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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
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

ame 514 applications of combustion

AME 514Applications of Combustion

Lecture 4: Microcombustionscience I

microscale reacting flows and power generation
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

what is microcombustion
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

the seductive lure of chemical fuels
The seductive lure of chemical fuels

AME 514 - Spring 2013 - Lecture 4

the challenge of microcombustion
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

the challenge of microcombustion1
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

smallest existing combustion engine
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

some power mems concepts
Some power MEMS concepts

Wankel rotary engine

(Berkeley)

Free-piston

engines

(U. Minn,

Georgia Tech)

AME 514 - Spring 2013 - Lecture 4

some power mems concepts1
Some power MEMS concepts

Liquid piston magnetohydrodynamic (MHD) engine (Honeywell / U. Minn)

Pulsed combustion driven turbine (UCLA)

AME 514 - Spring 2013 - Lecture 4

some power mems concepts gas turbine mit
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

some power mems concepts p 3 wash st univ
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

fuel cells
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

hydrogen storage
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

direct methanol fuel cell
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

formic acid fuel cell
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

scaling of micro power generation quenching
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

scaling gas phase vs catalytic reaction
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

scaling flame quenching revisited
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

scaling blow off limit at high u
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

scaling turbulence
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

scaling friction
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

scaling speed of sound
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

microscale power generation challenges
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

catalytic combustion
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

catalytic combustion1
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

catalytic combustion2
Catalytic combustion
  • Deutschman et al. (1996)

AME 514 - Spring 2013 - Lecture 4

catalytic combustion modeling objectives
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

model maruta et al 2002
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

results fuel air mixtures
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

results fuel air mixtures1
Results - fuel/air mixtures
  • Ratio of heat loss to heat generation ≈ 1 at low-velocity extinction limits

AME 514 - Spring 2013 - Lecture 4

results fuel air mixtures2
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

results fuel air mixtures3
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

results fuel o 2 n 2 mixtures
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

experiments
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

simplified model for propane cat comb
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

effect of wall heat conduction
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

effect of wall heat conduction1
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

conclusions catalytic combustion
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

simple model of heat recirculating combustors
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

simple model of heat recirculating combustors1
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

approach ronney 2003
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

energy balances
Energy balances

Reactant side

Dividing wall

Product side

dx

AME 514 - Spring 2013 - Lecture 4

non dimensional equations
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

nomenclature
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

temperature profiles
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

peak temperatures w
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

extinction limits
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

effect of wall thermal conduction
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

scaling for microcombustors
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

conclusions thermal conductivity effects
Conclusions - thermal conductivity effects
  • 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 514 - Spring 2013 - Lecture 4

references
References

Benard, P. et al.,“Comparison of hydrogen adsorption on nanoporous materials,” J. Alloys and Compounds, 446-447:380-284 (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. 26:1747-1754 (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, 119-124.

Jones, A.R., Lloyd, S. A., Weinberg, F. J., “Combustion in heat exchangers,”Proc. Roy. Soc. Lond. A. 360:97-115 (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. 1098 – 1116.

Karagiannidis, S., Mantzaras, J., Jackson, G., Boulouchos, K., “Hetero-/homogeneous combustion and stability maps in methane-fueled catalystic microreactors,”Proc. Combust. Inst. 31:3309-3317 (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. 957-963 (2002).

Ohadi, M.M. and Buckley, S.G., Experimental Thermal Fluid Sci. 25:207-217 (2001).

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.

AME 514 - Spring 2013 - Lecture 4

references1
References

Ronney, P. D., "Analysis of non-adiabatic heat-recirculating combustors," Combustion and Flame, Vol 135, pp. 421-439 (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 514 - Spring 2013 - Lecture 4