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Turbulent dispersion from line sources in grid turbulence
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10.1063/1.3006069
/content/aip/journal/pof2/20/10/10.1063/1.3006069
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/10/10.1063/1.3006069

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the experimental setup showing the wind tunnel. The source (dot) is at a distance from the turbulence generating grid.

Image of FIG. 2.
FIG. 2.

Comparison of the centerline intensity of fluctuations obtained using the laminar thermal wake model: (dot-dashed line) and (solid line); Warhaft (Ref. 7) data (▼) and Warhaft (Ref. 7) data (▲); Sawford’s (Ref. 23) model calculations (dashed line) plotted against flight time from the source for source position and source size .

Image of FIG. 3.
FIG. 3.

Comparison of mixing rate definitions with flight time from the source: Modified mixing model (dashed line); IECM model (thick solid line), (thin solid line); Sawford’s (Ref. 23) empirical mixing rate (dot-dashed line).

Image of FIG. 4.
FIG. 4.

Width of the mean scalar profile normalized by the turbulence length scale at the source against normalized flight time from the source for source position ; from Eq. (11) (solid line) and from the present model calculations (◼).

Image of FIG. 5.
FIG. 5.

Comparison of the centerline intensity of fluctuations, , plotted against flight time from the source. Warhaft (Ref. 7) data: , (◼), , (▼), , (▲), and , (◆). Sawford’s (Ref. 23) calculations using the mixing rate given by Eq. (44): , (thin solid line) and , (thin dashed line). Present calculations: , (thick solid line), , (thick dashed line), and , (dotted line).

Image of FIG. 6.
FIG. 6.

Comparison of IECM model calculations with the mixing rate given by Eq. (17) with the model calculations done with Eq. (50) showing the centerline intensity of fluctuations, , against flight time from the source. IECM model calculations using mixing rate given by Eq. (17): , (thick dot-dashed line). Present calculations: , (thick dashed line) and , (thick solid line). Warhaft (Ref. 7) data: , (◼), , (▼), and , (▲).

Image of FIG. 7.
FIG. 7.

Radial profiles of rms scalar normalized by its centerline value at . Warhaft (Ref. 7) data: (▲), (◼), (●), and (◆). Present calculations: (dotted line), (dot-dashed line), (solid line), and (dashed line).

Image of FIG. 8.
FIG. 8.

Integral measure of the scalar variance in nondimensional form against flight time from the source. Present calculations (solid line); Warhaft (Ref. 7) data (●). The source of size is at .

Image of FIG. 9.
FIG. 9.

Higher moments on the centerline against flight time from the source: Present calculations (solid line); Sawford (Ref. 23) IECM calculations (dashed line); Sawford and Tivendale (Ref. 23) data (●): (a) skewness and (b) kurtosis .

Image of FIG. 10.
FIG. 10.

Radial profiles of higher-order moments measured at varying distances from the source. Present calculations (solid line); Sawford (Ref. 23) IECM calculations (dashed line); Sawford and Tivendale (Ref. 23) data (●): (a) skewness at , (b) skewness at , (c) skewness at , (d) kurtosis at , (e) kurtosis at , and (f) kurtosis at .

Image of FIG. 11.
FIG. 11.

Evolution of the centerline cross-correlation coefficient for various source spacings, . The sources are placed at a distance of from the turbulence generating grid: Warhaft (Ref. 7) data (●); Sawford (Ref. 23) model calculations (dot-dashed line); present calculations (solid line).

Image of FIG. 12.
FIG. 12.

Radial profiles of rms scalar normalized by their respective centerline values when the sources are positioned at from the turbulence grid for different spacings between the sources, : (a) and , (b) and , and (c) and ; present model calculations (solid line); Warhaft (Ref. 7) data: (●), (◼), and (◆).

Image of FIG. 13.
FIG. 13.

Radial profiles of the cross-correlation coefficient between sources 1 and 2 for different spacings between the two sources, . The sources are positioned at from the turbulence generating grid: (a) , (b) , (c) , and (d) . Present model calculations (solid line). Warhaft (Ref. 7) data: (●), (▲), (◼), (▼), and (◆).

Image of FIG. 14.
FIG. 14.

(a) Radial profiles of rms scalar corresponding to each of the four sources in an array, normalized by their respective centerline values at ; (b) radial profiles of rms scalar corresponding to ; (c) radial profiles of rms scalar corresponding to ; (d) radial profiles of rms scalar corresponding to ; (e) radial profiles of rms scalar corresponding to all the four sources. The radial profiles in (b)–(e) are normalized by the mean centerline value obtained from (a). Present model calculations (solid line); Warhaft (Ref. 7) data (●).

Image of FIG. 15.
FIG. 15.

Radial profiles of the cross-correlation coefficient between pairs of sources at . Diffusion behind an array of four sources is considered. The sources are positioned at from the turbulence grid: (a) , sources 2 and 3; (b) , sources 2 and 4; (c) , sources 1 and 4. Present model calculations (solid line); Warhaft (Ref. 7) data (●).

Image of FIG. 16.
FIG. 16.

Experimental data of decay of normalized scalar fluctuations, , downstream of a heated mandoline from the turbulence generating grid. Relevant parameters are listed in Table III: and (●), and (◼), and and (◆).

Image of FIG. 17.
FIG. 17.

Decay of normalized scalar fluctuations, , downstream of a heated mandoline from the turbulence generating grid. Experimental data: and (●), and (◼), and and (◆). Present model calculations are denoted by lines: and (solid line), and (dashed line), and and (dot-dashed line).

Image of FIG. 18.
FIG. 18.

Decay of normalized scalar fluctuations, , against flight time from the source. Experimental data: and (●), and (◼), and and (◆). Present model calculations are denoted by lines: and (solid line), and (dashed line), and and (dot-dashed line). A dashed line of slope is shown for reference.

Image of FIG. 19.
FIG. 19.

Effect of model coefficients and on scalar fluctuations. (a) Maximum centerline intensity of fluctuations, , against different placements of the source with respect to the turbulence grid, . (b) Centerline intensity of fluctuations, , against where . Symbols are from present calculations for different combinations of and : and (●), and (◼), and (▲), and (◆), and (▼), and and (). Solid horizontal lines correspond to the experimental data.

Image of FIG. 20.
FIG. 20.

Correlation coefficient between a pair of line sources at plotted for different source separations, , for various combinations of and . Symbols are from present calculations for different combinations of and : and (●), and (◼), and (▲), and (◆), and (▼), and and (). Solid horizontal lines correspond to the experimental data.

Image of FIG. 21.
FIG. 21.

Centerline intensity of fluctuations, , vs flight time from the source for and different values of : (solid line), (dashed line), and (dotted line).

Image of FIG. 22.
FIG. 22.

Mean plume width normalized by the turbulence integral scale at the source, , against flight time from the source for and different values of : (solid line), (dashed line), and (dotted line).

Image of FIG. 23.
FIG. 23.

Integral of scalar variance, , normalized by against flight time from the source for and different values of : (solid line), (dashed line), and (dotted line).

Image of FIG. 24.
FIG. 24.

Skewness and kurtosis against flight time from the source for and different values of : (solid line), (dashed line), and (dotted line).

Image of FIG. 25.
FIG. 25.

Maximum centerline intensity of fluctuation against for . The solid lines indicate 95% confidence intervals. Dashed line of slope 1/3 is shown for reference.

Image of FIG. 26.
FIG. 26.

Estimate of the centerline intensity of fluctuation as against for . The lines indicate 95% confidence intervals.

Image of FIG. 27.
FIG. 27.

Maximum centerline intensity of fluctuation against for : (●) and (◼). The lines indicate 95% confidence intervals.

Image of FIG. 28.
FIG. 28.

Estimate of the centerline intensity of fluctuation as against for : (●) and (◼). The lines indicate 95% confidence intervals.

Image of FIG. 29.
FIG. 29.

Centerline intensity of fluctuations, , vs flight time from the source at for different values of : (solid line), (dashed line), and (dotted line).

Image of FIG. 30.
FIG. 30.

Mean plume width normalized by the turbulence integral scale at the source, , against flight time from the source at for different values of : (solid line), (dashed line), and (dotted line).

Image of FIG. 31.
FIG. 31.

Integral of scalar variance, , normalized by against flight time from the source at for different values of : (solid line), (dashed line), and (dotted line).

Image of FIG. 32.
FIG. 32.

Skewness and kurtosis against flight time from the source at for different values of : (solid line), (dashed line), and (dotted line).

Image of FIG. 33.
FIG. 33.

Normalized mean plume width minus the effect of the source plotted against flight time from the source at for different values of : (solid line), (dashed line), and (dotted line). (The lines are indistinguishable.)

Image of FIG. 34.
FIG. 34.

Centerline intensity of fluctuations, , vs time, , at for different values of : (solid line), (dashed line), and (dotted line). (The lines are indistinguishable.)

Image of FIG. 35.
FIG. 35.

Maximum centerline intensity of fluctuation against for . The lines indicate 95% confidence intervals.

Image of FIG. 36.
FIG. 36.

Estimate of the centerline intensity of fluctuation as against for . The lines indicate 95% confidence intervals.

Tables

Generic image for table
Table I.

Parameters in the laboratory measurements for diffusion behind a single line source in grid turbulence (Ref. 7), effective source size , mesh spacing , position of the source with respect to the grid, , mean speed , velocity standard deviation at one mesh length from the grid, , velocity variance decay exponent , and molecular diffusivity .

Generic image for table
Table II.

Characteristics of the velocity field corresponding to the parameters in Table I; effective source size , source position relative to the grid, , Kolmogorov length scale , turbulence length scale , integral scale Reynolds number, , and Taylor scale Reynolds number at the source.

Generic image for table
Table III.

Parameters in the laboratory measurements of Warhaft and Lumley (Ref. 6). Definitions are given in Table I.

Generic image for table
Table IV.

Parameters corresponding to the cases performed in Sec. V F. Velocity variance at the source location (isotropic turbulence), , Velocity variance decay exponent , turbulence mesh spacing , mean speed , source size , Taylor scale Reynolds number at the source location, , and ratio of source to turbulence integral scale at the source location, .

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/content/aip/journal/pof2/20/10/10.1063/1.3006069
2008-10-31
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Turbulent dispersion from line sources in grid turbulence
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/10/10.1063/1.3006069
10.1063/1.3006069
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