采用改进的时空守恒元/解元（CE/SE）格式和新型二步化学反应模型，对小扰动情况下方管通道中的氢氧气相爆轰传播过程进行了数值模拟，对不同截面尺寸和两种扰动模式下的爆轰波三波线结构进行了详细计算和分析。数值模拟花费了相对较少的计算代价，清晰地得到了方形截面通道中3种相对稳定的爆轰波传播结构，即直角模式、对角模式和螺旋模式。随着截面尺寸的减小，爆轰波胞格图样与波阵面结构随之产生适应性的变形，乃至出现胞格数目的减少和部分三波线的消失；最终，直角模式和对角模式都会转化为顺时针或逆时针的螺旋模式；临界尺寸下，得到了转换过程中新的过渡结构和压力脉冲振幅的变化，并以此初步讨论了直角和对角传播模式的稳定性。
Using an improved space-time Conservation Element and Solution Element (CE/SE) scheme, the three-dimensional detonation propagation in square ducts filled with H2-O2 mixtures is simulated. A series of detonation structures under different cross-sectional sizes and two kinds of initial perturbation are calculated and analyzed. It costs relatively little computational resource to reproduce the three typical kinds of detonation propagation structure, namely the rectangular mode, the diagonal mode, and the spinning mode. As the cross-sectional size decreases, the detonation cellular pattern and the wave front structure will produce an adaptive deformation, until the number of cellular pattern decreases and some of the triple point lines disappear. Eventually, the rectangular mode and the diagonal mode will both transform into the clockwise or anticlockwise spinning mode. At the critical cross-sectional size, the new detonation structure and its maximum pressure histories during the transformation process are obtained, and the stability of the rectangular and diagonal propagation mode are preliminarily discussed.
[1] HANANA M, LEFEBVRE M H, VAN TIGGELEN P J. Pressure profiles in detonation cells with rectangular and diagonal structures[J]. Shock Waves, 2001, 11(2):77-88.
[2] 周凯, 汪球, 胡宗民, 等. 爆轰驱动膨胀管性能研究[J]. 航空学报, 2016, 37(3):810-816. ZHOU K, WANG Q, HU Z M, et al. Performance study of a detonation-driven expansion tube[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(3):810-816(in Chinese).
[3] ZHENG D F, WANG B. Acceleration of DDT by non-thermal plasma in a single-trial detonation tube[J]. Chinese Journal of Aeronautics, 2018, 31(5):1012-1019.
[4] ORAN E S, WEBER J W, STEFANIW E I, et al. A numerical study of a two-dimensional H2-O2-Ar detonation using a detailed chemical reaction model[J]. Combustion and Flame, 1998, 113(1-2):147-163.
[5] SICHEL M, TONELLO N A, ORAN E S, et al. A two-step kinetics model for numerical simulation of explosions and detonations in H2-O2 mixtures[J]. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 2014, 470(2168):20140413.
[6] TAKI S, FUJIWARA T. Numerical Analysis of two-dimensional nonsteady detonations[J]. AIAA Journal, 1978, 16(1):73-77.
[7] TSUBOI N, KATOH S, HAYASHI A K. Three dimensional numerical simulation for hydrogen/air detonation:Rectangular and diagonal structures[J]. Proceedings of the Combustion Institute, 2002, 29(2):2783-2788.
[8] TSUBOI N, ASAHARA M, ETO K, et al. Numerical simulation of spinning detonation in square tube[J]. Shock Waves, 2008, 18(4):329-344.
[9] TSUBOI N, HAYASHI A K. Numerical study on spinning detonations[J]. Proceedings of the Combustion Institute, 2007, 31(2):2389-2396.
[10] TSUBOI N, DAIMON Y, HAYASHI A K. Three dimensional numerical simulation of detonations in coaxial tubes[J]. Shock Waves, 2008, 18(5):379-392.
[11] DOU H S, TSAI H M, KHOO B C, et al. Simulations of detonation wave propagation in rectangular ducts using a three-dimensional WENO scheme[J]. Combustion and Flame, 2008, 154(4):644-659.
[12] DOU H S, KHOO B C. Effect of initial disturbance on the detonation front structure of a narrow duct[J]. Shock Waves, 2010, 20(2):163-173.
[13] WANG C, SHU C W, HAN W H, et al. High resolution WENO simulation of 3D detonation waves[J]. Combustion and Flame, 2013, 160(2):447-462.
[14] WANG C, LI P, GAO Z, et al. Three-dimensional detonation simulations with the mapped WENO-Z finite difference scheme[J]. Computers and Fluids, 2016, 139:105-111.
[15] WENG C S, GORE J P. A numerical study of two-and three-dimensional detonation dynamics of pulse detonation engine by the CE/SE method[J]. Acta Mechanica Sinica, 2005, 21(1):32-39.
[16] SHEN H, LIU K X, ZHANG D L. Three-dimensional simulation of detonation propagation in a rectangular duct by an improved CE/SE scheme[J]. Chinese Physics Letters, 2011, 28(12):124-135.
[17] IVANOV M F, KIVERIN A D, YAKOVENKO I S, et al. Hydrogen oxygen flame acceleration and deflagration to detonation transition in three-dimensional rectangular channels with no-slip walls[J]. International Journal of Hydrogen Energy, 2013, 38(36):16427-16440.
[18] CAI X D, LIANG J H, DEITERDING R, et al. Adaptive mesh refinement based simulations of three dimensional detonation combustion in supersonic combustible mixtures with a detailed reaction model[J]. International Journal of Hydrogen Energy, 2016, 41(4):3222-3239.
[19] HUANG Y, JI H, LIAN F S, et al. Three-dimensional parallel simulation of formation of spinning detonation in a narrow square tube[J]. Chinese Physics Letters, 2012, 29(11):114701.
[20] HUANG Y, JI H, LIAN F S, et al. Numerical study of three-dimensional detonation structure transformations in a narrow square tube:From rectangular and diagonal modes into spinning modes[J]. Shock Waves, 2014, 24(4):375-392.
[21] CHANG S C. The method of space-time conservation element and solution element-A new approach for solving the Navier-Stokes and Euler equations[J]. Journal of Computational Physics, 1995, 119(2):295-324.
[22] CHANG S C. New developments in the method of space-time conservation element and solution element:Applications to the Euler and Navier-Stokes equations:NASA-TM-106226[R]. Washington, D.C.:NASA, 1993.
[23] WANG X Y. Accuracy study of the space-time CE/SE method for computational aeroacoustics problems involving shock waves:AIAA-2000-0474[R]. Reston, VA:AIAA, 2000.
[24] ZHANG M, YU S T, CHANG S C. Solving the Navier-Stokes equations by the CE/SE method:AIAA-2004-0075[R]. Reston, VA:AIAA, 2004.
CJA