Lambda Presentation

Lambda Calculation from Exhaust Gas MeasurementsDetermining how close the A/F ratio is to the stoichiometric point using exhaust gas analysis.Presented to East Bay ATA, Hayward, CAMay 5, 2004By: Robert J. Schrader President, Bridge Analyzers, Inc.

What is Lambda? Lambda is Oxygen Balance

Why is Lambda Important?Lambda control is necessary for peak combustion efficiency in the Engine.Lambda control is necessary for peak CAT efficiency.Lambda Control Improves Reliability, Fuel Economy and Lowers Emissions.

Combustion Efficiency (CE)Engine out CE for Gasoline Fuel is no better than 95%.Tailpipe-out CE for CAT equipped vehicles improves to 99.0-99.5%.Factor of 10 improvementRequired for Current Emission StandardsCAT CE is very Lambda-Dependent

Engine-Out Gas Values

CO2

3.27883073561.092943578511.72116926440

2.96711334540.989037781812.03288665460

2.5968214520.865607150712.4031785480

2.18685712280.728952374312.81314287720

1.75746122060.585820406913.24253877940

1.33025032380.443416774613.66974967620

0.92825404560.309418015214.07174595440

0.57595275220.191984250714.42404724780

0.29931568030.099771893414.70068431970

0.12583945390.041946484614.87416054610

0.0845870.0281956667150

0014.85148514850.209

0014.70588235290.418

0014.56310679610.627

0014.42307692310.836

0014.28571428571.045

0014.15094339621.254

0014.01869158881.463

0013.88888888891.672

0013.76146788991.881

0013.63636363642.09

CO2 - Carbon Dioxide

Lambda

% Concentration

CO_H2_O2

3.27883073561.092943578511.72116926440

2.96711334540.989037781812.03288665460

2.5968214520.865607150712.4031785480

2.18685712280.728952374312.81314287720

1.75746122060.585820406913.24253877940

1.33025032380.443416774613.66974967620

0.92825404560.309418015214.07174595440

0.57595275220.191984250714.42404724780

0.29931568030.099771893414.70068431970

0.12583945390.041946484614.87416054610

0.0845870.0281956667150

0014.85148514850.209

0014.70588235290.418

0014.56310679610.627

0014.42307692310.836

0014.28571428571.045

0014.15094339621.254

0014.01869158881.463

0013.88888888891.672

0013.76146788991.881

0013.63636363642.09

CO - Carbon Monoxide

H2 - Hydrogen

O2 - Oxygen

Lambda

% Concentration

Engine-Out Gases

LambdaCOH2CO2O2

0.9003.281.0911.70.00a-353.0

0.9102.970.9912.00.00b1258.8

0.9202.600.8712.40.00c-1460.1

0.9302.190.7312.80.00d554.4

0.9401.760.5913.20.00

0.9501.330.4413.70.00

0.9600.930.3114.10.00

0.9700.580.1914.40.00

0.9800.300.1014.70.00

0.9900.130.0414.90.00

1.0000.080.0315.00.00

1.0100.000.0014.90.21

1.0200.000.0014.70.42

1.0300.000.0014.60.63

1.0400.000.0014.40.84

1.0500.000.0014.31.05

1.0600.000.0014.21.25

1.0700.000.0014.01.46

1.0800.000.0013.91.67

1.0900.000.0013.81.88

1.1000.000.0013.62.09

CO2

3.27883073561.092943578511.72116926440

2.96711334540.989037781812.03288665460

2.5968214520.865607150712.4031785480

2.18685712280.728952374312.81314287720

1.75746122060.585820406913.24253877940

1.33025032380.443416774613.66974967620

0.92825404560.309418015214.07174595440

0.57595275220.191984250714.42404724780

0.29931568030.099771893414.70068431970

0.12583945390.041946484614.87416054610

0.0845870.0281956667150

0014.85148514850.209

0014.70588235290.418

0014.56310679610.627

0014.42307692310.836

0014.28571428571.045

0014.15094339621.254

0014.01869158881.463

0013.88888888891.672

0013.76146788991.881

0013.63636363642.09

CO2 - Carbon Dioxide

Lambda

% Concentration

CO_H2_O2

3.27883073561.092943578511.72116926440

2.96711334540.989037781812.03288665460

2.5968214520.865607150712.4031785480

2.18685712280.728952374312.81314287720

1.75746122060.585820406913.24253877940

1.33025032380.443416774613.66974967620

0.92825404560.309418015214.07174595440

0.57595275220.191984250714.42404724780

0.29931568030.099771893414.70068431970

0.12583945390.041946484614.87416054610

0.0845870.0281956667150

0014.85148514850.209

0014.70588235290.418

0014.56310679610.627

0014.42307692310.836

0014.28571428571.045

0014.15094339621.254

0014.01869158881.463

0013.88888888891.672

0013.76146788991.881

0013.63636363642.09


H2 - Hydrogen

O2 - Oxygen

Lambda

% Concentration

Engine-Out Gases

LambdaCOH2CO2O2

0.9003.281.0911.70.00a-353.0

0.9102.970.9912.00.00b1258.8

0.9202.600.8712.40.00c-1460.1

0.9302.190.7312.80.00d554.4

0.9401.760.5913.20.00

0.9501.330.4413.70.00

0.9600.930.3114.10.00

0.9700.580.1914.40.00

0.9800.300.1014.70.00

0.9900.130.0414.90.00

1.0000.080.0315.00.00

1.0100.000.0014.90.21

1.0200.000.0014.70.42

1.0300.000.0014.60.63

1.0400.000.0014.40.84

1.0500.000.0014.31.05

1.0600.000.0014.21.25

1.0700.000.0014.01.46

1.0800.000.0013.91.67

1.0900.000.0013.81.88

1.1000.000.0013.62.09

CAT Oxidation and Reduction Efficiency vs Lambda

CO_H2_O2

1.06420025910.1330250324640

0.69619053420.0870238168720

0.4089264540.0511158068800

0.19455519220.024319399960

0.06921169970.00865146251120

0.010.001251600

002400.209

003600.418

004800.627

006000.836

007201.045

&A

Page &P

H2 - Hydrogen

NOx - Oxides of Nitrogen


CAT Efficiency

0.920.2

0.910.25

0.90.29

0.880.35

0.860.45

0.80.75

0.70.8

0.550.82

0.40.84

0.250.86

0.10.88

Oxidation Efficiency

Reduction Efficiency

Nox Red. Eff

CO Oxy Eff

Engine-Out Gases

LambdaCOH2NOxCO2O2Nox Red. EffNox Red. IneffNOxCO Oxy EffCO Oxy Ineff

0.9501.060.136413.90.0092%8%80020%80%a-353.0

0.9600.700.097214.30.0091%9%80025%75%b1258.8

0.9700.410.058014.60.0090%10%80029%71%c-1460.1

0.9800.190.029614.80.0088%12%80035%65%d554.4

0.9900.070.0111214.90.0086%14%80045%55%

1.0000.010.0016015.00.0080%20%80075%25%

1.0100.000.0024015.00.2170%30%80080%20%

1.0200.000.0036015.00.4255%45%80082%18%

1.0300.000.0048015.00.6340%60%80084%16%

1.0400.000.0060015.00.8425%75%80086%14%

1.0500.000.0072015.01.0510%90%80088%12%

CAT Out Gases

CO_H2_O2

0.46558761330.0581984517640

0.27847621370.0348095267720

0.1439881880.0179985235800

0.06285629290.0078570366960

0.02516789080.00314598631120

0.010.001251600

002400.209

003600.418

004800.627

006000.836

007201.045

&A

Page &P

H2 - Hydrogen

NOx - Oxides of Nitrogen


Engine-Out Gases

LambdaCOH2NOxCO2O2Nox Red. EffNox Red. IneffCO Oxy EffCO Oxy Ineff

0.9500.470.066414.50.0092%8%80065%35%a-353.0

0.9600.280.037214.70.0091%9%80070%30%b1258.8

0.9700.140.028014.90.0090%10%80075%25%c-1460.1

0.9800.060.019614.90.0088%12%80079%21%d554.4

0.9900.030.0011215.00.0086%14%80080%20%

1.0000.010.0016015.00.0080%20%80080%20%

1.0100.000.0024015.00.2170%30%80081%19%

1.0200.000.0036015.00.4255%45%80082%18%

1.0300.000.0048015.00.6340%60%80083%17%

1.0400.000.0060015.00.8425%75%80084%16%

1.0500.000.0072015.01.0510%90%80085%15%

3-Way CAT vs LambdaNOx Reduction BedRequires Lambda to be not greater than 1.020.CO/HC Oxidation BedRequires Lambda to be not less than 0.980.Modulation DepthCycles Rich and Lean Between the Limits Above.

Brettschneider Equation- a balance equation that calculates Lambda

Calculating A/F Ratio from LambdaLambda = 1.000 when the Oxygen available and Combustible Oxygen demands are in balance.This is the point of perfect stoichometric balance.At this point the A/F ratio is 14.71 to 1.00 for Gasoline.Thus, A/F = 14.71 x Lambda

Sensitivity to Combustion Efficiency (Pre CAT vs Post CAT)Brettschneider Lambda uses all the oxygen-bearing and combustible-bearing gases.Balance Equation - Calculation not affected by the degree of oxidation.Method is insensitive to combustion efficiency.Either Pre-CAT or Post-CAT gases may be used.

Lambda for Emissions Control = 1.000 when Oxygen available and Combustible demands are in balance.ECM controls =1.000 at 0.5-1.0 Cycles/Sec using lambda sensor input.3-Way CAT operation requires 0.980 to 1.020 Lambda can be confirmed by exhaust gas measurement, either pre or post CAT.

Lambda for Fuel Control Diagnostics calculated from exhaust gas indicates air-fuel mixture independent of the engine controls. calculated from exhaust gas indicates air-fuel mixture independent of combustion efficiency.Cold (Open Loop) vs Hot (Closed Loop) vs CAT light-off operation can be evaluated. can be used to tune systems which do not have closed-loop control.

Qualifying EGA gas tightness prior to Lambda CalculationHigh Combustion Efficiency: Measure O2 post CAT - every 5% air leak adds 1.0% O2 to gases. Low Combustion Efficiency: Add CO and CO2 - should equal 15% for Gasoline.Compare both Methods. If O2 indicates air dilution - then confirm this with low CO and CO2 sum. They should agree.

iATN Lambda CalculatorCreated by iATN Tech Support staff, and available to iATN members on-line at http://members.iatn.net/tech/lambda.htmlPlug and Play either 4 or 5 gas values.Can select either US or European gasoline constants.Operates in Java - can be saved and run off-line by any Java-equipped net browser.

Bridge Excel WorksheetAvailable as email attached Excel file by contacting: [email protected] and Play either 4 or 5 gas values.Can select either US or European gasoline constants.Operates on any PC with Excel - can be saved and run off-line using Microsoft Excel.

iPaq Palm Computer WorksheetWritten by Miles Wada using the Brettschneider equation - ala Bridge.Available for download at: http://www.aeswave.com/Operates on the iPaq using CE Excel.Can operate on other CE-based units.

Palm Computer Worksheet in Excel.Written by Greg Meyer using the Brettschneider equation - ala Bridge.Available from Greg via email at: [email protected] on Palm OS computers in Excel.

A/F Ratio From LambdaA/F = 14.71 x Lambda

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Lambda Presentation