臺灣博碩士論文加值系統

我們在本文中提出了新的方法，以解兩相流介面的Eular五方程式模型。我們使用傳統的PPM方法加上BVD方法來調整處理後的介面及震波現象，在邊界處重建變量的不連續，從而有效地減少數值解的數值耗散。我們用該方法與原始的MUSCL法以及PPM法做比較，結果驗證本方法在捕獲多相流介面方面的能力，可以明確的處理多相流不連續的條件。因此我們提出的方法是一種簡單有效的模擬可壓縮多介面流的方法。

A new reconstruction scheme of cell state variables is presented to solve the five equation model for achieving high-resolution of interfaces and shock waves in two phase flows. We use a piecewise parabolic shock capturing scheme and the interface sharpening scheme as two building-blocks of spatial reconstruction to minimize the discontinuities of the reconstructed variables at cell boundaries, and thus the numerical dissipations is effectively reduced in numerical solutions. Benchmark test are shown to compare with original TVD scheme, to verify the ability of the present method in capturing the material interface as a well-defined sharp in volume fraction. The proposed scheme is a simple and effective method of practical significance for simulating compressible interfacial multiphase flows.

Nomenclature v
List of Figure ix
1. Introduction 1
1.1. Background 1
1.2. Numerical Algorithm Review 5
1.3. Shock-Bubble Interaction Review 10
2. Numerical Models 19
2.1. Governing Equations 19
2.2. Closures strategy 21
2.3. Numerical Methodology 23
2.4. Time Evolution 24
2.5. HLLC Numerical Flux 25
2.6. Interpolation Method 29
3. Numerical Results 39
3.1. Sod Problem 39
3.2. Two Interacting Blast Waves Problem 41
3.3. Grid Independence 45
3.4. Two-Component Shock Tube Problem 46
3.5. Two-Phase Gas-Liquid Shock Tube Problem 48
3.6. R22 Gas Bubble 51
3.7. Helium Bubble 54
4. Conclusions 59
5. References 61
Appendix 101
List of Figure
Figure 2.1 The solution of the HLLC scheme shows in the Star Region. 75
Figure 2.2 The intermediate fluxes shows in the Star Region. 75
Figure 3.1 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the Sod’s problem based on HLLC at time t = 0.25 76
Figure 3.2 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the Sod’s problem based on HLLC at time t = 0.25 77
Figure 3.3 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two interacting blast waves problem based on HLLC at time t = 0.38 78
Figure 3.4 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two interacting blast waves problem based on HLLC at time t = 0.38 79
Figure 3.5 Numerical solutions of the density in the two interacting blast waves problem based on HLLC at time t = 0.38 80
Figure 3.6 Numerical solutions of the density in the two interacting blast waves problem based on HLLC at time t =0.38 81
Figure 3.7 Numerical solutions of the density in the two interacting blast waves problem based on HLLC at time t =0.38 82
Figure 3.8 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two-component shock tube problem based on HLLC at time t = 0.1 83
Figure 3.9 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two-component shock tube problem based on HLLC at time t = 0.1 84
Figure 3.10 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two-phase gas-liquid shock tube problem based on HLLC in gamma model at time t = 0.1 85
Figure 3.11 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two-phase gas-liquid shock tube problem based on HLLC in alpha model at time t = 0.1 86
Figure 3.12 Comparison between Schlieren plots and experiments. (a) t = 55 μs, (b) t = 115 μs, (c) t = 135 μs and (d) t = 187 μs 87
Figure 3.13 Comparison between Schlieren plots and experiments. (e) t = 247 μs, (g) t = 342 μs, (h) t = 417 μs and (i) t = 1020 μs 88
Figure 3.14 Comparison between Schlieren plots and experiments. (a) t = 55 μs, (b) t = 115 μs, (c) t = 135 μs and (d) t = 187 μs 89
Figure 3.15 Comparison between Schlieren plots and experiments. (e) t = 247 μs, (g) t = 342 μs, (h) t = 417 μs and (i) t = 1020 μs 90
Figure 3.16 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular R22 gas bubble 91
Figure 3.17 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular R22 gas bubble 92
Figure 3.18 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular R22 gas bubble 93
Figure 3.19 Comparison between Schlieren plots and experiments. (a) t = 32 μs, (b) t = 52 μs, (c) t = 62 μs and (d) t = 72 μs 94
Figure 3.20 Comparison between Schlieren plots and experiments. (f) t = 102 μs, (g) t = 245 μs, (h) t = 427 μs and (i) t = 67μs 95
Figure 3.21 Comparison between Schlieren plots and experiments. (a) t = 32 μs, (b) t = 52 μs, (c) t = 62 μs and (d) t = 72 μs 96
Figure 3.22 Comparison between Schlieren plots and experiments. (f) t = 102 μs, (g) t = 245 μs, (h) t = 427 μs and (i) t = 674 μs 97
Figure 3.23 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular helium-air bubble 98
Figure 3.24 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular helium-air bubble 99
Figure 3.25 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular helium-air bubble 100

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