在超音速衝壓引擎模擬中，涉及到多相流與化學反應等複雜的物理現象，為了瞭解這些複雜的物理現象，本文目的在於發展出一套分析超音速衝壓引擎內部流場結構的數值模擬程式。在本研究中，我們首先透過五方程多相流模型與拉格朗日方法，模擬側向噴流問題中震波與液滴霧化蒸發間的交互作用，經比較結果後發現五方程多相流模型相較於單相的Navier-Stokes 方程在震波的捕捉上有較好的解析度。接著結合五方程多相流模型與單步的化學反應模型，模擬不同測試條件下無限長爆震管中胞格結構的形成與發展，並找到合適的單步化學反應模型模擬複雜的化學反應。最後將前兩個算例結合，針對DLR超燃衝壓引擎進行了初步的模擬，模擬結果顯示，在氣態燃料與液態燃料注入燃燒的模擬中，皆顯示了與實驗相似的流場結構。

In the simulation of scramjet engines, many complex physical phenomena are involved, such as the fuel atomization, mass transition, and chemical reactions. In order to understand these complex physical phenomena, the purpose of the current thesis is to develop an in-house code for analyzing the flow structures of the scramjet engine. In this study, we first used the five-equation multiphase flow model and the Lagrangian method to reproduce the process of the fuel atomization and evaporation in a flow over side jet problem. Shock waves, recirculation zones and breakup processes of droplet particles were well captured. Comparing the results, we found that the five-equation multiphase model shows a better resolution in the shock capturing, comparing with the single phase Navier-Stokes equations. Then, we combined the five-equation multi-phase model and the single-step reaction model to simulate the formation of the cell structures in the detonation tube. The detonation waves under various operating conditions were discussed based on a single-step reaction model to model the complex reactions. Finally, a preliminary simulation of the DLR scramjet is performed. The current works have achieved satisfactory agreement compared to the experimental data no matter in reacting flow case or non-reacting flow case.

Table of Contents iii
Nomenclature v
List of Figure ix
1. Introduction	1
1.1. Background	1
1.2. Literature Review	3
1.2.1. Review of flow over a side jet	3
1.2.2. Review of Multi-Phase Flow Model	9
1.2.3. Review of the single-step reactive model	13
1.2.4. Review of the cellular structure	15
2. Numerical Methodology 19
2.1. Governing Equations 19
2.1.1. Closures strategy 21
2.2. Turbulence Model 22
2.3. Single-Step Reactive model 24
2.4. Numerical Schemes 26
2.4.1. HLLC Approximate Riemann Solver	26
2.4.2. MUSCL 29
2.4.3. THINC-EM	30
2.4.4. HMT scheme (Hybrid MUSCL & THINC-EM) 32
2.4.5. PPM 33
2.4.6. Strang Splitting and 3th order Runge-Kutta method 35
2.5. Eulerian-Lagrangian Method	36
2.5.1. Droplet Motion Equations	37
2.5.2. Droplet Momentum Coupling 38
2.5.3. KH-RT Breakup Model 39
2.5.4. Droplet Evaporation 42
2.6. Parallel Computing 45
3. Numerical Results 46
3.1. Numerical simulation of flow over a side jet part-I	46
3.2. Numerical simulation of flow over a side jet part-II	50
3.2.1. Droplet trajectory of five equation multi-phase model 52
3.2.2. Influence of injector diameter 53
3.2.3. Influence of momentum flux ratio 53
3.2.4. Difference in shock capturing 54
3.3. Cellular structure in a detonation tube 59
3.3.1. Formulation of the triple point system 60
3.3.2. Grid independence on the cellular structure 64
3.3.3. Influence of Courant Friedrichs Lewy number 65
3.3.4. Influence of computational domain 67
3.3.5. Influence of the pre-exponential factor 69
3.3.6. Influence of the activation energy 70
3.4. Preliminary simulation of DLR scramjet combustion 89
3.4.1. Computational domain 89
3.4.2. Non-reactive case of Hydrogen injection 91
3.4.3. Reactive case of the Hydrogen injection 99
3.4.4. Non-reactive case of the liquid fuel injection 101
3.4.5. Reactive case of the liquid fuel injection 104
4. Conclusions 107
5. References 109
6. Appendix 117

Figure 1：Solution in the Star Region consists of two constant states separated from each other by a middle wave of speed S*. 26
Figure 2：Computing time of different scheme with the number of CPUs.	45
Figure 3：Computational domain of the flow field, 800×400 grids. 47
Figure 4：Experimental schlieren of the flow over a side jet [78]. 47
Figure 5：Numerical schlieren of the flow over a side jet. 47
Figure 6：Breakup process of the side jet over time [78]. 49
Figure 7：Computational domain of the flow field 51
Figure 8：The location of the injector and the flow condition 51
Figure 9：Droplet trajectory by using five equation model	52
Figure 10：Influence of injector diameter 53
Figure 11：Influence of momentum flux ratio 54
Figure 12：Comparison between single phase Navier Stokes equations and the multiphase five-equations model.	55
Figure 13：Comparison between single phase Navier Stokes equations [2] and the multiphase five-equations model. (dj=0.1 mm,q=10) 57
Figure 14：Comparison between single phase Navier Stokes equations [2] and the multiphase five-equations model. (dj=0.5 mm,q=5)	58
Figure 15：Initial condition of the detonation tube	59
Figure 16： (a) - (f) are the pressure contour in different time step and the (g) is the cellular structure	61
Figure 17：Evolution of the triple wave structure over the time. 62
Figure 18：The triple wave structure. 63
Figure 19： Evolution of the cellular structure over time. 63
Figure 20：Cellular structure in different grid sizes.	65
Figure 21：Cellular structure in different CFL numbers.	66
Figure 22：Cellular structure with different tube width.	68
Figure 23：Cellular structure with different pre-exponential factor. 70
Figure 24：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of weakly unstable detonation wave with PPM scheme. 72
Figure 25：Cellular structure record for weakly unstable detonation wave with PPM scheme. 73
Figure 26：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of weakly unstable detonation wave with MUSCL scheme. 74
Figure 27： Cellular structure record for weakly unstable detonation wave with MUSCL scheme. 75
Figure 28：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of weakly unstable detonation wave with THINC-EM scheme. 75
Figure 29： Cellular structure record for weakly unstable detonation wave with THINC-EM scheme. 76
Figure 30：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of weakly unstable detonation wave with HMT scheme. 76
Figure 31：Cellular structure record for weakly unstable detonation wave with HMT scheme. 77
Figure 32：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of moderately unstable detonation wave with PPM scheme. 79
Figure 33：Cellular structure record for moderately unstable detonation wave with PPM scheme. 80
Figure 34：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of moderately unstable detonation wave with MUSCL scheme. 80
Figure 35： Cellular structure record for moderately unstable detonation wave with MUSCL scheme. 81
Figure 36：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of moderately unstable detonation wave with THINC-EM scheme. 81
Figure 37：Cellular structure record for moderately unstable detonation wave with THINC-EM scheme. 82
Figure 38：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of moderately unstable detonation wave with HMT scheme. 82
Figure 39：Cellular structure record for moderately unstable detonation wave with HMT scheme. 83
Figure 40：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of highly unstable detonation wave with MUSCL scheme.	85
Figure 41：Cellular structure record for highly unstable detonation wave with MUSCL scheme. 86
Figure 42：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of highly unstable detonation wave with THINC-EM scheme. 86
Figure 43：Cellular structure record for highly unstable detonation wave with THINCM scheme. 87
Figure 44：Snapshots of pressure contours (line) and distributions of the reaction progress variable for different pre-exponential factors, illustrating structures of highly unstable detonation wave with HMT scheme. 87
Figure 45：Cellular structure record for highly unstable detonation wave with HMT scheme. 88
Figure 46：Geometry and configuration of the DLR supersonic combustion chamber. 90
Figure 47：Computational domain of the DLR supersonic combustion chamber. 90
Figure 48：Experimental Schlieren image of the combustion chamber with nonreacting flow. 92
Figure 49：Numerical Schlieren image of the combustion chamber with nonreacting flow. 93
Figure 50：Numerical contour plot of density in the combustion chamber with nonreacting flow. 93
Figure 51：Numerical Schlieren image calculated by four different sharp interface algorithms. 94
Figure 52：Numerical contour plot of density and pressure calculated with four different schemes. 95
Figure 53：Transverse profiles of mean axial velocity at x=85 mm, x=125 mm, x=233 mm in the non-reactive case, compared with available experimental data from Waidmann et al. [81] 98
Figure 54：Experimental Schlieren image of the combustion chamber with reacting flow. 100
Figure 55：Numerical Schlieren image and the density contour plot of the combustion chamber with reacting flow. 101
Figure 56：The enlargement figure of the density (left) and pressure (right) contour plots. The gray shaded area indicates the region of the combustion zone. 101
Figure 57：Numerical Schlieren image (a) and numerical contour plot of density (b), pressure (c) in the combustion chamber, with non-reacting flow. 103
Figure 58：Enlargement figure of density (left) and pressure (right) contour plots of the combustion chamber.	104
Figure 59：Numerical Schlieren image (a) and density contour plot of the combustion chamber with Propane combustion. 105
Figure 60：Enlargement figure of density (left) and pressure (right) contour plots of the combustion chamber with Propane combustion. 106

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