Date of Award

December 2021

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

Committee Member

Chenning Tong

Committee Member

Richard Miller

Committee Member

Jay Ochterbeck

Committee Member

Xiangchun Xuan


The scalar-scalar-gradient filtered joint density function (FJDF) and its transport equation for large eddy simulation (LES) of turbulent combustion is studied experimentally. Measurements are made in the fully developed region of an axisymmetric turbulent jet (with jet Reynolds number UjDj/ν = 40000) using an array consisting of three X-wires and three resistance-wire temperature probes. Filtering in the cross-stream and streamwise directions are realized by using the array and by invoking Taylor’s hypothesis, respectively. The FJDF and the terms in the transport equation are analyzed using their means conditional on the filtered scalar and the subgrid-scale (SGS) scalar variance. The FJDF is unimodal when the SGS scalar variance is small compared to its mean value. The scalar gradient depends weakly on the SGS scalar. For large SGS variance the FJDF is bimodal and the gradient depends strongly on the SGS scalar; therefore the often-invoked independence assumption is not valid. The SGS scalar under such a condition contains a diffusion layer structure and the SGS mixing is similar to the early stages of binary mixing. The iso-scalar surface in the diffusion layer has a lower surface-to-volume ratio than those in a well mixed scalar. The conditionally filtered diffusion of the scalar gradient has a S- shaped dependence on the scalar gradient, which is expected to be qualitatively different from that of a reactive scalar under fast chemistry conditions. However, because modeling is performed at a higher level and because the scalar-scalar- gradient FJDF contains the information about the scalar dissipation and the surface-to-volume ratio, the FJDF approach is expected to be more accurate than scalar filtered density function approaches and has the potential to model turbulent combustion over a wide range of Damköhler numbers.

An alternative for LES, the self-conditioned fields approach, is studied experimentally using the three-scalar mixing setup. This flow approximates the mixing process in turbulent non-premixed flames as mixing between the center jet scalar and the co-flow air must involve the annulus scalar. The physical-space scalar structures are investigated using the self-conditioned JPDF and the terms in the self-conditioned JPDF transport equation. The self-conditioned JPDF conditioning on the filtered fields (the filtered scalar and SGS variance) is studied first. The results are consistent with the FJDF results with additional spatial structures obtained. The transition of the peaks in the self-conditioned JPDF directly indicates a ramp-cliff structure in the physical space. The self-conditioned JPDF conditioning on the proper orthogonal decomposition (POD) coefficients is also studied. Unlike the locally filtered scalars, POD can best capture scalar structures and is a full-field parameter. The conditioning variables in the self-conditioned JPDF and their values are the same. Therefore the spatial variations of self-conditioned JPDF can be investigated in the entire field. Similar to conditioning on the locally filtered scalar and SGS variance, POD coefficients of scalar field and scalar square field are used as the conditioning variables. Our analysis shows the mixing process depends on the POD coefficient of the scalar square field. For small POD coefficient of the scalar square field, the scalars are well mixed with unimodal self-conditioned JPDF and the initial three-scalar mixing configuration is lost. For large POD coefficient of the scalar square field, the scalars are highly segregated with bimodal self-conditioned JPDF at radial locations near the peak of the variance of the center jet scalar. For the higher velocity ratio cases, the peak value of variance is larger and also the variance value is larger close to the centerline, hence resulting in stronger bimodality and appearance of the bimodal self-conditioned JPDF closer to the jet centerline. For the lower velocity ratios cases, the bimodal range extends further towards the jet edge due to a wider variance profile and larger values of variance. For the self-conditioned diffusion, the streamlines first converge to a manifold in the scalar space and continue along with the manifold to a stagnation point. The manifold is well defined at locations with bimodal self-conditioned JPDF, providing a mixing path between the center jet scalar and co-flow air. The initial three-scalar mixing configuration is maintained. The self-conditioned dissipation result further reveals the scalar structures in the flow. For the bimodal self-conditioned JPDF, the ramp-cliff structure is less steep at location with the strongest bimodality, i.e., smaller dissipation rate of the center jet scalar. The center jet scalar is similar to the mixture fraction in the non-premixed flames. The spatial structures obtained in the self-conditioned approach provides a better understanding of the mixing process in the turbulent reactive flows.

Calculation of the self-conditioned field generally requires 2-D images due to its spatial dependence. However, 2-D measurements of mixture fraction in flames remain a challenge due to the limitations of existing measurement techniques, such as weak signals, requiring quenching corrections or limited to certain flames. A new technique that overcomes these limitations is developed to obtain 2-D images in piloted methane/air flames by utilizing the much stronger two-photon laser-induced fluorescence (TPLIF) of iodine atoms. Photodissociation characteristics of iodine are analyzed with 532nm and 266 nm lasers.



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