Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mechanical Engineering

Committee Chair/Advisor

Tong, Chenning

Committee Member

Ma , Lin

Committee Member

Miller , Richard S

Committee Member

Park , Chanseok


The filtered mass density function (FMDF) of mixture fraction, temperature and species used in large eddy simulation (LES) of turbulent combustion is studied experimentally using line images obtained in turbulent partially premixed methane flames (Sandia flames D and E). Cross-stream filtering is employed to obtain the FMDF and other filtered variables. The mean of the FMDF conditional on the subgrid-scale (SGS) scalar variance at a given location are found to vary from unimodal to bimodal, corresponding to quasi-equilibrium distributed reaction zones and laminar flamelets (including extinguished flamelets), respectively. The conditionally filtered mixture fraction dissipation for small SGS variances has a relatively weak dependence on the mixture fraction, and is not sensitive to temperature for extinguished samples. For large SGS variance the large dissipation is concentrated in the cliffs and increases with decreasing temperature. The conditionally filtered temperature dissipation for small SGS variances is the highest for intermediate temperature. For large SGS variance the dependence is more complex and the pilot gas appears to be playing an important role. The conditionally filtered scalar and temperature diffusion for small SGS variance have a simple structure. For large SGS variance the diffusion structure is much more complex, with the pilot and local extinction also playing important roles. The results show that it is important that mixing models for filtered density function methods be able to account for the different SGS mixture fraction and temperature structures for small and large SGS variance. The different SGS mixture fraction structures for small and large SGS variances, as reflected by the unimodal and bimodal FMDF, have a strong impact on the small-scale mixing and turbulence-chemistry interaction, as reflected by the results for the conditionally filtered dissipation rates and diffusion. The results have implications for understanding and modeling multiple reactive scalar SGS mixing.
Scalar dissipation rate is an important quantity in turbulent mixing and combustion. Its measurement depends on two opposite trends, noise and resolution effects, making their separation and accurate corrections difficult. A major task in dissipation rate correction, therefore, is to isolate each effect. A conditional sampling-based method for correcting noise and resolution effects for scalar dissipation rate measurements is developed. The conditional-sampling method uses instantaneous local scalar mean and variance as conditioning variables, and is based in part on Kolmogorov's refined similarity hypotheses. It ensures selection of instantaneous fully resolved local scalar fields, which are analyzed to determine the measurement noise. Noise correction is applied to potentially under-resolved local scalar fields, also selected using the conditional-sampling procedure, effectively separating the effects of noise from those of resolution. The error function is used as a model for the potentially under-resolved local scalar fields to evaluate their dissipation length scales and to make corrections for the dissipation rate. The present method uses local instead of spectral analysis; therefore, can be applied to the mean scalar dissipation rate conditional on the scalar values. Applications of the method to scalar dissipation rate in a slightly heated turbulent jet and turbulent flames show excellent results, validating the method.



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