Characterisation and Design of Direct Numerical Simulations of Turbulent Statistically Planar Flames
Abstract
:1. Introduction
2. Theoretical Background
2.1. Laminar Flame Theory
2.2. Turbulent Flame Theory
- For the function behind in Equation (13), it is sufficient to rearrange Equation (3).
- The function for is the result of Equation (8) being plugged into Equation (10), leading to . That expression can be rearranged to create Equation (14).
- The function for is derived from Equation (4), where statements from Equations (11) and (6) are plugged, in leading to . Here, Equation (10) and then Equation (8) can be plugged in, resulting in . A simple rearrangement leads to Equation (15).
- For the derivation of , Equation (5) is combined with Equation (6) to create ()/(). Here, the statement from Equation (10) is plugged in, leading to . The insertion of Equation (8) results in Now, Equation (16) can be inferred.
2.3. Simulative Setup
3. Results and Discussion
3.1. Mathematical Relations of Design Parameters
3.2. Trade-Off of Design Parameters
3.3. Definition of a Representative Point for Characteristic Flame Properties
3.4. Adaption of the Regime Diagram
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Latin: | |
Heat capacity at constant pressure | |
Damköhler number | |
Karlovitz number | |
Turbulent kinetic energy | |
Molecular Prandtl number | |
Pressure | |
Reynolds number | |
Flame front propagation velocity | |
Temperature | |
Time | |
Velocity | |
Turbulent fluctuations | |
X | Molar Fraction |
Indices | |
Average between reactants and products | |
Burned | |
Chemical | |
char | Characteristic |
Initial | |
Laminar | |
Length-scale | |
max | Maximum |
Turbulence | |
Unburned | |
Based on the characteristic length of eddies | |
Based on the Kolmogorov scale | |
s | Species index |
Greek: | |
Thermal diffusivity | |
Empirical constant for the Karman spectrum. Usually, it equals 2.7. | |
Flame front thickness | |
Flame front thickness based on the turbulence | |
Flame front thickness based on the reaction zone | |
Dissipation | |
Kolmogorov scale | |
Domain size divided by characteristic length of eddies | |
Wave number (=1/wave length) | |
Characteristic length of eddies | |
Heat conductivity | |
Molecular viscosity | |
Density | |
Time scale | |
Aspect ratio | |
ϕ | Equivalence ratio |
Flame front resolution | |
Mesh size (=number of cells) | |
Abbreviations: | |
DNS | Direct numerical simulation |
HIT | Homogeneous isotropic turbulence |
TCI | Turbulence–chemistry interaction |
ML | Machine learning |
TKE | Turbulent kinetic energy |
RAM | Random-access memory |
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Case | A | B | C |
---|---|---|---|
2.2 | 4.59 | 7.55 | |
40.6 | 31 | 30.7 | |
1.5 | 0.81 | 0.56 | |
0.74 | 1.37 | 1.98 | |
3.072 | 3.072 | 3.072 | |
5.46 | 5.46 | 5.46 | |
1.11 | 1.11 | 1.11 | |
11.8 | 11.8 | 11.8 | |
80.5 | 128 | 209 | |
0.87 | 1.37 | 5.48 | |
10.38 | 3.8 | 2.3 | |
8 | 8 | 8 | |
7 | 7 | 7 | |
4 | 4 | 4 |
Point | Definition | Determination Method | Pr | |
---|---|---|---|---|
variable constant | from reactants | 0.066 | 1.11 | |
Favre-averaged ν | 0.817 | 13.7 | ||
Averaged ν | 1.564 | 26.2 | ||
2.014 | 33.8 | |||
Whole Pr term as a local variable | from reactants | 0.717 | 1.11 | |
Position of autoignition temperature | 0.704 | 4.45 | ||
Favre averaged Pr | 0.691 | 22.1 | ||
Averaged Pr | 0.676 | 29.1 | ||
0.675 | 29.9 | |||
Intersection of both definitions | 0.706 | 11.8 |
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Sternin, A.; Martinez, D.; Sternin, D.; Haidn, O.; Tajmar, M. Characterisation and Design of Direct Numerical Simulations of Turbulent Statistically Planar Flames. Aerospace 2022, 9, 530. https://doi.org/10.3390/aerospace9100530
Sternin A, Martinez D, Sternin D, Haidn O, Tajmar M. Characterisation and Design of Direct Numerical Simulations of Turbulent Statistically Planar Flames. Aerospace. 2022; 9(10):530. https://doi.org/10.3390/aerospace9100530
Chicago/Turabian StyleSternin, Andrej, Daniel Martinez, Daniel Sternin, Oskar Haidn, and Martin Tajmar. 2022. "Characterisation and Design of Direct Numerical Simulations of Turbulent Statistically Planar Flames" Aerospace 9, no. 10: 530. https://doi.org/10.3390/aerospace9100530
APA StyleSternin, A., Martinez, D., Sternin, D., Haidn, O., & Tajmar, M. (2022). Characterisation and Design of Direct Numerical Simulations of Turbulent Statistically Planar Flames. Aerospace, 9(10), 530. https://doi.org/10.3390/aerospace9100530