近年來由於超臨界二氧化碳布雷登循環擁有高效率、體積小、以及低污染等優勢，所以成為目前學術研究的一個主要方向。而在小型渦輪發電系統方面，向心式渦輪已經成為渦輪擴散器的主要選擇。本論文將針對低溫餘熱回收的超臨界布雷登循環100kW以及500kW級渦輪發電系統，運用子午面(meanline) 葉片設計方法產生多種向心式的渦輪設計方案。運用比速率(specific speed)以及速度比(velocity ratio)這兩項重要的參數，設計出不同的向心式的渦輪，再與計算流體力學軟體(CFD)的模擬結果來做比對與驗證。研究結果成功的設計出能夠產生最大渦輪輸出性能的向心式渦輪設計方案。針對100kW渦輪發電機在每秒3公斤的流量時，最佳比速率(specific speed)是在0.3到0.5，而最佳的速度比(velocity ratio)則是落在0.52到0.68。至於500kW渦輪發電機在每秒10公斤的流量時，無法有效提升比速率(specific speed)超過0.6，原因是已經產生了區域性的穿音速擾流，而且是在低轉速的運作情況下就發生了。至於提高速度比(velocity ratio)則會在定流量的情況下，提升擴散比;而在定擴散比的情況下，降低流量。運用上述兩項最佳化的參數來設計最大效率的向心式渦輪，結果顯示速度比會隨著比速率的降低而減少。總之，本研究所開發的向心式渦輪葉片設計系統顯示可以有效地運用在小型渦輪發電系統，而且能夠達成86% 轉子效率以及84 % 整體渦輪效率。
最後，為了要驗證本研究所開發的設計系統，論文中採用了文獻中所提及的向心式空氣渦輪設計方法(Balje diagram)來做比對。結果顯示本研究適用於超臨界二氧化碳向心式渦輪機葉片設計之餘，同樣也可適用於向心式空氣渦輪機。而且超臨界二氧化碳向心式渦輪機的各方面的損耗，也與向心式空氣渦輪非常類似。同時本研究也驗證了超臨界二氧化碳向心式渦輪不同於超臨界二氧化碳壓縮機的部分，就是渦輪機展現了非常低的可壓縮性而且與理想氣體非常類似。

In recent years, supercritical CO2 (sCO2) Brayton cycles have drawn the attention of researchers due to their high cycle efficiencies, compact turbomachinery, and environmental friendliness. For small scale cycles, radial inflow turbines are the prevailing choice for the turboexpander and one of the key components. Different meanline design paths for radial inflow turbines are outlined, and aerodynamic design space exploration is conducted for one 100 kW-class and one 500 kW-class turbine test case for a low-temperature waste-heat utilization sCO2 Brayton cycle. By varying the two design parameters, specific speed, and velocity ratio, different turbine configurations are set up and compared numerically by means of CFD simulations. Results are analyzed to conclude on best design parameters with regard to maximum turbine performance. Specific speeds from 0.3 to 0.5 and velocity ratios from 0.52 to 0.68 are recommended for sCO2 radial inflow turbines with small throughflow (3 kg/s). For the radial inflow turbines intended for the medium scale sCO2 power cycle, despite the higher mass flow rate (10 kg/s), no significant increase in specific speed (above 0.6) could be achieved, as local transonic flow occurred already at considerably lower rotational speeds. Higher velocity ratios result in bigger expansion ratios if the mass flow rate is fixed, and in smaller throughflows, if the expansion ratio is fixed. Pairs of optimum design parameters that effectuate maximum efficiency are identified, with smaller velocity ratios prevailing for lower specific speeds. By achieving total-to-static stage and rotor efficiencies of 84% and 86%, respectively, the developed meanline design procedure has proven to be an effective and easily applicable tool for the preliminary design of small scale sCO2 RIT.
Moreover, the turbine simulation results for sCO2 are compared to well-established recommendations for the design of air turbines from literature, such as the Balje diagram. It is concluded that for the design of sCO2 radial inflow turbines, similar design principles and parameters can be used as those for air turbines. Also, losses occurring in sCO2 radial inflow turbines are similarly distributed as those of air turbines. These outcomes support the understanding that supercritical CO2, in the working range of a sCO2 turbine, shows very little compressibility and behaves similar to ideal gas (in contrary to a sCO2 compressor.)

摘 要 I
ABSTRACT II
ACKNOWLEDGEMENTS III
RELATED PUBLICATIONS IV
CONTENTS V
LIST OF FIGURES IX
LIST OF TABLES XIII
NOMENCLATURE XIV
1. Introduction 1
1.1 Motivation 1
1.2 The Supercritical CO2 Brayton Cycle 3
1.3 Historical Background of the Supercritical CO2 Brayton Cycle 6
1.4 Supercritical CO2 Brayton Cycle Test Facility Development 7
1.5 Current Supercritical CO2 Brayton Cycle Research Areas 9
2. Literature Review 12
2.1 Supercritical CO2 Turbomachinery 12
2.2 Supercritical CO2 Turbines 13
2.3 Design Challenges for sCO2 Radial Inflow Turbines 13
2.4 Meanline Design Approach for Radial Inflow Turbines 14
2.5 Numerical Approach for Investigation of Different sCO2 Radial Inflow Turbine Designs 16
3. Thesis Aim and Outline 17
4. Thermodynamic Cycle Analysis 20
4.1 Cycle Layouts for the sCO2 Brayton Cycle 20
4.1.1 The Simple Recuperated Brayton Cycle Layout 21
4.1.2 The Intercooling Cycle Layout 22
4.1.3 The Reheating Cycle Layout 22
4.1.4 The Recompression Split Flow Cycle Layout 23
4.2 Cycle Analysis Case Study – Effect of Different Turbine Inlet Pressures and Temperatures 24
4.2.1 Ideal Case and Real Case Assumptions 25
4.2.2 Cycle Efficiency Results 26
4.2.3 Power Output Results 33
4.3 Summary of Cycle Analysis Case Study 35
5. Radial Inflow Turbine Meanline Design 38
5.1 Radial Inflow Turbines 38
5.1.1 Radial Inflow Turbine Components 38
5.1.2 Thermodynamics of a Radial Inflow Turbine Stage 40
5.1.3 Basic Physical Principles for Turbomachinery 43
5.1.4 Loss Correlations for Radial Inflow Turbines 46
5.2 Input Parameters for the Radial Inflow Turbine Design 50
5.3 Radial Inflow Turbine Meanline Design Outcome 51
5.4 Meanline Design Procedure 53
5.4.1 General Turbine Calculations (Steps 1 to 3) 53
5.4.2 Rotor Inlet Calculations (Steps 4 to 8) 55
5.4.3 Rotor Outlet Calculations (Steps 9 to 12) 61
5.4.4 Determination of Remaining Turbine Rotor Geometry (Steps 13 to 16) 63
5.4.5 Determination of Turbine Stator Geometry (Steps 17 and 18) 65
5.5 Other Radial Inflow Turbine Design Constraints 67
5.5.1 Structural Constraints 67
5.5.2 Vibration Constraints 67
5.5.3 Mach Number Constraints 67
5.6 Design Paths 68
5.7 Summary of Non-Dimensional Parameters 71
6. Numerical Method 73
6.1 Numerical Method for sCO2 Radial Inflow Turbine Flow Modeling 73
6.1.1 3D Turbine Models 73
6.1.2 Grid Generation 74
6.1.3 CFD Setup 76
6.1.4 RGP File Generation 77
6.2 Validation of the Numerical Method 78
6.2.1 Air Turbine Simulation Setup 80
6.2.2 Validation of the Numerical Method 82
6.2.3 Validation of the Meanline Design Approach 85
7. CFD Simulation Results for Supercritical CO2 Radial Inflow Turbines 89
7.1 Small Scale Turbine Test Case 89
7.1.1 Design Parameters 91
7.1.2 Analyzed Design Space 92
7.1.3 Numerical Method 92
7.1.4 Performance Evaluation of Small Scale sCO2 Radial Inflow Turbines 94
7.2 Medium Scale Turbine Test Case 100
7.2.1 Design Parameters 102
7.2.2 Analyzed Design Space 102
7.2.3 Numerical Method 103
7.2.4 Performance Evaluation of Medium Scale sCO2 Radial Inflow Turbines 105
7.3 Rotor Inlet Flow Field Analysis 109
7.3.1 Influence of Design Parameters on the Flow Field at the Turbine Inlet 109
7.3.2 Flow Disturbances at the Rotor Inlet 110
7.3.3 Turbine Slip at Rotor Inlet 112
7.4 Effect of Design Parameters on Turbine Geometry 113
7.5 Comparison of Best Design Parameters for sCO2 Radial Inflow Turbines to Gas Turbine Design Charts 115
7.6 Comparison of Loss Contributions in Radial Inflow Turbines Using sCO2 and Air 117
8. Conclusions and Future Research 120
REFERENCES 124

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