AME 514 Applications of Combustion Lecture 5: Microcombustion science II

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, … 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 2017 - Lecture 4

Heat recirculating combustors minimizes heat losses - can be used as heat source for thermoelectric or other power generator Toroidal 3D geometry: further reduces losses - minimizes external T on all surfaces Cold reactants Hot Products Combustion zone Heat exchange 2D “Swiss roll” combustor (Lloyd & Weinberg, 1974, 1975) 1D counterflow heat exchanger and combustor AME 514 - Spring 2017 - Lecture 5

“Swiss roll” experiments Key issues Extinction limits, especially at low Reynolds number (Re) Re  Ud/; U = inlet velocity, d = channel width,  = viscosity Catalytic vs. gas-phase combustion Control of temperature, mixture & residence time for thermoelectric or solid oxide fuel cell generator (Lecture 6) Implementation of experiments – baseline case 3.5 turn 2-D rectangular Swiss roll PC control and data acquisition using LabView Mass flow controllers for fuel (propane) & air (butane, isobutane not shown but similar) Thermocouples - 1 in each inlet & outlet turn (7 total) Bare metal Pt foil catalyst in center of burner AME 514 - Spring 2017 - Lecture 5

Swiss roll experiments Mass Flow Controllers Air PC with LabView Fuel O2 or N2 Flashback arrestor NI-DAQ board Gas Chromatograph PC with PeakSimple Thermocouples Outgoing products Incoming reactants AME 514 - Spring 2017 - Lecture 5

Swiss roll experiments 3.5 mm channel width, 0.5 mm wall thickness Top & bottom sealed with ceramic blanket insulation AME 514 - Spring 2017 - Lecture 5

Swiss roll experiments – extinction limits Ahn et al., 2005 Propane-air 3.5-turn Swiss roll AME 514 - Spring 2017 - Lecture 5

Swiss roll experiments – extinction limits Gas-phase extinction limits ≈ symmetrical about  = 1 Minimum Re ≈ 40 Catalytic Low Re Very low Re (≈ 1) possible Lean limit rich of stoichiometric (!), limits very asymmetrical about  = 1 - due to need for excess fuel to scrub O2 from catalyst surface (consistent with computations - Lecture 4) Pre-conditioning Pt catalyst by burning NH3 very beneficial Rearranging catalyst or 4x increase in area: practically no effect! - not transport limited Intermediate Re: only slight improvement with catalyst Still higher Re: no effect of catalyst Near stoichiometric, higher Re: strong combustion, heat recirculation not needed, reaction zone not centered, not stable (same result with or without catalyst) AME 514 - Spring 2017 - Lecture 5

Swiss roll experiments – limit temperatures AME 514 - Spring 2017 - Lecture 5

Swiss roll experiments – limit temperatures Much lower limit T with catalyst but only slightly leaner mixtures For a given  and Re supporting gas-phase combustion, catalyst actually hurts slightly - only helps when gas-phase fails Limit temperatures ≈ same lean & rich Limit temperatures down to 650˚C (non-cat), 125˚C (cat), 75˚C (!) (cat, with NH3 treatment) Limit temperatures follow Arrhenius law Ln(Relimit) ~ -Ln(residence time) ~ 1/T Activation energies ≈ 19 kcal/mole (gas-phase), 6.4 kcal/mole (catalytic) Mechanism At limit, heat loss ~ heat generation Heat loss ~ Tmax-T∞ Heat generation ~ exp(-E/RTmax) ~ ∞U∞AYfQR Limit temperatures approx. ~ ln(U∞) ~ ln(Re) AME 514 - Spring 2017 - Lecture 5

Out-of-center regime Near lean or rich limits – maximum possible heat recirculation needed to obtain high enough T for reaction - flame centered Near-stoichiometric – heat recirculation not needed - flame self-sustaining - reaction zone moves toward inlet - center cool due to heat losses AME 514 - Spring 2017 - Lecture 5

Exhaust gas composition All cases: > 80% conversion of scarce reactant Low Re No CO or non-propane hydrocarbons found, even for ultra-rich mixtures! Only combustion products are CO2 and (probably) H2O Additional catalyst has almost no effect NH3 catalyst treatment increases fuel conversion substantially for very low Re cases Moderate Re Some CO formed in rich mixtures, less with catalyst High Re Catalyst ineffective, products same with or without catalyst AME 514 - Spring 2017 - Lecture 5

Exhaust gas composition AME 514 - Spring 2017 - Lecture 5

Scale-down experiments Wire-EDM fabrication, Pt igniter wire / catalyst Can’t reach as low Re as macroscale burner! Wall thick and has high thermal conductivity - loss mechanism! 2D mini Swiss Roll AME 514 - Spring 2017 - Lecture 5

Polymer combustors Theoretical study showed importance of wall thermal conductivity on combustor performance - counterintuitive: lower is better - heat transfer across thin wall is easy, but need to minimize streamwise conduction Low Tmax demonstrated in metal burners with catalytic combustion - no need for high-temperature metals (high k) or ceramics (k = 1 - 2 W/m˚C but fragile, hard to fabricate) Use polymers??? Low k (DuPont Vespel SP-1 polyimide, k = 0.29 W/m˚C), rated to T > 400˚C, even in oxidizing atmosphere Easy to fabricate, not brittle AME 514 - Spring 2017 - Lecture 5

Plastic combustor - implementation World’s first all polymer combustors? (Sanford et al., 2008) CNC milling: 3.5 turn Swiss roll, 3 mm channel width, 0.5 mm wall thickness, 2.5 cm tall NH3-treated bare metal Pt catalyst in central region General performance No damage even at T > 400˚C (high enough for SOFCs) Thermal expansion coefficient of Vespel ≈ 4x inconel, but no warping Sustained combustion at 2.9 W thermal (birthday candle ≈ 50 W) 5.5 cm Catalyst region AME 514 - Spring 2017 - Lecture 5

Results - polymer burner - extinction limits Extinction limit behavior similar to metal burner at larger Re Improved “lean” and “rich” limit performance compared to macroscale burner at 2.5 < Re < 20 Sudden, still unexplained cutoff at Re ≈ 2.5 in polymer burner Sanford et al., 2008 AME 514 - Spring 2017 - Lecture 5

Swiss roll - numerical modeling Kuo & Ronney, 2007; Chen & Ronney 2011, 2013 FLUENT, 2D & 3D Conduction (solid & gas), convection (gas), radiation (solid-solid only, DO method,  = 0.35) k- turbulence model - useful for qualitative evaluations but not quantitatively accurate for low Re 1-step chemistry, pre-exponential adjusted for agreement between model & expt. at Re = 1000 All gas & solid properties chosen to simulate Inconel burner experiments Boundary conditions: Inlet: 300K, plug flow Outlet: pressure outlet 2D simulations: heat loss at boundaries + volumetric term to simulate heat loss in 3rd dimension AME 514 - Spring 2017 - Lecture 5

Swiss roll - numerical modeling “Virtual thermocouple” locations inlet outlet 7 6 5 4 3 2 d 1 AME 514 - Spring 2017 - Lecture 5

Swiss roll - numerical modeling User-Defined Function to simulate heat loss in 3rd dimension (includes radiation to ambient) T_gas T_blanket T_plate T_outside T_ambient Intake Exhaust h = 10 W/m2K  = 0.35 T_ambient T_wall T_plate T_blanket Since this is a 2-D model, we cannot have the behavior in 3rd dimension. So, using User-Defined Function is a way to simulate heat loss in 3rd dimension. UDF is a way to specify the boundary, heat source etc. by user. In our case, the heat loss from top and bottom plane. So, the heat loss is calculated by this equation with the solid and air thermal resistant. T1 T_gas Heat loss in 3rd dimension blanket AME 514 - Spring 2017 - Lecture 5

Model results - comparison to experiment Temperatures too high to conduct experiments above this Re! AME 514 - Spring 2017 - Lecture 5

Model results - comparison to experiment Reasonable agreement between model & experiment for all Re when turbulence included High-Re “blow-off” limit - insufficient residence time compared to chemical time scale At high Re, wider limits with turbulence - increases heat transfer (gas  wall), thus increases heat recirculation At low Re, limits same with or without turbulence (reality check) Low-Re limit due to heat loss Heat generation ~ Yf,∞; ~ U ~ Re Heat loss ~ (Tmax - Tambient) ≈ const  Heat loss / heat generation increases as Re decreases - need more fuel (larger Yf,∞) to avoid extinction Model & experiment show low-U limit at Re ≈ 40, even for stoichiometric mixture (nothing adjusted to get this agreement at low Re!) When the turbulent included, the variables in the governing equation are averaged. Turbulent viscosity should be calculated by turbulent kinetic energy and dissipation rate. AME 514 - Spring 2017 - Lecture 5

Model results - turbulence effects Extinction limit with laminar flow deviates from turbulent flow at higher Re Higher heat transfer coefficient (h ~ u’ ~ U) for turbulent flow compared to h = constant for laminar flow Adiabatic reactor temperature (homework…): If h ~ U ~ , Treactor (thus limit Yf,∞) ≈ independent of U (thus independent of Re) Vital to include turbulence effects in macroscale model to obtain correct pre-exponential factor When the turbulent included, the variables in the governing equation are averaged. Turbulent viscosity should be calculated by turbulent kinetic energy and dissipation rate. AME 514 - Spring 2017 - Lecture 5

Model results – temperatures at extinction Tmax Tad AME 514 - Spring 2017 - Lecture 5

Model results – temperatures at extinction “Virtual thermocouples” - 1 mm x 1 mm region at same locations at thermocouples in experiments Maximum temperatures at limit higher for 1-step model than experiments - typical result for 1-step model without chain branching steps Low Re: Tmax < Tad due to heat loss - even with heat recirculation Higher Re: heat loss less important, Tmax > Tad due to heat recirculation Tmax at extinction nearly same with or without turbulence even though limit mixtures (thus Tad) are different At high Re, extinction is caused by insufficient residence time compared to reaction time - determined by flow velocity (Re) Reaction time far more sensitive to temperature than mixture strength Re determines T required to avoid extinction, regardless of transport environment required to obtain this temperature AME 514 - Spring 2017 - Lecture 5

Model results - extinction limits Temperatures too high to conduct experiments above this Re! AME 514 - Spring 2017 - Lecture 5

Model results - heat loss & radiation Radiation: effect similar to heat loss Causes heat to be conducted along the walls and subsequently lost to ambient Less important at smaller scales Conduction ~ k(T/x) Radiation ~ (T4-T4) Radiation/Conduction ~ x … but unless you include radiation, you get the wrong answer when you calibrate a macroscale model then apply it to microscales! High Re: convection dominates heat transfer, finite residence time dominates extinction, all models yield almost same predictions We done some previous work at high Re, this shows…… (last point) AME 514 - Spring 2017 - Lecture 5

Model results - out of center limit Model shows that when fuel mole % increases, reaction zone moves out of center - consistent with experiments Semi-quantitative agreement between simulations & experiments - NO ADJUSTABLE PARAMETERS Again need to include turbulence at high Re AME 514 - Spring 2017 - Lecture 5

Model results - wall conductivity Heat recirculation requires spanwise conduction across wall from products to reactants … but conduction to wall also causes streamwise heat conduction - removes thermal energy from reaction zone which can be lost to ambient, narrows extinction limits (Ronney, 2003; Chen & Buckmaster, 2004) BUT if wall k = 0, no heat recirculation  THERE MUST BE AN OPTIMUM WALL THERMAL CONDUCTIVTY Computational predictions High Re: convection >> conduction, wall k doesn’t matter unless it’s too small Lower Re: convection ≈ conduction, heat loss dominant; optimal k exists, but is less than air! Optimal k roughly where thermal resistance across wall ≈ thermal resistance air  wall AME 514 - Spring 2017 - Lecture 5

Model results – wall conductivity AME 514 - Spring 2017 - Lecture 5

Model results - 3D effects Q: Does 2D model properly account for heat loss in 3rd dimension? A: (Chen & Ronney, 2011) Generally yes, but new effects arise - Dean vortices in flow in curved channels - additional heat transport - heat recirculation (thus extinction limits) similar with or without turbulence (RSM = Reynolds Stress model) included, whereas 2D model (no Dean vortices possible) shows very different results! Equivalence ratio at ext. limit Equivalence ratio at ext. limit AME 514 - Spring 2017 - Lecture 5

Model results - 3D effects Turbulence model suppressed With turbulence model Vorticity (1/s) AME 514 - Spring 2017 - Lecture 5

Model results - chemistry effects Q: One-step model: pre-exponential term (Z) adjusted to match experiments – can Swiss-roll combustors be modeled without adjustable parameters and/or complex chemistry? A: Yes – 4-step model (Hautmann et al., 1981) designed to model flow reactor experiments (not flames) works well with zero adjustable parameters 4-step 1-step Reaction rate map: Re = 55 4-step Equivalence ratio at ext. limit 1-step Reaction rate map: Re = 1760 AME 514 - Spring 2017 - Lecture 5

Scale effects revisited Simplified analysis (Chen and Ronney, 2013) Adiabatic energy balance across heat exchanger: equate heat transfer QT to enthalpy increase of reactants due to QT yields excess enthalpy (E) UT = overall heat transfer coefficient, AT = exchanger area N = Number of Transfer Units (common in heat exchanger literature) Non-adiabatic analysis using “mixing cup” (average) temperatures AME 514 - Spring 2017 - Lecture 5

Scale effects revisited Heat transfer Laminar flow: UT ~ h ~ (k/d)Nu ~ (k/d)Re0 h = heat transfer coefficient, Nu = Nusselt number N ~ UTAT/ CP ~ (k/d)d2/(rUd2)CP ~ Re-1 ~ 1/d Turbulent flow: UT ~ (k/d)Nu ~ (k/d)Re0.8, N ~ Re-0.2 Either way, Re (which is known a priori) is uniquely related to N, so can use Re as a scaling parameter instead place of N (which depends on h and isn’t known a priori) Heat loss UL generally independent of scale (for buoyant convection or radiation), AL ~ AT, thus for laminar flow with UT ~ 1/d, a ~ d Thus, at low Re, for the same Re performance is poorer for large scale combustors AME 514 - Spring 2017 - Lecture 5

Scale effects revisited Chemical reaction Reaction_rate/volume ~ Yf,∞Zgasexp(–Egas/RT) ~ 1/(Reaction time) Residence time ~ V/(mdot/) ~ V/((UA)/) ~ (V/A)/U (V = volume, U = velocity) V/A ~ d3/d2 = d1  Residence time ~ d/U Residence time / reaction time ~ Yf,∞Zgasd/U exp(–Egas/RT)] ~ Da/(exp(–Egas/RT)])Red-1; Da = Yf,∞Zgasd2/n Blowoff at high U occurs more readily for small d (small residence time / chemical time); at same Red, need Z ~ 1/d2 to maintain same extinction limit Radiation Convective transfer per unit area between walls i and j ~ UT(Ti – Tj) Radiative heat transfer ~ [e/(2-e)]s(Ti4 – Tj4) Radiation / convection Surface radiation effects more important at larger scale; as previously discussed, hurts performance in a manner similar to streamwise wall heat conduction AME 514 - Spring 2017 - Lecture 5

Scale effects revisited Simulations in 3D, 3.5 turn Swiss roll, without and with property values adjusted to obtain constant a, Da and R Without adjustments, at small Re heat loss effects result in worse performance for large combustor whereas at large Re, residence time (Da effects) results in worse performance for small combustor; with adjustments, all scales similar Property Half Full Double hL (W/m2K) 10 5 2.5 εL (external wall) 0.8 0.4 0.2 εL (insulation) 1 0.5 0.25 Z (m-sec-kmole units) 1.44 x 1011 3.6 x 1010 9.0 x 109 εi (internal wall) 0.2857 Without property adjustment With property adjustment AME 514 - Spring 2017 - Lecture 5

Linear exchanger vs. spiral Swiss roll Create pseudo-3-turn spiral exchanger from linear exchanger cut into 3 pieces, again use mixing-cup temperatures AME 514 - Spring 2017 - Lecture 5

Linear exchanger vs. spiral Swiss roll Adiabatic linear exchanger performance much better than spiral exchanger at large N (low Re) With increasing heat loss (a), linear exchanger performance deteriorates substantially compared to spiral exchanger (homework problem!) … but this is all just heat transfer assuming complete combustion, what about with finite-rate chemical reaction? Linear Simulated spiral AME 514 - Spring 2017 - Lecture 5

Linear exchanger vs. spiral Swiss roll Consistent with detailed calculations (Chen & Ronney, 2013) Adiabatic Linear better (leaner extinction limit) at low Re (large N) Same performance at high Re (small N) (Swiss roll has 2x larger AT than linear device, so 2x lower equivalence ratio at limit) Non-adiabatic Swiss roll MUCH better at low Re (need to reduce for linear device heat loss coefficients by 4x just to get plots on the same scale!) AME 514 - Spring 2017 - Lecture 5

Model results - number of turns Make practical comparison – assume same overall dimension and same wall thickness (fabrication limitation) More turns means larger N but more material, thus more thermal conduction (and heat loss) in 3rd dimension – optimum exists, but relatively flat; optimal n larger at higher Re (lower N, more “starved” for additional heat recirculation) 12-turn Swiss roll AME 514 - Spring 2017 - Lecture 5

References AME 514 - Spring 2017 - Lecture 5 Ahn, J., Eastwood, C., Sitzki, L., Ronney, P. D. (2005). “Gas-phase and catalytic combustion in heat- recirculating burners,” Proceedings of the Combustion Institute, Vol. 30, pp. 2463-2472. Chen, C.-H., Ronney, P. D. (2013), “Scale and geometry effects on heat-recirculating combustors,” Combustion Theory and Modelling, Vol. 17, pp. 888-905 (2013) Chen, C.-H., Ronney, P. D. (2011) “Three-dimensional Effects in Counterflow Heat-Recirculating Combustors,” Proceedings of the Combustion Institute, Vol. 33, pp. 3285-3291. Hautman, D. J., Dryer, F. L., Schug, K. P., Glassman, I. (1981). “A Multiple-step Overall Kinetic Mechanism for the Oxidation of Hydrocarbons,” Combustion Science and Technology Vol. 25, pp. 219-235. Kuo, C.-H., Ronney, P. D. (2007). Numerical Modeling of Heat Recirculating Combustors, Proceedings of the Combustion Institute, Vol. 31, pp. 3277 - 3284. Lloyd, S.A., Weinberg, F.J., Nature 251:47-49 (1974). Lloyd, S.A., Weinberg, F.J., Nature 257:367-370 (1975). Maruta, K., Muso, K., Takeda, K., Niioka, T., Proc. Combust. Inst. 28:2117-2123 (2000). Ronney, P. D. (2015). “Heat-Recirculating Combustors,” Chapter 8 in Microscale Combustion and Power Generation (Y. Ju, C. Cadou and K. Maruta, Eds.), Momentum Press LLC, New York. Sanford, L. L., Huang, S. Y. J., Lin, C. S., Lee, J. M., Ahn, J. M., Ronney, P. D. (2008). “Plastic mesoscale combustors/heat exchangers,” Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Nov. 11 – 15, 2007, Seattle, WA, pp. 141 – 145. Targett, M., Retallick, W., Churchill, S. (1992). “Solutions in closed form for a double-spiral heat exchanger,” Industrial and Engineering Chemical Research 31, 658-669. AME 514 - Spring 2017 - Lecture 5