1. AME 514 Applications of Combustion
Lecture 4: Microcombustion science I

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, …
Flameless & 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. 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 Spring Lecture 4

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 Spring Lecture 4

5. The seductive lure of chemical fuels
AME Spring 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
> $40 billion/yr of disposable batteries ends up in landfills
> $6 billion/yr market for rechargables (increasing rapidly due to Electric vehicles)
AME Spring 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: > 25 projects, > $50M)
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 Spring Lecture 4

8. The challenge of microcombustion
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 Spring Lecture 4

9. Smallest existing combustion engine
Application: model airplanes Weight: oz. Bore: ” = 6.02 mm Stroke: ” = 5.74 mm Displacement: in3 (0.163 cm3)
RPM: ,000
Power: ≈ 5 watts
Ignition: Glow plug
Typical fuel: castor oil (20%),
nitromethane (10%), balance methanol (much
lower heating value than pure hydrocarbons,
22 MJ/kg vs. ≈ 45 MJ/kg)
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) = high enough for turbulence (barely)
Size > quenching distance at 1 atm, nowhere near quenching post-compression
Test data (for 2.45 cm3 2-stroke engine) (Menon et al., 2007): max. efficiency 8%, max. power 140 Watts at 10,000 RPM (Brake Mean Effective Pressure = 3.38 atm, vs. typically atm for automotive engines)
Cox Tee Dee .010
AME Spring Lecture 4

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

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

12. 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 Spring Lecture 4

13. Some power MEMS concepts - P3 - Wash. St. Univ.
P3 engine (Whalen et al., 2003) - heating/cooling of 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 Spring Lecture 4

14. 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 ( ˚C)
Formic acid (O=CH-OH) - low energy density but good electrochemistry
PEM fuel cell
Solid Oxide Fuel Cell
AME Spring Lecture 4

15. Hydrogen storage Hydrogen is a great fuel But how to store it???
High energy density (1.2 x 108 J/kg, ≈ 3x hydrocarbons)
Much higher  than hydrocarbons (≈ x at same T)
Excellent electrochemical properties in fuel cells
Ignites near room temperature on Pt catalyst
But how to store it???
Cryogenic liquid - 20K,  = g/cm3 (by volume, gasoline has 64% more H than LH2); also, how to insulate for long-duration storage?
Compressed gas, 200 atm:  = 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 ( - 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 Spring Lecture 4

16. 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 Spring Lecture 4

17. 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 Spring Lecture 4

18. Scaling of micro power generation - quenching
Heat losses vs. heat generation
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 Spring Lecture 4

19. 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 Spring Lecture 4

20. 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 Spring Lecture 4

21. 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/U exp(–Egas/RT)] ~ (Yf,∞Zgasd2/n)Red-1
Blowoff occurs more readily for small d (small residence time / chemical time)
AME Spring Lecture 4

22. 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) = high enough for turbulence
Cox Tee Dee: Re ≈ (2 x (0.6 cm)2 x (30000/60s)) / (0.15 cm2/s) = 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 Spring Lecture 4

23. Scaling - friction Friction 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)] ≈ 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 Spring Lecture 4

24. 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 Spring Lecture 4

25. Catalytic combustion
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 Spring 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 Spring Lecture 4

27. Catalytic combustion
Deutschman et al. (1996) – methane oxidation on platinum
AME Spring 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 ( )
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 Spring 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 Spring 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 Spring Lecture 4

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

36. Experiments
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
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!
AME Spring Lecture 4

37. 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 Spring Lecture 4

38. Effect of wall heat conduction
Karagiannidis et al., 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 Spring Lecture 4

39. 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
Gas-phase reaction has modest benefit
5 atm, 700K:
with gas-phase reaction (squares)
5 atm, 600K:
with gas-phase reaction (circles)
Without gas-phase reaction (triangles)
Without gas-phase reaction (crosses)
AME Spring Lecture 4

40. 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 Spring Lecture 4

41. 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 Spring Lecture 4

42. Energy balances Reactant side Dividing wall Product side dx
AME Spring Lecture 4

43. Non-dimensional equations
Wall conduction
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 Spring Lecture 4

44. Nomenclature AME 514 - Spring 2015 - Lecture 4 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
k Thermal 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 Spring Lecture 4

45. 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 Spring Lecture 4

46. 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 Spring Lecture 4

47. 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 Spring Lecture 4

48. 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 Spring Lecture 4

49. 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 = (d/do)-2
AME Spring Lecture 4

50. Summary – 1D analysis
Heat-recirculating combustors show both high velocity (high M or Re) “blowoff” and low-M heat loss induced extinction limits
Low-M limits are dominated by heat conduction along the walls that is not a loss process by itself but re-distributes thermal energy within the exchanger
Microscale heat-recirculating combustors require large B (thin walls, low conductivity)
Very different from linear reactors - streamwise heat conduction aids heat recirculation (no spanwise heat conduction)
Current results can be used to predict scale-down of macroscale test devices to microscale target applications (with some limitations…)
AME Spring Lecture 4

51. References AME 514 - Spring 2015 - Lecture 4
Benard, P. et al., “Comparison of hydrogen adsorption on nanoporous materials,” J. Alloys and Compounds, : (2007)
Deshmukh, S.R., Vlachos, D.G. (2007). A reduced mechanism for methane and one-step rate expressions for fuel-lean catalytic combustion of small alkanes on noble metals. Combustion Flame 149, 366–383.
Deutschmann, O., Schmidt, R., Behrendt, F., Warnatz, J., Proc. Comb. Inst. 26: (1996).
Glassman, I., Combustion (3rd Ed.), Academic Press, 1996.
Ha, S., Adams, B., Masel, R. I. (2004). “A miniature air breathing direct formic acid fuel cell,” J. Power Sources, 128,
Jones, A.R., Lloyd, S. A., Weinberg, F. J., “Combustion in heat exchangers,” Proc. Roy. Soc. Lond. A. 360: (1978).
Kaisare, N. S. Deshmukh, S. R.Vlachos, D. G. (2008). “Stability and performance of catalytic microreactors: Simulations of propane catalytic combustion on Pt.” Chemical Engineering Science 63, pp – 1116.
Karagiannidis, S., Mantzaras, J., Jackson, G., Boulouchos, K., “Hetero-/homogeneous combustion and stability maps in methane-fueled catalystic microreactors,” Proc. Combust. Inst. 31: (2007)
Maruta, K., Takeda, K., Ahn, J., Borer, K., Sitzki, L, Ronney, P. D., Deutchman, O., "Extinction Limits of Catalytic Combustion in Microchannels," Proceedings of the Combustion Institute, Vol. 29, pp (2002).
Menon, S., Moulton, N., Cadou, C., “Development of a Dynamometer for Measuring Small Internal-Combustion Engine Performance,” J. Propulsion Power 23: (2007).
Ohadi, M.M. and Buckley, S.G., Experimental Thermal Fluid Sci. 25: (2001).
AME Spring Lecture 4

52. References AME 514 - Spring 2015 - Lecture 4
Papac, J., Figueroa, I., Dunn-Rankin, D., “Performance Assessment of a Centimeter-Scale Four-Stroke Engine,” Paper 03F-91, Fall Technical Meeting, Western States Section, Combustion Institute, October 2003, UCLA.
Ronney, P. D., "Analysis of non-adiabatic heat-recirculating combustors," Combustion and Flame, Vol 135, pp (2003).
Shah, R.K., London, A.L., Laminar Flow: Forced Convection in Ducts, Academic Press, 1978.
Whalen, S., Thompson, M., Bahr, D., Richards, C., Richards, R. (2003). “Design, fabrication and testing of the P3 micro heat engine”, Sensors and Actuators A 104, 290–298.
Zhu, Y. , Ha, S., Masel, R. I. (2004). “High power density direct formic acid fuel cells ,” J. Power Sources, 130, 8-14.
AME Spring Lecture 4