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ME 475/675 Introduction to Combustion Lecture 34 Flammability limits, Flame quenching Announcements • HW 14 Ch. 8 (1, 13, 15, 16) • Due Friday, November 20, 2015 • Integrated BS/MS Degree • http://www.unr.edu/engineering/academics/accelerated • Term Project • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH.475.675.Combustion/TermProjectAssignment.pdf Mixture Flammability Limits, Ignition, and Quenching for Premixed Flame • What mixtures (equivalence ratios) can ignite? • What does it take to ignite a flammable mixture? • What does it take to extinguish a self-sustaining flame? Flammability Limits, Table𝐴8.4 page 291 𝜈= 𝐹 𝑠𝑡𝑜𝑖𝑐 𝜒𝐶𝐻4,𝐿𝑒𝑎𝑛 • Flames only propagate within certain fuel/oxidizer mixture equivalence ratio ranges • Φ𝑚𝑖𝑛 < Φ < Φ𝑚𝑎𝑥 • For some hydrocarbons Φ𝑚𝑖𝑛 ≈ 0.5 • But smaller for • Φ𝑚𝑖𝑛 = Φ𝑙𝑜𝑤𝑒𝑟 = Φ𝑙𝑒𝑎𝑛 • Φ𝑚𝑎𝑥 = Φ𝑢𝑝𝑝𝑒𝑟 = Φ𝑟𝑖𝑐ℎ • See page 291, Table 8.4 for limits • Φ= 𝐴 𝐹 𝑠𝑡𝑜𝑖𝑐 𝐴 𝐹 • 𝜒𝐶𝐻4,𝐿𝑒𝑎𝑛 = 𝜈 =𝐴 = 𝐹 𝑁𝐶𝐻4 𝑚𝐹 𝑚𝐴,𝑆𝑡 𝑚𝐹,𝑆𝑡 𝑚𝐴 1 𝑁𝐶𝐻4 +𝑁𝐴𝑖𝑟 = 𝑁 1+𝑁 𝐴𝑖𝑟 𝐶𝐻4 = 1 𝑚 𝑀𝑊𝐶𝐻 1+𝑚 𝐴𝑖𝑟 𝑀𝑊 4 𝐶𝐻4 𝐴𝑖𝑟 • • • • • acetylene (C2H2) (very wide range) Carbon monoxide (CO) N-Decane (C10H22) Ethylene (ethane) (C2H4) Hydrogen (H2) 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 (0.464 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? 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) Cold Wall Quenching 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 Simplified Quenching Analysis for a Slot 𝐿 𝛿 𝑄𝑐𝑜𝑛𝑑 𝑄𝑐𝑜𝑛𝑑 𝑄 ′′′ 𝑉 𝑑 𝑇 b>2 b=2 ′′′ 𝑥 • To quench, we need: 𝑄 𝑉 < 𝑄𝑐𝑜𝑛𝑑 = • • 𝑑𝑇 −𝐴𝑘 𝑑𝑥 𝑇𝑏 −𝑇𝑤 ′′′ −𝑚𝐹 Δℎ𝐹 𝛿𝐿𝑑 < 2𝛿𝐿 𝑘 𝑑 𝑏 2𝑏𝑘 𝑇 −𝑇 2𝑏𝑘 𝑇 −𝑇 𝑤 𝑢 𝑏 𝑏 𝑑2 < = 2𝜌 ′′′ Δℎ 𝑆 −𝑚𝐹 𝑐 𝐿 𝑢 𝑐𝑝 𝜈+1 𝑇𝑏 −𝑇𝑢 = 2𝛼 1+𝜈 • If 𝑇𝑤 = 𝑇𝑢 ; and since Δℎ𝑐 = 𝑐𝑝 𝜈 + 1 𝑇𝑏 − 𝑇𝑢 and 𝑆𝐿2 4𝑏𝛼 2 , 2 𝑆𝐿 so need 𝑑 < = 2𝛼 1 + 𝜈 ′′′ −𝑚𝐹 𝜌𝑢 𝛼 2 𝑆𝐿 𝑏 Quenching will take place when 𝐿 𝛿 𝑄𝑐𝑜𝑛𝑑 𝑑 𝑄𝑐𝑜𝑛𝑑 𝑄 ′′′ 𝑉 𝛿 𝑑 𝑇 b>2 b=2 𝛼 •𝑑 < 2 𝑏 𝑆𝐿 2𝛼 • But 𝛿 = 𝑥 = 𝑏𝛿, 𝑏 = 2 or larger 𝑆𝐿 • See data for methane/air mixtures • For non-stoichiometric mixtures, flame temperature decreases • Flame thickness and quenching distance both increases Data, Table 8.4 page 291 • • Highest temperature and thinnest flame at Φ > 1, • Also smallest 𝑑 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 below. Fuelair 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 End 2015 • Ran out of time by ~2 minutes Ignition 𝑑𝑇 𝑑𝑥 𝑅𝐶𝑟𝑖𝑡 • 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 > 𝑄𝑐𝑜𝑛𝑑 • −𝑚𝐹′′′ 2 • 𝑅𝑐𝑟𝑖𝑡 ≥ • 𝑆𝐿2 Δℎ𝑐 4 3 𝜋𝑅𝑐𝑟𝑖𝑡 3 3𝑘 𝑇𝑏 −𝑇𝑢 ′′′ Δℎ −𝑚𝐹 𝑐 = 2𝛼 1 + 𝜈 = ′′′ −𝑚𝐹 𝜌𝑢 𝑑𝑇 𝑇𝑏 −𝑇𝑢 2 >𝑘 ~𝑘 4𝜋𝑅𝑐𝑟𝑖𝑡 𝑑𝑥 𝑅𝐶𝑟𝑖𝑡 𝑅𝑐𝑟𝑖𝑡 2𝛼 1+𝜈 3𝑘 𝑇𝑏 −𝑇𝑢 6𝛼2 𝛼 6 = ; 𝑅 ≥ 6 = 𝛿 𝑐𝑟𝑖𝑡 𝜌𝑢 𝑆𝐿2 𝑐𝑝 1+𝜈 𝑇𝑏 −𝑇𝑢 𝑆𝐿2 𝑆𝐿 2 ; 2 4𝜋𝑅𝑐𝑟𝑖𝑡 1 ′′′ −𝑚𝐹 = 2𝛼 1+𝜈 𝜌𝑢 𝑆𝐿2 ; Δℎ𝑐 = 𝑐𝑝 1 + 𝜈 𝑇𝑏 − 𝑇𝑢 ; 𝛼 = 𝑘 ; 𝜌𝑢 𝑐𝑝 𝛿= 2𝛼 𝑆𝐿 Energy to bring critical volume to Tb • 𝐸𝑖𝑔𝑛 = 𝑚𝑐𝑟𝑖𝑡 𝑐𝑝 𝑇𝑏 − 𝑇𝑢 • 𝑚𝑐𝑟𝑖𝑡 = 4 3 𝜋𝑅𝑐𝑟𝑖𝑡 𝜌𝑏 3 • 𝐸𝑖𝑔𝑛 = 61.56𝑃 • • = 4 𝜋 3 𝛼 3 6 𝜌𝑏 𝑆𝐿 𝛼 3 𝑐𝑝 𝑇𝑏 −𝑇𝑢 𝑆𝐿 𝑅𝑏 𝑇𝑏 𝑇𝑢 𝑇 0.75 𝛼~ ; 𝑃 𝐸𝐴 0.375 0 𝑆𝐿 ~𝑇 𝑃 𝑒𝑥𝑝 2𝑅𝑢 𝑇𝑏 = 61.56 𝑃 ~ 3 ~𝑃−2 𝑃 • 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 • 𝐸𝑖𝑔𝑛 decreases as Tu increases • Table 8.5 page 298 Different fuels 𝛼 3 𝑃 𝑆𝐿 𝑅𝑏 𝑇 𝑏 •