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Direct numerical simulation of heated flows at supercritical pressure in a vertical annulus at
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10.1063/1.2927488
/content/aip/journal/pof2/20/5/10.1063/1.2927488
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/5/10.1063/1.2927488

Figures

Image of FIG. 1.
FIG. 1.

Properties of at : (a) and , (b) , , and . These property data are obtained from a computer program called PROPATH (Ref. 2) and compiled in the form of the thermodynamic tables to be used in the simulation.

Image of FIG. 2.
FIG. 2.

Schematic of the flow regions and boundary conditions.

Image of FIG. 3.
FIG. 3.

Inflow simulation results for fully developed annular flow at : (a) mean velocity profiles, (b) turbulence intensities (root-mean-square velocity fluctuations): (—), the present DNS; (-⋅⋅-⋅⋅-), Chung et al. (Ref. 18), (-⋅-⋅-), Kim et al. (Ref. 19).

Image of FIG. 4.
FIG. 4.

Time history of the mean pressure gradients at the inlet obtained from the inflow generator and at the exit averaged over the outlet plane, and the Nusselt number at the exit for case M2.

Image of FIG. 5.
FIG. 5.

Local Nusselt number distributions along the heated inner wall as compared with the empirical correlations for forced convection: (a) case F1, (b) case F3: (—), the present DNS; (----), modified Krasnoshchekov–Protopopov correlation; (-⋅⋅-⋅⋅-), Jackson–Fewster correlation; (⋯), Dittus–Boelter equation for fully established flows.

Image of FIG. 6.
FIG. 6.

Local Nusselt number distributions along the heated inner wall as compared with the empirical correlation for mixed convection: (a) case M2, (b) case M4: (—), the present DNS; (-⋅⋅-⋅⋅-), Kirillov correlation; (----), the present DNS for case M2G in (a).

Image of FIG. 7.
FIG. 7.

Nusselt number ratio vs the buoyancy parameter for cases of mixed convection as compared to the experimental data for circular pipe flows (Ref. 22): (◼), case M1; (▲), case M2; (▼), case M3; and (●), case M4. Open circles are the experimental data for circular pipe flows obtained from Fewster (Ref. 22).

Image of FIG. 8.
FIG. 8.

Heated wall temperature distributions for each heating condition: (a) , (b) , (c) , and (d) . For cases in (d), the inlet temperature is higher than the pseudocritical temperature .

Image of FIG. 9.
FIG. 9.

Mean velocity profiles at for cases C3, F3, and M3: (a) vs ; (b) vs near the heated wall, where the subscript VD denotes the van Driest transformation: (----), case C3; (-⋅-⋅-), case F3; (—), case M3.

Image of FIG. 10.
FIG. 10.

Mean density and temperature profiles at for (a) case F3 and (b) case M3.

Image of FIG. 11.
FIG. 11.

Normalized shear stress profiles at for (a) case C3, (b) case F3, and (c) case M3: (-⋅⋅-⋅⋅-), ; (----), ; (—), , where , , and denotes the inner wall shear stress at the inlet.

Image of FIG. 12.
FIG. 12.

Distributions of TKE, , at (a) and (b) : (----), case C3; (-.-.-), case F3; and (—), case M3. Note that .

Image of FIG. 13.
FIG. 13.

TKE production terms for cases F3 and M3 at (a) and (b) : (-⋅-⋅-), for case F3; (—), for case M3; (----), for case M3, plotted in scale of the other terms.

Image of FIG. 14.
FIG. 14.

Normalized mean temperature profiles at : (a) vs , (b) vs near the heated wall: (----), case C3; (-⋅-⋅-), case F3; and (—), case M3.

Image of FIG. 15.
FIG. 15.

Normalized mean temperature profiles at : (a) vs , (b) vs near the heated wall: (----), case C3; (-⋅-⋅-), case F3; and (—), case M3.

Image of FIG. 16.
FIG. 16.

Normalized mean temperature profiles for cases F4 and M4 at : (a) vs , (b) vs near the heated wall: (-⋅-⋅-), case F4; and (—), case M4.

Image of FIG. 17.
FIG. 17.

Local Prandtl number distributions at (a) and (b) : (-⋅-⋅-), case F3; (—), case M3.

Image of FIG. 18.
FIG. 18.

Distributions of the normalized radial turbulent heat flux at (a) and (b) : (----), case C3; (-⋅-⋅-), case F3; and (—), case M3.

Image of FIG. 19.
FIG. 19.

Distributions of the normalized streamwise turbulent heat flux at (a) and (b) : (----), case C3; (-⋅-⋅-), case F3; and (—), case M3.

Image of FIG. 20.
FIG. 20.

Instantaneous isodensity surfaces for case F3: (a) near the heated wall, at ; (b) the pseudocritical point, at . This figure shows a view of the flow looking upstream between . The black and white photo in each subfigure (permission granted by Experimental Thermal and Fluid Science) shows an experimental visualization of the flows formed above a heated wire placed in stagnant at a supercritical pressure of (Ref. 32), with arrows indicating the flow pattern approximately corresponding to the present view.

Image of FIG. 21.
FIG. 21.

Instantaneous isodensity surfaces at the pseudocritical temperature for case M3: (a) , (b) .

Image of FIG. 22.
FIG. 22.

Instantaneous (left column) and (right column) contours superimposed on the instantaneous cross-stream velocity vector plots for case M3 at (a) and (b) . The vector size is reduced in (b) for clarity.

Image of FIG. 23.
FIG. 23.

Near-wall streaky patterns of the velocity field for case M3. Instantaneous contours are shown at for the entire heated length. Low-speed streaks appear as dark gray contours elongated in the streamwise direction: (a) , (b) , (c) , (d) , (e) , (f) , (g) , (h) , (i) , (j) , (k) , and (l) .

Image of FIG. 24.
FIG. 24.

Near-wall streaky thermal patterns for case M3. Instantaneous contours are shown at . Streaks of low-density hot fluids appear as dark gray contours.

Tables

Generic image for table
Table I.

Grid resolution for inflow simulation at .

Generic image for table
Table II.

Summary of the flow conditions. For all simulations, and . at , and property, convection, convection.

Generic image for table
Table III.

Values of .

Generic image for table
Table IV.

Values of and for cases F3 and M3.

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/content/aip/journal/pof2/20/5/10.1063/1.2927488
2008-05-29
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Direct numerical simulation of heated CO2 flows at supercritical pressure in a vertical annulus at Re=8900
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/5/10.1063/1.2927488
10.1063/1.2927488
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