1. ME 475/675 Introduction to Combustion
Lecture 34
Flammability limits, Flame quenching

2. Announcements HW 14 Ch. 8 (1, 13, 15, 16) Integrated BS/MS Degree
Due Wednesday
Integrated BS/MS Degree
Term Project
Discuss on Monday

3. Laminar Premixed flames
So far, we talked about flame speeds and thickness
Now
What mixtures (equivalence ratios) can ignite?
How much energy is required ignite a flammable mixture?
What does it take to extinguish a self-sustaining flame?

4. Stoichiometric Air to Fuel Mass ratio, Table 8.4 page 291
𝜈= 𝐴 𝐹 𝑠𝑡𝑜𝑖𝑐
Stoichiometric Air to Fuel Mass ratio, 𝜈= 𝐴 𝐹 𝑠𝑡𝑜𝑖𝑐
For hydrocarbons ~15-17
Less for CO and Oxygenated hydrocarbons (contain O atoms)
Greater for H2

5. Flammability Limits, Table 8.4 page 291
𝜈= 𝐴 𝐹 𝑠𝑡𝑜𝑖𝑐
𝜒 𝐶 𝐻 4 ,𝐿𝑒𝑎𝑛
Flames only propagate within certain fuel/oxidizer mixture equivalence ratio ranges
Φ 𝑚𝑖𝑛 <Φ< Φ 𝑚𝑎𝑥
Φ 𝑚𝑖𝑛 = Φ 𝑙𝑜𝑤𝑒𝑟 = Φ 𝑙𝑒𝑎𝑛
Φ 𝑚𝑎𝑥 = Φ 𝑢𝑝𝑝𝑒𝑟 = Φ 𝑟𝑖𝑐ℎ
See page 291, Table 8.4 for limits
Φ= 𝐴 𝐹 𝑠𝑡𝑜𝑖𝑐 𝐴 𝐹 = 𝜈 𝐴 𝐹 = 𝑚 𝐹 𝑚 𝐹,𝑆𝑡 𝑚 𝐴,𝑆𝑡 𝑚 𝐴
𝜒 𝐶 𝐻 4 ,𝐿𝑒𝑎𝑛 = 𝑁 𝐶 𝐻 𝑁 𝐶 𝐻 𝑁 𝐴𝑖𝑟 = 𝑁 𝐴𝑖𝑟 𝑁 𝐶 𝐻 = 𝑚 𝐴𝑖𝑟 𝑚 𝐶 𝐻 𝑀𝑊 𝐶 𝐻 4 𝑀𝑊 𝐴𝑖𝑟
For some hydrocarbons Φ 𝑚𝑖𝑛 ≈0.5
But smaller for
acetylene (C2H2) (very wide range)
Carbon monoxide (CO)
N-Decane (C10H22)
Ethylene (ethane) (C2H4)
Hydrogen (H2)

6. Example 8.5, p 294 (turn in next time for EC)
A full propane cylinder from a camp stove leaks its contents of 1.02 lbm ( kg) into a 12’x14’x8’ (3.66 m x 4.27 m x 2.44 m) room at 20°C and 1 atm. After a long time, the fuel gas and room are well mixed.
Is the mixture in the room flammable?

7. Williams Criteria How much energy is required to ignite a mixture?
What does it take to extinguish a flame?
“Williams Criteria” (rule of thumb)
Ignition will occur if enough energy is added to a slab of thickness 𝛿 (laminar flame thickness) to raise it to the adiabatic flame temperature, Tad.
A flame will be sustained if its rate of chemical heat release insides a slab is roughly equal to heat loss by conduction out of the slab (why not radiation?)
Example extinguishment methods
Pass a flame through a narrow tube or slot so it losses too much heat to the surfaces
Dilute using water (or thermal?)
Interrupt chemical kinetics (halogens)
Blow reaction away (loses fuel or heat)

8. Cold Wall Quenching Define Quenching Distance, 𝑑
dTube
dSlot
Define Quenching Distance, 𝑑
Smallest dimension that allows flame to pass
Experimentally determined by shutting off flow of a premixed stabilized flame
dTube = (1.2 to 1.5) dSlot

9. Simplified Quenching Analysis for a Slot𝐿 𝛿
𝑄 𝑐𝑜𝑛𝑑
𝑄 ′′′ 𝑉
𝑄 𝑐𝑜𝑛𝑑 𝑑
b>2 𝑇
b=2 𝑥
To quench, we need: 𝑄 ′′′ 𝑉< 𝑄 𝑐𝑜𝑛𝑑 =−𝐴𝑘 𝑑𝑇 𝑑𝑥
− 𝑚 𝐹 ′′′ Δ ℎ 𝐶 𝛿𝐿𝑑 < 2𝛿𝐿 𝑘 𝑇 𝑏 − 𝑇 𝑤 𝑑 𝑏
𝑑 2 < 2𝑏𝑘 𝑇 𝑏 − 𝑇 𝑤 − 𝑚 𝐹 ′′′ Δ ℎ 𝑐 = 2𝑏𝑘 𝑇 𝑏 − 𝑇 𝑢 𝑆 𝐿 2 𝜌 𝑢 2𝛼 1+𝜈 𝑐 𝑝 𝜈+1 𝑇 𝑏 − 𝑇 𝑢 = 4𝑏 𝛼 2 𝑆 𝐿 2 , so need 𝑑<2 𝛼 𝑆 𝐿 𝑏
If 𝑇 𝑤 = 𝑇 𝑢 ; and since Δ ℎ 𝑐 = 𝑐 𝑝 𝜈+1 𝑇 𝑏 − 𝑇 𝑢 and 𝑆 𝐿 2 =2𝛼 1+𝜈 − 𝑚 𝐹 ′′′ 𝜌 𝑢

10. Quenching will take place when
𝑄 ′′′ 𝑉
𝑄 𝑐𝑜𝑛𝑑 𝑑 𝛿 𝐿 𝑇 𝑥
b=2
b>2 𝑑 𝛿
𝑑<2 𝛼 𝑆 𝐿 𝑏 = 𝑏 𝛿, 𝑏 = 2 or larger
But 𝛿= 2𝛼 𝑆 𝐿
See data for methane/air mixtures
Flame temperature decreases and thickness increases for non-stoichiometric mixtures
Quenching distance increases (follows flame thickness behavior)

11. Data, Table 8.4 page 291
Highest temperature and thinnest flame at Φ>1,
Also smallest 𝑑

12. Example 8.4, page 290 Turn in next time for EC
Consider the design of a laminar-flow, adiabatic, flat-flame burner consisting of a square arrangement of thin-walled tubes as illustrated in the sketch. Fuel-air mixture flows through both the tubes and the interstices between the tubes. It is desired to operate the burner with a stoichiometric methane-air mixture exiting the burner tubes at 300 K and 5 atm.
Determine the mixture mass flow rate per unit cross-sectional area at the design condition.
Estimate the maximum tube diameter allowed so that flashback will be prevented.
Methane (CH4)/air, Φ=1, T=300 K, P=5 atm

13. End 2017
Ran out of time by a 2 minutes

14. Ignition
𝑑𝑇 𝑑𝑥 𝑅 𝐶𝑟𝑖𝑡
The minimum electrical spark energy capable of igniting a flammable mixture.
It is dependent on the temperature, pressure and equivalence ratio of the mixture
What is the critical (minimum) radius of a spark that will propagate
𝑄 ′′′ 𝑉> 𝑄 𝑐𝑜𝑛𝑑
− 𝑚 𝐹 ′′′ Δ ℎ 𝑐 𝜋 𝑅 𝑐𝑟𝑖𝑡 3 >𝑘 4𝜋 𝑅 𝑐𝑟𝑖𝑡 𝑑𝑇 𝑑𝑥 𝑅 𝐶𝑟𝑖𝑡 ~𝑘 4𝜋 𝑅 𝑐𝑟𝑖𝑡 2 𝑇 𝑏 − 𝑇 𝑢 𝑅 𝑐𝑟𝑖𝑡
𝑅 𝑐𝑟𝑖𝑡 2 ≥ 3𝑘 𝑇 𝑏 − 𝑇 𝑢 − 𝑚 𝐹 ′′′ Δ ℎ 𝑐 = 2𝛼 1+𝜈 𝜌 𝑢 𝑆 𝐿 2 3𝑘 𝑇 𝑏 − 𝑇 𝑢 𝑐 𝑝 1+𝜈 𝑇 𝑏 − 𝑇 𝑢 = 6 𝛼 2 𝑆 𝐿 2 ; 𝑅 𝑐𝑟𝑖𝑡 ≥ 6 𝛼 𝑆 𝐿 = 𝛿
𝑆 𝐿 2 =2𝛼 1+𝜈 − 𝑚 𝐹 ′′′ 𝜌 𝑢 ; 1 − 𝑚 𝐹 ′′′ = 2𝛼 1+𝜈 𝜌 𝑢 𝑆 𝐿 2 ; Δ ℎ 𝑐 = 𝑐 𝑝 1+𝜈 𝑇 𝑏 − 𝑇 𝑢 ; 𝛼= 𝑘 𝜌 𝑢 𝑐 𝑝 ; 𝛿= 2𝛼 𝑆 𝐿

15. Energy to bring critical volume to Tb
𝐸 𝑖𝑔𝑛 = 𝑚 𝑐𝑟𝑖𝑡 𝑐 𝑝 𝑇 𝑏 − 𝑇 𝑢
𝑚 𝑐𝑟𝑖𝑡 = 4 3 𝜋 𝑅 𝑐𝑟𝑖𝑡 3 𝜌 𝑏 = 4 3 𝜋 𝛼 𝑆 𝐿 𝜌 𝑏 = 𝛼 𝑆 𝐿 𝑃 𝑅 𝑏 𝑇 𝑏
𝐸 𝑖𝑔𝑛 =61.56𝑃 𝛼 𝑆 𝐿 𝑐 𝑝 𝑅 𝑏 𝑇 𝑏 − 𝑇 𝑢 𝑇 𝑏 ~ 𝑃 𝑃 3 ~ 𝑃 −2
𝛼~ 𝑇 𝑢 𝑇 𝑃 ;
𝑆 𝐿 ~ 𝑇 𝑃 0 𝑒𝑥𝑝 𝐸 𝐴 2 𝑅 𝑢 𝑇 𝑏
not normally considered reliable
Agrees with measurements at low pressure
Need lots of energy at low pressure
Hard to restart jet engines at low pressures
𝐸 𝑖𝑔𝑛 decreases as Tu increases
Table 8.5 page 298 Different fuels