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A streamwise-constant model of turbulent pipe flow
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View: Figures


Image of FIG. 1.
FIG. 1.

The coordinate system used to project the Navier-Stokes equations.

Image of FIG. 2.
FIG. 2.

(a) Streamfunctions Ψ1,ac (η) and (b) corresponding velocity profiles u 0(η) for Ψ1,a (η) = 0.033(η − 3η 3 + 2η 4) (thin solid), Ψ1,b (η) = 0.7(η − 3η 3 + 2η 4)2 (dashed), and Ψ1,c (η) = 14(η − 3η 3 + 2η 4)3 (dash-dot) and experimental velocity profile of Ref. 38 at Re = 24 600 (thick solid).

Image of FIG. 3.
FIG. 3.

Model output for deterministic forcing: (a) contours of the streamfunction Ψ = 0.033 (η − 3η 3 + 2η 4) sin φ, (b) vector plot of the corresponding in-plane velocities, and (c) contours of the resulting axial velocity field.

Image of FIG. 4.
FIG. 4.

Contours of the axial velocity induced by the streamfunction Ψ6(η, φ) = (η 4 − 2η 5 + η 6) sin(6φ), the light and dark filled contours correspond to regions of the flow, respectively, faster and slower than laminar.

Image of FIG. 5.
FIG. 5.

Time traces of the centerline velocity from three different simulations, respectively, at Re = 2200 with 0.0005 and 0.002 rms noise levels (a) and (c) and at Re = 10 000 with 0.002 rms noise level (b). The resolution in the radial direction is N = 48. (d) Zoom on the time interval during which the samples of Figure 6 are taken. The vertical lines indicate the sampling instants.

Image of FIG. 6.
FIG. 6.

(Color online) Contours of the axial velocity, subfigures (a) to (c), and of the swirling strength for the in-plane velocities, subfigures (d) to (f), computed, respectively, at t = 1620, t = 1700, and t = 1740 dimensionless time units.

Image of FIG. 7.
FIG. 7.

Diagram detailing the different stages of the QSSP. The dashed lines represent unmodeled effects.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A streamwise-constant model of turbulent pipe flow