Extensive Discussions of the Eddy Dissipation Concept Constants and Numerical Simulations of the Sandia Flame D
Abstract
:1. Introduction
2. Reaction Rates
3. Fine-Structures Model
4. EDC Model Constants and the Effects on Reaction Rate
5. Results and Discussion
5.1. Axial Velocity Profiles
5.2. Reynolds Normal Stress Profiles
5.3. Mean Temperature Profiles
5.4. Major Species Profiles
5.5. Minor Species Profiles
6. Conclusions
- (1)
- (2)
- The limiting Reynolds number for the validity of EDC is concluded. Thus, the turbulent Reynolds number should be larger than with different combinations of the primary EDC constants and , or the EDC constants need to be adjusted according to the criteria.
- (3)
- The secondary constant, , should be less than unity with the proposed EDC constant combinations because it is the time–scale ratio of the fine structure to the Kolmogorov scale. The upper limit of is determined from the unity .
- (4)
- The mean reaction rate is expressed as a function of the secondary constants, and its dependence on the EDC constant is presented. The dependence shows that decreasing the mean reaction rate requires deceases in or , and vice versa.
- (5)
- Comprehensive comparison of the predictions of axial velocity, Reynolds stress, temperature, and major and minor species with experimental data shows that case 8, with the secondary constant or the primary constants and can properly reproduce the Sandia flames D.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
, , , | - | primary constants of EDC |
, , , , | - | secondary constants of EDC |
k | m2/s2 | turbulence energy |
L | m | length scale |
s−1 | mass inflow rate to EDC reactor per reactor mass | |
q | m2/s3 | mechanical work rate dissipated into heat in the energy cascade model, Figure 2 |
kg/(s·m3) | volumetric reaction rate of species k | |
Re | - | Reynolds number |
ReT | - | turbulence Reynolds number, |
T | K | temperature |
u | m/s | velocity scale |
w | m2/s3 | mechanical work rate transferred in the energy cascade model, Figure 2 |
Yk | - | mass fraction of species k |
Greeks | ||
- | mass of fine structures divided by total mass | |
- | mass of fine-structure regions divided by total mass | |
ε | m2/s3 | turbulence energy dissipation rate |
- | numerical constant | |
η | m | Kolmogorov length scale |
ν | m2/s | kinematic viscosity |
ρ | kg/m3 | mass density |
τ | s | Time scale |
m/s | Kolmogorov velocity scale | |
χ | - | reacting fraction of fine structures |
ω | s−1 | turbulence strain rate or frequency |
Superscripts | ||
- | average | |
~ | mass-weighted (Favre) average | |
* | fine-structure (reactor) quantity of EDC | |
0 | surroundings of EDC fine-structure reactor |
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Case | Ref. | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.1350 | 0.5000 | 2.1298 | 0.4082 | 11.11 | 27 | 0.0900 | 0.54 | 21 | 1.42 | 2.47 | 222 | 0.2825 | 0.8264 | 20.6 | [2,5] |
2 | 0.1350 | 0.2700 | 1.8257 | 0.3000 | 11.11 | 15 | 0.0900 | 0.46 | 11 | 0.89 | 1.33 | 120 | 0.1930 | 0.7718 | 11.1 | [21] |
3 | 0.1296 | 0.4860 | 2.1584 | 0.4025 | 11.57 | 29 | 0.0864 | 0.54 | 22 | 1.42 | 2.50 | 234 | 0.2909 | 0.8306 | 21.7 | [1,2] |
4 | 0.1340 | 0.5000 | 2.1377 | 0.4082 | 11.19 | 28 | 0.0893 | 0.54 | 21 | 1.43 | 2.49 | 226 | 0.2848 | 0.8276 | 20.9 | [5] |
5 | 0.1340 | 0.2500 | 1.7976 | 0.2887 | 11.19 | 14 | 0.0893 | 0.45 | 10 | 0.85 | 1.24 | 113 | 0.1850 | 0.7655 | 10.4 | [19] |
6 | 0.1340 | 1.0000 | 2.5420 | 0.5773 | 11.19 | 56 | 0.0893 | 0.64 | 42 | 2.40 | 4.97 | 451 | 0.4004 | 0.8747 | 41.8 | |
7 | 0.1340 | 27.0000 | 5.7950 | 3.0000 | 11.19 | 1504 | 0.0893 | 1.46 | 1128 | 28.39 | 134.33 | 12,180 | 0.8335 | 0.9745 | 1127.8 | |
8 | 0.1357 | 0.1100 | 1.4549 | 0.1915 | 11.05 | 6 | 0.0905 | 0.37 | 4 | 0.45 | 0.54 | 48 | 0.0973 | 0.6661 | 4.5 | [21] |
9 | 0.1357 | 0.2100 | 1.7101 | 0.2646 | 11.05 | 11 | 0.0905 | 0.43 | 9 | 0.74 | 1.03 | 92 | 0.1607 | 0.7445 | 8.6 | |
10 | 0.1357 | 0.3100 | 1.8850 | 0.3215 | 11.05 | 17 | 0.0905 | 0.47 | 13 | 0.99 | 1.52 | 136 | 0.2101 | 0.7842 | 12.6 | |
11 | 0.1357 | 0.4100 | 2.0215 | 0.3697 | 11.05 | 22 | 0.0905 | 0.51 | 17 | 1.22 | 2.01 | 180 | 0.2503 | 0.8093 | 16.7 | |
12 | 0.1357 | 0.5100 | 2.1349 | 0.4123 | 11.05 | 28 | 0.0905 | 0.54 | 21 | 1.44 | 2.51 | 224 | 0.2840 | 0.8272 | 20.8 | |
13 | 0.1357 | 0.6100 | 2.2326 | 0.4509 | 11.05 | 33 | 0.0905 | 0.56 | 25 | 1.64 | 3.00 | 268 | 0.3128 | 0.8407 | 24.8 | |
14 | 0.1357 | 0.7100 | 2.3189 | 0.4865 | 11.05 | 39 | 0.0905 | 0.58 | 29 | 1.84 | 3.49 | 312 | 0.3380 | 0.8514 | 28.9 | |
15 | 0.1357 | 0.8100 | 2.3966 | 0.5196 | 11.05 | 44 | 0.0905 | 0.60 | 33 | 2.03 | 3.98 | 356 | 0.3602 | 0.8602 | 33.0 | |
16 | 0.1357 | 0.9100 | 2.4674 | 0.5508 | 11.05 | 49 | 0.0905 | 0.62 | 37 | 2.22 | 4.47 | 400 | 0.3800 | 0.8675 | 37.1 | |
17 | 0.6108 | 6.4827 | 1.9000 | 1.4700 | 2.46 | 17 | 0.4072 | 0.48 | 13 | 4.56 | 7.08 | 141 | 0.2145 | 0.7872 | 13.0 | [18] |
18 | 0.6638 | 9.3987 | 2.0000 | 1.7700 | 2.26 | 21 | 0.4425 | 0.50 | 16 | 5.78 | 9.44 | 173 | 0.2439 | 0.8057 | 16.0 | |
19 | 0.2686 | 2.0172 | 2.1400 | 0.8200 | 5.58 | 28 | 0.1791 | 0.54 | 21 | 2.87 | 5.01 | 227 | 0.2855 | 0.8279 | 21.0 | |
20 | 0.3275 | 3.0000 | 2.1400 | 1.0000 | 4.58 | 28 | 0.2184 | 0.54 | 21 | 3.49 | 6.11 | 227 | 0.2855 | 0.8280 | 21.0 |
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He, D.; Yu, Y.; Ma, H.; Liang, H.; Wang, C. Extensive Discussions of the Eddy Dissipation Concept Constants and Numerical Simulations of the Sandia Flame D. Appl. Sci. 2022, 12, 9162. https://doi.org/10.3390/app12189162
He D, Yu Y, Ma H, Liang H, Wang C. Extensive Discussions of the Eddy Dissipation Concept Constants and Numerical Simulations of the Sandia Flame D. Applied Sciences. 2022; 12(18):9162. https://doi.org/10.3390/app12189162
Chicago/Turabian StyleHe, Di, Yusong Yu, Hao Ma, Hongbo Liang, and Chaojun Wang. 2022. "Extensive Discussions of the Eddy Dissipation Concept Constants and Numerical Simulations of the Sandia Flame D" Applied Sciences 12, no. 18: 9162. https://doi.org/10.3390/app12189162
APA StyleHe, D., Yu, Y., Ma, H., Liang, H., & Wang, C. (2022). Extensive Discussions of the Eddy Dissipation Concept Constants and Numerical Simulations of the Sandia Flame D. Applied Sciences, 12(18), 9162. https://doi.org/10.3390/app12189162