What makes fast flames fast: influence of hydrodynamic instabilities

We just submitted our new paper on the fast flame supersonic regime in gases. A pre-print, along with the high speed videos, are available on ArXiv.

Our work investigates the structure of fast supersonic turbulent flames typically observed as precursors to the onset of detonation. These high speed deflagrations are obtained after the interaction of a detonation wave with cylindrical obstacles.

Two mixtures having the same propensity for local hot spot formation were considered, namely hydrogen-oxygen (2H₂+O₂) and methane-oxygen (CH₄+2O₂).

We show that the methane mixture sustains turbulent fast flames, while the hydrogen mixture does not.

An incident detonation wave in 2H₂+O₂ coming from the left interacts with a row of cylinders.  The subsequent fast flame, consisting of a system of discrete hot spots and transverse shock system, fails; the figure consists of an overlay of frames showing the evolution; See Video.

A supersonic turbulent fast flame is established in CH₄+2O₂ and slowly accelerates towards DDT; see Video.

Detailed high speed visualizations of nearly two-dimensional flow fields permitted to identify the key mechanism involved. The strong vorticity generation associated with shock reflections in methane permitted to drive jets. These provided local enhancement of mixing rates, sustenance of pressure waves, organization of the front in stronger fewer modes and eventually the transition to detonation.

Hot spot re-ignition in CH₄+2O₂ and entrainment by a Mach jet; see Video.

Shock reflection flow field before the onset of the hot spot in CH₄+2O₂, illustrating the Mach jet formed and lead shock bifurcations; see Video.

The structure of the supersonic fast flame in CH₄+2O₂ far from the obstacles: hot spot ignitions,  jet entrainments, amplification of transverse pressure waves and ultimately the onset of detonation; see Video.

 In the hydrogen system, for similar thermo-chemical parameters, the absence of these jets did not permit to establish such fast flames.

Hot spot ignition in 2H₂+O₂ from shock reflections; see Video.

Shock reflection flow field before the onset of the hot spot in H2-O2, illustrating the Mach reflection configuration; see Video.

This jetting slip line instability in shock reflections (and lack thereof in hydrogen) was correlated with the value of the isentropic exponent and its control of Mach shock jetting instability (Mach & Radulescu - I still have to write the full length paper :(  but see Mach's Masters' thesis or our PROCI 2011 paper).

Structure of the Mach reflection in  a) 2H₂+O₂, and b) CH₄+2O₂, illustrating the Mach jet in the methane mixture, typical of low isentropic exponent reflections; calculated with James Quirk's AMRITA.

Update 4-2-2014.  The reviews from our Combustion Symposium submission are now out.  I am reproducing them here, hopefully, to inspire others to leave comments/feedback to these posts and provide criticisms everybody can benefit from.

Reviewer #1: Excellent

The English in this paper needs to be improved? (1 = Yes; 2 = No; 3 = See comment below) [1-3] 2
This paper requires review by a native English speaker or a translation service? (1 = Yes; 2 = No; 3 = See comment below) [1-3] 2

This paper has experimentally and numercally investigated for the structure of fast supersonic turbulent flames typically observed as precursors to the onset of detonation using high speed shadowgraphy and pressure measurement on two mixture of 2H2-O2 and CH4-2O2.  Authors showed clearly the process of hydrodynamic instabilities in experiment and discussion with the aid of numerical simulation for Mach reflection in cold flow.

Eveything is clear, and well discussed. However, this reviewer wishes to suggest authors to try a numerical simulation for the same setting as experiment of CH4-2O2 where hydrodynamic instability occurs, in order to directly reveal the core physical processes in it.

Reviewer #3: Marginal

The English in this paper needs to be improved? (1 = Yes; 2 = No; 3 = See comment below) [1-3] 2
This paper requires review by a native English speaker or a translation service? (1 = Yes; 2 = No; 3 = See comment below) [1-3] 2

Compared to authors' previous published work, it is a rather incremental study but with very nice flow vizualisations and quite an interesting scenario proposed to explain the conditions of sustainability of fast flame propagation in a reacting mixture prior to the transition to detonation.

If my present rating is "marginal", a "good" rating could be granted if the following issues are properly dealt with:

1) the recourse to the term "turbulent" made several times by the authors is somehow quite too speculative: please substantiate the fact that the observed complex and unsteady structures are indeed turbulent and 2) if so, what is granting the relevance of the recourse to "standard" equilibrium turbulence relationships to estimate turbulence time scales (p. 18) ? 

2) The title of the paper contains the term "hydrodynamic instabilities..." but the main mechanism exhibited (mostly in a qualitative/speculative way though) by the authors to discriminate between the two mixtures is much more the level of vorticity induced by the various interactions between the different flow structures as well as with the obstacle(s) wall. If they are mentioning the Kelvin-Helmoltz shear layer instability or that of the jet formed by the wall jetting effect in the Mach reflection, the link between these instabilities and the vorticity level is not sufficiently firmly established. In that respect, the link with the study of Henderson et al. (JFM, 2003, 479:259-286) who proposed to discriminate between weak and strong jetting effect could be beneficial. The title could be modified to insist more on vorticity.
3) The writing of the vorticity equation to illustrate the impact of the baroclinic torque would be a plus.   
4) Since you are describing rather complex flow patterns you should pinpoint directly on the figures the various prominent structures (e.g. slip line, triple point, incident shock,....)
5) What are the uncertainties associated with the velocity estimation leading to the curves of Figs.3 and 5 ?
7) Some typos must be corrected. The English could be marginally improved although it is far from being critical.


Reviewer #4: Very Good

The English in this paper needs to be improved? (1 = Yes; 2 = No; 3 = See comment below) [1-3] 2
This paper requires review by a native English speaker or a translation service? (1 = Yes; 2 = No; 3 = See comment below) [1-3] 2

This is an interesting experimental examination on the strange wave, traveling at half the CJ velocity of a hydrocarbon mixture. Strange wave is referred to as the fast supersonic turbulent flames (deflagration) which is a precursor to the onset of a full detonation. This type of deflagration flame occurs after the interaction of a detonation wave with cylindrical obstacles. Authors developed and analyzed the jetting slip line instability in shock reflections, correlated with the value of the isentropic exponent and its control of Mach shock jetting instability. Their study focuses on the mechanism controlling the fast flame propagation in the far field with a focus on the hydrodynamic effects.

The paper shows new discussion on the origin of the different behaviors in methane and hydrogen mixtures. In particular, shock reflections are the mechanism to enhance the mixing in the reaction zone of the high speed deflagration. Presented results are sufficient to support their claims.


Reviewer #5: Very Good

The English in this paper needs to be improved? (1 = Yes; 2 = No; 3 = See comment below) [1-3] 2
This paper requires review by a native English speaker or a translation service? (1 = Yes; 2 = No; 3 = See comment below) [1-3] 2

The paper presents an experimental study on the mechanisms that control fast flame propagation with a focus on the hydrodynamic effects. In this work, high speed deflagrations are obtained from self-sustained cellular detonations that diffract around single or multiple cylindrical obstacles.
Two reactive systems (stoichiometric H2/O2 and CH4/O2 mixtures) were chosen for their similar chemical-kinetics properties and for their different isentropic exponent. Different initial pressures were considered in order to vary the mixture reactivity. The visualizations were conducted using two different techniques, the Z-type Schlieren technique and the Edgerton shadowgraph technique.

The visualizations indicate that generation of vorticity by hydrodynamic instabilities is favored in mixtures with a lower isentropic exponent and the propensity of reactive mixture to support fast flame is related to its ability to generate vorticity by hydrodynamic instabilities.

I recommend this paper for publication in the Proceeding of the International Combustion Symposium 2014 because it presents detailed pictures and analysis of a specific stage of the DDT phenomenon that are useful both for physical understanding and as benchmarks for numerical simulations. Such work help to better understand the DDT complex phenomena just before detonation onset.

Update 13-2-2014:

Our rebuttal:

Reviewer 1

Reviewer # 1 finds our paper “Excellent” and further suggests detailed numerical simulations in the future. We agree with the importance for detailed numerical simulations, including viscous effects in 3D, in order to allow for turbulent cascading.  Considering the formidable task to carry these out accurately, we leave these exclusively for future study.

Reviewer # 3

Reviewer # 3 gauges the present study against our previous work, and finds it rather incremental, but with very nice flow visualizations and quite an interesting scenario proposed to explain the conditions of sustainability of fast flame propagation in a reacting mixture prior to the transition to detonation.  She/he finds our paper  “conditionally good” (from an initial “marginal” evaluation) if her/his comments/suggestions are addressed in our MS. 

This reviewer expresses doubts about the turbulent nature of the flowfield obtained.  We can infer that the flow field is turbulent by direct observation of the photographs and by evaluating the Reynolds numbers on the shear layers and forward jets.  This new information will be incorporated in the revision of our manuscript. 

Firstly, the experimental images show the coherent structures caused by the Kelvin-Helmholtz break down into a much more complex flow along the slip-stream (Figure 9), indicating the onset of turbulence.  This has also been observed in detail in our previous work (Figure 3 of Bhatacharjee et. al. PROCI 2012).   We will report these observations and annotate the figures accordingly.

 

Secondly, we have now estimated the Reynolds number of the slip lines (in Figure 7 frame 6 of this paper the Reynolds number half way along the slip line is 10^5).   We find it to be an order of magnitude larger than the typical value for the onset of turbulence on mixing layers (approximately 10^4 according to the survey by Dimotakis. Ann. Rev. Fluid. Mech. 2000).  This again permits to us to infer that the burning occurring along the shear layers and forward jets is in the turbulent regime.

Given the universality of turbulence at small scales, the inference of turbulence permits us to use standard Kolmogorov arguments for the characteristic scales. We note that these are just scaling laws for order of magnitude estimates.   

This reviewer also recommends a more thorough discussion of the mechanism for the forward jet formation, and the variables that favor this effect (gama, Mach number and incidence angle).   We will now refer to the study of Mach (MASc thesis, U. Ottawa 2011) and Mach & Radulescu (PROCI 2011) who have investigated this phenomenon, extending previous arguments made by Hornung (1986) and Henderson (2002) on the role of pressure build-up on the stagnation streamline in shock reflections and its role in forward jetting.  Part of this discussion will be included in the revised MS. 

This reviewer also suggests we include the vorticity equation. We concur.  With the appropriate scaling, this will show unambiguously how the level of vorticity increases with an increase in density gradients, which are favored by a decrease in gama.   The Newtonian limit of infinite compressibility (gama -> 1) will also be discussed, where very large density gradients are expected.

Finally, the reviewer recommends we provide uncertainty measures for the speed measurements reported in Figs. 3 & 5. We now estimated these to approximately 6 - 9% for the range of speed recorded and the spatial and temporal resolution of our recordings.  We will provide these as error bars in the revised MS. 

Reviewer 4 finds the MS “Very Good” and recommends publication as is.  We concur.

Reviewer 5 finds the MS “Very Good” and recommends publication as is.  We concur.