1. AME 514 Applications of Combustion
Lecture 5: Microcombustion science II

2. 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 Spring Lecture 4

3. 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 Spring Lecture 5

4. “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 Spring Lecture 5

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 Spring Lecture 5

6. Swiss roll experiments
3.5 mm channel width, 0.5 mm wall thickness
Top & bottom sealed with ceramic blanket insulation
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7. Swiss roll experiments – extinction limits
Ahn et al., 2005
Propane-air
3.5-turn Swiss roll
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8. 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)
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9. Swiss roll experiments – limit temperatures
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10. 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 Spring Lecture 5

11. 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 Spring Lecture 5

12. 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
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13. Exhaust gas composition
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14. 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
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15. 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 = 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 Spring Lecture 5

16. 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 Spring Lecture 5

17. 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 Spring Lecture 5

18. 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 Spring Lecture 5

19. Swiss roll - numerical modeling
“Virtual thermocouple” locations
inlet
outlet 7 6 5 4 3 2 d 1
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20. 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 Spring Lecture 5

21. Model results - comparison to experiment
Temperatures too high to conduct experiments above this Re!
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22. 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 Spring Lecture 5

23. 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.
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24. Model results – temperatures at extinction
Tmax
Tad
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25. 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 Spring Lecture 5

26. Model results - extinction limits
Temperatures too high to conduct experiments above this Re!
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27. 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 Spring Lecture 5

28. 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 Spring Lecture 5

29. 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
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30. Model results – wall conductivity
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31. 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
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32. Model results - 3D effects
Turbulence model suppressed
With turbulence model
Vorticity (1/s)
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33. 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 Spring Lecture 5

34. 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 Spring Lecture 5

35. 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 Spring Lecture 5

36. 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 Spring Lecture 5

37. 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 Spring Lecture 5

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

40. 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 Spring Lecture 5

41. 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
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42. 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
Chen, C.-H., Ronney, P. D. (2013), “Scale and geometry effects on heat-recirculating combustors,” Combustion Theory and Modelling, Vol. 17, pp (2013)
Chen, C.-H., Ronney, P. D. (2011) “Three-dimensional Effects in Counterflow Heat-Recirculating Combustors,” Proceedings of the Combustion Institute, Vol. 33, pp
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
Kuo, C.-H., Ronney, P. D. (2007). Numerical Modeling of Heat Recirculating Combustors, Proceedings of the Combustion Institute, Vol. 31, pp
Lloyd, S.A., Weinberg, F.J., Nature 251:47-49 (1974).
Lloyd, S.A., Weinberg, F.J., Nature 257: (1975).
Maruta, K., Muso, K., Takeda, K., Niioka, T., Proc. Combust. Inst. 28: (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,
AME Spring Lecture 5