Air–fuel ratio - Wikipedia

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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Air-fuel_ratio_meters" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Air-fuel_ratio_meters"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Air-fuel ratio meters</span> </div> </a> <ul id="toc-Air-fuel_ratio_meters-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Internal_combustion_engines" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Internal_combustion_engines"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Internal combustion engines</span> </div> </a> <ul id="toc-Internal_combustion_engines-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Engine_management_systems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Engine_management_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Engine management systems</span> </div> </a> <ul id="toc-Engine_management_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_types_of_engines" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_types_of_engines"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Other types of engines</span> </div> </a> <ul id="toc-Other_types_of_engines-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_terms_used" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_terms_used"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Other terms used</span> </div> </a> <button aria-controls="toc-Other_terms_used-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Other terms used subsection</span> </button> <ul id="toc-Other_terms_used-sublist" class="vector-toc-list"> <li id="toc-Mixture" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mixture"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Mixture</span> </div> </a> <ul id="toc-Mixture-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fuel–air_ratio_(FAR)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fuel–air_ratio_(FAR)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Fuel–air ratio (FAR)</span> </div> </a> <ul id="toc-Fuel–air_ratio_(FAR)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Air–fuel_equivalence_ratio_(λ)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Air–fuel_equivalence_ratio_(λ)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Air–fuel equivalence ratio (<i>λ</i>)</span> </div> </a> <ul id="toc-Air–fuel_equivalence_ratio_(λ)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fuel–air_equivalence_ratio_(Φ)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fuel–air_equivalence_ratio_(Φ)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Fuel–air equivalence ratio (<i>Φ</i>)</span> </div> </a> <ul id="toc-Fuel–air_equivalence_ratio_(Φ)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mixture_fraction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mixture_fraction"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Mixture fraction</span> </div> </a> <ul id="toc-Mixture_fraction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Percent_excess_combustion_air" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Percent_excess_combustion_air"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Percent excess combustion air</span> </div> </a> <ul id="toc-Percent_excess_combustion_air-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown 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class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Sou%C4%8Dinitel_p%C5%99ebytku_vzduchu" title="Součinitel přebytku vzduchu – Czech" lang="cs" hreflang="cs" data-title="Součinitel přebytku vzduchu" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Verbrennungsluftverh%C3%A4ltnis" title="Verbrennungsluftverhältnis – German" lang="de" hreflang="de" data-title="Verbrennungsluftverhältnis" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Relaci%C3%B3n_aire-combusti%C3%B3n" title="Relación aire-combustión – Spanish" lang="es" hreflang="es" data-title="Relación aire-combustión" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D8%B3%D8%A8%D8%AA_%D9%87%D9%88%D8%A7-%D8%B3%D9%88%D8%AE%D8%AA" title="نسبت هوا-سوخت – Persian" lang="fa" hreflang="fa" data-title="نسبت هوا-سوخت" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rapport_de_m%C3%A9lange_(combustion)" title="Rapport de mélange (combustion) – French" lang="fr" hreflang="fr" data-title="Rapport de mélange (combustion)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%B5%EC%97%B0%EB%B9%84" title="공연비 – Korean" lang="ko" hreflang="ko" data-title="공연비" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Aria_teorica_di_combustione" title="Aria teorica di combustione – Italian" lang="it" hreflang="it" data-title="Aria teorica di combustione" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Lambdawaarde_(motortechniek)" title="Lambdawaarde (motortechniek) – Dutch" lang="nl" hreflang="nl" data-title="Lambdawaarde (motortechniek)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%A9%BA%E7%87%83%E6%AF%94" title="空燃比 – Japanese" lang="ja" hreflang="ja" data-title="空燃比" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wsp%C3%B3%C5%82czynnik_nadmiaru_powietrza" title="Współczynnik nadmiaru powietrza – Polish" lang="pl" hreflang="pl" data-title="Współczynnik nadmiaru powietrza" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Amestec_carburant" title="Amestec carburant – Romanian" lang="ro" hreflang="ro" data-title="Amestec carburant" data-language-autonym="Română" data-language-local-name="Romanian" 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href="https://uk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%85%D1%96%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D1%81%D0%BA%D0%BB%D0%B0%D0%B4_%D0%B3%D0%BE%D1%80%D1%8E%D1%87%D0%BE%D1%97_%D1%81%D1%83%D0%BC%D1%96%D1%88%D1%96" title="Стехіометричний склад горючої суміші – Ukrainian" lang="uk" hreflang="uk" data-title="Стехіометричний склад горючої суміші" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%A9%BA%E7%87%83%E6%AF%94" title="空燃比 – Chinese" lang="zh" hreflang="zh" data-title="空燃比" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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searchaux" style="display:none">Mass ratio of air to a fuel</div> <p><b>Air–fuel ratio</b> (<b>AFR</b>) is the mass ratio of <a href="/wiki/Air" class="mw-redirect" title="Air">air</a> to a solid, liquid, or gaseous <a href="/wiki/Fuel" title="Fuel">fuel</a> present in a <a href="/wiki/Combustion" title="Combustion">combustion</a> process. The combustion may take place in a controlled manner such as in an <a href="/wiki/Internal_combustion_engine" title="Internal combustion engine">internal combustion engine</a> or industrial furnace, or may result in an explosion (e.g., a <a href="/wiki/Dust_explosion" title="Dust explosion">dust explosion</a>). The air–fuel ratio determines whether a mixture is combustible at all, how much energy is being released, and how much unwanted pollutants are produced in the reaction. Typically a range of fuel to air ratios exists, outside of which ignition will not occur. These are known as the lower and upper explosive limits. </p><p>In an <a href="/wiki/Internal_combustion_engine" title="Internal combustion engine">internal combustion engine</a> or industrial furnace, the air–fuel ratio is an important measure for anti-pollution and performance-tuning reasons. If exactly enough air is provided to completely burn all of the fuel (<b><a href="/wiki/Stoichiometric" class="mw-redirect" title="Stoichiometric">stoichiometric</a> combustion</b>), the ratio is known as the <b>stoichiometric mixture</b>, often abbreviated to <b>stoich</b>. Ratios lower than stoichiometric (where the fuel is in excess) are considered "rich". Rich mixtures are less efficient, but may produce more power and burn cooler. Ratios higher than stoichiometric (where the air is in excess) are considered "lean". Lean mixtures are more efficient but may cause higher temperatures, which can lead to the formation of <a href="/wiki/Nitrogen_oxide" title="Nitrogen oxide">nitrogen oxides</a>. Some engines are designed with features to allow <a href="/wiki/Lean-burn" title="Lean-burn">lean-burn</a>. For precise air–fuel ratio calculations, the <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> content of combustion air should be specified because of different <a href="/wiki/Density_of_air" title="Density of air">air density</a> due to different altitude or intake air temperature, possible dilution by ambient <a href="/wiki/Water_vapor" title="Water vapor">water vapor</a>, or enrichment by oxygen additions. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Air-fuel_ratio_meters">Air-fuel ratio meters</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=1" title="Edit section: Air-fuel ratio meters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An <b>air-fuel ratio meter</b> monitors the air–fuel ratio of an <a href="/wiki/Internal_combustion_engine" title="Internal combustion engine">internal combustion engine</a>. Also called <b>air–fuel ratio gauge</b>, <b>air–fuel meter</b>, or <b>air–fuel gauge</b>, it reads the voltage output of an <a href="/wiki/Oxygen_sensor" title="Oxygen sensor">oxygen sensor</a>, sometimes also called <b>AFR sensor</b> or lambda sensor. </p><p>The original narrow-band oxygen sensors became factory installed standard in the late 1970s and early 1980s. In recent years a newer and much more accurate wide-band sensor, though more expensive, has become available. </p><p>Most stand-alone narrow-band meters have 10 <a href="/wiki/Light-emitting_diode" title="Light-emitting diode">LEDs</a> and some have more. Also common, narrow band meters in round housings with the standard mounting <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style>52 and 67 mm (<span class="frac">2<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">16</span></span> and <span class="frac">2<span class="sr-only">+</span><span class="num">5</span>⁄<span class="den">8</span></span> in) diameters, as other types of car 'gauges'. These usually have 10 or 20 LEDs. Analogue 'needle' style gauges are also available. </p> <div class="mw-heading mw-heading2"><h2 id="Internal_combustion_engines">Internal combustion engines</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=2" title="Edit section: Internal combustion engines"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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. </p><p>Most of the combustion process is completed in approximately 2 milliseconds at an engine speed of <span class="nowrap"><span data-sort-value="7003600000000000000♠"></span>6,000 <a href="/wiki/Revolutions_per_minute" title="Revolutions per minute">revolutions per minute</a></span> (100 revolutions per second, or 10 milliseconds per revolution of the crankshaft. For a four-stroke engine this would mean 5 milliseconds for each piston stroke, and 20 milliseconds to complete one 720 degree <a href="/wiki/Otto_cycle" title="Otto cycle">Otto cycle</a>). This is the time that elapses from the spark plug firing until 90% of the fuel–air mix is combusted, typically some 80 degrees of crankshaft rotation later. <a href="/wiki/Catalytic_converter" title="Catalytic converter">Catalytic converters</a> are designed to work best when the <a href="/wiki/Exhaust_gas" title="Exhaust gas">exhaust gases</a> passing through them are the result of nearly perfect combustion. </p><p>A perfectly stoichiometric mixture 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, the detonation of the fuel-air mix while approaching or shortly after maximum cylinder pressure is possible under high load (referred to as <a href="/wiki/Engine_knocking" title="Engine knocking">knocking</a> or pinging), specifically a "pre-detonation" event in the context of a spark-ignition engine model. Such 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 to low-moderate load conditions. For acceleration and high-load conditions, a richer mixture (lower air–fuel ratio) is used to produce cooler combustion products (thereby utilizing <a href="/wiki/Evaporative_cooling" class="mw-redirect" title="Evaporative cooling">evaporative cooling</a>), and so avoid overheating of the <a href="/wiki/Cylinder_head" title="Cylinder head">cylinder head</a>, and thus prevent detonation. </p> <div class="mw-heading mw-heading2"><h2 id="Engine_management_systems">Engine management systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=3" title="Edit section: Engine management systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Stoichiometric" class="mw-redirect" title="Stoichiometric">stoichiometric</a> mixture for a gasoline engine is the ideal ratio of air to fuel that burns all fuel with no excess air. For <a href="/wiki/Gasoline" title="Gasoline">gasoline</a> fuel, the stoichiometric air–fuel mixture is about 14.7:1<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> i.e. for every one gram of fuel, 14.7 grams of air are required. For pure <a href="/wiki/Octane" title="Octane">octane</a> fuel, the oxidation reaction is: </p> <dl><dd>25 O<sub>2</sub> + 2 C<sub>8</sub>H<sub>18</sub> → 16 CO<sub>2</sub> + 18 H<sub>2</sub>O + energy</dd></dl> <p>Any mixture greater than 14.7:1 is considered a <a href="/wiki/Lean_burn" class="mw-redirect" title="Lean burn">lean mixture</a>; any less than 14.7:1 is a <a href="/wiki/Rich_burn" class="mw-redirect" title="Rich burn">rich mixture</a> – given perfect (ideal) "test" fuel (gasoline consisting of solely <i>n</i>-<a href="/wiki/Heptane" title="Heptane">heptane</a> and <a href="/wiki/Iso-octane" class="mw-redirect" title="Iso-octane">iso-octane</a>). In reality, most fuels consist of a combination of heptane, octane, a handful of other <a href="/wiki/Alkanes" class="mw-redirect" title="Alkanes">alkanes</a>, plus additives including detergents, and possibly oxygenators such as MTBE (<a href="/wiki/Methyl_tert-butyl_ether" title="Methyl tert-butyl ether">methyl <i>tert</i>-butyl ether</a>) or <a href="/wiki/Ethanol" title="Ethanol">ethanol</a>/<a href="/wiki/Methanol" title="Methanol">methanol</a>. 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 the time of combustions; for <a href="/wiki/MTBE" class="mw-redirect" title="MTBE">MTBE</a>-laden fuel, a stoichiometric ratio can be as low as 14.1:1). Vehicles that use an <a href="/wiki/Oxygen_sensor" title="Oxygen sensor">oxygen sensor</a> or other feedback loops to control fuel to air ratio (lambda control), compensate automatically for this change in the fuel's stoichiometric rate by measuring the exhaust gas composition and controlling fuel volume. Vehicles without such controls (such as most motorcycles until recently, and cars predating the mid-1980s) may have difficulties running certain fuel blends (especially winter fuels used in some areas) and may require different <a href="/wiki/Carburetor" title="Carburetor">carburetor</a> jets (or otherwise have the fueling ratios altered) to compensate. Vehicles that use <a href="/wiki/Oxygen_sensor" title="Oxygen sensor">oxygen sensors</a> can monitor the air–fuel ratio with an <a href="/wiki/Air%E2%80%93fuel_ratio_meter" class="mw-redirect" title="Air–fuel ratio meter">air–fuel ratio meter</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Other_types_of_engines">Other types of engines</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=4" title="Edit section: Other types of engines"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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 II).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2013)">citation needed</span></a></i>]</sup> 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. </p> <div class="mw-heading mw-heading2"><h2 id="Other_terms_used">Other terms used</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=5" title="Edit section: Other terms used"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are other terms commonly used when discussing the mixture of air and fuel in internal combustion engines. </p> <div class="mw-heading mw-heading3"><h3 id="Mixture">Mixture</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=6" title="Edit section: Mixture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Mixture</b> is the predominant word that appears in training texts, operation manuals, and maintenance manuals in the aviation world. </p><p>Air–fuel ratio is the ratio between the <i>mass</i> of air and the mass of fuel in the fuel–air mix at any given moment. The mass is the mass of all constituents that compose the fuel and air, whether combustible or not. For example, a calculation of the mass of natural gas—which often contains <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">carbon dioxide</a> (<span class="chemf nowrap">CO<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>), <a href="/wiki/Nitrogen" title="Nitrogen">nitrogen</a> (<span class="chemf nowrap">N<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>), and various <a href="/wiki/Alkanes" class="mw-redirect" title="Alkanes">alkanes</a>—includes the mass of the carbon dioxide, nitrogen and all alkanes in determining the value of <i>m</i><sub>fuel</sub>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>For pure <a href="/wiki/Octane" title="Octane">octane</a> the stoichiometric mixture is approximately 15.1:1, or <i>λ</i> of 1.00 exactly. </p><p>In naturally aspirated engines powered by octane, maximum power is frequently reached at AFRs ranging from 12.5 to 13.3:1 or <i>λ</i> of 0.850 to 0.901.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2019)">citation needed</span></a></i>]</sup> </p><p>The air-fuel ratio of 12:1 is considered as the maximum output ratio, whereas the air-fuel ratio of 16:1 is considered as the maximum fuel economy ratio.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2019)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Fuel–air_ratio_(FAR)"><span id="Fuel.E2.80.93air_ratio_.28FAR.29"></span>Fuel–air ratio (FAR) <span class="anchor" id="Fuel-air_ratio"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=7" title="Edit section: Fuel–air ratio (FAR)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Fuel–air ratio</b> is commonly used in the <a href="/wiki/Gas_turbine" title="Gas turbine">gas turbine</a> industry as well as in government studies of <a href="/wiki/Internal_combustion_engine" title="Internal combustion engine">internal combustion engine</a>, and refers to the ratio of fuel to the air.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2013)">citation needed</span></a></i>]</sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {FAR} ={\frac {1}{\mathrm {AFR} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">R</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {FAR} ={\frac {1}{\mathrm {AFR} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/898466e23bbca948aeecfd830deaba009a3e4d75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.878ex; height:5.343ex;" alt="{\displaystyle \mathrm {FAR} ={\frac {1}{\mathrm {AFR} }}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Air–fuel_equivalence_ratio_(λ)"><span id="Air.E2.80.93fuel_equivalence_ratio_.28.CE.BB.29"></span>Air–fuel equivalence ratio (<i>λ</i>)<span class="anchor" id="Air-fuel_equivalence_ratio"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=8" title="Edit section: Air–fuel equivalence ratio (λ)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Air–fuel equivalence ratio, <i>λ</i> (lambda), is the ratio of actual AFR to stoichiometry for a given mixture. <i>λ</i> = 1.0 is at stoichiometry, rich mixtures <i>λ</i> < 1.0, and lean mixtures <i>λ</i> > 1.0. </p><p>There is a direct relationship between <i>λ</i> and AFR. To calculate AFR from a given <i>λ</i>, multiply the measured <i>λ</i> by the stoichiometric AFR for that fuel. Alternatively, to recover <i>λ</i> from an AFR, divide AFR by the stoichiometric AFR for that fuel. This last equation is often used as the definition of <i>λ</i>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda ={\frac {\mathrm {AFR} }{\mathrm {AFR} _{\text{stoich}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">R</mi> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>stoich</mtext> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ={\frac {\mathrm {AFR} }{\mathrm {AFR} _{\text{stoich}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/356ee66ce6dad42d9a71c0b2fc5d53a32478be3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.704ex; height:5.843ex;" alt="{\displaystyle \lambda ={\frac {\mathrm {AFR} }{\mathrm {AFR} _{\text{stoich}}}}}"></span></dd></dl> <p>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 <i>λ</i> values rather than AFR. </p><p>Most practical AFR devices actually measure the amount of residual oxygen (for lean mixes) or unburnt hydrocarbons (for rich mixtures) in the exhaust gas. </p> <div class="mw-heading mw-heading3"><h3 id="Fuel–air_equivalence_ratio_(Φ)"><span id="Fuel.E2.80.93air_equivalence_ratio_.28.CE.A6.29"></span>Fuel–air equivalence ratio (<i>Φ</i>)<span class="anchor" id="Fuel-air_equivalence_ratio"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=9" title="Edit section: Fuel–air equivalence ratio (Φ)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <b>fuel–air equivalence ratio</b>, <i>Φ</i> (phi), of a system is defined as the ratio of the fuel-to-oxidizer ratio to the stoichiometric fuel-to-oxidizer ratio. Mathematically, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi ={\frac {\mbox{fuel-to-oxidizer ratio}}{({\mbox{fuel-to-oxidizer ratio}})_{\text{st}}}}={\frac {m_{\text{fuel}}/m_{\text{ox}}}{\left(m_{\text{fuel}}/m_{\text{ox}}\right)_{\text{st}}}}={\frac {n_{\text{fuel}}/n_{\text{ox}}}{\left(n_{\text{fuel}}/n_{\text{ox}}\right)_{\text{st}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="false" scriptlevel="0"> <mtext>fuel-to-oxidizer ratio</mtext> </mstyle> <mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>fuel-to-oxidizer ratio</mtext> </mstyle> </mrow> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>fuel</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ox</mtext> </mrow> </msub> </mrow> <msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>fuel</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ox</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>fuel</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ox</mtext> </mrow> </msub> </mrow> <msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>fuel</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ox</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ={\frac {\mbox{fuel-to-oxidizer ratio}}{({\mbox{fuel-to-oxidizer ratio}})_{\text{st}}}}={\frac {m_{\text{fuel}}/m_{\text{ox}}}{\left(m_{\text{fuel}}/m_{\text{ox}}\right)_{\text{st}}}}={\frac {n_{\text{fuel}}/n_{\text{ox}}}{\left(n_{\text{fuel}}/n_{\text{ox}}\right)_{\text{st}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acc11252883232bf6e13eef2ece593a8f4889b98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:62.511ex; height:6.509ex;" alt="{\displaystyle \phi ={\frac {\mbox{fuel-to-oxidizer ratio}}{({\mbox{fuel-to-oxidizer ratio}})_{\text{st}}}}={\frac {m_{\text{fuel}}/m_{\text{ox}}}{\left(m_{\text{fuel}}/m_{\text{ox}}\right)_{\text{st}}}}={\frac {n_{\text{fuel}}/n_{\text{ox}}}{\left(n_{\text{fuel}}/n_{\text{ox}}\right)_{\text{st}}}}}"></span></dd></dl> <p>where <i>m</i> represents the mass, <i>n</i> represents a number of moles, subscript st stands for stoichiometric conditions. </p><p>The advantage of using equivalence ratio over fuel–oxidizer ratio is that it takes into account (and is therefore independent of) both mass and molar values for the fuel and the oxidizer. Consider, for example, a mixture of one mole of <a href="/wiki/Ethane" title="Ethane">ethane</a> (<span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span></span>) and one mole of <a href="/wiki/Oxygen" title="Oxygen">oxygen</a> (<span class="chemf nowrap">O<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sub></span></span></span>). The fuel–oxidizer ratio of this mixture based on the mass of fuel and air is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {m_{{\ce {C2H6}}}}{m_{{\ce {O2}}}}}={\frac {1\times (2\times 12+6\times 1)}{1\times (2\times 16)}}={\frac {30}{32}}=0.9375}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>×</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>×</mo> <mn>12</mn> <mo>+</mo> <mn>6</mn> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>1</mn> <mo>×</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>×</mo> <mn>16</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>30</mn> <mn>32</mn> </mfrac> </mrow> <mo>=</mo> <mn>0.9375</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {m_{{\ce {C2H6}}}}{m_{{\ce {O2}}}}}={\frac {1\times (2\times 12+6\times 1)}{1\times (2\times 16)}}={\frac {30}{32}}=0.9375}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fa5c4b3f44d6a153955f3362abbcf89bf9fd32b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:47.088ex; height:6.676ex;" alt="{\displaystyle {\frac {m_{{\ce {C2H6}}}}{m_{{\ce {O2}}}}}={\frac {1\times (2\times 12+6\times 1)}{1\times (2\times 16)}}={\frac {30}{32}}=0.9375}"></span></dd></dl> <p>and the fuel-oxidizer ratio of this mixture based on the number of moles of fuel and air is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n_{{\ce {C2H6}}}}{n_{{\ce {O2}}}}}={\frac {1}{1}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>1</mn> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n_{{\ce {C2H6}}}}{n_{{\ce {O2}}}}}={\frac {1}{1}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ee8b3872c80eba4b5419d0d5172de528a4aca4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:15.903ex; height:6.343ex;" alt="{\displaystyle {\frac {n_{{\ce {C2H6}}}}{n_{{\ce {O2}}}}}={\frac {1}{1}}=1}"></span></dd></dl> <p>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, </p> <dl><dd>C<sub>2</sub>H<sub>6</sub> + <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">7</span>⁄<span class="den">2</span></span> O<sub>2</sub> → 2 CO<sub>2</sub> + 3 H<sub>2</sub>O</dd></dl> <p>This gives </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\text{fuel-to-oxidizer ratio based on mass}})_{\text{st}}=\left({\frac {m_{{\ce {C2H6}}}}{m_{{\ce {O2}}}}}\right)_{\text{st}}={\frac {1\times (2\times 12+6\times 1)}{3.5\times (2\times 16)}}={\frac {30}{112}}=0.268}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>fuel-to-oxidizer ratio based on mass</mtext> </mrow> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>×</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>×</mo> <mn>12</mn> <mo>+</mo> <mn>6</mn> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>3.5</mn> <mo>×</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>×</mo> <mn>16</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>30</mn> <mn>112</mn> </mfrac> </mrow> <mo>=</mo> <mn>0.268</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\text{fuel-to-oxidizer ratio based on mass}})_{\text{st}}=\left({\frac {m_{{\ce {C2H6}}}}{m_{{\ce {O2}}}}}\right)_{\text{st}}={\frac {1\times (2\times 12+6\times 1)}{3.5\times (2\times 16)}}={\frac {30}{112}}=0.268}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45fba063b1a3cbf61ff3ec03b15bdf24cce2b701" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:94.162ex; height:7.676ex;" alt="{\displaystyle ({\text{fuel-to-oxidizer ratio based on mass}})_{\text{st}}=\left({\frac {m_{{\ce {C2H6}}}}{m_{{\ce {O2}}}}}\right)_{\text{st}}={\frac {1\times (2\times 12+6\times 1)}{3.5\times (2\times 16)}}={\frac {30}{112}}=0.268}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\text{fuel-to-oxidizer ratio based on number of moles}})_{\text{st}}=\left({\frac {n_{{\ce {C2H6}}}}{n_{{\ce {O2}}}}}\right)_{\text{st}}={\frac {1}{3.5}}=0.286}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>fuel-to-oxidizer ratio based on number of moles</mtext> </mrow> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3.5</mn> </mfrac> </mrow> <mo>=</mo> <mn>0.286</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\text{fuel-to-oxidizer ratio based on number of moles}})_{\text{st}}=\left({\frac {n_{{\ce {C2H6}}}}{n_{{\ce {O2}}}}}\right)_{\text{st}}={\frac {1}{3.5}}=0.286}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/819ab1cbd86958a956a65d68450cc0dcec5d816e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:80.477ex; height:7.676ex;" alt="{\displaystyle ({\text{fuel-to-oxidizer ratio based on number of moles}})_{\text{st}}=\left({\frac {n_{{\ce {C2H6}}}}{n_{{\ce {O2}}}}}\right)_{\text{st}}={\frac {1}{3.5}}=0.286}"></span></dd></dl> <p>Thus we can determine the equivalence ratio of the given mixture as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi ={\frac {m_{{\ce {C2H6}}}/m_{{\ce {O2}}}}{\left(m_{{\ce {C2H6}}}/m_{{\ce {O2}}}\right)_{\text{st}}}}={\frac {0.938}{0.268}}=3.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> </mrow> <msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0.938</mn> <mn>0.268</mn> </mfrac> </mrow> <mo>=</mo> <mn>3.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ={\frac {m_{{\ce {C2H6}}}/m_{{\ce {O2}}}}{\left(m_{{\ce {C2H6}}}/m_{{\ce {O2}}}\right)_{\text{st}}}}={\frac {0.938}{0.268}}=3.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a4a41975a42e7e06c5718ac83cf26b2ffb4dbab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:36.817ex; height:8.676ex;" alt="{\displaystyle \phi ={\frac {m_{{\ce {C2H6}}}/m_{{\ce {O2}}}}{\left(m_{{\ce {C2H6}}}/m_{{\ce {O2}}}\right)_{\text{st}}}}={\frac {0.938}{0.268}}=3.5}"></span></dd></dl> <p>or, equivalently, as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi ={\frac {n_{{\ce {C2H6}}}/n_{{\ce {O2}}}}{\left(n_{{\ce {C2H6}}}/n_{{\ce {O2}}}\right)_{\text{st}}}}={\frac {1}{0.286}}=3.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> </mrow> <msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>O</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>0.286</mn> </mfrac> </mrow> <mo>=</mo> <mn>3.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ={\frac {n_{{\ce {C2H6}}}/n_{{\ce {O2}}}}{\left(n_{{\ce {C2H6}}}/n_{{\ce {O2}}}\right)_{\text{st}}}}={\frac {1}{0.286}}=3.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/704c031238b9473aa61abaa425e925151672d131" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:35.526ex; height:8.676ex;" alt="{\displaystyle \phi ={\frac {n_{{\ce {C2H6}}}/n_{{\ce {O2}}}}{\left(n_{{\ce {C2H6}}}/n_{{\ce {O2}}}\right)_{\text{st}}}}={\frac {1}{0.286}}=3.5}"></span></dd></dl> <p>Another advantage of using the equivalence ratio is that ratios greater than one always mean there is more fuel in the fuel–oxidizer mixture than 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 takes different values for different mixtures. </p><p>The fuel–air equivalence ratio is related to the air–fuel equivalence ratio (defined previously) as follows: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi ={\frac {1}{\lambda }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>λ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi ={\frac {1}{\lambda }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c5118e2e3690f5d8447f6cbc35df1280797bba0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:6.675ex; height:5.343ex;" alt="{\displaystyle \phi ={\frac {1}{\lambda }}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Mixture_fraction">Mixture fraction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=10" title="Edit section: Mixture fraction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Mixture_fraction" title="Mixture fraction">Mixture fraction</a></div> <p>The relative amounts of oxygen enrichment and fuel dilution can be quantified by the <a href="/wiki/Mixture_fraction" title="Mixture fraction">mixture fraction</a>, Z, defined as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z=\left[{\frac {sY_{\mathrm {F} }-Y_{\mathrm {O} }+Y_{\mathrm {O,0} }}{sY_{\mathrm {F,0} }+Y_{\mathrm {O,0} }}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>s</mi> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> <mo>,</mo> <mn>0</mn> </mrow> </mrow> </msub> </mrow> <mrow> <mi>s</mi> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <mo>,</mo> <mn>0</mn> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> <mo>,</mo> <mn>0</mn> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z=\left[{\frac {sY_{\mathrm {F} }-Y_{\mathrm {O} }+Y_{\mathrm {O,0} }}{sY_{\mathrm {F,0} }+Y_{\mathrm {O,0} }}}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9aa5444be1bff9d96d84bdc3cd8cd70ef5e30317" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:24.499ex; height:6.176ex;" alt="{\displaystyle Z=\left[{\frac {sY_{\mathrm {F} }-Y_{\mathrm {O} }+Y_{\mathrm {O,0} }}{sY_{\mathrm {F,0} }+Y_{\mathrm {O,0} }}}\right]}"></span>,</dd></dl> <p>where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s=\mathrm {AFR} _{\mathrm {stoich} }={\frac {W_{\mathrm {O} }\times v_{\mathrm {O} }}{W_{\mathrm {F} }\times v_{\mathrm {F} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">h</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>×</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mrow> <mrow> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> </mrow> </mrow> </msub> <mo>×</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s=\mathrm {AFR} _{\mathrm {stoich} }={\frac {W_{\mathrm {O} }\times v_{\mathrm {O} }}{W_{\mathrm {F} }\times v_{\mathrm {F} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55b83893629faa44a6e5b4f0d78cec1f0c488ca6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:26.721ex; height:5.676ex;" alt="{\displaystyle s=\mathrm {AFR} _{\mathrm {stoich} }={\frac {W_{\mathrm {O} }\times v_{\mathrm {O} }}{W_{\mathrm {F} }\times v_{\mathrm {F} }}}}"></span>,</dd></dl> <p><i>Y</i><sub>F,0</sub> and <i>Y</i><sub>O,0</sub> represent the fuel and oxidizer mass fractions at the inlet, <i>W</i><sub>F</sub> and <i>W</i><sub>O</sub> are the species molecular weights, and <i>v</i><sub>F</sub> and <i>v</i><sub>O</sub> are the fuel and oxygen stoichiometric coefficients, respectively. The stoichiometric mixture fraction is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{\mathrm {st} }=\left[{\frac {1}{1+{\frac {Y_{\mathrm {F,0} }\times W_{\mathrm {O} }\times v_{\mathrm {O} }}{Y_{\mathrm {O,0} }\times W_{\mathrm {F} }\times v_{\mathrm {F} }}}}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <mo>,</mo> <mn>0</mn> </mrow> </mrow> </msub> <mo>×</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> <mo>×</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> </mrow> </msub> </mrow> <mrow> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> <mo>,</mo> <mn>0</mn> </mrow> </mrow> </msub> <mo>×</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> </mrow> </mrow> </msub> <mo>×</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{\mathrm {st} }=\left[{\frac {1}{1+{\frac {Y_{\mathrm {F,0} }\times W_{\mathrm {O} }\times v_{\mathrm {O} }}{Y_{\mathrm {O,0} }\times W_{\mathrm {F} }\times v_{\mathrm {F} }}}}}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504eafbadd594c1c11ade4e7f37aab3e349702c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:25.321ex; height:10.509ex;" alt="{\displaystyle Z_{\mathrm {st} }=\left[{\frac {1}{1+{\frac {Y_{\mathrm {F,0} }\times W_{\mathrm {O} }\times v_{\mathrm {O} }}{Y_{\mathrm {O,0} }\times W_{\mathrm {F} }\times v_{\mathrm {F} }}}}}\right]}"></span><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></dd></dl> <p>The stoichiometric mixture fraction is related to <i>λ</i> (lambda) and <i>Φ</i> (phi) by the equations </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{\text{st}}={\frac {\lambda }{1+\lambda }}={\frac {1}{1+\phi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>st</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>λ</mi> <mrow> <mn>1</mn> <mo>+</mo> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mi>ϕ</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{\text{st}}={\frac {\lambda }{1+\lambda }}={\frac {1}{1+\phi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf877bcde446ba5121997ed8c0281bd51acd45d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.723ex; height:5.843ex;" alt="{\displaystyle Z_{\text{st}}={\frac {\lambda }{1+\lambda }}={\frac {1}{1+\phi }}}"></span>,</dd></dl> <p>assuming </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {AFR} ={\frac {Y_{\mathrm {O,0} }}{Y_{\mathrm {F,0} }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> <mo>,</mo> <mn>0</mn> </mrow> </mrow> </msub> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">F</mi> <mo>,</mo> <mn>0</mn> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {AFR} ={\frac {Y_{\mathrm {O,0} }}{Y_{\mathrm {F,0} }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3543befdc76bde55ba76344c801979cc2250915a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:13.047ex; height:6.176ex;" alt="{\displaystyle \mathrm {AFR} ={\frac {Y_{\mathrm {O,0} }}{Y_{\mathrm {F,0} }}}}"></span><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Percent_excess_combustion_air">Percent excess combustion air</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=11" title="Edit section: Percent excess combustion air"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ideal-stoichiometry.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Ideal-stoichiometry.svg/220px-Ideal-stoichiometry.svg.png" decoding="async" width="220" height="247" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Ideal-stoichiometry.svg/330px-Ideal-stoichiometry.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Ideal-stoichiometry.svg/440px-Ideal-stoichiometry.svg.png 2x" data-file-width="437" data-file-height="491" /></a><figcaption>Ideal stoichiometry</figcaption></figure><p>In industrial <a href="/wiki/Industrial_furnace" title="Industrial furnace">fired heaters</a>, <a href="/wiki/Power_plant" class="mw-redirect" title="Power plant">power plant</a> steam generators, and large <a href="/wiki/Gas_turbine" title="Gas turbine">gas-fired turbines</a>, the more common terms are percent excess combustion air and percent stoichiometric air.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> For example, excess combustion air of 15 percent means that 15 percent more than the required stoichiometric air (or 115 percent of stoichiometric air) is being used. </p><p>A combustion control point can be defined by specifying the percent excess air (or oxygen) in the <a href="/wiki/Oxidizing_agent" title="Oxidizing agent">oxidant</a>, or by specifying the percent oxygen in the combustion product.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> An <a href="/wiki/Air%E2%80%93fuel_ratio_meter" class="mw-redirect" title="Air–fuel ratio meter">air–fuel ratio meter</a> may be used to measure the percent oxygen in the combustion gas, from which the percent excess oxygen can be calculated from stoichiometry and a <a href="/wiki/Mass_balance" title="Mass balance">mass balance</a> for fuel combustion. For example, for propane (<span class="chemf nowrap">C<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">3</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">8</sub></span></span></span>) combustion between stoichiometric and 30 percent excess air (AFR<sub>mass</sub> between 15.58 and 20.3), the relationship between percent excess air and percent oxygen is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\mathrm {Mass\%\ O_{2}\ in\ propane\ combustion\ gas} &\approx -0.1433(\mathrm {\%\ excess\ O_{2}} )^{2}+0.214(\mathrm {\%\ excess\ O_{2}} )\\\mathrm {Volume\%\ O_{2}\ in\ propane\ combustion\ gas} &\approx -0.1208(\mathrm {\%\ excess\ O_{2}} )^{2}+0.186(\mathrm {\%\ excess\ O_{2}} )\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">%</mi> <mtext> </mtext> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mtext> </mtext> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mtext> </mtext> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> <mtext> </mtext> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mtd> <mtd> <mi></mi> <mo>≈</mo> <mo>−</mo> <mn>0.1433</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">%</mi> <mtext> </mtext> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> <mtext> </mtext> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>0.214</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">%</mi> <mtext> </mtext> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> <mtext> </mtext> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">%</mi> <mtext> </mtext> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mtext> </mtext> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mtext> </mtext> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">e</mi> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">n</mi> <mtext> </mtext> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mtd> <mtd> <mi></mi> <mo>≈</mo> <mo>−</mo> <mn>0.1208</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">%</mi> <mtext> </mtext> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> <mtext> </mtext> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>0.186</mn> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">%</mi> <mtext> </mtext> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">x</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">s</mi> <mtext> </mtext> <msub> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\mathrm {Mass\%\ O_{2}\ in\ propane\ combustion\ gas} &\approx -0.1433(\mathrm {\%\ excess\ O_{2}} )^{2}+0.214(\mathrm {\%\ excess\ O_{2}} )\\\mathrm {Volume\%\ O_{2}\ in\ propane\ combustion\ gas} &\approx -0.1208(\mathrm {\%\ excess\ O_{2}} )^{2}+0.186(\mathrm {\%\ excess\ O_{2}} )\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebc60b058ae104918f66b516bd5c3b1affb7d990" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:89.641ex; height:6.509ex;" alt="{\displaystyle {\begin{aligned}\mathrm {Mass\%\ O_{2}\ in\ propane\ combustion\ gas} &\approx -0.1433(\mathrm {\%\ excess\ O_{2}} )^{2}+0.214(\mathrm {\%\ excess\ O_{2}} )\\\mathrm {Volume\%\ O_{2}\ in\ propane\ combustion\ gas} &\approx -0.1208(\mathrm {\%\ excess\ O_{2}} )^{2}+0.186(\mathrm {\%\ excess\ O_{2}} )\end{aligned}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Adiabatic_flame_temperature" title="Adiabatic flame temperature">Adiabatic flame temperature</a></li> <li><a href="/wiki/AFR_sensor" class="mw-redirect" title="AFR sensor">AFR sensor</a></li> <li><a href="/wiki/Air%E2%80%93fuel_ratio_meter" class="mw-redirect" title="Air–fuel ratio meter">Air–fuel ratio meter</a></li> <li><a href="/wiki/Mass_flow_sensor" title="Mass flow sensor">Mass flow sensor</a></li> <li><a href="/wiki/Combustion" title="Combustion">Combustion</a></li> <li><a href="/wiki/Stoichiometry#Stoichiometric_air-to-fuel_ratios_of_common_fuels" title="Stoichiometry">Stoichiometric air-to-fuel ratio of common fuels</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFHillierPittuck1966" class="citation book cs1">Hillier, V.A.W.; Pittuck, F.W. (1966). "Sub-section 3.2". <i>Fundamentals of Motor Vehicle Technology</i>. London: <a href="/wiki/Hutchinson_(publisher)" class="mw-redirect" title="Hutchinson (publisher)">Hutchinson Educational</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-09-110711-3" title="Special:BookSources/0-09-110711-3"><bdi>0-09-110711-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Sub-section+3.2&rft.btitle=Fundamentals+of+Motor+Vehicle+Technology&rft.place=London&rft.pub=Hutchinson+Educational&rft.date=1966&rft.isbn=0-09-110711-3&rft.aulast=Hillier&rft.aufirst=V.A.W.&rft.au=Pittuck%2C+F.W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAir%E2%80%93fuel+ratio" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">See Example 15.3 in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFÇengelBoles2006" class="citation book cs1">Çengel, Yunus A.; Boles, Michael A. (2006). <a rel="nofollow" class="external text" href="http://www.abebooks.com/Thermodynamics-Engineering-Approach-5th-Cengel-Yunus/1943380167/bd"><i>Thermodynamics: An Engineering Approach</i></a> (5th ed.). Boston: <a href="/wiki/McGraw-Hill_Education" class="mw-redirect" title="McGraw-Hill Education">McGraw-Hill</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780072884951" title="Special:BookSources/9780072884951"><bdi>9780072884951</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thermodynamics%3A+An+Engineering+Approach&rft.place=Boston&rft.edition=5th&rft.pub=McGraw-Hill&rft.date=2006&rft.isbn=9780072884951&rft.aulast=%C3%87engel&rft.aufirst=Yunus+A.&rft.au=Boles%2C+Michael+A.&rft_id=http%3A%2F%2Fwww.abebooks.com%2FThermodynamics-Engineering-Approach-5th-Cengel-Yunus%2F1943380167%2Fbd&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAir%E2%80%93fuel+ratio" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKumferSkeenAxelbaum2008" class="citation journal cs1">Kumfer, B.; Skeen, S.; Axelbaum, R. (2008). <a rel="nofollow" class="external text" href="http://cccu.wustl.edu/Publications%20list/Soot%20Inception%20limits%20in%20laminar%20diffusion%20flames%20with%20application%20to%20oxyfuel%20combustion.pdf">"Soot inception limits in laminar diffusion flames with application to oxy-fuel combustion"</a> <span class="cs1-format">(PDF)</span>. <i>Combustion and Flame</i>. <b>154</b> (3): 546–556. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.combustflame.2008.03.008">10.1016/j.combustflame.2008.03.008</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Combustion+and+Flame&rft.atitle=Soot+inception+limits+in+laminar+diffusion+flames+with+application+to+oxy-fuel+combustion&rft.volume=154&rft.issue=3&rft.pages=546-556&rft.date=2008&rft_id=info%3Adoi%2F10.1016%2Fj.combustflame.2008.03.008&rft.aulast=Kumfer&rft.aufirst=B.&rft.au=Skeen%2C+S.&rft.au=Axelbaum%2C+R.&rft_id=http%3A%2F%2Fcccu.wustl.edu%2FPublications%2520list%2FSoot%2520Inception%2520limits%2520in%2520laminar%2520diffusion%2520flames%2520with%2520application%2520to%2520oxyfuel%2520combustion.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAir%E2%80%93fuel+ratio" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://eyrie.shef.ac.uk/eee/cpe630/comfun1.html"><i>Introduction to Fuel and Energy: 1) MOLES, MASS, CONCENTRATION AND DEFINITIONS</i></a>, accessed 2011-05-25</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www1.eere.energy.gov/manufacturing/tech_assistance/pdfs/42110.pdf">"Energy Tips – Process Heating – Check Burner Air to Fuel Ratios"</a> <span class="cs1-format">(PDF)</span>. U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy. November 2007<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Energy+Tips+%E2%80%93+Process+Heating+%E2%80%93+Check+Burner+Air+to+Fuel+Ratios&rft.pub=U.S.+Department+of+Energy%2C+Office+of+Energy+Efficiency+and+Renewable+Energy&rft.date=2007-11&rft_id=http%3A%2F%2Fwww1.eere.energy.gov%2Fmanufacturing%2Ftech_assistance%2Fpdfs%2F42110.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAir%E2%80%93fuel+ratio" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.engineeringtoolbox.com/stoichiometric-combustion-d_399.html">"Stoichiometric combustion and excess of air"</a>. The Engineering ToolBox<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Stoichiometric+combustion+and+excess+of+air&rft.pub=The+Engineering+ToolBox&rft_id=http%3A%2F%2Fwww.engineeringtoolbox.com%2Fstoichiometric-combustion-d_399.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAir%E2%80%93fuel+ratio" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEckerlin" class="citation web cs1">Eckerlin, Herbert M. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140327143946/http://www.mae.ncsu.edu/eckerlin/courses/mae406/chapter3.pdf">"The Importance of Excess Air in the Combustion Process"</a> <span class="cs1-format">(PDF)</span>. <i>Mechanical and Aerospace Engineering 406 - Energy Conservation in Industry</i>. North Carolina State University. Archived from <a rel="nofollow" class="external text" href="http://www.mae.ncsu.edu/eckerlin/courses/mae406/chapter3.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 27 March 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Mechanical+and+Aerospace+Engineering+406+-+Energy+Conservation+in+Industry&rft.atitle=The+Importance+of+Excess+Air+in+the+Combustion+Process&rft.aulast=Eckerlin&rft.aufirst=Herbert+M.&rft_id=http%3A%2F%2Fwww.mae.ncsu.edu%2Feckerlin%2Fcourses%2Fmae406%2Fchapter3.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAir%E2%80%93fuel+ratio" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Air%E2%80%93fuel_ratio&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>HowStuffWorks: <a rel="nofollow" class="external text" href="http://auto.howstuffworks.com/fuel-injection.htm">fuel injection</a>, <a rel="nofollow" class="external text" href="http://auto.howstuffworks.com/catalytic-converter.htm">catalytic converter</a></li> <li>University of Plymouth: <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070206060439/http://www.tech.plym.ac.uk/sme/ther305-web/Combust1.PDF">Engine Combustion primer</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKamm" class="citation journal cs1">Kamm, Richard W. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101120124152/http://amtonline.com/publication/article.jsp?pubId=1&id=1171">"Mixed Up About Fuel Mixtures?"</a>. <i>Aircraft Maintenance Technology</i> (February 2002). 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Air–fuel ratio - Wikipedia