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Direct numerical simulation of turbulence in injection-driven plane channel flows
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10.1063/1.2963137
/content/aip/journal/pof2/20/10/10.1063/1.2963137
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/10/10.1063/1.2963137

Figures

Image of FIG. 1.
FIG. 1.

Schematic representation of a solid-propellant rocket showing casing, propellant, and nozzle (top) and an idealized injection-driven flow (bottom), which models a solid rocket by replacing the evolution of gas by combustion at the propellant surface with mass injection through the walls.

Image of FIG. 2.
FIG. 2.

Schematic representation of the model solid rocket motor.

Image of FIG. 3.
FIG. 3.

Actual (—) and modeled (-⋅-⋅-) values of (a) , (b) , and (c) near the center of the channel measured in the spatially developing injection-driven flow of Wasistho and Moser (Ref. 18). Other locations are similar or have better agreement.

Image of FIG. 4.
FIG. 4.

[(a) and (b)] One-dimensional velocity spectra and [(c) and (d)] premultiplied spectra, [(a) and (c)] near the wall and [(b) and (d)] near the channel center . Shown are the spectra for (—), (----), and (-⋅-⋅-). The quantity is defined in Sec. IV A.

Image of FIG. 5.
FIG. 5.

rms value of the residual normalized by the rms value of the time derivative, . The -spline knots are spaced according to , where is the knot spacing at the center line and is the knot spacing at a given location. 192 collocation points are used in the wall normal direction.

Image of FIG. 6.
FIG. 6.

Mean streamwise and wall normal velocities over half the channel width for the turbulent (—) and laminar (-⋅-⋅-) cases. The center of the channel is at , and the streamwise and wall-normal velocities are symmetric and antisymmetric about the center, respectively.

Image of FIG. 7.
FIG. 7.

Terms in the mean streamwise momentum equation, normalized by : (a) Turbulent case and (b) laminar case. (—), (⋯), (----), (---), and (-⋅-⋅-).

Image of FIG. 8.
FIG. 8.

Mean density and temperature profiles: Turbulent case (—) and laminar case (-⋅-⋅-).

Image of FIG. 9.
FIG. 9.

Terms in the mean kinetic energy equation, normalized by . Convection of mean kinetic energy (—), convection of Reynolds stress (----), production of turbulent kinetic energy (⋯), contribution from slow growth terms (-⋅-⋅-), work done by mean pressure gradient (–◇–), mean pressure diffusion (–⊖–), mean pressure dilatation (–◻–), mean viscous diffusion (×), and mean dissipation (∗).

Image of FIG. 10.
FIG. 10.

rms velocity fluctuation profiles normalized by (a) and (b) for the transpiration-driven channel and for a nontranspired turbulent channel at . Shown are (—) (----), and (-⋅-⋅). The curves for the nontranspired channel are indicated with the ● symbol.

Image of FIG. 11.
FIG. 11.

Rate of turbulent kinetic energy dissipation (—) and streamwise convection (slow growth term) (----) normalized by the volume-averaged rate of turbulent kinetic energy production in the transpired (current) and nontranspired channels (●). (b) is a zoomed version of (a) to show the central region of the channels.

Image of FIG. 12.
FIG. 12.

Rate of turbulent kinetic energy dissipation normalized by in the transpired (current) and nontranspired channels (●). Note that this quantity is unbounded at the wall because goes to zero.

Image of FIG. 13.
FIG. 13.

Normalized two-point correlations at the channel center line with separations in the (a) and (b) directions from the current transpiration-driven flow and the nontranspired channel (●). Shown are (—), , (----), and .(-⋅-⋅-)

Image of FIG. 14.
FIG. 14.

Terms in the Reynolds stress transport equation, normalized by the average production of turbulent kinetic energy. (a) , (b) , (c) , and (d) . Convection of Reynolds stress (—), production (⋯), turbulent diffusion (----), pressure diffusion (-⋅-⋅-), pressure strain (–⊖–), viscous diffusion (–◻–), dissipation (–◇–), contribution from slow growth terms (×), and compressibility terms (∗).

Image of FIG. 15.
FIG. 15.

Terms in the Reynolds stress transport equation for nontranspired turbulent channel flow at , normalized by the average production of turbulent kinetic energy. (a) , (b) , (c) , and (d) . Production (⋯), turbulent diffusion (----), pressure diffusion (-⋅-⋅-), pressure strain (–⊖–), viscous diffusion (–◻–), and dissipation (–◇–).

Image of FIG. 16.
FIG. 16.

Terms in the turbulent kinetic energy equation for the (a) transpiration-driven (b) and non-transpired channels, normalized by the average production of turbulent kinetic energy. Convection of turbulent kinetic energy (—), production (⋯), turbulent diffusion (----), pressure diffusion (-⋅-⋅-), pressure dilatation (–⊖–), viscous diffusion (–◻–), dissipation (–◇–), contribution from slow growth terms (×), and compressibility terms (∗).

Image of FIG. 17.
FIG. 17.

Streamwise vorticity fluctuations obtained for the transpiration-driven channel.

Image of FIG. 18.
FIG. 18.

Two-point autocorrelation for velocities in the spanwise direction at . (—), (----), and (-⋅-⋅-).

Image of FIG. 19.
FIG. 19.

Contours of streamwise velocity fluctuations. (a) Present study: . Turbulent channel flow at : (b) and (c) . In all three plots, blue represents negative values of and red represents positive values of .

Image of FIG. 20.
FIG. 20.

PDF of (a) and (b) in the transpiration-driven channel, where is the angle made by the vorticity vector with the positive vertical axis and is the angle made with the positive streamwise axis. Curves are for (—), (⋯), (----), and (-⋅-⋅-).

Image of FIG. 21.
FIG. 21.

Joint PDF of and for the present study and for plane turbulent channel flow at . Present study: (a) and (b) . Turbulent channel flow at : (c) and (d) .

Image of FIG. 22.
FIG. 22.

Conditionally averaged vorticity magnitude at and for the present study and for plane turbulent channel flow at . The magnitude of vorticity has been normalized by the square root of enstrophy at that particular wall normal location. Present study: (a) and (b) . Turbulent channel flow at : (c) and (d) .

Image of FIG. 23.
FIG. 23.

Contours of spanwise vorticity velocity fluctuations in an plane for (a) the present study and (b) the turbulent channel flow at . Blue represents negative values of and red represents positive values of .

Image of FIG. 24.
FIG. 24.

Spanwise vorticity contours in a spanwise plane from a LES of spatially developing solid rocket motor flow conducted by Wasistho and Moser (Ref. 18). The parameters and the geometry used in the simulation are the same as those used in the experiment of Traineau et al. (Ref. 5). The streamwise and wall normal coordinates in the figure are in meters.

Image of FIG. 25.
FIG. 25.

rms density and temperature fluctuations normalized by their corresponding mean values.

Image of FIG. 26.
FIG. 26.

(a) Mean Mach number . (b) Turbulent Mach number (-⋅-⋅-) and rms Mach number (----).

Image of FIG. 27.
FIG. 27.

Ratio of (a) mean square dilatation to enstrophy and (b) pressure dilatation to homogeneous solenoidal dissipation .

Tables

Generic image for table
Table I.

Comparison of parameters used in numerical simulations of injection-driven flows including the current study. reported by Apte and Yang (Ref. 7) is evaluated at the head end. Liou et al. (Ref. 6) performed a two-dimensional simulation of the Euler equations.

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2008-10-10
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Direct numerical simulation of turbulence in injection-driven plane channel flows
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/10/10.1063/1.2963137
10.1063/1.2963137
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