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Near-wall passive scalar transport at high Prandtl numbers
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10.1063/1.2739402
/content/aip/journal/pof2/19/6/10.1063/1.2739402
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/6/10.1063/1.2739402

Figures

Image of FIG. 1.
FIG. 1.

Mean temperature profiles predicted by DNS of Schwertfirm and Manhart, empirical correlation of Kader, and three overlapping profiles predicted by the present computation: (1) under-resolved computation on points, (2) computation on points with spectral turbulent diffusivity, (3) under-resolved computation on grid.

Image of FIG. 2.
FIG. 2.

Various wall regions in the channel/flume flow at Prandtl numbers 25–500. Velocity—momentum layers (Pope, Ref. 28): viscous sublayer, buffer layer, log-law region. Temperature–thermal layers at : diffusive sublayer, thermal buffer layer, viscous-thermal buffer layer, thermal log-law region.

Image of FIG. 3.
FIG. 3.

Temperature rms fluctuations predicted by DNS of Schwertfirm and Manhart, and profiles predicted by the present computation.

Image of FIG. 4.
FIG. 4.

Turbulent heat flux profiles (top, streamwise; bottom, wall-normal) predicted by DNS of Schwertfirm and Manhart (Ref. 15) and three overlapping profiles predicted by the present computation.

Image of FIG. 5.
FIG. 5.

Budget of the temperature variance: comparison of Schwertfirm, Manhart DNS (solid lines) and the present computation (dashed lines)—first temperature field—under-resolved DNS.

Image of FIG. 6.
FIG. 6.

Temporal behavior of the volume averaged mean velocity and mean temperature (top) and volume averaged friction velocity and friction temperature (bottom).

Image of FIG. 7.
FIG. 7.

Mean temperature profiles of the calculations from Table I and temperature profiles of Kader (Ref. 33) (double-dotted-dashed line) and Mitrovic (Ref. 14) (dashed-dotted line) at and . Thin solid lines: cases 1a–5a from the Table I, long dashed lines: cases 1b–4b, short dashed line: case 5c.

Image of FIG. 8.
FIG. 8.

RMS-temperature fluctuations at and . Thin solid lines: cases 1a–5a from Table I; long dashed lines: cases 1b–4b; short dashed line: case 5c. Order in the legend corresponds to the top-to-down order of the curves maxima in the small inset graph.

Image of FIG. 9.
FIG. 9.

Skewness of the temperature fluctuations at and . Order in the legend corresponds to the top-to-down order of the curves in the graph at .

Image of FIG. 10.
FIG. 10.

Streamwise (top) and wall-normal (bottom) turbulent heat fluxes at and . Thin solid lines: cases 1a–5a from Table I; long dashed lines: cases 1b–4b; short dashed line: case 5c. Order in the legend of the top figure corresponds to the top-to-down order of the curves maxima in the small inset graph. Only two runs—cases 4a, 4b, 5a, 5c are shown in the small inset graph of the bottom figure.

Image of FIG. 11.
FIG. 11.

Streamwise (left) and spanwise (right) spectra of the temperature fluctuations at and , above the diffusive sublayer at , at the top of the thermal buffer layer at , and in the center of the channel at . Curves of the cases 1a, 3a, 5a are distinguishable due to the different length: case 1a, shortest; case 5a, longest curves.

Image of FIG. 12.
FIG. 12.

Temperature profiles at , and .

Image of FIG. 13.
FIG. 13.

Temperature profiles at various Reynolds numbers and at and .

Image of FIG. 14.
FIG. 14.

Temperature profiles at and and . Comparison of the present results, Kader correlation and LES results of Calmet and Magnaudet (Ref. 25).

Image of FIG. 15.
FIG. 15.

Temperature rms fluctuations at and .

Image of FIG. 16.
FIG. 16.

Relative heat transfer coefficient fluctuations, see Tables I, III, and IV to identify various runs.

Image of FIG. 17.
FIG. 17.

Turbulent Prandtl number profiles at and .

Image of FIG. 18.
FIG. 18.

Turbulent Prandtl number profiles at and ; comparison of the fluctuating and nonfluctuating temperature boundary condition.

Image of FIG. 19.
FIG. 19.

Streamwise (left) and spanwise (right) autocorrelation functions of the temperature and velocity fluctuations at and above the diffusive sublayer at and at the top of the thermal buffer layer at .

Tables

Generic image for table
Table I.

Sensitivity of the results to the grid density and time step at and . Cases ending with “a” and “b” denote results obtained with and without the model of spectral turbulent diffusivity, respectively. Temperature field of the case 200-5c was calculated on the grid.

Generic image for table
Table II.

Influence of the wall-normal grid density on the friction temperature: -“exact” friction temperature obtained on wall-normal grid of 193 point, , -friction temperatures recalculated on 97 and 65 points, respectively.

Generic image for table
Table III.

Computations at (channel geometry). Cases ending with “a” and “b” denote results obtained with and without the model of spectral turbulent diffusivity, respectively.

Generic image for table
Table IV.

Computations at (flume geometry).

Generic image for table
Table V.

Heat transfer coefficient at various Reynolds and Prandt numbers. Value of the coefficient at and (denoted with ) was obtained with extrapolation from and results. Correlation of Shaw and Hanratty (Ref. 36) .

Generic image for table
Table VI.

Thickness of the diffusive sublayer at various Reynolds and Prandt numbers (with accuracy). Value at and (denoted with ) was obtained with extrapolation from and results. Correlation of Shaw and Hanratty (Ref. 36) .

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/content/aip/journal/pof2/19/6/10.1063/1.2739402
2007-06-13
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Near-wall passive scalar transport at high Prandtl numbers
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/6/10.1063/1.2739402
10.1063/1.2739402
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