Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras Advanced Transport Phenomena Module 8 Lecture 35 1 Illustrative Example: Flame Propagation

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FLAME SPREAD ACROSS IC ENGINE CYLINDER SuSu Flame spread across a carbureted internal combustion (piston) engine 3

 Spark plug is fired  Is the spark adequate for ignition?  Time required for combustion reaction to consume fuel vapor + air mixture in the cylinder space (defined by instantaneous piston location)?  What factors govern necessary spark energy per unit volume, flame propagation speed across chamber? FLAME SPREAD ACROSS IC ENGINE CYLINDER 4

 Considerations:  If spark energy is too small, or gas velocities past gap too large, incipient combustion zone will be quickly extinguished (unfavorable rate of heat loss to heat generation)  Ratio of energy diffusion from burned gas to unburnt gas determines rate of temperature rise to critical value at which combustion reactions can be supported FLAME SPREAD ACROSS IC ENGINE CYLINDER 5

 Considerations:  Chaotic gas motion (turbulence) can enhance this transfer rate  Premixed gas loses energy to water-cooled cylinder walls, becoming difficult to ignite & causing local extinction FLAME SPREAD ACROSS IC ENGINE CYLINDER 6

GASEOUS FUEL JET Horizontal gaseous fuel jet issuing into a turbulent, co-flowing, oxidizer containing gas stream FUEL JET 7

 Fuel & oxidizer vapors do not co-exist initially, but “find each other” in a narrow reaction zone  Hot combustion products mix in both directions  Unreacted fuel side & surrounding air side  Locally diluting, but heating, both GASEOUS FUEL JET 8

 Advantages over premixed counterparts:  Little explosion hazard in recycling energy (otherwise lost) into one or both of reactant feed streams  Better heat radiators in furnaces, owing to presence of hot soot particles in diffusion flames GASEOUS FUEL JET 9

 Shape & length of flame required to completely burn fuel vapor dominated by turbulent transport (rather than chemical kinetics)  Increase in jet velocity does not lengthen flame!  Large changes in fuel chemistry have only a small influence on flame length & shape! GASEOUS FUEL JET 10

 Kinetic factors do control pollutant (e.g., soot, NO(g)) emission  Physical transport processes control overall volumetric energy release rate (flame length, etc.) GASEOUS FUEL JET 11

GASEOUS FUEL JET Gaseous fuel jet in confined furnace space: characteristic macroscopic lengths 12

 Macroscopic dimensions of problem: Typically, r j < r f < L f < L c GASEOUS FUEL JET 13

GASEOUS FUEL JET  Each macroscopic dimension very large compared to “microscopic” lengths:  Hence, continuum formulation possible  Molecularity or granularity of gaseous medium neglected 14

 Equivalent statement in terms of characteristic macroscopic times:  Usually >> 1 ms GASEOUS FUEL JET 15

 Microscopic times: Ordinarily, t interaction < t collision < t chem But in combustion, first two are much smaller than t chem and macroscopic times (for a gaseous system with p = 1 atm and T = 1000K, t interaction ≈ 0.5 ps and t collision ≈ 0.2 ns) GASEOUS FUEL JET 16

 For a continuum fluid, average properties per unit volume become relevant:   limiting value of mass/ volume when volume is small compared to cube of any macroscopic length, but larger than cube of microscopic dimensions (such as mean free path)  “field variable” GASEOUS FUEL JET 17

GASEOUS FUEL JET Operational definition of continuum density “at a point”; illustrative case of total mass density 18

 Scalar fields often displayed at each instant by giving snapshot contours of constant field values, e.g.: isobars contours of constant pressure (cf. meteorological map); isotherms contours of constant temperature; isopleths contours of constant species density, etc. GASEOUS FUEL JET 19

 Flows may be locally chaotic (turbulent), but time- averaged field variables steady at each point  Steady velocity fields: “streamlines”  Representative fields of combustion interest: slides to follow GASEOUS FUEL JET 20

GASEOUS FUEL JET Temperature distributions and streamlines in a natural gas/air premixed flame (adapted from Lewis and von Elbe (1956)) 21

GASEOUS FUEL JET Time-averaged temperature distributions and streamlines in the wake of a pre mixed flame “gutter” – type stabilizer (adapted from Bespalov, et al. (1967)) 22

GASEOUS FUEL JET Species and temperature distributions in a one-dimensional methane/air flame (adapted from Goodings, et al. (1956)) 23

GASEOUS FUEL JET Time- averaged NO profiles (ppm by volume) in a turbulent diffusion flame furnace (adapted from Owen, et al. (1967)) 24

GASEOUS FUEL JET Time-averaged streamlines in a swirling turbulent annular jet containing a recirculation zone (adapted from Beer and Chiger (1974)) 25

GASEOUS FUEL JET Sketch of time-averaged streamlines in a gas turbine combustion chamber 26

GASEOUS FUEL JET  Flow fields complicated, difficult to measure or predict  However, “field” viewpoint conceptually valuable in quantitative treatment of reacting fluid-flow problems, such as combustion 27

SINGLE FUEL DROPLET, DROPLET SPRAY Envelope flame model of isolated fuel droplet combustion in an ambient gas containing oxidizer (adapted from Rosner (1972)) 28

SINGLE FUEL DROPLET, DROPLET SPRAY  Many fuels stored as liquids, but burned by spraying into combustion space  e.g., oil-fired furnaces, diesel-engine cylinders  Droplet surrounded by envelope of diffusion flame when  Oxidizer concentration is adequate, and  Relative velocity between droplet & gas sufficiently small  Fuel vapors generated at droplet surface meet inflowing oxygen  Energy generated at flame zone fed back to sustain endothermic fuel vaporization process 29

SINGLE FUEL DROPLET, DROPLET SPRAY  Again, physical processes control overall combustion rate  Time to completely consume a fuel droplet depends quadratically on initial droplet diameter  Droplet lifetime only weakly dependent on ambient gas temperature & pressure level  Even on fuel chemistry  Insensitive to intrinsic chemical kinetic properties of fuel/air system 30

SINGLE FUEL DROPLET, DROPLET SPRAY  Can define contours of constant time-averaged liquid fuel density (mass of liquid per unit volume of space)  Additional local info:  Statistics of turbulent fluctuations about local mean  Local distribution of liquid fuel wrt droplet size at each position x and time t, etc. 31

 Exploit macroscopic, continuum mechanics; but….  Do not neglect insights from microscopic theories  Phenomenological versus concerns with individual substances  Conservation laws versus constitutive relationships USES OF CONSERVATION/ CONSTITUTIVE PRINCIPLES IN SCIENCE & TECHNOLOGY 32

USES OF CONSERVATION/ CONSTITUTIVE PRINCIPLES IN SCIENCE & TECHNOLOGY 33

 Inference based on Analysis & Measurement of Simple Flows:  Constitutive laws & coefficients determined by comparing experimental measurements with predictions  Employ systems with simple geometry, minimum number of physicochemical interactions  e.g., steady flow through straight channels, circular ducts USES OF CONSERVATION/ CONSTITUTIVE PRINCIPLES IN SCIENCE & TECHNOLOGY 34

 Solution of Simpler Prototype Problems:  To understand transport processes in practical devices, probe relevant “unit processes”  Interactions in simpler, smaller-scale systems  e.g., flame ignition & flame propagation, characterized by measuring oxidation rate of isolated spherical fuel droplet  Emphasis not on accuracy, but understanding of relevant groupings & functional dependencies USES OF CONSERVATION/ CONSTITUTIVE PRINCIPLES IN SCIENCE & TECHNOLOGY 35

 Design of Experiments & Interpretation of Results:  Measurements of all properties at all points not possible, not required  Prediction of full-scale behavior based on small-scale data requires careful design  Similitude analysis is useful tool for DOE  Interpretation of results should be on basis of conservation/ constitutive laws  e.g., thermocouple measurements USES OF CONSERVATION/ CONSTITUTIVE PRINCIPLES IN SCIENCE & TECHNOLOGY 36

USES OF CONSERVATION/ CONSTITUTIVE PRINCIPLES IN SCIENCE & TECHNOLOGY  Computer Modeling:  Comprehensive computer codes can predict/ optimize chemical processes  Seriously initiated in 1970s  Can ultimately reduce design and development cost  Has had huge effects already on research strategies  Directs attention to areas of uncertainty having greatest influence on device performance 37