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<div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Critical considerations in combustion phenomenon</span> </div> </a> <ul id="toc-Critical_considerations_in_combustion_phenomenon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simple_chemical_reacting_system_model" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Simple_chemical_reacting_system_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Simple chemical reacting system model</span> </div> </a> <ul id="toc-Simple_chemical_reacting_system_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Eddy_break–up_model" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eddy_break–up_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Eddy break–up model</span> </div> </a> <ul id="toc-Eddy_break–up_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Laminar_flamelet_model" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Laminar_flamelet_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Laminar flamelet model</span> </div> </a> <ul id="toc-Laminar_flamelet_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Presumed_probability_distribution_function_model" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Presumed_probability_distribution_function_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Presumed probability distribution function model</span> </div> </a> <ul id="toc-Presumed_probability_distribution_function_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conditional_moment_closure" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Conditional_moment_closure"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Conditional moment closure</span> </div> </a> <ul id="toc-Conditional_moment_closure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_models" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_models"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Other models</span> </div> </a> <ul id="toc-Other_models-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">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>Combustion models for CFD</b> refers to combustion models for <a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">computational fluid dynamics</a>. <a href="/wiki/Combustion" title="Combustion">Combustion</a> is defined as a chemical reaction in which a fuel reacts with an oxidant to form products, accompanied with the release of energy in the form of heat. Being the integral part of various engineering applications like: <a href="/wiki/Internal_combustion_engine" title="Internal combustion engine">internal combustion engines</a>, <a href="/wiki/Aircraft_engine" title="Aircraft engine">aircraft engines</a>, <a href="/wiki/Rocket_engine" title="Rocket engine">rocket engines</a>, <a href="/wiki/Industrial_furnace" title="Industrial furnace">furnaces</a>, and <a href="/w/index.php?title=Power_station_combustor&action=edit&redlink=1" class="new" title="Power station combustor (page does not exist)">power station combustors</a>, combustion manifests itself as a wide domain during the design, analysis and performance characteristics stages of the above-mentioned applications.<sup id="cite_ref-one_1-0" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> With the added complexity of chemical kinetics and achieving reacting flow mixture environment, proper modeling physics has to be incorporated during <a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">computational fluid dynamic (CFD)</a> simulations of combustion. Hence the following discussion presents a general outline of the various adequate models incorporated with the Computational fluid dynamic code to model the process of combustion.<sup id="cite_ref-two_2-0" class="reference"><a href="#cite_note-two-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Combustion_models_for_CFD&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Computational fluid dynamics modeling of combustion calls upon the proper selection and implementation of a model suitable to faithfully represent the complex physical and chemical phenomenon associated with any combustion process. The model should be competent enough to deliver information related to the species concentration, their volumetric generation or destruction rate and changes in the parameters of the system like enthalpy, temperature and mixture density. The model should be capable of solving the general transport equations for fluid flow and heat transfer as well as the additional equations of combustion chemistry and <a href="/wiki/Chemical_kinetics" title="Chemical kinetics">chemical kinetics</a> incorporated into that as per the simulating environment desired<sup id="cite_ref-one_1-1" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Critical_considerations_in_combustion_phenomenon">Critical considerations in combustion phenomenon</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Combustion_models_for_CFD&action=edit&section=2" title="Edit section: Critical considerations in combustion phenomenon"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The major consideration during any general combustion process includes the mixing time scale and the reacting time scale elapsed for the process. The flame type and the type of mixing of flow streams of the constituents also have to be taken into account. Apart from that as far as the kinetic complexity of the reaction is concerned, the reaction proceeds in multiple steps and what appears as a simple one line reaction actually completes after a series of reactions.<sup id="cite_ref-one_1-2" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-two_2-1" class="reference"><a href="#cite_note-two-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Also the transport equations for mass fractions of all the species as well as the enthalpy generated during the reaction have to be solved. Hence even the simplest combustion reaction involves very tedious and rigorous calculation if all the intermediate steps of the combustion process, all transport equations and all flow equations have to be satisfied simultaneously. All these factors will have a significant effect on the computational speed and time of the simulation. But with proper simplifying assumptions Computational fluid dynamic modeling of combustion reaction can be done without substantial compromise on the accuracy and convergence of the solution.<sup id="cite_ref-two_2-2" class="reference"><a href="#cite_note-two-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The basic models used for the same are covered in the following paragraphs. </p> <div class="mw-heading mw-heading2"><h2 id="Simple_chemical_reacting_system_model">Simple chemical reacting system model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Combustion_models_for_CFD&action=edit&section=3" title="Edit section: Simple chemical reacting system model"><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">Main article: <a href="/wiki/Simple_chemical_reacting_system" title="Simple chemical reacting system">Simple chemical reacting system</a></div> <p>This model takes into consideration only the final concentration of species and takes into account only the global nature of combustion process where the reaction proceeds infinitely fast as a single step process without much stress on the detailed kinetics involved.<sup id="cite_ref-one_1-3" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The reactants are assumed to react in <a href="/wiki/Stoichiometric" class="mw-redirect" title="Stoichiometric">stoichiometric</a> proportions. The model also deduces a linear relationship between the mass fractions of fuel, oxidant and the non dimensional variable mixture fraction.<sup id="cite_ref-two_2-3" class="reference"><a href="#cite_note-two-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The model also takes into account an additional assumption that the mass diffusion coefficients of all species are equal.<sup id="cite_ref-six_3-0" class="reference"><a href="#cite_note-six-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Owing to this additional assumption the model only solves one extra partial differential equation for mixture fraction and after solving the transport equation for the mixture fraction the corresponding mass fractions for fuel and oxidant are calculated. </p><p>This model can very well be applied to a combustion environment where laminar diffusion effects are dominant and the combustion proceeds via non premixed fuel and oxidant streams diffusing into each other giving rise to a laminar flame.<sup id="cite_ref-one_1-4" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Eddy_break–up_model"><span id="Eddy_break.E2.80.93up_model"></span>Eddy break–up model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Combustion_models_for_CFD&action=edit&section=4" title="Edit section: Eddy break–up model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Eddy_break-up_model_for_combustion" class="mw-redirect" title="Eddy break-up model for combustion">Eddy break-up model for combustion</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Combustor-Temp-Plane.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Combustor-Temp-Plane.png/300px-Combustor-Temp-Plane.png" decoding="async" width="300" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Combustor-Temp-Plane.png/450px-Combustor-Temp-Plane.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Combustor-Temp-Plane.png/600px-Combustor-Temp-Plane.png 2x" data-file-width="3984" data-file-height="2892" /></a><figcaption>Simulation of can combustor using eddy dissipation model.</figcaption></figure> <p>This model is used when <a href="/w/index.php?title=Turbulent_mixing&action=edit&redlink=1" class="new" title="Turbulent mixing (page does not exist)">turbulent mixing</a> of the constituents has to be taken into consideration. The k/Ɛ turbulent time scale is used to calculate the reaction rate. A comparison between the turbulent dissipation rates of the fuel, oxidant and products is done and the minimum amongst all is taken as the rate of the reaction. The transport equations for the mass fractions of the constituents are solved using this rate of reaction.<sup id="cite_ref-one_1-5" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Apart from this a mean enthalpy equation is also solved and temperature, density and viscosity are calculated accordingly. The model can also be implemented when finite rate kinetically controlled reaction is to be simulated. In such situation while deciding the rate of the reaction the Arrhenius kinetic rate expression is also taken into account and the rate of reaction is taken as minimum amongst the turbulent dissipation rates of all the constituents and the Arrhenius kinetic rate expression.<sup id="cite_ref-two_2-4" class="reference"><a href="#cite_note-two-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Since turbulent mixing governs the characteristics of this model, there exists a limit to the quality of the combustion simulation depending upon the type of the turbulent model implemented to represent the flow. The model can also be modified to account for mixing of fine structures during the turbulent reaction. This modification of the model results in the eddy dissipation model which consider the mass fraction of fine structures in its calculations.<sup id="cite_ref-one_1-6" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Laminar_flamelet_model">Laminar flamelet model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Combustion_models_for_CFD&action=edit&section=5" title="Edit section: Laminar flamelet model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Laminar_flamelet_model" title="Laminar flamelet model">Laminar flamelet model</a></div> <p>This model approximates the turbulent flame as a series of laminar flamelet regions concentrated just around the stoichiometric surfaces of the reacting mixture.<sup id="cite_ref-one_1-7" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> This model exploits the use of experimental data for determining relations between the variables considered like mass fraction, temperature etc. The nature and type of dependence of the variables is predicted through experimental data obtained during laminar diffusion flame experiment and laminar flamelet relationship is deduced based on the same. These relationships are then used to solve the transport equations for species mass fraction and mixture composition.<sup id="cite_ref-two_2-5" class="reference"><a href="#cite_note-two-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The model can very well be implemented for situations where concentration of minor species in the combustion is to be computed like quantifying the generation of pollutants.<sup id="cite_ref-one_1-8" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A simple enhancement to the model results in the flamelet time scale model which takes finite rate kinetics effect into consideration. The flamelet time scale model produces steady laminar flamelet solution when reaction proceeds very fast and captures the finite rate effects when reaction chemistry is dominant.<sup id="cite_ref-three_4-0" class="reference"><a href="#cite_note-three-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Presumed_probability_distribution_function_model">Presumed probability distribution function model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Combustion_models_for_CFD&action=edit&section=6" title="Edit section: Presumed probability distribution function model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This model takes into account a statistical approach for calculating the variables like species mass fractions, temperature and density while the mixture composition is calculated at the grids.<sup id="cite_ref-two_2-6" class="reference"><a href="#cite_note-two-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Then these all variables are calculated as functions of the mixture fraction around a presumed <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a> function.<sup id="cite_ref-one_1-9" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-five_5-0" class="reference"><a href="#cite_note-five-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The model can produce satisfactory results for turbulent reactive flows where convection effects due to mean and fluctuating components of velocity are dominant.<sup id="cite_ref-four_6-0" class="reference"><a href="#cite_note-four-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The model can be extended for adiabatic as well as non adiabatic conditions. </p> <div class="mw-heading mw-heading2"><h2 id="Conditional_moment_closure">Conditional moment closure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Combustion_models_for_CFD&action=edit&section=7" title="Edit section: Conditional moment closure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Conditional moment closure (CMC) is an advanced combustion model. The basic idea is to model the chemical source based on <a href="/wiki/Conditional_expectation" title="Conditional expectation">conditional averages</a>. The model was first introduced for non-premixed flows and hence the conditioning is done in the mixture fraction.<sup id="cite_ref-Cant_Mastorakos_2007_7-0" class="reference"><a href="#cite_note-Cant_Mastorakos_2007-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Other_models">Other models</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Combustion_models_for_CFD&action=edit&section=8" title="Edit section: Other models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following are some of the other relevant models used for computational fluid dynamic modeling of combustion. </p> <ul><li>The <a href="/w/index.php?title=Chemical_equilibrium_model&action=edit&redlink=1" class="new" title="Chemical equilibrium model (page does not exist)">chemical equilibrium model</a></li> <li>The <a href="/wiki/Flamelet_generated_manifold" title="Flamelet generated manifold">Flamelet generated manifold</a> model</li> <li>The <a href="/w/index.php?title=Flame_surface_density_model&action=edit&redlink=1" class="new" title="Flame surface density model (page does not exist)">flame surface density model</a></li> <li>The <a href="/w/index.php?title=Large_eddy_simulation_model&action=edit&redlink=1" class="new" title="Large eddy simulation model (page does not exist)">large eddy simulation model</a></li></ul> <p>The chemical equilibrium model considers the effect of intermediate reactions during turbulent combustion.<sup id="cite_ref-one_1-10" class="reference"><a href="#cite_note-one-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The concentration of species is calculated when the combustion reaction reaches equilibrium state. The species concentration is calculated as a function of mixture fraction by deploying certain equilibrium calculation programs available to serve the purpose. The conditional closure model solves the transport equations for the mean components of the flow properties without considering the fluctuating composition of the reaction mixture.<sup id="cite_ref-four_6-1" class="reference"><a href="#cite_note-four-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <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=Combustion_models_for_CFD&action=edit&section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-one-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-one_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-one_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-one_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-one_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-one_1-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-one_1-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-one_1-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-one_1-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-one_1-8"><sup><i><b>i</b></i></sup></a> <a href="#cite_ref-one_1-9"><sup><i><b>j</b></i></sup></a> <a href="#cite_ref-one_1-10"><sup><i><b>k</b></i></sup></a></span> <span class="reference-text">“An introduction to Computational Fluid Dynamics-- the finite volume method” H.K. Versteeg and W.Malalasekara Pearson Education limited.p.357</span> </li> <li id="cite_note-two-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-two_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-two_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-two_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-two_2-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-two_2-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-two_2-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-two_2-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text">An introduction to Computational Fluid Dynamics-- the finite volume method” H.K. Versteeg and W. Malalasekera Longman Group limited.p.210</span> </li> <li id="cite_note-six-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-six_3-0">^</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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.cham.co.uk/phoenics/d_polis/d_lecs/general/combust.htm#2">"Combust.HTM"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Combust.HTM&rft_id=http%3A%2F%2Fwww.cham.co.uk%2Fphoenics%2Fd_polis%2Fd_lecs%2Fgeneral%2Fcombust.htm%232&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACombustion+models+for+CFD" class="Z3988"></span></span> </li> <li id="cite_note-three-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-three_4-0">^</a></b></span> <span class="reference-text">9-rao-rutland.pdf---“A Flamelet Time Scale combustion model for turbulent combustion in KIVA” Shrikanth Rao and Christopher J. Rutland( Engine Research Center, UW Madison.)</span> </li> <li id="cite_note-five-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-five_5-0">^</a></b></span> <span class="reference-text">Pope_NACM_91.pdf—“combustion modeling using probability density function methods” S.B.Pope.</span> </li> <li id="cite_note-four-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-four_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-four_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Pope_ACAC_97.pdf---“Turbulence Combustion Modelling: fluctuations and chemistry (advanced computation and analysis of combustion: 310-320)” S.B.Pope (Sibley School of Mechanical and Aerospace Engineering Cornell University, Ithaca NY).</span> </li> <li id="cite_note-Cant_Mastorakos_2007-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cant_Mastorakos_2007_7-0">^</a></b></span> <span class="reference-text">Cant, R.S. & Mastorakos, E. <i>An Introduction to Turbulent Reacting Flows</i>. Imperial College Press, London. 2007.</span> </li> </ol></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Combustion_models_for_CFD&oldid=1241937587">https://en.wikipedia.org/w/index.php?title=Combustion_models_for_CFD&oldid=1241937587</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Computational_fluid_dynamics" title="Category:Computational fluid dynamics">Computational fluid dynamics</a></li><li><a href="/wiki/Category:Combustion_engineering" title="Category:Combustion engineering">Combustion engineering</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 24 August 2024, at 00:59<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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