Notes5 Simple Reactors

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Simple Reactors

Coupled Thermodynamic and Chemical Systems


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Four Simple Reactor Models


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SUMMARY OF USEFUL RELATIONS

i

i

i

ii

mix

i

iimix

i i

imix

iiii

j

j

ii

mix

iii

j

jj

iii

i

i

i

imixi

i

mixii

X

MWX

MW

MWMW

MW

YMW

MWXY

X

X

MWRT

PX

MWX

MWX

Y

MW

Y

RTMW

YPMWX

MWMWY

1

Mole / mass fraction relation

Mass fraction / molar concentration

Mole fraction / molar concentration

Mass concentration

MWmix defined in terms of mass fractions

MWmix defined in terms of mole fractions

MWmix defined in terms of molar concentrations

i: mole fractionYi: mass fraction

[Xi]: molar concentration


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1. CONSTANT PRESSURE, FIXED MASS REACTOR

dt

dT

TX

X

dt

Xd

MWX

mV

cX

hV

Q

dt

dT

Vdt

dN

XVN

dt

dTcdt

dT

T

h

dt

hd

dt

hdN

dt

dNh

mdt

dh

dt

dh

mQ

ii

i

i

iii

i

ii

i

pi

i

ii

ii

ii

ipii

i i

iii

i

1

1

,

1st

Law

Differentiation of enthalpy

Note that enthalpys are on per mole basis

Calorically perfect gas

short hand notation for net production rate for

complete mechanism

Substitution into 1st Law

Volume expression

Expression for rate of change of molar concentrations

i


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2. CONSTANT VOLUME, FIXED MASS REACTOR

i

i

i

i

ipi

i

ii

i

i

i

vi

i

ii

dt

dTXRRT

dt

dP

RcX

hRTV

Q

dt

dT

cX

uV

Q

dt

dT

dtdumQ

i

i

1st

Law

Substitution into 1st

Law

In terms of molar enthalpys (instead of

internal energy)

Expression for time rate of change of pressure

Very useful for explosion calculations


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Constant Volume Combustion: Engine Knock

Compressed gasoline-air mixtures have atendency to ignite prematurely rather thanburning smoothly Engine Knock

Octane number of gasoline - resistance toknock

Octane number is determined bycomparing the characteristics of agasoline to isooctane (2,2,4-

trimethylpentane) and heptane. Isooctane is assigned an octane

number of 100. It is a highlybranched compound that burnssmoothly, with little knock.

Heptane is given an octane rating ofzero. It is an unbranched compoundand knocks badly.


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EXAMPLE: ENGINE KNOCK

In spark ignition engines, knock occurs when unburned fuel-air mixture ahead of flame reacts

homogeneously, i.e., it autoignites

Rate of pressure rise is a key parameter in determining knock intensity and propensity for mechanical

damage to piston-crank engine assembly

Pressure vs. time traces for normal and knocking combustion in a spark-ignition engine shown below

Note very rapid pressure rise in case of heavy knock.

Piston exposed to long

terms effects of knockhttp://www-cms.llnl.gov/s-t/int_combustion_eng.html


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EXAMPLE: ENGINE KNOCK Create a simple constant volume model of autoignition process and determine temperature, pressure and fuel

and product concentrations as a function of time

Assume that initial conditions corresponding to compression of a fuel-air mixture from 300 K and 1 atm toTDC for a compression ratio of 10:1. Initial volume before compression is 3.68x10-4 m3 which corresponds to

an engine with both bore and a stroke of 75 mm. Use ethane, C2H6, as fuel.

Other assumptions:

1. One-step global kinetics using rate parameters for ethane

2. Fuel, air and products all have equal molecular weights, MW=293. Specific heats for the fuel, air, and products are constant and equal, cp=1,200 J/kg K

4. Enthalpy of formation of air and products is zero and enthalpy of formation of fuel is 4x107 J/kg

5. Stoichiometric air-fuel ratio is 16, and combustion is restricted to stoichiometric or lean cases

nmyxayx

k

yx

OHCRT

EA

dt

HCd

OHy

xCOOy

xHCglobal

2

222

exp

24


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SOLUTION: MATLAB SIMULATION, CONSTANT VOLUME

Fuel

OxidizerProducts


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SOLUTION: EXPANDED SCALE ON TOP PLOT

Fuel

Oxidizer

Products

Large temperature increase in ~0.1 ms


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EXAMPLE RESULTS AND COMMENTS

Equations are integrated numerically using Excel

Temperature increases only about 200 K in first 3 ms, then T rises extremelyrapidly to adiabatic flame temperature, Tad ~ 3300 K, in less than 0.1 ms

This rapid temperature rise and rapid consumption of fuel is characteristic of athermal explosion, where the energy released and temperature rise from reactionfeeds back to produce ever-increasing reaction rates because of the (-Ea/RT)temperature dependence of the reaction rate.

It can also be shown that huge pressure derivatives are associated with exploding

stage of reaction, with peak values of dP/dt ~ 1.9x1013

Pa/s !!!

Although this model predicted explosive combustion of mixture after an initialperiod of slow combustion, as is observed in real knocking combustion, single-stepkinetics mechanism does not model true behavior of autoigniting mixtures

In reality, induction period, or ignition delay, is controlled by formation ofintermediate species (radicals)

To accurately model knock, a more detailed mechanism would be required


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EXAMPLE 1: WSR MODELING

Develop a WSR model using same simplified chemistry and thermodynamic used in previous example

Equal constant cps, MWs, one-step global kinetics for C2H6 Use model to develop blowout characteristics of a spherical reactor with premixed reactants (C2H6 and

Air) entering at 298 K. Diameter of reactor is 80 mm.

Plot at blowout as a function of mass flow rate for 1.0 and assume that reactor is adiabatic

0

01

023.0

023.0

,,

Pr

65.11.0

75.1

,

65.11.0

75.1

,

inPinFFFf

OxF

OxFGOxinOx

OxFGFinF

TTcYYh

YYY

YYRT

PMWVkFAYYm

YYRT

PMWVkYYm

Set of 4 coupled nonlinear algebraic equations with unknowns, YF, YOx, YPr, and T

Treat mass flow rate and volume as known parameters

To determine reactor blowout characteristic, solve nonlinear algebraic equations on previous slide for a

sufficiently small value of mass flow rate that allows combustion at given equivalence ratio Increase mass flow rate until failure to achieve a solution or until solution yields input values


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EXAMPLE 1: RESULTS AND COMMENTS

Decreasing conversion of fuel to products as mass flow rate is increased to blowout condition

Decreased temperature as flow rate is increased to blowout condition

Mass flow rate for blowout is about 0.193 kg/s

Ratio of blowout temperature to adiabatic flame temperature is 1738 / 2381 = 0.73

Repeat calculations at various equivalence ratios generates the blowout characteristic curve

Reactor is more easily blown out as the fuel-air mixture becomes leaner Shape of blowout curve is similar to experimental for gas turbine engine combustors


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GAS TURBINE COMBUSTOR CHALLENGES

Based on material limits of turbine (Tt4), combustors must operate belowstoichiometric values

For most relevant hydrocarbon fuels, s ~ 0.06 (based on mass)

Comparison of actual fuel-to-air and stoichiometric ratio is called equivalence ratio Equivalence ratio = = stoich For most modern aircraft ~ 0.3-0.4

Summary

If = 1: Stoichiometric

If > 1: Fuel Rich

If < 1: Fuel Lean


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SOLUTION: BURNING REGIONS

Air

C

ompressor

Turbine

~ 1.0T>2000 K

~0.3

Primary

Zone


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COMBUSTOR ZONES: MORE DETAILS

1. Primary Zone Anchors Flame

Provides sufficient time, mixing, temperature for complete oxidation of fuel

Equivalence ratio near=1

2. Intermediate (Secondary Zone)

Low altitude operation (higher pressures in combustor)

Recover dissociation losses (primarily CO CO2) and Soot Oxidation

Complete burning of anything left over from primary due to poor mixing

High altitude operation (lower pressures in combustor)

Low pressure implies slower rate of reaction in primary zone

Serves basically as an extension of primary zone (increased res)

L/D ~ 0.7

3. Dilution Zone (critical to durability of turbine)

Mix in air to lower temperature to acceptable value for turbine

Tailor temperature profile (low at root and tip, high in middle)

Uses about 20-40% of total ingested core mass flow

L/D ~ 1.5-1.8


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Assumptions

Input


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Important


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EXCELFile


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Notes5 Simple Reactors

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