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ME 475/675 Introduction to Combustion Lecture 31 Laminar flame speed and thickness dependence on unburned temperature, pressure, fuel and dilution, Ex. 8.2, Announcements • HW 13 • Due Monday, November 9, 2015 • Midterm 2 • Review Monday, Nov. 9, 2015 • Tutorial: Thursday, November 12, 2015, 5-7 pm, SEM 257 • Exam: Friday, November 13, 2015 • PE 104, 8 to 9:30 (or 9:45?) AM • Project • In groups of two, construct a backpacking stove • Materials will be supplied in lab • Determine how long it takes and how much fuel is required to boil water • Form your group by Monday, November 9 • Inform TA: Hasibul Alam [email protected] • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH.475.675.Combustion/TermProjectAssignment.pdf Pressure and temperature dependence of SL and 𝛿 𝑆𝐿 𝑆𝐿 𝑆𝐿 2𝛼 1 + 𝜈 • For methane: ′′′ −𝑚𝐹 𝜌𝑢 ~𝑃0 𝑇𝑢 𝑇 0.375 𝑇𝑏−1 𝑒𝑥𝑝 • Actually decreases as P increases: 𝑆𝐿 •𝛿= Φ 𝑇𝑢 𝑃 • 𝑆𝐿 = 𝛿 Φ 𝐸𝑎 𝑅𝑢 − 2𝑇𝑏 ≠ 𝑓𝑛 𝑃 (for HC fuels, N=2) 0.2 cm s = cm 43 0.168 0.15 𝑃 [𝑎𝑡𝑚] • Increases with unburned temperature: 𝑆𝐿 s = 10 + 3.71 × 10−4 𝑇𝑢2 𝐾 • Decreases for Φ above or below 1.05 (because that decreases temperature) 2𝛼 𝐸 𝑅 ~𝑃−1 𝑇 0.375 𝑇𝑏1 𝑒𝑥𝑝 𝑎 𝑢 𝑆𝐿 2𝑇𝑏 SL ( Tu ) 0.1 0.05 0.015 0 400 273 0.375 d ( Tu) Ta ( Tu) Tb ( Tu) • Fast (high temperature) flame are thin (slow and think and large and small Φ) 600 800 Tu EaRu 2 Tb ( Tu) exp 3 110 1000 Dependence on Fuel Type 𝑆𝐿 𝑆𝐿,𝐶3 𝐻8 𝑇𝑓 [K] at max 𝑆𝐿 • Table 8.2, P = 1 atm, Φ = 1, Tu = Room temperature • Fig. 8.17: ratio flame speed some hydrocarbons [C2-C6 alkanes (single bonds), alkenes (double bonds), and alkynes (triple bonds)] to propane speed (C3H8) versus 𝑇𝑓 at max 𝑆𝐿 (Φ = 1.05?) • • • • • 𝑚 𝑆𝐿,𝐶3 𝐻8 = 44 ? 𝑠 C3-C6 follow same trend (hotter flames are faster) Methane CH4 is somewhat slower Ethylene (C2H4) and acetylene (C2H2) somewhat faster Hydrogen (H2) is much faster (fast diffusion and reaction kinetics, no slow 𝐶𝑂 → 𝐶𝑂2 ) • Consistency of data for Methane with P = 1 atm, Tu = 298K • Table 8.2: 𝑆𝐿 = 40 cm cm ; 𝑆𝐿 s s = 43 𝑃 [𝑎𝑡𝑚] = 43 cm cm ; 𝑆𝐿 s s = 10 + 3.71 × 10−4 𝑇𝑢2 𝐾 = 43 cm s Flame Speed Correlations for Selected Fuels • 𝑆𝐿 = 𝑆𝐿,𝑟𝑒𝑓 𝑇𝑢 𝑇𝑢,𝑟𝑒𝑓 𝛾 𝑃 𝑃𝑟𝑒𝑓 𝛽 1 − 2.1𝑌𝑑𝑖𝑙 • 𝑇𝑢 > ~350𝐾, 𝑇𝑟𝑒𝑓 = 298 𝐾, 𝑃𝑟𝑒𝑓 = 1 𝑎𝑡𝑚 2 • 𝑆𝐿,𝑟𝑒𝑓 = 𝐵𝑀 + 𝐵2 Φ − Φ𝑚 • 𝛾 = 2.18 − 0.8 Φ − 1 • 𝛽 = −0.16 + 0.22 Φ − 1 • RMFD-303 is a research fuel that simulates gasolines Example 8.3, p. 286 • Compare the laminar flame speeds of gasoline-air mixtures with Φ = 0.8 for the following three cases: i. At reference conditions of T = 298 K, and P = 1 atm. ii. At conditions typical of a spark-ignition engine operating at wide-open throttle: T = 685 K and P = 18.38 atm iii. Same as condition II above, but with 15 percent (by mass) exhaust-gas recirculation. • Simple or complex problem? Graduate Research topic using combustion • Large Fire Heat transfer • Dependence of Fire Time of Concern on Package Location for a 1 PWR Transport Package • Paper Dependence of Fire Time of Concern on Package Location for a 1 PWR Transport Package Ketan Mittal Miles Greiner Research Assistant Professor of Mechanical Engineering University of Nevada, Reno University of Nevada, Reno Ahti Suo-Anttila Computational Engineering Analysis LLC Albuquerque, New Mexico Funded by the US Nuclear Regulatory Commission, Contract NRC-HQ-12-P-02-0200 Packaging and Transportation of Radioactive Materials August 20, 2013 –San Francisco, California Motivation • Consider a package designed to transport one used nuclear fuel assembly in proximity to a long-lasting, 12-m diameter jet fuel fire • If the package is centered over the pool, how long will it take before the fuel’s cladding reaches its possible burst temperature, 750°C? • How far must the package be from the pool’s center so that its cladding will not reach this temperature, even for an infinitely-long-lasting fire? (Safe distance) Package Response Finite Element Model Models fuel block, steel-lead-steel construction surrounded by water tank Inside package, heat generation within the fuel, conduction and surface-to-surface radiation heat transfer Normal Conditions of Transport Temperatures Fuel heat generation , Solar heat flux Natural convection and radiation heat transfer to 38° C environment External surface temperature, hottest at center Internal Temperature Comparison to Previous studies Container Analysis Fire Environment Simulations 800 Tests 1 and 2 Light Winds DT [°C] 600 Simulations Measurements Test 3 Strong Winds 400 200 0 0 10 20 30 40 Time, t [min] • Employs computational fluid dynamics and radiation heat models to calculate fire behavior and heat transfer to nearby or engulfed objects (Others simply use Tfire = 800°C and 𝜀𝐹𝑖𝑟𝑒 = 0.9) • Model parameters were adjusted to agree with temperatures we measured in jet fuel fires at Sandia National Laboratories for a range of wind conditions • FE model calculates package response to this heat transfer Max Cladding Temperature vs time for package Centered over 12-m Pool • Simulations were performed for a range of modeling parameters • Calculated fire time of concern for the cladding tc (when the cladding reaches 750°C) is between 11.8 and 13.3 hours Dependence on Package Location • The fire time of concern for the cladding increases as the distance between the package and fuel centers increases • For Sx > 6.4 m (package over the pool edge) the cladding temperature never reaches its burst condition. • This work helps risk analysts determine which actual fires have the potential to affect safety and require further study Time of Concern versus Package Position Flame Quenching, Mixture Flammability, Ignition • What does it take 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 • 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 d d • Quenching distance d • Smallest dimension d that allows flame to pass • Experimentally determined by shutting off flow of a premixed stabilized flame • dtube = (1.2 to 1.5) dtube • Could we design and build an experiment to observe this using different sized screens? 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 𝑆𝐿2 = 2𝛼 1 + 𝜈 ′′′ −𝑚𝐹 𝜌𝑢 = 4𝑏𝛼 2 , 2 𝑆𝐿 so need 𝑑 < and Δℎ𝑐 = 𝑐𝑝 𝜈 + 1 𝑇𝑏 − 𝑇𝑢 𝛼 2 𝑆𝐿 𝑏 Quenching will take place when 𝐿 𝛿 𝑄𝑐𝑜𝑛𝑑 𝑄𝑐𝑜𝑛𝑑 𝑄 ′′′ 𝑉 𝑑 𝑇 b>2 b=2 𝛼 •𝑑 < 2 𝑏 𝑆𝐿 2𝛼 • But 𝛿 = 𝑆𝐿 𝑥 = 𝑏𝛿, 𝑏 = 2 or larger 𝛿 𝑑 • Example 8.4, page 290 • 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 flowrate 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