Center for TurbulenceResearch Annual Research Briefs Incorp orating realistic chemistry into direct numerical simulations of turbulent nonpremixed combustion By W K Bushe R W Bilger AND G R Ruetsch Motivation and ob jectives Combustion is an imp ortant phenomenon in many engineering applications Com bustion of hydro carb ons is still by far the most common source of energy in the world In many devices of interestsuch as in furnaces diesel engines and gas turbinesthe combustion takes place in what is known as the nonpremixed regime The fuel and oxidizer are initially unmixed and in order for chemical reac tion to take place they must rst mix together In this regime the rate at which fuel and oxidizer are consumed and at which heat and pro duct sp ecies are pro duced is therefore to a large extent controlled by mixing In virtually all engineering applications of combustion pro cesses the ow in which the combustion takes place is turbulent Furthermore the combustion pro cess it self is usually describ ed byavery large system of elementary chemical reactions These chemical kinetic mechanisms are usually extremely sti and involve for longer chain hydro carb on sp ecies hundreds of chemical sp ecies The governing equations describing the chemical comp osition are closely coupled to those describing the turbulent transp ort Also the chemical reaction rates are nonlinear and strongly dep end on the instantaneous comp osition and temp erature Modeling turbulent combustion In order to mo del turbulent combustion one must circumvent what is known as the chemical closure problem The chemical source term in the Reynolds averaged sp ecies transp ort equation must b e mo deled Several mo dels have b een prop osed to achievechemical closure but many of these are only applicable to limited ow or chemistry regimes For example in the fast chemistry limit the chemistry is assumed to b e innitely fast in comparison to the turbulent mixing pro cess Bil ger which completely neglects the inuence of nite rate chemistry on the combustion pro cess Laminar amelet mo dels Peters are only applicable in what is known as the amelet regime where the chemical reactions take place along an interface which is thinner than the smallest turbulent length scale The PDF mo del Pop e where the transp ort equation for the joint probability density function of the comp osition vector is solved is only practical for systems with very simple chemical kinetic mechanismssuch as reduced chemical kinetic mechanisms The University of Sydney Australia W K Bushe R W Bilger G R Ruetsch A new metho d for closing the chemical source term was recently prop osed in dep endently by Klimenko and Bilger a b In the Conditional Moment Closure CMC metho d the transp ort equations are conditionally aver aged with the condition b eing some variable on which the chemical reaction rates are known to dep end For nonpremixed combustion an appropriate conditioning variable is the mixture fraction This is a conserved scalar suitably dened to haveavalue of zero in pure oxidizer and unity in pure fuel The average of the mass fraction Y of a particular sp ecies I conditional on the I mixture fraction Z having some value is Q x t hY x tjZ x t i I k I k k Foraowinwhich the velo city and mixture fraction elds are b oth isotropic and homogeneous the conditionally averaged transp ort equation for Y b ecomes Smith I Q Q Z Z I I h jZ i hD jZ i I t x x i i the righthand side of which has two unclosed terms the conditionally averaged reaction rate and a mixing term in which app ears the conditionally averaged scalar Z Z dissipation hD jZ i x x i i There are several mo dels available for the scalar dissipation such as presumed PDF mo dels Mell et al and mapping closure mo dels Bushe Clo sure of the reaction term can b e achieved through the rst order CMC hyp othesis that the conditional average of the chemical source term of some sp ecies I which is a function of the comp osition vector Y and the temp erature T can b e mo d J eled byevaluating the chemical reaction rates using the conditional averages of the comp osition vector Q and temp erature hT jZ iThus J h Y T jZ i Q hT jZ i J I J I Various renements to the closure hyp othesis for the chemical reaction term have b een prop osed using either a second conditioning variable Bilger Bushe or a second moment Li Bilger Smith which are intended to extend the validity of the closure hyp othesis to account for ignition and extinction phenomenon and to improve the p erformance of the mo del for chemical reactions where the activation energies are very large Validation of turbulent combustion models Work attempting to improve and validate mo dels for turbulent combustion has b een hamp ered byalack of adequate exp erimental results Only recently have exp erimental techniques b een devised whichmightprovide the necessary insight these exp eriments metho ds are still quite limited in the information they provide and are also extremely exp ensive and dicult to p erform As an alternative to exp eriments Direct Numerical Simulation DNS of the governing equations can b e p erformed however to date suchsimulations have b een Incorporating realistic chemistry into DNS of combustion limited byavailable computer resourcesand by the complexity and stiness of the asso ciated equationsto simple chemical kinetic mo dels Vervisch With the advent of new techniques for the systematic reduction of chemical ki netic mechanisms new reduced kinetic mechanisms are nowavailable which are still relatively simple but which retain sucient complexity from the original mecha nism to provide go o d predictions of ame structure and reaction rates In a previous study which implements such a reduced mechanism in DNS Swaminathan and Bil ger a b the owwas assumed to b e incompressible so that eects of heat release on the owwere neglected While the results of this study havebeen encouraging validation of the CMC metho d against this constant prop erty DNS data is not completely convincing There is clearly a need to obtain DNS data using realistic chemical kinetics in turbulence where eects of the heat release on the ow are included In the present study a reduced kinetic mechanism has b een incorp orated into a fully compressible DNS co de The results of the simulations will b e used for the validation and hop efully improvement of current combustion mo dels such as the CMC mo del describ ed ab ove Accomplishments Chemistry Original kinetic mechanism The chemical kinetic mechanism that was used in the simulations is one repre sentative of the oxidation of a methanenitrogen mixture byanoxygennitrogen mixture There are three reactions in the mechanism the rst two represent the oxidation of the methane Williams and the third represents the formation of nitric oxide The reactions are Fuel Oxi Int Prod I Int Oxi Prod I I N Oxi NO I I I where Fuel is CH Oxi is O Int is H CO andProd is H O CO Rates for reactions I and I I expressed in terms of mass fractions are given by mol cm K T exp Y Y I Fuel H g s K T and K cm T Y Y II Oxi H M g s The mass fraction of Hydrogen which app ears in the b oth of these reaction rate expressions is given by the steady state approximation Y Y K Oxi Int T exp K T Y e H Y Prod W K Bushe R W Bilger G R Ruetsch with Y K F uel exp K T exp Y T Oxi The inuence of the enhanced third b o dy M app earing in the rate expression for reaction I I is Y Y Y Y M F uel Oxi Int Prod The rate expression for reaction I I I is obtained by placing the oxygen free radical in the simple Zeldovichmechanism ON NON NO NOO in steady state The concentration of the oxygen free radical is estimated by assum ing it is in partial equilibrium with the hydrogen and hydroxyl free radicals The resulting rate expression is mol cm Y Y Y K Prod N H exp III g s T Y Int The rate expressions in Eqs and eachgive the reaction rates in units of mol g s The rates of change of mass fractions can b e calculated by mixtur e multiplying the reaction rates by each participating sp ecies molecular weight gmol F uel I g mol Oxi I II III g mol I II Int g mol Prod I II g mol NO III The rate of change of energy due to chemical reaction is calculated bymultiplying the reaction rates byeach reactions enthalpy of formation k J mol k J mol k J mol e I II III Simplifying the mechanism In order to reduce computational costs and to make the mechanism more tractable for mo deling purp oses the reaction rate expressions were simplied Incorporating realistic chemistry into DNS of combustion The equation for Eq contains the function f T T exp T which over a temp erature range from to K iswell approximated as b eing constantas seen in Fig a This was taken to b e which over that temp erature range predicts Eq within The expression for reaction I Eq contains the function g T T exp T This function can b e approximated by g T exp T as shown in Fig b also to within o ver the range of K The expression for the hydrogen freeradical mass fraction b ecomes Y K F uel Y exp H T Y Oxi Y Y Oxi Int exp K T Y Prod and the expression for the reaction rate of reaction I b ecomes mol cm K exp Y Y I Fuel H g s T Nondimensionalizing the mechanism The DNS co de for which the mechanism was b eing mo died uses the constant pressure sp ecic heat C the ratio of sp ecic heats