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Paper review format

Paper review format. Prepare a critical review of the article, not to exceed 2 pages, structured as follows : Motivation: Why the author(s) conducted the work Summary of the methods and results Summary of the conclusions Merits: Your opinion of the merits of the work

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Paper review format

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  1. Paper review format • Prepare a critical review of the article, not to exceed 2 pages, structured as follows: • Motivation: Why the author(s) conducted the work • Summary of the methods and results • Summary of the conclusions • Merits: Your opinion of the merits of the work • Weaknesses: Your opinion of the shortcomings of the work • Suggestions: • Don’t repeat text that is in the paper. Summarize in your own words – it shows me that you really do understand the paper. • Don’t use buzz words from the paper without defining them. If you don’t understand them and don’t feel inclined to learn what they are (which is ok, I don’t expect you to understand every detail of the paper) then leave the buzz words out! In other words: “everything you say can and will be used against you…” (Sounds harsh, but that’s the way real science is – anything you write in a paper is subject to evaluation and criticism). • Points 1 and 5 are the most important. Say more than 1 line about item 5, in particular. This really shows what you learned from the paper. It also helps you to generate your own ideas for research. AME 514 - Spring 2013 - Lecture 4

  2. AME 514Applications of Combustion Lecture 4: Microcombustionscience I

  3. Microscale reacting flows and power generation • Micropower generation: what and why (Lecture 4) • “Microcombustion science” (Lectures 4 - 5) • Scaling considerations - flame quenching, friction, speed of sound, … • Flameless & catalytic combustion • Effects of heat recirculation • Devices (Lecture 6) • Thermoelectrics • Fuel cells • Microscale internal combustion engines • Microscale propulsion • Gas turbine • Thermal transpiration AME 514 - Spring 2013 - Lecture 6

  4. What is microcombustion? • PDR’s definition: microcombustion occurs in small-scale flames whose physics is qualitatively different from conventional flames used in macroscopic power generation devices, specifically • The Reynolds numbers is too small for the flow to be turbulent and thus allow the flame reap the benefits of flame acceleration by turbulence AND • The flame dimension is too small (i.e. smaller than the quenching distance, Pe < 40), thus some additional measure (heat recirculation, catalytic combustion, reactant preheating, etc.) is needed to sustain combustion AME 514 - Spring 2013 - Lecture 4

  5. The seductive lure of chemical fuels AME 514 - Spring 2013 - Lecture 4

  6. The challenge of microcombustion • Hydrocarbon fuels have numerous advantages over batteries • ≈ 100 X higher energy density • Much higher power / weight & power / volume of engine • Inexpensive • Nearly infinite shelf life • More constant voltage, no memory effect, instant recharge • Environmentally superior to disposable batteries > $30 billion/yr of disposable batteries ends up in landfills > $6 billion/yr market for rechargables AME 514 - Spring 2013 - Lecture 4

  7. The challenge of microcombustion • … but converting fuel energy to electricity with a small device has not yet proved practical despite numerous applications • Foot soldiers (past DARPA funding: > 15 projects, > $30M) • Portable electronics - laptop computers, cell phones, … • Micro air and space vehicles (enabling technology) • Most approaches use scaled-down macroscopic combustion engines, but may have problems with • Heat losses - flame quenching, unburned fuel & CO emissions • Heat gains before/during compression • Limited fuel choices for premixed-charge engines – need knock-resistant fuels, etc. • Friction losses • Sealing, tolerances, manufacturing, assembly AME 514 - Spring 2013 - Lecture 4

  8. Smallest existing combustion engine Cox Tee Dee .010 • Application: model airplanesWeight: 0.49 oz.Bore: 0.237” = 6.02 mmStroke: 0.226” = 5.74 mmDisplacement: 0.00997 in3 (0.163 cm3) RPM: 30,000 Power: ≈ 5 watts Ignition: Glow plug • Typical fuel: castor oil (10 - 20%), nitromethane (0 - 50%), balance methanol (much lower heating value than pure hydrocarbons!) • Poor performance • Low efficiency (≈ 5%) • Emissions & noise unacceptable for indoor applications • Not “microscale” • Re = Ud/ ≈ (2 x 0.6cm x (30000/60s)) (0.6cm) / (0.15 cm2/s) = 2400 - high enough for turbulence (barely) • Size > quenching distance even at 1 atm, nowhere near quenching distance at post-compression condition • Test data (for 4.89 cm3 4-stroke engine) (Papac et al., 2003): max efficiency 9.3%, power 83 Watts at 13,500 RPM (Brake Mean Effective Pressure = 1.37 atm, vs. typically 8 - 10 atm for automotive engines) AME 514 - Spring 2013 - Lecture 4

  9. Some power MEMS concepts Wankel rotary engine (Berkeley) Free-piston engines (U. Minn, Georgia Tech) AME 514 - Spring 2013 - Lecture 4

  10. Some power MEMS concepts Liquid piston magnetohydrodynamic (MHD) engine (Honeywell / U. Minn) Pulsed combustion driven turbine (UCLA) AME 514 - Spring 2013 - Lecture 4

  11. Some power MEMS concepts - gas turbine (MIT) • Friction & heat losses • Manufacturing tolerances • Very high rotational speed (≈ 2 million RPM) needed for compression (speed of sound doesn’t scale!) AME 514 - Spring 2013 - Lecture 4

  12. Some power MEMS concepts - P3 - Wash. St. Univ. • P3 engine (Whalen et al., 2003) - heating/cooling of trapped vapor bubble • Flexing but no sliding or rotating parts - more amenable to microscales - less friction losses • Layered design more amenable to MEMS fabrication • Stacks - heat out of higher-T engine = heat in to next lower-T engine • Efficiency? Thermal switch? Self-resonating? • To date: 0.8 µW power out for 1.45 W thermal power input AME 514 - Spring 2013 - Lecture 4

  13. Fuel cells • Basically a battery with a continuous feed of reactants to electrodes • Basic parts • Cathode: O2 decomposed, electrons consumed, • Anode: fuel decomposed, electrons generated • Membrane: allows H+ or O= to pass, but not electrons • Fuel cells not limited by 2nd Law efficiencies - not a heat engine • Several flavors including • Hydrogen - air: simple to make using Proton Exchange Membrane (PEM) polymers (e.g. DuPont Nafion™, but how to store H2?) • Methanol - easy to store, but need to “reform” to make H2 or find “holy grail” membrane for direct conversion (Nafion: “crossover” of methanol to air side) • Solid oxide - direct conversion of hydrocarbons, but need high temperatures (500 - 1000˚C) • Formic acid (O=CH-OH) - low energy density but good electrochemistry PEM fuel cell Solid Oxide Fuel Cell AME 514 - Spring 2013 - Lecture 4

  14. Hydrogen storage • Hydrogen is a great fuel • High energy density (1.2 x 108 J/kg, ≈ 3x hydrocarbons) • Much higher  than hydrocarbons (≈ 10 - 100x at same T) • Excellent electrochemical properties in fuel cells • Ignites near room temperature on Pt catalyst • But how to store it??? • Cryogenic liquid - 20K,  = 0.070 g/cm3 (by volume, gasoline has 64% more H than LH2); also, how to insulate for long-duration storage? • Compressed gas, 200 atm:  = 0.018 g/cm3; weight of tank >> weight of fuel; spherical tank, high-strength aluminum (50,000 psi working stress), (mass tank)/(mass fuel) ≈ 15 (note CH4 has 2x more H for same volume & pressure) • Borohydride solution or powder + H2O • NaBH4 + 2H2O  NaBO2 (Borax) + 3H2 • (mass solution)/(mass fuel) ≈ 9.25 • 4.05 x 106 J/kg “bonus” heat release • Safe, no high pressure or dangerous products, but solution has limited lifetime • Palladium - absorbs 900x its own volume in H2 (www.psc.edu/science/Wolf/Wolf.html) - but Pd/H = 164 (mass basis) • Carbon nanotubes - many claims…currently < 1% plausible (Benard et al., 2007) • Long-chain hydrocarbon (CH2)x: (Mass C)/(mass H) = 6, plus C atoms add 94.1 kcal of energy release to 57.8 for H2! AME 514 - Spring 2013 - Lecture 4

  15. Direct methanol fuel cell Methanol is much more easily stored than H2, but has ≈ 6x lower energy/mass and requires a lot more equipment! (CMU concept shown) AME 514 - Spring 2013 - Lecture 4

  16. Formic acid fuel cell • Zhu et al. (2004); Ha et al. (2004) • HCOOH  H2 + CO2 - good hydrogen storage, chemistry amenable to fuel cells, low “crossover” compared to methanol, but low energy density (5.53 x 106 J/kg, 8.4x lower than hydrocarbons) • …but it works! AME 514 - Spring 2013 - Lecture 4

  17. Scaling of micro power generation - quenching • Heat losses vs. heat generation – discussed in AME 513 • Heat loss / heat generation ≈ 1/ at limit • Premixed flames in tubes: PeSLd/ ≈ 40 - as d , need SL  (stronger mixture) to avoid quenching • SL = 40 cm/s,  = 0.2 cm2/s  quenching distance ≈ 2 mm for stoichiometric HC-air • Note  ~ P-1, but roughly SL ~ P-0.1, thus can use weaker mixture (lower SL) at higher P • Also: Pe = 40 assumes cold walls - less heat loss, thus quenching problem with higher wall temperature (obviously) AME 514 - Spring 2013 - Lecture 4

  18. Scaling - gas-phase vs. catalytic reaction • Heat release rate H (in Watts) • Gas-phase: H = QR* *(reaction_rate/volume)*volume • Reaction_rate/volume ~ Yf,∞Zgasexp(–Egas/RT), volume ~ d3  H ~ Yf,∞QRZgasexp(–Egas/RT)d3 d = channel width or some other characteristic dimension • Catalytic: H = Yf,∞QR*(rate/area)*area, area ~ d2; rate/area can be transport limited or kinetically limited • Transport limited (large scales, low flow rates) Rate/area ~ diffusivity*gradient ~ DYf,∞ (1/d)  H ~ (D/d)*d2*QR H ~ Yf,∞QRDd • Kinetically limited (small scales, high flow rates, near extinction) Rate/area ~ Zsurfexp(–Esurf/RT)  H ~ Yf,∞QRd2Zsurfexp(–Esurf/RT) • Ratio gas/surface reaction • Transport limited: Hgas/Hsurf = Zgasexp(–Egas/RT)d2/D ~ d2 • Kinetically limited: Hgas/Hsurf = Zgasexp(–Egas/RT)d/(Zsurfexp(–Esurf/RT)) ~ d  Catalytic combustion will be faster than gas-phase combustion at sufficiently small scales AME 514 - Spring 2013 - Lecture 4

  19. Scaling - flame quenching revisited • Heat loss (by conduction) ~ kg(Area)T/d ~ kgd2T/d ~ kgdT • Define = Heat loss / heat generation (H) • Gas-phase combustion  ~ (kgdT)/(QRZgasexp(–Egas/RT)d3) fQR ~ CPT; SL ~ (g)1/2 ~ (gZgasexp(–Egas/RT))1/2  ~ (g/SLd)2 ~ (1/Pe)2(i.e. quenching criterion is a constant Pe as already discussed) • Surface combustion, transport limited  ~ (kgdT)/(QRDd) ~ (CPT/QR)(kg/CP)/D ~ 1 (i.e. no effect of scale or transport properties, not really a limit criterion) • Surface combustion, kinetically limited, relevant to microcombustion  ~ (kgdT)/QRd2Zsurfexp(–Esurf/RT) ~ (kg/CP)(CPT/QR)(1/Zsurfd)  ~ g/Zsurfd ~ 1/d • Catalytic combustion:  decreases more slowly with decreasing d (~ 1/d) than in gas combustion (~1/d2), may be necessary at small scales to avoid quenching by heat losses! AME 514 - Spring 2013 - Lecture 4

  20. Scaling – blow-off limit at high U • Reaction_rate/volume ~ Yf,∞Zgasexp(–Egas/RT) ~ 1/(Reaction time) • Residence time ~ V/(mdot/) ~ V/((UA)/) ~ (V/A)/U(V = volume) • V/A ~ d3/d2 = d1 Residence time ~ d/U • Residence time / reaction time ~ Yf,∞Zgasd/Uexp(–Egas/RT)] ~ (Yf,∞Zgasd2/n)Red-1 • Blowoff occurs more readily for small d (small residence time / chemical time) AME 514 - Spring 2013 - Lecture 4

  21. Scaling - turbulence • Example: IC engine, bore = stroke = d • Re = Upd/n ≈ (2dN)d/n = 2d2N/n Up = piston speed; N = engine rotational speed (rev/min) • Minimum Re ≈ several 1000 for turbulent flow • Need N ~ 1/d2 or Up ~ 1/d to maintain turbulence (!) • Typical auto engine at idle: Re ≈ (2 x (10 cm)2 x (600/60s)) / (0.15 cm2/s) = 13000 - high enough for turbulence • Cox Tee Dee: Re ≈ (2 x (0.6 cm)2 x (30000/60s)) / (0.15 cm2/s) = 2400 - high enough for turbulence (barely) (maybe) • Why need turbulence? Increase burning rate - but how much? • Turbulent burning velocity (ST) ≈ turbulence intensity (u’) • u’ ≈ 0.5 Up (Heywood, 1988) ≈ dN • ≈ 67 cm/s > SL (auto engine at idle, much more at higher N) • ≈ 300 cm/s >> SL (Cox Tee Dee) AME 514 - Spring 2013 - Lecture 4

  22. Scaling - friction • Fricton due to fluid flow in piston/cylinder gap • Shear stress (t) = µoil(du/dy) = µoilUp/h • Friction power = t x area x velocity = 4µoilUpL2/h = 4µoilRe2n2/h • Thermal power = mass flux x Cp x DTcombustion = rSTd2CpDT = r(Up/2)d2CpDT = rRe)dCpDT/2 • Friction power / thermal power = [8µoil(Re)n]/[rCpDThd)] ≈ 0.002 for macroscale engine • Implications • Need Re ≥ Remin to have turbulence • Material properties µoil, n, rCp,DT essentially fixed  For geometrically similar engines (h ~ d), importance of friction losses ~ 1/d2 ! • What is allowable h? Need to have sufficiently small leakage • Simple fluid mechanics: volumetric leak rate = (P)h3/3µ • Rate of volume sweeping = Ud2 - must be >> leak rate • Need h << (3ndRemin/P)1/3 • Don’t need geometrically similar engine, but still need h ~ d1/3, thus importance of friction loss ~ 1/d4/3! AME 514 - Spring 2013 - Lecture 4

  23. Scaling - speed of sound • For gas turbine compressors, pressure rise ∆P occurs due to dynamic pressure P ~ 1/2rU2 • To get ∆P/P∞ ≈ 1, need rU2/P∞ ≈ 2 or U ~ (RT)1/2 ~ c (sound speed), which doesn’t change with scale or pressure! • Proper compressible flow analysis: for ∆P/P∞ ≈ 1, u = 2(-1)/2 c∞ ≈ 1.1 c∞ ≈ 383 m/s • Macroscopic gas turbine, d ≈ 30 cm, need N ≈ 24,000 rev/min • MEMS (MIT microturbine: d ≈ 4 mm), need 1.8 million RPM! AME 514 - Spring 2013 - Lecture 4

  24. Microscale power generation - challenges • How to avoid flame quenching? • Catalytic combustion • Heat recirculation (e.g. Swiss roll) • Combustion behavior likely to be different from “conventional” macroscale systems… • Other issues • Modeling - gas-phase & surface chemistry submodels • Characterization of catalyst degradation & restoration • Heat rejection - 10% efficiency means 10x more heat rejection than battery, 5% = 20x, etc. • Auxiliary components - valves, pumps, fuel tanks • Packaging AME 514 - Spring 2013 - Lecture 4

  25. Catalytic combustion • Development of micro-scale combustors challenging, especially due to heat losses • Catalysis may help - generally can sustain catalytic combustion at lower temperatures than gas-phase combustion - reduces heat loss and thermal stress problems • Higher surface area to volume ratio at small scales beneficial to catalytic combustion • Key feature of hydrocarbon-air catalytic combustion on typical (e.g. Pt) catalyst • Low temperature: O(s) (oxygen atoms) coat surface, fuel molecules unable to reach surface (exception: H2) • Higher T: some O(s) desorbs, opens surface sites, allows hydrocarbon molecules to adsorb AME 514 - Spring 2013 - Lecture 4

  26. Catalytic combustion • Advantages of catalytic combustion NOT mainly due to lower heat loss, but rather higher reaction rate at a given temperature AME 514 - Spring 2013 - Lecture 4

  27. Catalytic combustion • Deutschman et al. (1996) AME 514 - Spring 2013 - Lecture 4

  28. Catalytic combustion modeling - objectives • Maruta et al., 2002; • Model interactions of chemical reaction, heat loss, fluid flow in simple geometry at small scales • Examine effects of • Heat loss coefficient (H) • Flow velocity or Reynolds number (2.4 - 60) • Fuel/air AND fuel/O2 ratio - conventional experiments using fuel/air mixtures might be misleading because both fuel/O2 ratio and adiabatic flame temperatures are changed simultaneously! AME 514 - Spring 2013 - Lecture 4

  29. Model (Maruta et al, 2002) • Cylindrical tube reactor, 1 mm dia. x 10 mm length • FLUENT + detailed catalytic combustion model (Deutchmann et al.) • Gas-phase reaction neglected - not expected under these conditions (Ohadi & Buckley, 2001) • Thermal conduction along wall neglected • Pt catalyst, CH4-air and CH4-O2-N2 mixtures AME 514 - Spring 2013 - Lecture 4

  30. Results - fuel/air mixtures • “Dual-limit” behavior similar to experiments observed when heat loss is present • Heat release inhibited by high O(s) coverage (slow O(s) desorption) at low T - need Pt(s) sites for fuel adsorption / oxidation AME 514 - Spring 2013 - Lecture 4

  31. Results - fuel/air mixtures • Ratio of heat loss to heat generation ≈ 1 at low-velocity extinction limits AME 514 - Spring 2013 - Lecture 4

  32. Results - fuel/air mixtures • Surface temperature profiles show effects of • Heat loss at low flow velocities • Axial diffusion (broader profile) at low flow velocities AME 514 - Spring 2013 - Lecture 4

  33. Results - fuel/air mixtures • Heat release inhibited by high O(s) coverage (slow O(s) desorption) at low temperatures - need Pt(s) sites for fuel adsorption / oxidation a b Heat release rates and gas-phase CH4 mole fraction Surface coverage AME 514 - Spring 2013 - Lecture 4

  34. Results - fuel/O2/N2 mixtures • Computations with fuel:O2 fixed, N2 (not air) dilution • Minimum fuel concentration and flame temperatures needed to sustain combustion much lower for even slightly rich mixtures! • Combustion sustained at much smaller total heat release rate for even slightly rich mixtures • Behavior due to transition from O(s) coverage for lean mixtures (excess O2) to CO(s) coverage for rich mixtures (excess fuel) AME 514 - Spring 2013 - Lecture 4

  35. Experiments • Predictions qualitatively consistent with experiments (propane-O2-N2) in 2D Swiss roll (not straight tube) at low Re: sharp decrease in % fuel at limit upon crossing stoichiometric fuel:O2 ratio • Lean mixtures: % fuel at limit lower with no catalyst • Rich mixtures: opposite! • Temperatures at limit always lower with catalyst • Similar results found with methane, but minimum flame temperatures for lean mixtures exceed materials limitation of our burner! • No analogous behavior seen without catalyst - only conventional rapid increase in % fuel at limit for rich fuel:O2 ratios AME 514 - Spring 2013 - Lecture 4

  36. Simplified model for propane cat. comb. • Kaisare et al. (2008); Deshmukh & Vlachos (2007) • Only reaction rates considered are adsorption of C3H8 & O2 and desorption of O2 • Adsorption has low activation energy (but has “sticking probability”: so); O2 desorption has high E which depends on O(s) • Transcendental equation for kdesO2! AME 514 - Spring 2013 - Lecture 4

  37. Effect of wall heat conduction • Karagiannidis et al., 2007 - extension of Maruta et al. (2002) to include streamwise wall heat conduction & gas-phase reaction • Conduction significantly narrows extinction limits - need preheated reactants (≈ 600K) to avoid extinction • Some wall heat conduction beneficial (maximum heat loss coefficient (h) higher) - conduction causes heat recirculation AME 514 - Spring 2013 - Lecture 4

  38. Effect of wall heat conduction • Low-velocity and high-velocity extinction limits • Low velocity - heat loss • High velocity - insufficient reaction time • Limits much broader with more reactant preheating • Limits much broader with increasing pressure Without gas-phase reaction (crosses) Without gas-phase reaction (triangles) AME 514 - Spring 2013 - Lecture 4

  39. Conclusions - catalytic combustion • Computations of catalytic combustion in a 1 mm diameter channel with heat losses reveal • Dual limit behavior - low-speed heat loss limit & high-speed blow-off limit • Behavior dependent on surface coverage - Pt(s) promotes reaction, O(s) inhibits reaction • Effect of equivalence ratio very important - transition to CO(s) coverage for rich mixtures, less inhibition than O(s) • Behavior of catalytic combustion in microchannels VERY different from “conventional” flames • Results qualitatively consistent with experiments, even in a different geometry (Swiss roll vs. straight tube) even with different fuels (propane, methane) • Typical strategy to reduce flame temperature: dilute with excess air, but for catalytic combustion at low temperature, slightly rich mixtures with N2 or exhaust gas dilution to reduce temperature is a much better operating strategy! • Impact of streamwise wall heat conduction AME 514 - Spring 2013 - Lecture 4

  40. Simple model of heat recirculating combustors • Work on heat recirculating combustors to minimize heat losses and/or provide large surface area for thermoelectric power generation at small scales • Experimental results in Swiss-roll burners show • Flow velocity or Reynolds number effects (dual limits) • Effects of wall material (inconel vs. Ti vs. plastic) • Macro vs. mesoscale - can’t reach as low Re in mesoscale burner! • Weinberg’s burners showed poor low-Re performance - no combustion at Re < 500 - unacceptable for microscale applications • How to get good low-Re performance necessary for microscale applications? AME 514 - Spring 2013 - Lecture 4

  41. Simple model of heat recirculating combustors • First work: Jones, Lloyd, Weinberg, 1978 • Prescribed minimum reactor temperature • Prescribed heat loss rate (not just prescribed coefficient) • Showed two limits, one at high Re and one at low Re • Not predictive because of prescribed parameters • Did not consider heat conduction along dividing wall • Objective • Develop simplest possible analytical model of counterflow heat-recirculating burners including • Heat transfer between reactant and product streams • Finite-rate chemical reaction • Heat loss to ambient • Streamwise thermal conduction along wall • No prescribed or ad hoc modeling parameters AME 514 - Spring 2013 - Lecture 4

  42. Approach (Ronney, 2003) • Quasi-1D - use constant coefficients for heat transfer to wall (h1) and heat loss (h2) - realistic for laminar flow • Chemical reaction in Well-Stirred Reactor (WSR) (e.g. Glassman, 1996) (simplified but realistic model for “flameless combustion” observed in Swiss-rolll combustors) with one-step Arrhenius reaction • WSR model probably applicable to catalytic combustion also at low Re where kinetically rather than transport limited • “Thermally thin” wall - neglect T across dividing wall compared to T between gas streams and wall • Dividing wall assumed adiabatic at both ends AME 514 - Spring 2013 - Lecture 4

  43. Energy balances Reactant side Dividing wall Product side dx AME 514 - Spring 2013 - Lecture 4

  44. Non-dimensional equations Wall conduction Gas (reactant side) Gas (reactant side) Assume thermally thin wall: Tw,e - Tw,i << Te - Ti; Tw ≈ (Tw,e + Tw,i)/2 Combining leads to: Da = 107, T = 5  = 10, Ti = 1 WSR equation (e.g. Glassman, 1996): Typical WSR response curve AME 514 - Spring 2013 - Lecture 4

  45. Nomenclature AR WSR area B Scaled Biot number = 2h1L2/kw Da Damköhler number = gCPARZ/Lh1 H Dimensionless heat loss coefficient = h2/h1 h1 Heat transfer coefficient to divider wall (= 3.7 k/d for plane channel of height d) h2 Heat loss coefficient to ambient kThermal conductivity L Heat exchanger length M Dimensionless mass flux = CP/h1L = Re(d/L)Pr/Nu Nu Nusselt number for heat transfer = h1d/k (assumed constant) Pr Prandtl number Re Reynolds number Mass flow rate per unit depth Dimensionless temperature = T/T∞ x Streamwise coordinate Dimensionless streamwise coordinate = x/L Z Pre-exponential factor in reaction rate expression Non-dimensional activation energy = E/RT∞ Temperature rise for adiabatic complete combustion ~ fuel concentration  Dividing wall thickness Subscripts e product side of heat exchanger g gas i reactant side of heat exchanger w dividing wall ∞ ambient conditions AME 514 - Spring 2013 - Lecture 4

  46. Temperature profiles • TOP: Temperature profile along heat exchanger is linear with no heat loss (H = 0) and no wall conduction (B = ∞). • MIDDLE: With massive heat loss or low mass flux (M), only WSR end of exchanger is above ambient temperature. • BOTTOM: With wall heat conduction but no heat loss, wall re-distributes thermal energy, reducing WSR temperature even though the system is adiabatic overall! H = dimensionless heat loss B-1 = dimensionless wall conduction effect Da = dimensionless reaction rate AME 514 - Spring 2013 - Lecture 4

  47. Peak temperatures ( w) • Infinite reaction rate (Da = ∞) • No wall conduction (B = ∞): WSR temperature does not drop at low mass flux (M) but instead asymptotes to fixed value • With wall conduction, WSR temperature is a maximum at intermediate M and drops at low M! • Finite reaction rate • B = ∞ (green curve), WSR temperature does not drop at M but instead asymptotes to fixed values • Finite B: wall conduction, the C-shaped response curves become isolas (purple and black curves), thus both upper and lower limits on M exist AME 514 - Spring 2013 - Lecture 4

  48. Extinction limits • Wall heat conduction effects (~1/B) dominate minimum fuel concentration required to support combustion (vertical axis) at low velocity (or low mass flux, M) limit, but high-M limit is hardly affected. Note dual-limit behavior, similar to experimental findings • As wall heat conduction effects increase (decreasing B), the range of M sustaining combustion decreases, however, for adiabatic conditions no low-M extinction limit exists AME 514 - Spring 2013 - Lecture 4

  49. Effect of wall thermal conduction • Predictions consistent with experiments in 2D Swiss roll combustors made of inconel (k = 11 W/mK) vs. titanium (k = 7 W/mK) - higher T, wider extinction limits with lower k AME 514 - Spring 2013 - Lecture 4

  50. Scaling for microcombustors • Scaled-up experiments useful for predicting microscale performance since microscale devices difficult to instrument • ….but how to scale d, U, etc.? • For geometrically similar devices (d ~ L ~ w ~ w) & laminar flow (h ~ kg/d), M ~ Ud/g, B ~ kg/kw, Da ~ d2Z/g & H = const. • How to keep M & Da constant as d decreases? • Could change pressure (P); would require (since g ~ P-1), P ~ d-2, U ~ d, but Z and E are generally pressure-dependent • If P fixed, cannot use geometrical similarity; could use U = constant, L ~ d3, w ~ d & w ~ d5 - not practical! • Could use geometrical similarity, constant P, U ~ d-1 (thus constant M & Re) & adjust fuel concentration T to keep RHS of WSR equation constant (even though Da decreases with decreasing d) • Example: M = 0.01, B = 104, H = 0.05,  = 70 and initial values To = 1.1 and Da = 107, as d is decreased from do the required T are fit by T/ To = 1.07+0.03(d/do)-2 AME 514 - Spring 2013 - Lecture 4

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