Lambda Calculation from Exhaust Gas Measurements

Determining how close the A/F ratio is to the stoichiometric point using

exhaust gas analysis.

Presented to East Bay ATA, Hayward, CA

May 5, 2004

By: Robert J. Schrader President, Bridge Analyzers, Inc.

What is Lambda?

point. ricstoichometperfect the- balancein are

O2for Demand eCombustibl and O2 when 1.000 toequal is Lamdba

oxidation. completeattain toO2for Demand eCombustibl

the vsProcess Combustion the toavailable O2 of ratio theis Lambda

)( OxygenfordemandesCombustibl

availableOxygenLambda

• 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 improvement– Required for Current Emission Standards– CAT CE is very Lambda-Dependent

Engine-Out Gas Values

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10

Lambda

% C

on

cen

trati

on

CO - Carbon Monoxide

H2 - Hydrogen

O2 - Oxygen

11.00

11.50

12.00

12.50

13.00

13.50

14.00

14.50

15.00

15.50

16.00

0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10

Lambda

% C

on

cen

trati

on

CO2 - Carbon Dioxide

CAT Oxidation and Reduction Efficiency vs Lambda

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.950 0.960 0.970 0.980 0.990 1.000 1.010 1.020 1.030 1.040 1.050

Oxidation Efficiency

Reduction Efficiency

CAT Out Gases

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.950 0.960 0.970 0.980 0.990 1.000 1.010 1.020 1.030 1.040 1.050

0

100

200

300

400

500

600

700

800

900

1000

H2 - Hydrogen

NOx - Oxides of Nitrogen

CO - Carbon Monoxide

3-Way CAT vs Lambda

• NOx Reduction Bed– Requires Lambda to be not greater than 1.020.

• CO/HC Oxidation Bed– Requires Lambda to be not less than 0.980.

• Modulation Depth– Cycles Rich and Lean Between the Limits

Above.

Brettschneider Equation- a balance equation that

calculates Lambda

point. ricstoichometperfect the-

balancein are demand eCombustibl and O2 when 1.000 toequal is Lambda

oxidation. completeattain toO2for demand ecombustibl

the toO2) (as availableOxygen of ratio theas calculated is Lambda

)(OxygenfordemandeCombustibl

availableOxygenLambda

Calculating A/F Ratio from Lambda

• Lambda = 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 Calculation

• High 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 Calculator

• Created by iATN Tech Support staff, and available to iATN members on-line at http://members.iatn.net/tech/lambda.html

• Plug 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 Worksheet

• Available as email attached Excel file by contacting: support@bridgeanalyzers.com

• Plug 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 Worksheet

• Written by Miles Wada using the Brettschneider equation - a’la 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 - a’la Bridge.

• Available from Greg via email at: gsmeyer@attbi.com

• Operates on Palm OS computers in Excel.

A/F Ratio From Lambda

A/F = 14.71 x Lambda