# Mass Fraction Burned

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Burn rate analysis is commonly used with spark ignition engines to determine the mass fraction burned. Rassweiler and Withrow1 developed a technique in 1938 that is still considered today to be both accurate and computationally efficient.

During combustion, the pressure rise, Δp, during a crank interval, Δθ, is considered to consist of pressure rise due to combustion, Δpc, and pressure change due to change in volume, Δpv.

Deltap=Deltap_c+Deltap_v (Equation 1)

As the crank angle increments from θi to θi+1 the volume changes from Vi to Vi+1 and the pressure from pi to pi+1. Assuming that the change in pressure due to volume change can be calculated from a polytropic process of constant k:

p_(i+1) - p_i = Deltap_c+p_i[(V_i/V_(i+1))^k-1] (Equation 2)

Deltap_c=p_(i+1)-p_i(V_i/V_(i+1))^k (Equation 3)

Because the combustion process does not occur at constant volume, the pressure rise rate due to combustion is not directly proportional to the mass of fuel burned. Therefore the pressure rise due to combustion must be referenced to a datum volume, such as that at TDC, Vtdc.

Deltap_c^(**)=Deltap_cV_i/V_(tdc) (Equation 4)

By identifying the end of combustion and the number of crank angle intervals between start and finish of combustion, N, the mass fraction burned can be calculated:

mfb=(sum_0^iDeltap_c^(**))/(sum_0^N Deltap_c^(**)) (Equation 5)

For the purpose of cycle-to-cycle analysis, the crank angle at which burn rate percentages of 1%, 2%, 5%, 10%, 20%, 25%, 50%, 75%, 80%, 90%, 95%, 98% and 99% mass fraction burned are determined. Additionally, the ignition delay and combustion duration are determined from mass fraction burned curves. The ignition delay is the crank angle between start of combustion and typically 1,2 or 5% mfb. Combustion duration is calculated as the crank angle between the end of the ignition delay and typically 90, 95 or 99% mfb. Determining small or large percentages such as 1 or 99% can be difficult due to the susceptibility of the calculation to the effects of noise with small pressure changes.

This method of calculating mass fraction burned was chosen because of its proven reliability and its widespread use. Also, research has shown that more complex models provide little additional accuracy.

#### catool

The following calculations are made available in catool:

• MFB - Crank angle based Mass Fraction Burned curve
• MFB01_ - Crank angle of 1% Mass Fraction Burned
• MFB02_ - Crank angle of 2% Mass Fraction Burned
• MFB05_ - Crank angle of 5% Mass Fraction Burned
• MFB10_ - Crank angle of 10% Mass Fraction Burned
• MFB20_ - Crank angle of 20% Mass Fraction Burned
• MFB25_ - Crank angle of 25% Mass Fraction Burned
• MFB50_ - Crank angle of 50% Mass Fraction Burned
• MFB75_ - Crank angle of 75% Mass Fraction Burned
• MFB80_ - Crank angle of 80% Mass Fraction Burned
• MFB90_ - Crank angle of 90% Mass Fraction Burned
• MFB95_ - Crank angle of 95% Mass Fraction Burned
• MFB98_ - Crank angle of 98% Mass Fraction Burned
• MFB99_ - Crank angle of 99% Mass Fraction Burned
• B0002_ - Crank angle between Start of Combustion and 2% Mass Fraction Burned
• B0005_ - Crank angle between Start of Combustion and 5% Mass Fraction Burned
• B0010_ - Crank angle between Start of Combustion and 10% Mass Fraction Burned
• B0090_ - Crank angle between Start of Combustion and 90% Mass Fraction Burned
• B0290_ - Crank angle between 2% and 90% Mass Fraction Burned
• B0590_ - Crank angle between 5% and 90% Mass Fraction Burned
• B1090_ - Crank angle between 10% and 90% Mass Fraction Burned
• MXBRN - Maximum Burn Rate
• AMXBRN - Crank angle of Maximum Burn Rate
catool Implementation: See Return_MFB_Data() and Return_Burn_Angles() in analysis.c

#### References

1. Rassweiler, G. M., Withrow, L., "Motion Pictures of Engine Flames Correlated with Pressure Cards," SAE Proceedings May 1938, 1938.