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Research Papers

Computation of the Flow Over a Sphere at Re = 3700: A Comparison of Uniform and Turbulent Inflow Conditions

[+] Author and Article Information
Y. Bazilevs

Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093
e-mail: yuri@ucsd.edu

J. Yan

Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093

M. de Stadler, S. Sarkar

Department of Mechanical and
Aerospace Engineering,
University of California–San Diego,
La Jolla, CA 92093

Contributed by the Applied Mechanics of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 30, 2014; final manuscript received October 1, 2014; accepted manuscript posted October 10, 2014; published online October 20, 2014. Assoc. Editor: Kenji Takizawa.

J. Appl. Mech 81(12), 121003 (Oct 20, 2014) (16 pages) Paper No: JAM-14-1346; doi: 10.1115/1.4028754 History: Received July 30, 2014; Revised October 01, 2014; Accepted October 10, 2014

A highly resolved computation of the flow past a sphere at Reynolds number Re = 3700 using a finite element method (FEM)-based residual-based variational multiscale (RBVMS) formulation is performed. Both uniform and turbulent inflow conditions are considered with the uniform flow case validated against a previous direct numerical simulation (DNS) study. We find that, as a result of adding free-stream turbulence of moderate intensity, the drag force on the sphere is increased, the length of the recirculation bubble is reduced dramatically, and the near-wake turbulence is significantly more energetic than in case of uniform inflow. In the case of uniform inflow, we find that the solution exhibits low temporal frequency modes, which necessitate long-time simulations to obtain high-fidelity statistical averages. Subjecting the sphere to turbulent inflow removes the low-frequency modes from the solution and enables shorter-time simulations to achieve converged flow statistics.

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Figures

Grahic Jump Location
Fig. 1

2D slice of the mesh of the computational domain. Top left: uniform inflow case. Top right: turbulent inflow case. Bottom: zoom on the sphere boundary-layer mesh. Note the two cylindrical regions used for mesh refinement in the top plots. The cylindrical regions appear rectangular due to a 2D slice used for mesh visualization.

Grahic Jump Location
Fig. 2

Time history (left) and power spectra (right) of the radial velocity at different spatial locations: From top to bottom, the probes are located at (x/D = 1.0, r/D = 0.6), (x/D = 2.4, r/D = 0.6), (x/D = 3.0, r/D = 0.6), and (x/D = 5.0, r/D = 0.6).

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Fig. 3

Time history of the drag coefficient Cd. The time window of t ∈ [150.0, 1350.0] was used for the computation of the mean Cd.

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Fig. 4

Left: time-averaged streamwise velocity along the centerline. Right: RMS of the streamwise velocity along the centerline. Flow statistics are computed over three time windows corresponding to t ∈ [300.0, 675.0], t ∈ [600.0, 975.0], and t ∈ [900.0, 1,275.0], denoted in the figure by (W1), (W2), and (W3), respectively.

Grahic Jump Location
Fig. 5

Mean velocity profiles in the sphere wake. Left: streamwise velocity profile. Right: radial velocity profile. Flow statistics are computed over the time window corresponding to t ∈ [300.0, 675.0].

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Fig. 6

RMS of the velocity fluctuations in the sphere wake. Left: streamwise velocity fluctuations. Right: radial velocity fluctuations. Flow statistics are reported for three different time windows.

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Fig. 7

Left: ensemble-averaged pressure coefficient distribution as a function of the angular position. DNS results of Ref. [30] and experimental results of Ref. [32] are plotted for comparison. Right: mean skin-friction coefficient distribution as a function of the angular position. DNS results of Ref. [30] are plotted for comparison.

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Fig. 8

Triangular mesh of the sphere inflow domain boundary. The blue circle is used to denote the projection of the sphere outer boundary to the inlet plane.

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Fig. 9

Velocity fluctuation magnitude at final time on one of the planes of the isotropic turbulence simulation. Left: before projection. Right: after projection.

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Fig. 10

The data transfer employed for the turbulent inflow generation is validated by comparison of the temporally and spatially evolving simulations. Evolution of the turbulent kinetic energy (tke) and the viscous dissipation (ε) rate are shown. The x1-axis is taken in place of time for the spatially evolving simulation.

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Fig. 11

The time history of the drag coefficient

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Fig. 12

Left: ensemble-averaged pressure coefficient distribution as a function of the angular position. Right: mean skin-friction coefficient distribution as a function of the angular position. Turbulent and uniform flow results are plotted for comparison.

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Fig. 13

Contours of instantaneous out-of-plane vorticity component on a planar cut. Top: uniform inflow. Bottom: turbulent inflow.

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Fig. 14

Mean velocity streamlines on a planar cut. Top: uniform inflow. Bottom: turbulent inflow.

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Fig. 15

Top: time-averaged streamwise velocity along the centerline. Bottom: RMS of streamwise velocity fluctuations along the centerline. Turbulent and uniform inflow results are presented for comparison. Flow statistics from two time windows for the turbulent inflow case are plotted to show that the results are invariant with the choice of the time window.

Grahic Jump Location
Fig. 16

Top: time-averaged streamwise defect velocity along the centerline. Bottom: RMS of streamwise defect velocity fluctuations along the centerline. Both are scaled with the mean inflow speed. Turbulent and uniform inflow results are presented for comparison. The results are plotted on a log scale and the differences between the uniform and turbulent cases in the near and far wake become apparent.

Grahic Jump Location
Fig. 17

Mean velocity profiles in the sphere wake. Left: streamwise velocity profile. Right: radial velocity profile. Turbulent and uniform inflow results are presented for comparison. Flow statistics from two time windows for the turbulent inflow case are plotted to show that the results are invariant with the choice of the time window.

Grahic Jump Location
Fig. 18

RMS of the velocity fluctuations in the sphere wake. Left: streamwise velocity fluctuations. Right: radial velocity fluctuations. Turbulent and uniform inflow results are presented for comparison. Flow statistics from two time windows for the turbulent inflow case are plotted to show that the results are invariant with the choice of the time window.

Grahic Jump Location
Fig. 19

Time history (left) and power spectra (right) of the radial velocity at different spatial locations: From top to bottom, the probes are located at (x/D = 1.0, r/D = 0.6), (x/D = 2.4, r/D = 0.6), (x/D = 3.0, r/D = 0.6), and (x/D = 5.0, r/D = 0.6).

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