ME 475/675 Introduction to

CombustionLecture 38

Announcements• HW16 Ch. 9 (8, 10,12) • Due Monday, 12/1/2013

• Term Project (3% of grade) • Nothing dangerous please! • Instructions:

• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH.475.675.Combustion/TermProjectAssignment.pdf

• Must meet with Rachel to discuss proposal before the end of day Wednesday 26th

• Times to meet with Rachel Green about projects • Wednesdays, 11-3 pm HREL 306• Fridays, 1-3pmHREL 306• Mondays, 11-4 pm HREL 306• Schedule other times by emailing rmgreen@unr.edu

Last time: Non-reacting, constant-density laminar fuel jet

• In quiescent air• Assume • Temperature and Pressure are

constant

• Schmidt number, • before

• Axial diffusion small compared to advection outside core • Potential core not affected by

viscosityFuel

Centerline:Dimensionless

Speed, Fuel Mass Fraction

Constant in CoreThen decreases

due to spreading

Axial SpeedProfiles versus r

Spreads out asx increases

Max magnitudeDecreases

Now: Burning Fuel Jet (Diffusion Flame)• Laminar Diffusion flame structure• T and Y versus r at different x

• Flame shape• Assume flame surface is located

where , stoichiometric mixture• No reaction inside or outside this

• Products form in the flame sheet and then diffuse inward and outward• No oxidizer inside the flame envelop

• Over-ventilated: enough oxidizer to burn all fuel

Fuel

Soot

• Soot particles form from incomplete reaction of the HC fuels• Forms on the fuel side (inside) of the flame surface and

radiate orange and yellow• Most soot is consumed as it flows through the hot flame

• “Wings” form when unburned soot breaks through burning zone

• Smoke is soot that breaks through• Roughly how long will the flame be?

Flame length (a measurable quantity)• Flame length

• ;

• For un-reacting fuel jet (no buoyancy) • For Schmidt number ,

• Dimensionless Similarity Variable • Jet Reynold number:

• Flame length, where at

• Increases with (not dependent on separately)

• Decreases with increasing and ;

• Depend on fuel

• For fuel, ,

• For y = 2x+2 (alkanes), decreases with increasing x

• What about ?

• What is the effect of buoyancy?

Y x y( )1

1 4.76 xy

4

28.85

12.011 x 1.00794y

X x y( )1

1 4.76 xy

4

Ya x( ) 2 x( ) 2

2 4 6 8 100

0.02

0.04

0.06

0.08

0.095

0

Y x Ya x( )( )

X x Ya x( )( )

111 x

Momentum versus Buoyancy controlled flames

• Ratio of initial momentum to buoyancy can affect flame behavior• Froude number

• : Momentum-Controlled• : Mixed (transitional)• : Buoyancy-Controlled

• Affect flames from slots, but not from square or round ducts.

Buoyancy effects• Buoyancy causes differences between a non-reacting fuel jet and a burning flame• Makes the flow accelerate and narrows flame• The narrowed flame has higher and diffusion than fuel jets. • Buoyancy and diffusion effects on flame length “tend” to cancel, allowing models that

neglect both to be roughly correct (within order of magnitude)

• Variable-Density (and viscosity) Approximation (J. Fay)• Assumes

• ambient density far from flame• Flame density• page 335 table• =? (turns out we can perform calculation without knowing it)

Buoyant Length Estimate

• For hydrocarbon fueled flames:

• , • Table 9.2 gives ;

• This buoyant model predicts flame length is 2.4 times longer than unburned models• But same order of magnitude

Experimentally-Confirmed Numerical Solutions• Roper Correlations pp. 336-9; Table

9.3, Equations 9.59 to 9.70• Subscripts:

• thy = Theoretical• expt = Experimental

• Experimental results • round nozzles,

• square nozzles,

• Metric units (m, m3/s)• S = Molar Stoichiometric ratio =

4.75*(x+y/4) for CxHy fuel

• Temperatures: oxidizer, Fuel, mean-flame

• Inverse Gaussian error function “inverf” from Table 9.4

Slot Burners

• Slot burners are dependent on Froude number

• : Momentum-Controlled, : Mixed (transitional), : Buoyancy-Controlled• , • ; for plug nozzle velocity profile: ; for parabolic: • Need to iterate since se are trying to find

• Slot Nozzle Experimental results (stagnant oxidizer); • Momentum Controlled:

• Buoyancy Controlled:

• Transitional:

• These are independent of mean diffusion coefficient for oxidizer at stream temperature

Example 9.3 page 339 (turn in next time for EC)• It is desired to operate a square-port diffusion flame burner with a 50-mm-

high flame in a laboratory. Determine the volumetric flow rate required if the fuel is propane. Also determine the heat release of the flame. What flow rate is required if methane is substituted for propane?