On self-sustained detonation

Figures & data

Table 1. The input parameters

	Case 1	Case 2	Case 3
Heat of combustion ($q_0$)	4.0	4.0	4.0
Ratio of specific heats ($\gamma$)	1.25	1.25	1.25
Preexponential factor ($A$)	$2\times {10}^5$	$2\times {10}^5$	$2\times {10}^5$
Activation energy ($E_a$)	15	20	25
Re, Pr, M, Sc	$1.0\times {10}^6$, 0.78, 0.8704, 1.0

Table 2. Modes of self-sustained detonation for $q_0=4.0$, $E_a=15.0$ and $A=2\times {10}^5$

Mode	$M_0$	$M_{vonNeumann}$	$M_b$
1	3.376743	0.414326	0.526127
2	3.315874	0.417547	0.534179
3	3.086795	0.431175	0.569955
4	2.980451	0.438432	0.590382
5	2.929255	0.442168	0.601356
6	2.830782	0.449843	0.625065
7	2.783512	0.453774	0.637918
8	2.737575	0.457759	0.651532
9	2.347324	0.499725	0.904438

Table 3. Modes of self-sustained detonation for $q_0=4.0$, $E_a=20.0$ and $A=2\times {10}^5$

Mode	$M_0$	$M_{vonNeumann}$	$M_b$
1	3.394151	0.413433	0.523917
2	3.081351	0.431530	0.570932
3	2.999363	0.437093	0.586529
4	2.920474	0.442826	0.603324
5	2.736526	0.457852	0.651858
6	2.668285	0.464100	0.674635
7	2.635349	0.467262	0.686947
8	2.603229	0.470442	0.699970
9	2.571958	0.473634	0.713795
10	2.456424	0.486314	0.779776
11	2.430386	0.489379	0.799976
12	2.405806	0.492349	0.822336
13	2.362338	0.497788	0.876312

Table 4. Modes of self-sustained detonation for $q_0=4.0$, $E_a=25.0$ and $A=2\times {10}^5$

Mode	$M_0$	$M_{vonNeumann}$	$M_b$
1	3.459172	0.410199	0.516000
2	3.343662	0.416058	0.530439
3	3.306379	0.418064	0.535483
4	3.269685	0.420097	0.540652
5	3.198022	0.424242	0.551383
6	3.163033	0.426355	0.556956
7	3.128592	0.428495	0.562676
8	3.094691	0.430661	0.568550
9	3.061322	0.432854	0.574587
10	2.996145	0.437319	0.587177
11	2.964323	0.439591	0.593751
12	2.902183	0.444212	0.607508
13	2.871852	0.446561	0.614717
14	2.812648	0.451331	0.629868
15	2.783767	0.453752	0.637845
16	2.755364	0.456196	0.646117
17	2.727436	0.458662	0.654706
18	2.699984	0.461148	0.663639
19	2.673008	0.463655	0.672947
20	2.646512	0.466179	0.682664
21	2.620500	0.468720	0.692832
22	2.594979	0.471275	0.703499
23	2.569959	0.473841	0.714722
24	2.545456	0.476416	0.726568
25	2.521487	0.478995	0.739122
26	2.498081	0.481573	0.752485
27	2.453114	0.486699	0.782186
28	2.431671	0.489226	0.798905
29	2.411043	0.491710	0.817235

Figure 1. Structures of detonation calculated from the eigenvalue problem, (a) density of mixture, (b) pressures of mixture, (c) temperatures of mixture, (d) Mach numbers in flame, (e) fraction of product, (f) reaction rate

Figure 2. Reaction rates of three detonation propagation modes corresponding to the mode 10, mode 11 and mode 12 in Table 3

Figure 3. Ratios of the minimal detonation speeds produced by the eigenvalue problem and their C–J detonation speeds, here E_a is the activation energy (${\mathit{q}}_{\mathbf{0}}=5.0$, $\mathit{A}={10}^5$ and $\gamma \mathbf{=}\mathbf{1.25}$)

Figure 4. Comparison of the speed of detonations produced by DNS with the detonation speed predicted by the eigenvalue problem and C–J detonation speed (${\mathit{q}}_{\mathbf{0}}=5.0$, $\mathit{A}=2\times {10}^5$, ${\mathit{E}}_{\mathit{a}}=15$ and $\mathit{\gamma }=\mathrm{1..32}$)