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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93427完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 薛克民 | zh_TW |
| dc.contributor.advisor | Keh-Ming Shyue | en |
| dc.contributor.author | 張祐瑜 | zh_TW |
| dc.contributor.author | You-Yu Chang | en |
| dc.date.accessioned | 2024-07-31T16:16:28Z | - |
| dc.date.available | 2024-08-01 | - |
| dc.date.copyright | 2024-07-31 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-07-26 | - |
| dc.identifier.citation | [1] B. Andreotti, Y. Forterre, and O. Pouliquen. Granular Media: Between Fluid and Solid. Cambridge University Press, 2013.
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Dense shearing flows of inelastic disks. Physics of Fluids, 18(10):103307, 2006. [25] J. T. Jenkins. Dense inclined flows of inelastic spheres . Granular Matter, 10:47–52, 2007. [26] J. T. Jenkins and M. W. Richman. Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. The Physics of Fluids, 28(12):3485–3494, 1985. [27] J. T. Jenkins and S. B. Savage. A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. Journal of Fluid Mechanics, 130:187–202, 1983. [28] P. C. Johnson and R. Jackson. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics, 176:67–93, 1987. [29] P. C. Johnson, P. Nott, and R. Jackson. Frictional-collisional equations of motion for participate flows and their application to chutes. Journal of Fluid Mechanics, 210:501–535, 1990. [30] P. Jop, Y. Forterre, and O. Pouliquen. A constitutive law for dense granular flows. 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Shah, editors, Numencal/Laboratoiy Computer Methods in Fluid Mechanics, pages 13–28. ASME, New York, 1979. [45] P. M. Morse and H. Feshbach. Methods of Theoretical Physics. McGraw-Hill, New York, 1st edition, 1953. [46] R. H. Pletcher, J. C. Tannehill, and D. Anderson. Computational Fluid Mechanics and Heat Transfer. CRC Press, Florida, 2nd edition, 1997. [47] O. Pouliquen. Scaling laws in granular flows down rough inclined planes. Physics of Fluids, 11(3):542–548, 1999. [48] O. Pouliquen and F. Chevoir. Dense flows of dry granular material. Comptes Rendus Physique, 3(2):163–175, 2002. [49] O. Pouliquen and Y. Forterre. Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. Journal of Fluid Mechanics, 453:133–151, 2002. [50] O. Pouliquen and Y. Forterre. A non-local rheology for dense granular flows. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 367:5091–5107, 2009. [51] M. Prochnow. 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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93427 | - |
| dc.description.abstract | 顆粒流展現出多相的流動模式，包括以碰撞為主的類氣體區、以摩擦為主的類固體區，以及碰撞與摩擦同時作用的類液體區。本論文旨在分析類液體區的流變模型穩定性，並對不同流場進行連續體模擬。其中，討論了經典的μ(I)和Φ(I)流變模型在完全發展流中的穩定性，並以無因次參數χ作為穩定性的判斷標準；此外，也引入近年提出的CIDR和iCIDR流變模型，推導降伏函數和膨脹函數的解析解，並以顯式形式表示正向壓力和偏剪應力。
本研究也在卡氏坐標和極坐標系中開發了iCIDR 模型的數值模擬方法，通過無因次化統御方程式，將其表示為保守形式，形成一個混合雙曲—拋物系統，並應用分裂法將其分為雙曲系統和拋物系統兩步驟。透過模擬完全發展剪切流、斜坡流，以及軸對稱環形剪切流的暫態流況，與解析解和文獻的實驗與模擬結果相互驗證，確認方法論的可用性。最後，運用超限插值法定義曲線坐標系，將複雜的物理區域轉化為精簡的計算區域，保持數值近似的準確性，並以模擬具有弧形上板的二維剪切流的暫態發展過程來進行收斂性驗證。 | zh_TW |
| dc.description.abstract | Granular flow exhibits multiphase patterns: gas-like (collision-dominated), solid-like (friction-dominated), and liquid-like (both collision and friction). This thesis analyzes the stability of the rheological model in the liquid-like regime and performs continuum simulations of various flow fields. We examine the stability of classical μ(I) and Φ(I) rheology models in fully-developed flow using the dimensionless parameter χ. The CIDR and iCIDR rheology models are introduced with analytical solutions for yielding and dilation functions, explicitly expressing normal pressure and deviatoric shear stress.
Numerical methods for the iCIDR model in Cartesian and polar coordinates are developed, representing the dimensionless governing equations in a conservative form to create a mixed hyperbolic-parabolic system, solved by the fractional step method. Validity is verified by simulating transient responses of fully-developed simple shear, fully-developed inclined surface, and axisymmetric annular shear flows. Furthermore, the transfinite interpolation method is applied to simplify complex physical domains while maintaining numerical accuracy. The transient development of a shear flow with an arched upper plate is simulated for convergence verification. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-31T16:16:28Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-31T16:16:28Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員審定書 i
致謝 iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xv Chapter 1 Introduction 1 1.1 Flow interaction mechanisms . . . . . . . . . . . . . . . . . . . . . 1 1.2 Conservation laws and constitutive relations . . . . . . . . . . . . . . 4 1.3 Thesis work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 2 Stability Analysis of μ(I)- and Φ(I)-based Rheology Models 11 2.1 Hadamard stability in continuum simulation . . . . . . . . . . . . . . 11 2.2 Conventional μ(I) and Φ(I) models . . . . . . . . . . . . . . . . . . 13 2.2.1 Instability of μ(I) and Φ(I) models . . . . . . . . . . . . . . . . . 13 2.2.2 An unstable example: planar Couette flow . . . . . . . . . . . . . . 17 2.3 Novel development of rheology models . . . . . . . . . . . . . . . . 20 2.3.1 From CIDR to iCIDR modifications . . . . . . . . . . . . . . . . . 20 2.3.2 Stability of iCIDR model . . . . . . . . . . . . . . . . . . . . . . . 22 Chapter 3 Numerical Approximation of iCIDR Model on Cartesian Grids 27 3.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Fully-developed simple shear flows . . . . . . . . . . . . . . . . . . 30 3.2.1 Numerical discretization . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.3 Comparison with literature . . . . . . . . . . . . . . . . . . . . . . 36 3.3 Fully-developed inclined surface flows . . . . . . . . . . . . . . . . 37 3.3.1 Numerical discretization . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.3.3 Comparison with literature . . . . . . . . . . . . . . . . . . . . . . 43 3.4 Simple shear flows in finite domains . . . . . . . . . . . . . . . . . . 44 3.4.1 Numerical discretization . . . . . . . . . . . . . . . . . . . . . . . 45 3.4.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Chapter 4 Numerical Approximation of iCIDR Model on Polar Grids 51 4.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2 Axisymmetric annular shear flows . . . . . . . . . . . . . . . . . . . 54 4.2.1 Numerical discretization . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2.3 Comparison with literature . . . . . . . . . . . . . . . . . . . . . . 61 4.3 General annular shear flows . . . . . . . . . . . . . . . . . . . . . . 62 4.3.1 Numerical discretization . . . . . . . . . . . . . . . . . . . . . . . 63 4.3.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Chapter 5 Numerical Approximation of iCIDR Model on Quadrilateral Grids 69 5.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2 Simple shear flows with arched upper plate . . . . . . . . . . . . . . 72 5.2.1 Numerical discretization . . . . . . . . . . . . . . . . . . . . . . . 73 5.2.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Chapter 6 Conclusion 81 6.1 Thesis summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.2.1 Extension to non-monotonic rheology models . . . . . . . . . . . . 82 6.2.2 Extension to numerical methods . . . . . . . . . . . . . . . . . . . 83 Bibliography 85 Appendix A — Steady-state Analytical Solutions 93 A.1 Fully-developed simple shear flows . . . . . . . . . . . . . . . . . . 93 A.2 Fully-developed inclined surface flows . . . . . . . . . . . . . . . . 95 A.3 Axisymmetric annular shear flows . . . . . . . . . . . . . . . . . . . 97 Appendix B — Reported Data for Fully-developed Flows 101 B.1 Simple shear flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 B.1.1 Experiment data in Miller et al. (2013) . . . . . . . . . . . . . . . . 101 B.1.2 Simulation data in Rognon et al. (2015) . . . . . . . . . . . . . . . 102 B.2 Inclined surface flows . . . . . . . . . . . . . . . . . . . . . . . . . 103 B.2.1 Experiment data in Azanza (1998) . . . . . . . . . . . . . . . . . . 103 B.2.2 Simulation data in Prochnow (2002) . . . . . . . . . . . . . . . . . 104 Appendix C — Mesh generation in curvilinear coordinate systems 107 C.1 Vector-valued transfinite interpolation . . . . . . . . . . . . . . . . . 108 C.2 Lagrange interpolant of primitive function . . . . . . . . . . . . . . . 110 C.3 An example: simple shear flow with bumping walls . . . . . . . . . 112 | - |
| dc.language.iso | en | - |
| dc.subject | 顆粒流 | zh_TW |
| dc.subject | 流變模型 | zh_TW |
| dc.subject | 穩定性分析 | zh_TW |
| dc.subject | 連續體模擬 | zh_TW |
| dc.subject | granular flow | en |
| dc.subject | continuum simulation | en |
| dc.subject | stability analysis | en |
| dc.subject | rheology model | en |
| dc.title | 可壓縮顆粒流μ(I)與Φ(I)基底流變模型之理論與數值研究 | zh_TW |
| dc.title | A Theoretical and Numerical Study of μ(I)- and Φ(I)-based Rheology Models for Compressible Granular Flows | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 牛仰堯;陳宜良;鍾雲吉 | zh_TW |
| dc.contributor.oralexamcommittee | Yang-Yao Niu;I-Liang Chern;Yun-Chi Chung | en |
| dc.subject.keyword | 顆粒流,流變模型,穩定性分析,連續體模擬, | zh_TW |
| dc.subject.keyword | granular flow,rheology model,stability analysis,continuum simulation, | en |
| dc.relation.page | 113 | - |
| dc.identifier.doi | 10.6342/NTU202401575 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2024-07-29 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 應用數學科學研究所 | - |
| 顯示於系所單位： | 應用數學科學研究所 | |
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