐿 = 퐿 − 퐿 − 퐿

퐴 = 퐿 휋퐷

푈퐴 NTU = 퐶,

푄̇, = 푚̇ 퐶,푇, − 푇,

128

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 − 푐) 휀 = 1 − 푐 exp (−NTU(1 − 푐) where 퐶 푐 = , 퐶,

푄̇, = 휀 푄̇,

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

푄̇, = 푚̇ ℎ, − ℎ

129

Parallel Flow Condenser

Superheated Control Volume

푄̇ = 푚̇ ℎ, −ℎ

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 + 푐) 휀 = 1 + 푐 where 퐶 푐 = , 퐶,

푈퐴 NTU = 퐶,

130

퐴 퐿 = 휋퐷

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

Two-Phase Control Volume

푄̇ = 푚̇ (ℎ −ℎ)

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 + 푐) 휀 = 1 + 푐 where 퐶 푐 = , 퐶,

푈퐴 NTU = 퐶,

퐴 퐿 = 휋퐷

131

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

Superheated Control Volume

퐿 = 퐿 − 퐿 − 퐿

퐴 = 퐿 휋퐷

푈퐴 NTU = 퐶,

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 + 푐) 휀 = 1 + 푐 where 퐶 푐 = , 퐶,

푄̇, = 휀 푄̇,

132

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

푄̇, = 푚̇ ℎ − ℎ,

Counter Flow Condenser

Superheated Control Volume

푄̇ = 푚̇ ℎ, −ℎ

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

133

1 − exp (−NTU(1 − 푐) 휀 = 1 − 푐 exp (−NTU(1 − 푐) where 퐶 푐 = , 퐶,

푈퐴 NTU = 퐶,

퐴 퐿 = 휋퐷

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

Two-Phase Control Volume

푄̇ = 푚̇ (ℎ −ℎ)

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

1 − exp (−NTU(1 − 푐) 휀 = 1 − 푐 exp (−NTU(1 − 푐)

134

where 퐶 푐 = , 퐶,

푈퐴 NTU = 퐶,

퐴 퐿 = 휋퐷

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

Superheated Control Volume

퐿 = 퐿 − 퐿 − 퐿

퐴 = 퐿 휋퐷

푈퐴 NTU = 퐶,

푄̇, = 푚̇ 퐶,푇, − 푇,

where 퐶, = 푚̇ 푐,

퐶, = 푚̇ 푐,

퐶, = min 퐶, , 퐶,

135

1 − exp (−NTU(1 − 푐) 휀 = 1 − 푐 exp (−NTU(1 − 푐) where 퐶 푐 = , 퐶,

푄̇, = 휀 푄̇,

푄̇, = 푄̇, + 푄̇,

where 푄̇, = 푚̇ ℎ, − ℎ,

푄̇, = 푚̇ ℎ − ℎ,

136

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