Home | About | Journals | Submit | Contact Us | Français |

**|**Scientific Reports**|**PMC5599604

Formats

Article sections

Authors

Related links

Sci Rep. 2017; 7: 11545.

Published online 2017 September 14. doi: 10.1038/s41598-017-11650-x

PMCID: PMC5599604

Vassilios Papapostolou,^{1} Daniel H. Wacks,^{2} Nilanjan Chakraborty,^{}^{1} Markus Klein,^{3} and Hong G. Im^{4}

Nilanjan Chakraborty, Email: ku.ca.lcn@ytobarkahc.najnalin.

Received 2017 June 1; Accepted 2017 August 29.

Copyright © The Author(s) 2017

Enstrophy is an intrinsic feature of turbulent flows, and its transport properties are essential for the understanding of premixed flame-turbulence interaction. The interrelation between the enstrophy transport and flow topologies, which can be assigned to eight categories based on the three invariants of the velocity-gradient tensor, has been analysed here. The enstrophy transport conditional on flow topologies in turbulent premixed flames has been analysed using a Direct Numerical Simulation database representing the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) combustion regimes. The flame in the CF regime exhibits considerable flame-generated enstrophy, and the dilatation rate and baroclinic torque contributions to the enstrophy transport act as leading order sink and source terms, respectively. Consequently, flow topologies associated with positive dilatation rate values, contribute significantly to the enstrophy transport in the CF regime. By contrast, enstrophy decreases from the unburned to the burned gas side for the cases representing the TRZ and BRZ regimes, with diminishing influences of dilatation rate and baroclinic torque. The enstrophy transport in the TRZ and BRZ regimes is governed by the vortex-stretching and viscous dissipation contributions, similar to non-reacting flows, and topologies existing for all values of dilatation rate remain significant contributors.

Turbulent flows are inherently rotational in nature and the extent of this rotation is often quantified in terms of vorticity

(i.e. curl of velocity vector ). An important and characteristic feature of turbulent flows is the vortex-stretching mechanism, which is responsible for spreading turbulent velocity fluctuations over different length scalesTurbulent flows exhibit eight generic canonical local flow configurations underneath an apparently random fluid motion^{2, 3}, and these distinct flow topologies are categorised depending on the values of first, second and third invariants (i.e. *P*, *Q* and *R*, respectively) of the velocity gradient tensor, *A*
_{ij}=*u*
_{i}/*x*
_{j}=*S*
_{ij}+*W*
_{ij}, where the symmetric strain-rate tensor is *S*
_{ij}=0.5(*A*
_{ij}+*A*
_{ji}) and the anti-symmetric rotation rate tensor is *W*
_{ij}=0.5(*A*
_{ij}−*A*
_{ji}). Three eigenvalues of *A*
_{ij}, *λ*
_{1}, *λ*
_{2}, and *λ*
_{3}, are the solutions of the characteristics equation *λ*
^{3}+*Pλ*
^{2}+*Qλ*+*R*=0 with its invariants *P*, *Q* and *R* as specified below^{2}:

1

2

3

The discriminant, *D*=[27*R*
^{2}+(4*P*
^{3}−18*PQ*)*R*+4*Q*
^{3}−*P*
^{2}
*Q*
^{2}]/108, of the characteristic equation *λ*
^{3}+*Pλ*
^{2}+*Qλ*+*R*=0 divides the *P*−*Q*−*R* phase-space into two regions: the focal (*D*>0) and nodal (*D*<0) topologies^{2, 3}. The *A*
_{ij} tensor exhibits one real eigenvalue and two complex conjugate eigenvalues for focal topologies, whereas *A*
_{ij} shows three real eigenvalues for nodal topologies. The surface *D* = 0 leads to two subsets *r*
_{1a} and *r*
_{1b} in *P*−*Q*−*R* phase space which are given by Refs. ^{2} and ^{3}: *r*
_{1a}=*P*(*Q*−2*P*
^{2}/9)/3−2(−3*Q*+*P*
^{2})^{3/2}/27 and *r*
_{1b} = *P*(*Q*−2*P*
^{2}/9)/3+2(−3*Q*+*P*
^{2})^{3/2}/27. In the region *D*>0, *A*
_{ij} has purely imaginary eigenvalues on the surface *r*
_{2}, which are given by *R*=*PQ*. The surfaces *r*
_{1a}, *r*
_{1b} and *r*
_{2}, where *r*
_{2} is desc*r*ibed by *PQ*−*R*=0, divide the *P*−*Q*−*R* phase space into eight generic flow topologies, referred to as S1-S8, as shown schematically in Fig. 1
^{2, 3}. To date, a large body of literature^{4–11} concentrated on the local flow topology distribution from various viewpoints for incompressible fluids where

(Left) Classification of S1–S8 topologies in the *P*−*Q*−*R* space. The lines *r*
_{1a} (red), *r*
_{1b} (blue) and *r*
_{2} (green) dividing the topologies are shown. Black dashed lines correspond to *Q*=0 **...**

In turbulent flow, the enstrophy (i.e. Ω=*ω*
_{i}
*ω*
_{i}/2 where *ω*
_{i} is the *i*
^{th} component of vorticity) and vorticity fields affect the statistical behaviours of the second and third invariants, *Q* and *R*, which in turn affect the distributions of local flow topologies S1–S8. The instantaneous transport equation of Ω=*ω*
_{i}
*ω*
_{i}/2 is given by^{23–30}:

4

The term *T*
_{I} is the vortex-stretching contribution to the enstrophy transport, whereas term *T*
_{II} arises due to misalignment of gradients of density and viscous stresses. The term *T*
_{III} is responsible for molecular diffusion and dissipation of enstrophy due to viscous action, whereas the term *T*
_{IV} signifies the dissipation of enstrophy due to dilatation rate. The term *T*
_{V} is the baroclinic torque term which arises due to misalignment between pressure and density gradients.

A number of recent studies^{23–29} investigated the Reynolds-averaged enstrophy transport equation in turbulent premixed flames by Reynolds-averaging eq. ^{4}:

5

Here

indicates the Reynolds-averaged value of a general quantityHamlington *et al*.^{23} concentrated on different mechanisms of vorticity generation and the alignment of vorticity with local principal strain rates in the flames representing the thin reaction zones regime of premixed turbulent combustion. Chakraborty^{25} showed that the alignment of vorticity with local principal strain rates is significantly affected by the regime of combustion and the characteristic Lewis number (i.e. ratio of thermal diffusivity to mass diffusivity). Both studies^{23, 25} reported a predominant alignment of vorticity with the intermediate principal strain rate in turbulent premixed flames, which is similar to non-reacting turbulent flows^{31}. However, the relative alignment of vorticity with the most extensive and most compressive principal strain rates is significantly affected by the strength of dilatation rate^{25}, which is influenced by the regime of combustion and the characteristic Lewis number. Hamlington *et al*.^{23} showed that enstrophy decays significantly in the burned gas across the flame brush, whereas Treurniet *et al*.^{24} demonstrated an opposite trend for the flames with high density ratio between the unburned and burned gases. This behaviour has been explained by Lipatnikov *et al*.^{26} by analysing the terms of enstrophy and vorticity transport equation for weakly turbulent premixed flames representing the corrugated flamelets regime.

Recent analyses by Chakraborty *et al*.^{27} and Dopazo *et al*.^{30} demonstrated that the characteristic Lewis number significantly affects the vorticity generation within the flame, and a combination of augmented flame normal acceleration and high extent of flame wrinkling for small values of Lewis number may give rise to a significant amount of vorticity generation within the flame brush due to baroclinic torque. Bobbit and coworkers^{28, 29} demonstrated that the enstrophy transport in statistically planar flames propagating in homogeneous isotropic turbulence for large values of Karlovitz number is governed by the relative balance between the vortex-stretching and viscous dissipation similar to its non-reacting counterpart, and also revealed that the choice of chemical reaction mechanism does not affect the qualitative nature of the enstrophy transport. The enstrophy field in turbulent premixed flames using cinema- stereoscopic particle image velocimetry (PIV) measurements of rim-stabilised turbulent premixed flames has been investigated^{32–34} and confirmed some of the observations based on DNS data.

The aforementioned analyses^{23–29, 31–34} provided invaluable insight into the flame-turbulence interaction, but the nature of the enstrophy transport conditional on generic local flow topologies S1–S8 in different premixed combustion regimes is yet to be analysed in detail. Such an analysis is expected to reveal the canonical flow configurations which make dominant contributions to the enstrophy transport for different combustion regimes.

In order to address the aforementioned gap in the existing literature and to meet the above objectives an existing detailed chemistry DNS database^{21, 35} has been considered consisting of three *H*
_{2}-air flames with an equivalence ratio of *ϕ*=0.7, representative of the combustion processes in the corrugated flamelets, thin reaction zones, and broken reaction zones regimes of combustion. A detailed chemical mechanism^{36} involving 9 steps and 19 chemical reactions is considered for this analysis. The unburned gas temperature *T*
_{0} is taken to be 300 K, which gives rise to an unstrained laminar burning velocity *S*
_{L}=135.62 cm/s under atmospheric pressure. The inlet values of normalised root-mean-square turbulent velocity fluctuation *u*′/*S*
_{L}, turbulent length scale to flame thickness ratio *l*
_{T}/*δ*
_{th}, Damköhler number *Da*=*l*
_{T}
*S*
_{L}/*u*′*δ*
_{th}, Karlovitz number *Ka*=(*ρ*
_{0}
*S*
_{L}
*δ*
_{th}/*μ*
_{0})^{0.5}(*u*′/*S*
_{L})^{1.5}(*l*
_{T}/*δ*
_{th})^{−0.5} and turbulent Reynolds number *Re*
_{t}=*ρ*
_{0}
*u*′*l*
_{T}/*μ*
_{0} for all cases are presented in Table 1, where *ρ*
_{0} is the unburned gas density, *μ*
_{0} is the unburned gas viscosity, *l*
_{T} is the most energetic length scale, *δ*
_{th} = (*T*
_{ad}−*T*
_{0})/*max*|*T*|_{L} is the thermal flame thickness with *T*, *T*
_{ad} and *T*
_{0} being the instantaneous dimensional temperature, adiabatic flame temperature and unburned gas temperature, respectively, and the subscript ‘*L*’ is used to refer to unstrained laminar flame quantities.

The cases investigated in this study are representative of three regimes of combustion: case A: corrugated flamelets (*Ka* < 1), case B: thin reaction zones (1<*Ka*<100) and case C: broken reaction zones regime (*Ka*>100)^{22}. The Karlovitz number can be scaled as

The distributions of natural logarithm (to cover the wide dynamic range) of normalised enstrophy field (

) in the central(Top row) Natural logarithm of instantaneous normalised enstrophy (Ω×(*δ*
_{th}/*S*
_{L})^{2}) fields: (left to right) case A, case B and case C (truncated domain). *c*
_{T}-isosurfaces are shown for *c*
_{T}=0.1, **...**

Figure 2 (top row) further shows that in case A the enstrophy value increases locally from the unburned to the burned gas side of the flame due to flame-induced vorticity generation. In contrast, the magnitude of enstrophy decreases from unburned to burned gas side of the flame for cases B and C. Furthermore, Fig. 2 indicates that S1, S2, S3 and S4 topologies are predominantly present in the burned gas in all cases, but the topology distribution within the flame is significantly different between cases A–C. This can be substantiated from Fig. 3 which shows the probability of finding each flow topology for different values of Favre-averaged reaction progress variable

, where the Favre-average of a general quantityVariation of topology populations (by %) with () for cases (left to right) A-C: focal topologies S1 (red solid line), S4 (blue solid line), S5 (green solid line), and S7 (magenta solid line) and nodal topologies S2 (red dashed line), S3 (blue dashed **...**

Figure 3 indicates that S1–S4 topologies remain major contributors within the flame front for all three cases. As shown in Fig. 1, S1–S4 appear for all values of *P*, and thus they remain dominant contributors, which is consistent with previous findings by Cifuentes *et al*.^{19}. The dilatation rate

The variation of the normalised Reynolds-averaged enstrophy

(where and is defined such that whereVariation of normalised with (), where {*i*=0} are the total enstrophies (black solid lines) and {*i*=1, ..., 8} are the percentage-topology-weighted enstrophies S1–8, respectively, for cases (left to right) A-C: **...**

In order to identify the physical mechanisms responsible for the difference in the enstrophy statistics between cases A-C, which are representative of combustion situations in three different combustion regimes, the variation of

, , , and with for cases A-C are shown in Fig. 5. Significant differences are seen in the behaviour of the enstrophy transport between cases A, B and C. The term due to the viscous diffusion and dissipation acts as a leading order sink, and the magnitude of the viscous torque contribution remains small in comparison to for all cases. In case A, the baroclinic torque contribution acts as the major source term, and its magnitude remains comparable to that of . The contribution of the vortex-stretching term remains weak in case A and its magnitude remains small in comparison to that for the terms of and , whereas the dilatation term acts a major sink term in this case and its magnitude remains comparable to that of the combined viscous diffusion and dissipation term . The relative contributions of the dilatation term and the baroclinic torque term are somewhat diminished in the flame representing the thin reaction zones regime (e.g. case B) and become negligible in the flame representing the broken reaction zones regimes of combustion (e.g. case C). In case B, the vortex-stretching term and the combined viscous diffusion and dissipation term remain the major source and sink terms, respectively. Although the baroclinic term and the dilatation term continue to be source and sink terms in case B, their magnitudes are generally small in comparison to and , respectively. In case C, the transport of enstrophy is determined by the source and sink contributions of the vortex-stretching term and the combined viscous diffusion and dissipation term , respectively and the magnitudes of , and remain negligible in comparison to and . The behaviour of the enstrophy transport in case C is qualitatively similar to a non-reacting flow in this configuration. The effects of dilatation rate and density change on the background fluid motion weaken with increasing Karlovitz numberVariation with () of normalised enstrophy transport equation terms, (*j* = *I*, *II*, *III*, *IV*, *V*), for (left to right) cases A-C: *T*
_{I} (red line), *T*
_{II} (blue line), *T*
_{III} (green line), *T*
_{IV} (magenta line), *T*
_{V} (cyan line). The *x*-axis is shown using a logarithmic **...**

The vortex-stretching term

can be expressed as: whereThe term-by-term contributions of each individual topology to the enstrophy transport (i.e.

whereVariation of normalised with (), where {*i*=0} are the total enstrophy transport equation terms (black solid lines) and {*i*=1, ..., 8} are the percentage-topology-weighted terms corresponding to S1–8, respectively, **...**

The topologies S2, S7, S8 and S4 contribute significantly to the viscous torque term

in the decreasing order of importance in the corrugated flamelets regime case A. The contribution of remains positive in case A and mostly positive except towards the unburned gas side of the flame brush in the thin reaction zones regime case B. The topologies S1, S2, S8, S7 and S4 contribute significantly to in case B and the positive contribution of towards the burned gas side of the flame brush originates principally due to the S7 topology. The topologies S4, S1 and S2, which can be obtained irrespective of the value ofFigure 6 suggests that the S4, S1 and S2 topologies are the leading order contributors to the combined viscous diffusion and dissipation term

for all three cases, but S7 and, to a lesser extent, S3 topologies also contribute significantly to this term for the case representing the corrugated flamelets regime (i.e. case A). In the thin reaction zones and broken reaction zones regime cases (i.e. in cases B and C), S4, S1 and S2 topologies are responsible for most of the viscous diffusion and dissipation.The S2, S7, S1, S4 and S8 (in decreasing order of significance) topologies contribute significantly to the dilatation rate

and baroclinic torque terms in the corrugated flamelets regime case A, whereas S7, S2, S1, S4 and S8 (in decreasing order of significance) topologies remain leading order contributors to in the thin reaction zones regime case B. The topologies S2, S7, S4, S1 and S8 (in decreasing order of significance) are the major contributors to the baroclinic torque term in the thin reaction zones regime case B. In the broken reaction zones regime case C, the dilatation rate and the baroclinic torque terms do not have much significance, but S4, S1 and S7 remain major contributors to these terms in this case.The topologies which are significant contributors to

, , , and in cases A-C are summarised in Table 2. From the foregoing discussion and Table 2 it is evident that S1–S4, S7 and S8 topologies play key roles in the enstrophy transport in the corrugated flamelets regime flame, but the contributions of S7 and S8 topologies, which are obtained only for positive dilatation rates, weaken with an increase in Karlovitz number and for the broken reaction zones regime flame the enstrophy transport is governed by S1, S2 and S4 topologies which are obtained for conditions irrespective of the value of dilatation rate. Thus, simple experimental configurations satisfying canonical features of S7, S8 and S1–S4 are likely to be necessary and sufficient in order to extract fundamental information regarding the enstrophy transport in the corrugated flamelets regime, whereas a simple configuration with predominant features of S1, S2 and S4 will be sufficient for physical understanding of the enstrophy transport in the broken reaction zones regime.An existing three-dimensional DNS database^{21, 35} containing three freely propagating statistically planar *H*
_{2}-air flames representing typical flame-turbulence interaction in the corrugated flamelets, thin reaction zones and broken reaction zones regimes of turbulent premixed combustion has been used to analyse the enstrophy transport conditional on flow topologies within the flame. The flow topologies have been characterized in terms of three invariants of velocity gradient tensor (*P*, *Q* and *R*), where the first invariant is the negative of dilatation rate and second and third invariants can be linked to strain rate and enstrophy, and their generation mechanisms^{2, 3, 11}. In this analysis the flow topologies have been categorized in 8 types (i.e. S1-S8) depending on the location of velocity gradient tensor in *P*−*Q*−*R* space^{2, 3}. It has been found that the weakening of dilatation rate with increasing Karlovitz number plays a key role in the enstrophy transport in turbulent premixed flames. The contributions to the enstrophy transport conditional on topology have been analysed in detail and it has been found that the enstrophy generation due to baroclinic torque weakens from the corrugated flamelets regime case to the broken reaction zones regime case. Further, the flow topologies S1–S4, which can be obtained for all values of dilatation rate, contribute significantly to the enstrophy and its transport in the thin reaction zones and broken reaction zones regimes of premixed turbulent combustion. However, the topologies (i.e. S7 and S8), which are obtained only for positive values of dilatation rate, also contribute significantly to the enstrophy transport in the corrugated flamelets regime.

A three-dimensional complex chemistry (9 steps and 19 chemical reactions according to a detailed chemical mechanism^{36}) compressible flow DNS database of freely-propagating statistically planar turbulent *H*
_{2}-air premixed flames with *ϕ*=0.7 has been considered for this analysis. An equivalence ratio of 0.7 is chosen because an *H*
_{2}-air mixture for this equivalence ratio is known to be thermo-diffusively neutral^{36}, such that the additional effects of the preferential diffusion are eliminated. Interested readers are referred to Im *et al*.^{35} and Wacks *et al*.^{21} for detailed information on the DNS database used for the current analysis and here a brief description of the numerical methodology is provided. The spatial discretisation is carried out using an 8^{th} order central difference scheme for internal grid points and the order of differentiation gradually decreases to a one-sided 4^{th} order scheme at the non-periodic boundaries. A fourth order Runge-Kutta scheme is used for explicit time advancement. The flame is initialised by a steady 1D planar laminar flame profile, and a pre-computed auxiliary divergence free, homogeneous, isotropic turbulence field generated using a pseudo-spectral method^{37} following Passot-Pouquet spectrum^{38} is injected through the inlet. The mean inlet velocity has been gradually modified to match turbulent flame speed as the simulation progresses. The temporal evolution of flame area has been monitored and the flame is taken to be statistically stationary when the flame area no longer varies with time. Turbulent inflow and outflow boundaries are specified in the direction of mean flame propagation and the transverse boundaries are taken to be periodic. The non-periodic boundaries are specified using an improved Navier Stokes characteristic boundary conditions (NSCBC) technique^{39}.

The domain size is taken to be 20 mm×10mm×10mm (8 mm×2mm×2mm) in cases A and B (case C) and the domain has been discretised by a uniform Cartesian grid of 512 × 256 × 256 (1280 × 320 × 320). The grid spacing was determined by the flame resolution, ensuring about 10 grid points across *δ*
_{th}, and in all cases the Kolmogorov length scale remains bigger than the grid spacing (i.e. *η*≥1.5Δ*x* where *η* and Δ*x* are the Kolmogorov length scale and DNS grid spacing, respectively). Simulations have been carried out for 1.0*t*
_{e}, 6.8*t*
_{e} and 6.7*t*
_{e} (i.e. *t*
_{e}=*l*
_{T}/*u*
^{′}) for cases A-C respectively, and this simulation time remains comparable to several previous analyses^{40–42}.

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

N.C. and D.H.W. are grateful to EPSRC and N8/ARCHER. HGI was sponsored by KAUST and made use of the resources of the KAUST Supercomputing Laboratory and computer clusters.

Author Contributions

V.P., N.C. and D.H.W. did the analysis and developed the post-processing code. The analysis was conceptualised by N.C. and M.K., H.G.I. generated the DNS data and M.K. helped with data processing and transfer.

The authors declare that they have no competing interests.

**Publisher's note:** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

1. Tennekes, H. & Lumley, J. L. *A first course in turbulence* (MIT press, 1972).

2. Perry AE, Chong MS. A description of eddying motions and flow patterns using critical-point concepts. Annual Review of Fluid Mechanics. 1987;19:125–155. doi: 10.1146/annurev.fl.19.010187.001013. [Cross Ref]

3. Chong MS, Perry AE, Cantwell BJ. A general classification of three-dimensional flow fields. Physics of Fluids A: Fluid Dynamics. 1990;2:765–777. doi: 10.1063/1.857730. [Cross Ref]

4. Soria J, Sondergaard R, Cantwell B, Chong M, Perry A. A study of the fine-scale motions of incompressible time-developing mixing layers. Physics of Fluids. 1994;6:871–884. doi: 10.1063/1.868323. [Cross Ref]

5. Blackburn HM, Mansour NN, Cantwell BJ. Topology of fine-scale motions in turbulent channel flow. Journal of Fluid Mechanics. 1996;310:269–292. doi: 10.1017/S0022112096001802. [Cross Ref]

6. Chong M, et al. Turbulence structures of wall-bounded shear flows found using dns data. Journal of Fluid Mechanics. 1998;357:225–247. doi: 10.1017/S0022112097008057. [Cross Ref]

7. Chacin JM, Cantwell BJ. Dynamics of a low reynolds number turbulent boundary layer. Journal of Fluid Mechanics. 2000;404:87–115. doi: 10.1017/S002211209900720X. [Cross Ref]

8. Ooi A, Martin J, Soria J, Chong M. A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. Journal of Fluid Mechanics. 1999;381:141–174. doi: 10.1017/S0022112098003681. [Cross Ref]

9. Elsinga G, Marusic I. Evolution and lifetimes of flow topology in a turbulent boundary layer. Physics of Fluids. 2010;22:015102. doi: 10.1063/1.3291070. [Cross Ref]

10. Tsinober, A. Vortex stretching versus production of strain/dissipation. *Turbulence Structure and Vortex Dynamics* 164–191 (2000).

11. Dopazo C, Martn J, Hierro J. Local geometry of isoscalar surfaces. Physical Review E. 2007;76:056316. doi: 10.1103/PhysRevE.76.056316. [PubMed] [Cross Ref]

12. Chen, J. H., Cantwell, B. J. & Mansour, N. N. The topology and vorticity dynamics of a three-dimensional plane compressible wake. In *Proc. Tenth Australasian Fluid Mechanics Conference*, 5–1 (1989).

13. Sondergaard R, Chen J, Soria J, Cantwell B. Local topology of small scale motions in turbulent shear flows. In 8th Symposium on Turbulent Shear Flows, Volume 1. 1991;1:16–1.

14. Suman, S. & Girimaji, S. S. Velocity gradient invariants and local flow-field topology in compressible turbulence. *Journal of Turbulence* N2 (2010).

15. Wang L, Lu X-Y. Flow topology in compressible turbulent boundary layer. Journal of Fluid Mechanics. 2012;703:255. doi: 10.1017/jfm.2012.212. [Cross Ref]

16. Tanahashi M, Fujimura M, Miyauchi T. Coherent fine-scale eddies in turbulent premixed flames. Proceedings of the Combustion Institute. 2000;28:529–535. doi: 10.1016/S0082-0784(00)80252-0. [Cross Ref]

17. Chen, J. H., Yoo, C. S., Grout, R. & Gruber, A. Direct numerical simulation of flame stabilization downstream of a transverse fuel jet in cross-flow. Tech. Rep., Sandia National Laboratories (SNL-CA), Livermore, CA (United States) (2010).

18. Cifuentes L, Dopazo C, Martin J, Jimenez C. Local flow topologies and scalar structures in a turbulent premixed flame. Physics of Fluids. 2014;26:065108. doi: 10.1063/1.4884555. [Cross Ref]

19. Cifuentes L, Dopazo C, Martin J, Domingo P, Vervisch L. Effects of the local flow topologies upon the structure of a premixed methane-air turbulent jet flame. Flow, Turbulence and Combustion. 2016;96:535–546. doi: 10.1007/s10494-015-9686-1. [Cross Ref]

20. Wacks D, Chakraborty N. Flow topology and alignments of scalar gradients and vorticity in turbulent spray flames: A direct numerical simulation analysis. Fuel. 2016;184:922–947. doi: 10.1016/j.fuel.2016.04.061. [Cross Ref]

21. Wacks DH, Chakraborty N, Klein M, Arias PG, Im HG. Flow topologies in different regimes of premixed turbulent combustion: A direct numerical simulation analysis. Physical Review Fluids. 2016;1:083401. doi: 10.1103/PhysRevFluids.1.083401. [Cross Ref]

22. Peters, N. *Turbulent combustion* (Cambridge university press, 2000).

23. Hamlington PE, Poludnenko AY, Oran ES. Interactions between turbulence and flames in premixed reacting flows. Physics of Fluids. 2011;23:125111. doi: 10.1063/1.3671736. [Cross Ref]

24. Treurniet T, Nieuwstadt F, Boersma B. Direct numerical simulation of homogeneous turbulence in combination with premixed combustion at low mach number modelled by the *G*-equation. Journal of Fluid Mechanics. 2006;565:25–62. doi: 10.1017/S0022112006002072. [Cross Ref]

25. Chakraborty N. Statistics of vorticity alignment with local strain rates in turbulent premixed flame. European Journal of Mechanics B/Fluids. 2014;46:201–220. doi: 10.1016/j.euromechflu.2014.01.002. [Cross Ref]

26. Lipatnikov A, Nishiki S, Hasegawa T. A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames. Physics of Fluids. 2014;26:105104. doi: 10.1063/1.4898640. [Cross Ref]

27. Chakraborty N, Konstantinou I, Lipatnikov A. Effects of lewis number on vorticity and enstrophy transport in turbulent premixed flames. Physics of Fluids. 2016;28:015109. doi: 10.1063/1.4939795. [Cross Ref]

28. Bobbitt B, Lapointe S, Blanquart G. Vorticity transformation in high karlovitz number premixed flames. Physics of Fluids. 2016;28:015101. doi: 10.1063/1.4937947. [Cross Ref]

29. Bobbitt B, Blanquart G. Vorticity isotropy in high karlovitz number premixed flames. Physics of Fluids. 2016;28:105101. doi: 10.1063/1.4962305. [Cross Ref]

30. Dopazo C, Cifuentes L, Chakraborty N. Vorticity budgets in premixed combusting turbulent flows at different lewis numbers. Physics of Fluids. 2017;29:045106. doi: 10.1063/1.4981219. [Cross Ref]

31. Moffatt H, Tsinober A. Helicity in laminar and turbulent flow. Annual review of fluid mechanics. 1992;24:281–312. doi: 10.1146/annurev.fl.24.010192.001433. [Cross Ref]

32. Steinberg AM, Driscoll JF, Ceccio SL. Measurements of turbulent premixed flame dynamics using cinema stereoscopic piv. Experiments in Fluids. 2008;44:985–999. doi: 10.1007/s00348-007-0458-0. [Cross Ref]

33. Steinberg AM, Driscoll JF. Straining and wrinkling processes during turbulence–premixed flame interaction measured using temporally-resolved diagnostics. Combustion and Flame. 2009;156:2285–2306. doi: 10.1016/j.combustflame.2009.06.024. [Cross Ref]

34. Steinberg AM, Driscoll JF, Ceccio SL. Three-dimensional temporally resolved measurements of turbulence–flame interactions using orthogonal-plane cinema-stereoscopic piv. Experiments in fluids. 2009;47:527–547. doi: 10.1007/s00348-009-0677-7. [Cross Ref]

35. Im HG, Arias PG, Chaudhuri S, Uranakara HA. Direct numerical simulations of statistically stationary turbulent premixed flames. Combustion Science and Technology. 2016;188:1182–1198. doi: 10.1080/00102202.2016.1198789. [Cross Ref]

36. Burke MP, Chaos M, Ju Y, Dryer FL, Klippenstein SJ. Comprehensive h2/o2 kinetic model for high-pressure combustion. International Journal of Chemical Kinetics. 2012;44:444–474. doi: 10.1002/kin.20603. [Cross Ref]

37. Rogallo, R. S. Numerical experiments in homogeneous turbulence. *NASA Technical Memorandum 81315* (1981).

38. Passot T, Pouquet A. Numerical simulation of compressible homogeneous flows in the turbulent regime. Journal of Fluid Mechanics. 1987;181:441–466. doi: 10.1017/S0022112087002167. [Cross Ref]

39. Yoo CS, Wang Y, Trouvé A, Im HG. Characteristic boundary conditions for direct simulations of turbulent counterflow flames. Combustion Theory and Modelling. 2005;9:617–646. doi: 10.1080/13647830500307378. [Cross Ref]

40. Han I, Huh KY. Roles of displacement speed on evolution of flame surface density for different turbulent intensities and lewis numbers in turbulent premixed combustion. Combustion and Flame. 2008;152:194–205. doi: 10.1016/j.combustflame.2007.10.003. [Cross Ref]

41. Reddy H, Abraham J. Two-dimensional direct numerical simulation evaluation of the flame-surface density model for flames developing from an ignition kernel in lean methane/air mixtures under engine conditions. Physics of Fluids. 2012;24:105108. doi: 10.1063/1.4757655. [Cross Ref]

42. Dopazo C, Cifuentes L, Martin J, Jimenez C. Strain rates normal to approaching iso-scalar surfaces in a turbulent premixed flame. Combustion and Flame. 2015;162:1729–1736. doi: 10.1016/j.combustflame.2014.11.034. [Cross Ref]

Articles from Scientific Reports are provided here courtesy of **Nature Publishing Group**

PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers. |