Air–fuel ratio

Air–fuel ratio (AFR) is the mass ratio of air to fuel present in an internal combustion engine. If exactly enough air is provided to completely burn all of the fuel, the ratio is known as the stoichiometric mixture, often abbreviated to stoich. AFR is an important measure for anti-pollution and performance-tuning reasons. The lower the excess air, the "richer" the flame.

Synopsis

In theory a stoichiometric mixture has just enough air to completely burn the available fuel. In practice this is never quite achieved, due primarily to the very short time available in an internal combustion engine for each combustion cycle. Most of the combustion process completes in approximately 4–5 milliseconds at an engine speed of 6000 rpm. This is the time that elapses from when the spark is fired until the burning of the fuel air mix is essentially complete after some 80 degrees of crankshaft rotation.

Catalytic converters are designed to work best when the exhaust gases passing through them are the result of nearly perfect combustion.

A stoichiometric mixture unfortunately burns very hot and can damage engine components if the engine is placed under high load at this fuel–air mixture. Due to the high temperatures at this mixture, detonation of the fuel air mix shortly after maximum cylinder pressure is possible under high load (referred to as knocking or pinging). Detonation can cause serious engine damage as the uncontrolled burning of the fuel air mix can create very high pressures in the cylinder. As a consequence stoichiometric mixtures are only used under light load conditions. For acceleration and high load conditions, a richer mixture (lower air-fuel ratio) is used to produce cooler combustion products and thereby prevent detonation and overheating of the cylinder head. (The Bourke engine does not encounter this problem because of its design.)

Engine management systems

A stoichiometric mixture is the working point that modern engine management systems employing fuel injection attempt to achieve in light load cruise situations. For gasoline fuel, the stoichiometric air–fuel mixture is approximately 14.7; i.e. for every one gram of fuel, 14.7 grams of air are required (the fuel oxydation reaction is: 25/2 O₂ + C₈H₁₈ -> 8 CO₂ + 9 H₂O). Any mixture less than 14.7 to 1 is considered to be a rich mixture; any more than 14.7 to 1 is a lean mixture – given perfect (ideal) "test" fuel (gasoline consisting of solely n-heptane and iso-octane). In reality, most fuels consist of a combination of heptane, octane, a handful of other alkanes, plus additives including detergents, and possibly oxygenators such as MTBE (methyl tert-butyl ether) or ethanol/methanol. These compounds all alter the stoichiometric ratio, with most of the additives pushing the ratio downward (oxygenators bring extra oxygen to the combustion event in liquid form that is released at time of combustions; for MTBE-laden fuel, a stoichiometric ratio can be as low as 14.1:1). Vehicles using an oxygen sensor(s) or other feedback-loop to control fuel to air ratios (usually by controlling fuel volume) will usually compensate automatically for this change in the fuel's stoichiometric rate by measuring the exhaust gas composition, while vehicles without such controls (such as most motorcycles until recently, and cars predating the mid-1980s) may have difficulties running certain boutique blends of fuels (esp. winter fuels used in some areas) and may need to be rejetted (or otherwise have the fueling ratios altered) to compensate for special boutique fuel mixes. Vehicles using oxygen sensors enable the air-fuel ratio to be monitored by means of an air–fuel ratio meter.

Other types of engine

In the typical air to natural gas combustion burner, a double cross limit strategy is employed to ensure ratio control. (This method was used in World War 2). The strategy involves adding the opposite flow feedback into the limiting control of the respective gas (air or fuel).This assures ratio control within an acceptable margin.

Other terms used

There are other terms commonly used when discussing the mixture of air and fuel in internal combustion engines.

Mixture

Mixture is the predominant word that appears in training texts, operation manuals and maintenance manuals in the aviation world.

Air–fuel ratio (AFR)

The air–fuel ratio is the most common reference term used for mixtures in internal combustion engines.

$AFR={\frac {m_{air}}{m_{fuel}}}$

It is the ratio between the mass of air and the mass of fuel in the fuel–air mix at any given moment. The mass used is the mass of all constituents that compose the fuel and air whether the constituents are combustible or not. For example, if calculating the mass of natural gas which often contains carbon dioxide ($CO_{2}$) and nitrogen ($N_{2}$) as well as various alkanes, the mass of the carbon dioxide and nitrogen are included in addition to all alkanes to determine the value of $m_{fuel}$.

For pure octane the stoichiometric mixture is approximately 14.7:1, or λ of 1.00 exactly.

In naturally aspirated engines powered by octane, maximum power is frequently reached at AFRs ranging from 12.5 to 13.3:1 or λ of 0.850 to 0.901.

Fuel–air ratio (FAR)

Fuel–air ratio is commonly used in the gas turbine industry as well as in government studies of internal combustion engine, and refers to the ratio of fuel to the air.

$FAR={\frac {1}{AFR}}$

Lambda

Lambda (λ) is the ratio of actual AFR to stoichiometry for a given mixture. Lambda of 1.0 is at stoichiometry, rich mixtures are less than 1.0, and lean mixtures are greater than 1.0.

There is a direct relationship between lambda and AFR. To calculate AFR from a given lambda, multiply the measured lambda by the stoichiometric AFR for that fuel. Alternatively, to recover lambda from an AFR, divide AFR by the stoichiometric AFR for that fuel. This last equation is often used as the definition of lambda:

$\lambda ={\frac {AFR}{AFR_{stoich}}}$

Because the composition of common fuels varies seasonally, and because many modern vehicles can handle different fuels, when tuning, it makes more sense to talk about lambda values rather than AFR.

Most practical AFR devices actually measure the amount of residual oxygen (for lean mixes) or unburnt hydrocarbons (for rich mixtures) in the exhaust gas as know in PPCHS.

Equivalence ratio

The equivalence ratio of a system is defined as the ratio of the fuel-to-oxidizer ratio to the stoichiometric fuel-to-oxidizer ratio. Mathematically,

$\phi ={\frac {\mbox{fuel-to-oxidizer ratio}}{({\mbox{fuel-to-oxidizer ratio}})_{st}}}={\frac {m_{fuel}/m_{ox}}{(m_{fuel}/m_{ox})_{st}}}={\frac {n_{fuel}/n_{ox}}{(n_{fuel}/n_{ox})_{st}}}$

where, m represents the mass, n represents number of moles, suffix st stands for stoichiometric conditions.

The advantage of using equivalence ratio over fuel–oxidizer ratio is that it does not have the same dependence as fuel–oxidizer ratio on the units being used. For example fuel–oxidizer ratio based on mass of fuel and oxidizer is not same as one define based on number of moles. This is not the case for equivalence ratio. The following example can help clarify the point. Consider a mixture of one mole of ethane (C₂H₆) and one mole of oxygen (O₂).

fuel–oxidizer ratio of this mixture based on the mass of fuel and air is ${\frac {m_{\rm {C_{2}H_{6}}}}{m_{\rm {O_{2}}}}}={\frac {1\cdot (2\cdot 12+6\cdot 1)}{1\cdot (2\cdot 16)}}={\frac {30}{32}}=0.938$

fuel-to-oxidizer ratio of this mixture based on the number of moles of fuel and air is ${\frac {n_{\rm {C_{2}H_{6}}}}{n_{\rm {O_{2}}}}}={\tfrac {1}{1}}=1.$

Clearly the two values are not equal. To compare it with the equivalence ratio, we need to determine the fuel–oxidizer ratio of ethane and oxygen mixture. For this we need to consider the stoichiometric reaction of ethane and oxygen,

${\rm {C_{2}H_{6}}}+{\tfrac {7}{2}}{\rm {O_{2}}}\rightarrow 2{\rm {CO_{2}}}+3{\rm {H_{2}O}}$

This gives,

$({\mbox{fuel-to-oxidizer ratio based on mass}})_{st}=\left({\frac {m_{\rm {C_{2}H_{6}}}}{m_{\rm {O_{2}}}}}\right)_{st}={\frac {1\cdot (2\cdot 12+6\cdot 1)}{3.5\cdot (2\cdot 16)}}={\frac {30}{112}}=0.268$

$({\mbox{fuel-to-oxidizer ratio based on number of moles}})_{st}=\left({\frac {n_{\rm {C_{2}H_{6}}}}{n_{\rm {O_{2}}}}}\right)_{st}={\tfrac {1}{3.5}}=0.286$

Thus we can determine the equivalence ratio of the given mixture as,

$\phi ={\frac {m_{\rm {C_{2}H_{6}}}/m_{\rm {O_{2}}}}{(m_{\rm {C_{2}H_{6}}}/m_{\rm {O_{2}}})_{st}}}={\tfrac {0.938}{0.268}}=3.5$

or equivalently as,

$\phi ={\frac {n_{\rm {C_{2}H_{6}}}/n_{\rm {O_{2}}}}{(n_{\rm {C_{2}H_{6}}}/n_{\rm {O_{2}}})_{st}}}={\tfrac {1}{0.286}}=3.5$

Another advantage of using the equivalence ratio is that ratios greater than one always represent excess fuel in the fuel–oxidizer mixture than would be required for complete combustion (stoichiometric reaction) irrespective of the fuel and oxidizer being used, while ratios less than one represent a deficiency of fuel or equivalently excess oxidizer in the mixture. This is not the case if one uses fuel–oxidizer ratio, which will take different values for different mixtures.

Equivalence ratio is related to λ (defined previously) as follows:

$\phi ={\frac {1}{\lambda }}$

Stoichiometric mixture fraction

The relative amounts of oxygen enrichment and fuel dilution can be quantified by the stoichiometric mixture fraction, Z_st, defined as $Z_{st}=\left[{\frac {Y_{O,0}\cdot W_{F}\cdot v_{F}}{1+Y_{F,0}\cdot W_{O}\cdot v_{O}}}\right]$, where $Y_{F,0}$ and $Y_{O,0}$ represent the fuel and oxidizer mass fractions at the inlet, $W_{F}$ and $W_{O}$ are the species molecular weights, and $v_{F}$ and $v_{O}$ are the fuel and oxygen stoichiometric coefficients, respectively.

Z_st is related to lambda and AFR by the equations:

$Z_{st}={\frac {\lambda }{1+\lambda }}={\frac {1}{1+AFR}}$

Percent excess combustion air

In industrial fired heaters, power plant steam generators, and large gas-fired turbines, the more common term is percent excess combustion air. For example, excess combustion air of 15 percent means that 15 percent more than the required stoichiometric air is being used.

Ideal-stoichiometry

See also

I am a Professor of Engineering. This entire page is a bunch of mumbo jumbo. Due to the improper use of Greek symbols, meaningless formulas and ratios, as a Professor of Engineering I'd give you a failing grade. I could start at the top of this page and find fault after fault but the more I read it, the more stupidity I find in it. It's not worth any more of my time.

• Adiabatic flame temperature
• AFR sensor
• Air–fuel ratio meter
• Lean burn
• Mass flow sensor
• Oxygen sensor

External links

• HowStuffWorks: fuel injection, catalytic converter
• University of Plymouth :Engine Combustion primer
• Kamm, Richard W. "Mixed Up About Fuel Mixtures?". Aircraft Maintenance Technology (February 2002). Retrieved 2009-03-18.