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A new particle interaction mixing model for turbulent dispersion and turbulent reactive flows
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10.1063/1.3327288
/content/aip/journal/pof2/22/3/10.1063/1.3327288
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/3/10.1063/1.3327288

Figures

Image of FIG. 1.
FIG. 1.

Simulation of single-scalar mixing with a mean scalar gradient. Scalar trajectories (a) of particle (solid line), the corresponding drift particles (dashed line) and (dashed-dotted line), and (b) the associated drift particle lifetimes.

Image of FIG. 2.
FIG. 2.

The first two columns show density plots of planar slices through the initial scalar fields and . Contour plots of the corresponding joint scalar PDFs are shown in the third column. The ten contour levels range from 0.01 to 1 (black) and represent the PDF normalized by its maximum value. The rows correspond to different length scale pairs listed in Table II.

Image of FIG. 3.
FIG. 3.

Temporal evolution of the mechanical-to-scalar time scale ratio based on Fig. 14 of the DNS study (Ref. 19). and of case C and of case D (solid line); and of case A, of case D, and of case E (dashed line); of case E (dashed-dotted line); and of case B (dotted line).

Image of FIG. 4.
FIG. 4.

Temporal evolution of the standard deviation of the first scalar (solid lines) and the second scalar (dashed lines) for the test cases (a) A to (e) E. The thick lines represent the mixing model results and the thin lines the DNS predictions (Fig. 12 in Ref. 19). The dotted lines correspond to a decay given by Eq. (5) with .

Image of FIG. 5.
FIG. 5.

Temporal evolution of the skewness (curves with values ) and the flatness (curves with values ) of the first scalar (solid lines) and the second scalar (dashed lines) for the test cases (a) A to (e) E. The thick lines represent the mixing model results and the thin lines the DNS predictions (Fig. 11 in Ref. 19).

Image of FIG. 6.
FIG. 6.

In the first column the normalized joint scalar PDF and in the second column standard normal PDFs (solid lines), the normalized marginal PDFs (dashed lines) and (dots) are plotted. Rows (a), (d), and (e) correspond to cases A, D, and E.

Image of FIG. 7.
FIG. 7.

Scalar flatness (solid line) in the three-stream problem as a function of the mixing model parameter . With the values for (dashed line) the correct scalar variance decay is resulting.

Image of FIG. 8.
FIG. 8.

Evolution of the joint scalar PDF for case A; (a) DNS, (b) mixing model; the ten contour levels range from 0.01 to 1 (black) and represent the PDF normalized by its maximum value.

Image of FIG. 9.
FIG. 9.

Marginal PDFs for case A; (a) , (b) ; DNS (thin lines), mixing model (thick lines).

Image of FIG. 10.
FIG. 10.

Evolution of the conditional average of the scalar diffusion rate for case A; (a) DNS, (b) mixing model; the ten contour levels range from 0.01 to 1 (black) and represent normalized by its maximum value; the streamlines are parallel to .

Image of FIG. 11.
FIG. 11.

Evolution of the joint scalar PDF for case B; same as Fig. 8.

Image of FIG. 12.
FIG. 12.

Evolution of the conditional average of the scalar diffusion rate for case B; same as Fig. 10.

Image of FIG. 13.
FIG. 13.

(a) Evolution of the joint scalar PDF and (b) the conditional average of the scalar diffusion rate for case C; the ten contour levels range from 0.01 to 1 (black) and represent in (a) the PDF normalized by its maximum value and in (b) normalized by its maximum value; the streamlines in (b) are parallel to .

Image of FIG. 14.
FIG. 14.

Evolution of the joint scalar PDF for case D; same as Fig. 8.

Image of FIG. 15.
FIG. 15.

Evolution of the conditional average of the scalar diffusion rate for case D; same as Fig. 10.

Image of FIG. 16.
FIG. 16.

Evolution of the conditional average of the scalar diffusion rate for case E; same as Fig. 10.

Image of FIG. 17.
FIG. 17.

Evolution of the joint scalar PDF for case E; same as Fig. 8.

Image of FIG. 18.
FIG. 18.

Nondimensional scalar variance resulting from the new mixing model as function of the integer parameter and the number of particles .

Image of FIG. 19.
FIG. 19.

Scalar flatness resulting from the new mixing model as function of the integer parameter and the number of particles .

Image of FIG. 20.
FIG. 20.

Conditional mean of the scalar diffusion rate as a function of the velocity sample space coordinate and for different values of the integer parameter .

Image of FIG. 21.
FIG. 21.

Correlation coefficient between the scalar diffusion rate and the velocity as function of the integer parameter and the number of particles .

Image of FIG. 22.
FIG. 22.

Nondimensional scalar variance resulting from the modified Curl mixing model as function of the integer parameter and the number of particles .

Image of FIG. 23.
FIG. 23.

Scalar flatness resulting from the modified Curl mixing model as function of the integer parameter and the number of particles .

Image of FIG. 24.
FIG. 24.

Nondimensional scalar variance (solid line), scalar flatness (dashed line), correlation coefficient (dashed-dotted line), and (dotted line) as a function of . Lines with and without symbols correspond to (no velocity conditioning) and , respectively.

Image of FIG. 25.
FIG. 25.

Conditional mean of the scalar diffusion rate as function of the velocity sample space coordinate and different ratios.

Image of FIG. 26.
FIG. 26.

Scalar flatness as function of the number of (a) particles and (b) scalars .

Image of FIG. 27.
FIG. 27.

In (a), the normalized joint scalar PDF that is resulting in the mean scalar gradient test case with and is plotted. In (b), the corresponding marginal PDFs (dashed line) and (dots) are compared to a standard normal PDF (solid line).

Image of FIG. 28.
FIG. 28.

Computational cost (CPU-time) as function of the number of (a) particles and (b) scalars ; (solid line) mixing model performance (dotted line) linear increase.

Tables

Generic image for table
Table I.

Mixing model assessment based on the requirements listed by Subramaniam and Pope (Ref. 12) and Fox (Ref. 17). The symbols ●, ○, and × refer to requirements that are completely, partly, and not fulfilled, respectively. The accuracy of a mixing model that includes initial scalar length scale dependencies, and Re, Sc or Pr number effects depends on the corresponding mixing time scale model.

Generic image for table
Table II.

Scalar field parameters of the different DNS cases in Ref. 19.

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/content/aip/journal/pof2/22/3/10.1063/1.3327288
2010-03-11
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A new particle interaction mixing model for turbulent dispersion and turbulent reactive flows
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/3/10.1063/1.3327288
10.1063/1.3327288
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