Kosaly, George

Mitarai, Satoshi

Riley, James J.

English

CaltechCONF

A Priori Testing of Turbulent Mixing Models for Subgrid-scaleMixing and Reaction ∗Satoshi Mitarai, James J. Riley, and George Kosa´lyDepartment of Mechanical Engineering,University of Washington, Seattle, WA 98195, USAUsing the data obtained from direct numerical simulations (DNS), a priori testingof turbulent mixing models for large-eddy simulations of non-premixed turbulentcombustion have been tested, in particular the IEM (Villermaux and Devillon[1]),the modified Curl (Janicka et al.[2]) and the EMST (Subramaniam and Pope[3]).The DNS is performed for single-step, non-premixed reactions developing in incom-pressible, isotropic, decaying turbulence where local flame extinction and re-ignitionoccur (cf. Figs. 1 and 2); the simulation domain is divided into subvolumes for test-ing. In order to demonstrate the ”true” performance of the mixing models, thetemporal evolution of the fluid particle positions and the exact value of the mixingfrequencies within each subvolume are obtained from the DNS, and are utilized intesting. Comparison of the model predictions with the DNS data shows that theEMST mixing model yields reasonable filtered quantities, such as the filtered tem-perature and filtered reaction rate, while the IEM and the modified Curl mixingmodels tend to underestimate the filtered quantities (cf. Figs. 3 and 4).A priori testing of a new mixing model proposed by the authors (Mitarai et al. [4])will also be presented. Among other things, this new mixing model accounts for thedifference between the mixing of passive and of reactive scalars, while the presentlyavailable mixing models do not distinguish between them. Given the Lagrangiantime series of the mixture fraction and its dissipation rate, this new model welldescribes the qualitative behavior of the Lagrangian time series of reactive scalars,and yields accurate quantitative statistics.∗ Supported by NSF grants CTS-9415280 and CTS-01339250.2FIG. 1: Temporal evolution of the mixture fractionfield on a two dimensional slice through the compu-tational domain.FIG. 2: Temporal evolution of temperature field onthe same two dimensional slice through the compu-tational domain as in Fig. 1.0 0.2 0.4 0.6 0.800.20.40.60.8 time=0.0 filtered T (DNS)filtered T (model)0 0.2 0.4 0.6 0.800.20.40.60.8 time=0.3 filtered T (DNS)filtered T (model)0 0.2 0.4 0.6 0.800.20.40.60.8 time=1.0 filtered T (DNS)filtered T (model)0 0.2 0.4 0.6 0.800.20.40.60.8 time=2.0 filtered T (DNS)filtered T (model)FIG. 3: The filtered temperatures computed fromthe modified Curl mixing model[2]) plotted againstthose from the DNS.0 0.2 0.4 0.6 0.800.20.40.60.8 time=0.0 filtered T (DNS)filtered T (model)0 0.2 0.4 0.6 0.800.20.40.60.8 time=0.3 filtered T (DNS)filtered T (model)0 0.2 0.4 0.6 0.800.20.40.60.8 time=1.0 filtered T (DNS)filtered T (model)0 0.2 0.4 0.6 0.800.20.40.60.8 time=2.0 filtered T (DNS)filtered T (model)FIG. 4: The filtered reaction rate computed fromthe EMST mixing model[3] plotted against thosefrom the DNS.[1] J. Villermaux and J. C. Devillon, in 2nd International Symposia on Chemical Reaction Engi-neering (ISCRE, Netherlands, 1972), p. B1.[2] J. Janicka, W. Kolbe, and W. Kollmann, J. Non-Equilib. Thermodyn. 4, 47 (1979).[3] S. Subramaniam and S. B. Pope, Combust. Flame 115, 487 (1998).[4] S. Mitarai, G. Kosa´ly, and J. J. Riley (2003), submitted to Combust. Flame.

A Priori Testing of Turbulent Mixing Models for Subgrid-scale Mixing and Reaction

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