Application of a Modified Vorticity- Velocity Formulation to Steady and Unsteady Laminar Diffusion Flames Seth B. Dworkin, Blair C. Connelly, Beth Anne V. Bennett, Andrew M. Schaffer, Marshall B. Long, Mitchell D. Smooke Yale University, New Haven, CT, USA Maria P. Puccio, Brendan McAndrews, J. Houston Miller George Washington University, Washington, DC, USA Journée des Doctorants du CMAP le mercredi 7 mars 2007 Ecole Polytechnique Palaiseau, France
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Seth B. Dworkin, Blair C. Connelly , Beth Anne V. Bennett ,
J ournée des D octorants d u CMAP le mercredi 7 mars 2007 Ecole Polytechnique Palaiseau, France. Application of a Modified Vorticity-Velocity Formulation to Steady and Unsteady Laminar Diffusion Flames. Seth B. Dworkin, Blair C. Connelly , Beth Anne V. Bennett , - PowerPoint PPT Presentation
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Application of a Modified Vorticity-Velocity Formulation to Steady and Unsteady Laminar
Diffusion Flames
Seth B. Dworkin, Blair C. Connelly, Beth Anne V. Bennett, Andrew M. Schaffer, Marshall B. Long, Mitchell D. Smooke
Yale University, New Haven, CT, USA
Maria P. Puccio, Brendan McAndrews, J. Houston MillerGeorge Washington University, Washington, DC, USA
Journée des Doctorants du CMAP le mercredi 7 mars 2007 Ecole PolytechniquePalaiseau, France
Outline
• The vorticity-velocity formulation– Background, motivation and derivation– Mass conservation and the vorticity-velocity formulation
• Derivation of a mass-conservative vorticity-velocity formulation
• Predictions for temperature, O2, CO2 and CO concentrations agree well with experiment
Application: Modified Vorticity-Velocity to Periodically Forced Flame
Goal: • Compare experimental and computational data
in order to validate computational model of transient combustion
Problem definition:• Axisymmetric, laminar methane/air diffusion flame• Previously observed lack of agreement in overall flame structure
– Artificial viscosity/discretization error?– Lack of soot/radiation models
• More accurate solution of the velocity field may help the comparison
Periodically Forced Flame:Problem Formulation
ftRrvz 2 and 3.or 5. wherecm/s )sin1(*1*70 22
• Employs the same governing equations except each PDE also contains one or more time-dependent terms, as needed • Methane chemistry using a kinetic mechanism containing 16 species and 46 reversible reactions• Second order, implicit temporal discretizations
Boundary Conditions
• Fuel tube inlet (transient boundary condition)
• Parabolic velocity profile with vavg = 35 cm/s (averaged both spatially and temporally) and T = 298 K
• Axial velocity is forced by a sinusoidal perturbation with amplitude of 30% or 50% at 20 Hz
• 35% CH4 (mole) in N2
• Air flows in the oxidizer tube with vavg = 35 cm/s and T = 298 K
• Boundary conditions are otherwise identical to the steady flame
Periodically Forced Flame:Results
– Temperature fields– Forced at 20 Hz – Each cycle corresponds
to 0.05 seconds of actual time
50% modulation
30% modulation
Periodically Forced Flame:Temperature Contours
– 30% modulation– 10 ms intervals– Computational (top) and experimental
(bottom) isotherms– Panels b, c, g and h between 3.5 cm and
5.0 not shown • Highest level of particulate interference in
– 30% modulation– 10 ms intervals– Computational (top) and
experimental (bottom) isopleths for CO2
– CO is oxidized to form CO2 via CO+OH→CO2+H downstream of hydrocarbon oxidation
Conclusions and Future Work
Periodically Forced Flame; Future Objectives• Implementation of 31-species C2 chemical mechanism • Implementation of a 66 species ethylene mechanism coupled to a
sectional soot model (total of 90 unknowns per grid point)– Parallel implementation– Implimentation of EGLIB, for multicomponent transport property
evaluation
• Modified vorticity-velocity formulation conserves mass while maintaining the overall structure of governing equations
• Particularly useful when high are present (such as corners, walls, shear flows, etc.)– Original formulation has been used successfully for flames without such
vorticity generators• Can be applied to a periodically forced methane/air diffusion flame
– Good qualitative agreement with experiment
AcknowledgementsYale University, New Haven, CT, USAProf. Mitchell D. SmookeProf. Marshall B. LongDr. Beth Anne V. BennettDr. Andrew M. SchafferBlair C. ConnellyGeorge Washington University, Washington, DC, USAProf. J. Houston MillerMaria P. PuccioBrendan McAndrewsFundingUS Department of Energy Office of Basic Energy Sciences (grant no. DE-FG02-88ER13966)National Science Foundation (grant no. CTS-0328296) Natural Sciences and Engineering Research Council of CanadaNational Defense Science and Engineering Graduate Fellowship (ASEE)