NDLI: Damköhler-Shelkin Paradox in the Theory of Turbulent Flame Propagation, and a Concept of the Premixed Flame at the Intermediate Asymptotic Stage

Content Provider	Springer Nature Link
Author	Zimont, Vladimir L.
Copyright Year	2016
Abstract	We formulated a paradox in the theory of turbulent premixed flame in the flamelet regime: discrepancy between the Damköhler (1940) and Shelkin (1943) estimate of the turbulence flame speed $U_{t} \sim {u}^{\prime }$ in the case of strong turbulence ( ${u}^{\prime }>>S_{L} $ ) and numerous experiments that show a strong dependence of U t on the speed of the instantaneous flame S L . We name this discrepancy the Damköhler-Shelkin paradox. The first aim of the research is to validate and clarify this estimate, which is based on intuitive considerations, as the paradox must be a statement that seems contradictory to observations but is actually true. We analysed the turbulent flame in the context of the original hyperbolic combustion equation that directly describes the leading edge of the flame, which is a locus of the Zel’dovich “leading points” controlling the speed of the turbulent flame. Analysis of the corresponding characteristic equations results in the expression for speed on the steady-state turbulent flame $U_{t} ={u}^{\prime }\sqrt {1+(S_{L} /{u}^{\prime })^{2}} $ , which is the case when ${u}^{\prime }>>S_{L} $ becomes $U_{t} \cong {u}^{\prime }$ . This result confirms and improves the Damköhler-Shelkin estimate $U_{t} \sim {u}^{\prime }$ . The second aim is to resolve the Damköhler-Shelkin paradox. We explain the discrepancy with observations by the fact that turbulent flames are transient due to insufficient residence time in the real burners to reach statistical equilibrium of wrinkle structures of the random flame surface. We consider the transient flame in the intermediate asymptotic stage when the small-scales wrinkles are in statistical equilibrium, while at the same time the large-scale wrinkles are far from equilibrium. The expressions for the flame speed and width, which we deduce using the dimensional analysis and general properties of the ransom surface, $U_{t} \sim ({u}^{\prime }S_{L})^{1/2}$ and $\delta _{t} \sim ({u}^{\prime }Lt)^{1/2}$ , show that this transient flame is in fact a turbulent mixing layer travelling with constant speed U t depending on S L , the intermediate steady propagation (ISP) flame. Qualitative estimations of the times required for the small-scale and large-scale wrinkles to reach statistical equilibrium show that the turbulent Bunsen- and V-flames correspond to the intermediated asymptotic stage, and the turbulent flames with a complete equilibrium structure of the wrinkled flamelet surface are not attainable under laboratory conditions. We present the results of numerical simulations of the impingent flames, which count in favour of the belief that these flames are also transient.
Starting Page	875
Ending Page	912
Page Count	38
File Format	PDF
ISSN	13866184
Journal	Flow, Turbulence and Combustion
Volume Number	97
Issue Number	3
e-ISSN	15731987
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-02-15
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Turbulent premixed flame Damköhler-Shelkin theory Hyperbolic combustion equation Engineering Fluid Dynamics Fluid- and Aerodynamics Engineering Thermodynamics, Heat and Mass Transfer Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Physical and Theoretical Chemistry Chemical Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Towards the Development of an Evolution Equation for Flame Turbulence Interaction in Premixed Turbulent Combustion

Self-Turbulent Flame Speeds

Combined Influence of Strain and Heat Loss on Turbulent Premixed Flame Stabilization

DNS Analysis of Wall Heat Transfer and Combustion Regimes in a Turbulent Non-premixed Wall-jet Flame

RANS Simulations of Statistically Stationary Premixed Turbulent Combustion Using Flame Speed Closure Model

Topology and Brush Thickness of Turbulent Premixed V-shaped Flames

Analysis of the Combined Modelling of Sub-grid Transport and Filtered Flame Propagation for Premixed Turbulent Combustion

Application of the Dynamic F-TACLES Combustion Model to a Lean Premixed Turbulent Flame

Evaluations of SGS Combustion, Scalar Flux and Stress Models in a Turbulent Jet Premixed Flame

Damköhler-Shelkin Paradox in the Theory of Turbulent Flame Propagation, and a Concept of the Premixed Flame at the Intermediate Asymptotic Stage

Similar Documents

Towards the Development of an Evolution Equation for Flame Turbulence Interaction in Premixed Turbulent Combustion

Self-Turbulent Flame Speeds

Combined Influence of Strain and Heat Loss on Turbulent Premixed Flame Stabilization

DNS Analysis of Wall Heat Transfer and Combustion Regimes in a Turbulent Non-premixed Wall-jet Flame

RANS Simulations of Statistically Stationary Premixed Turbulent Combustion Using Flame Speed Closure Model

Topology and Brush Thickness of Turbulent Premixed V-shaped Flames

Analysis of the Combined Modelling of Sub-grid Transport and Filtered Flame Propagation for Premixed Turbulent Combustion

Application of the Dynamic F-TACLES Combustion Model to a Lean Premixed Turbulent Flame

Evaluations of SGS Combustion, Scalar Flux and Stress Models in a Turbulent Jet Premixed Flame

Damköhler-Shelkin Paradox in the Theory of Turbulent Flame Propagation, and a Concept of the Premixed Flame at the Intermediate Asymptotic Stage