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Research Papers: Fluid-Structure Interaction

# Application of Models for Laminar to Turbulent Transition to Flow Around a Circular Cylinder

[+] Author and Article Information
C. Reichel, K. Strohmeier

Institute for Pressure Vessels and Plant Design, Technical University of Munich, Garching D-85748, Germany

J. Pressure Vessel Technol 130(3), 031301 (Jun 16, 2008) (8 pages) doi:10.1115/1.2937765 History: Received September 30, 2006; Revised April 09, 2007; Published June 16, 2008

## Abstract

In many technical fields, for example, in heat exchanger design, circular cylinders are involved in fluid structure interaction problems. Therefore, correct fluid forces are needed. Direct numerical simulation or large eddy simulation are too time expensive, but great errors can occur if fluid forces are evaluated with mainstream statistical turbulence models. In this paper, several models are applied to flow around a circular cylinder in the Reynolds number range from 500 up to $106$. Mainly 2D simulations are performed. Additionally, calculations are performed to evaluate the influence of three dimensional modeling. The incorrect prediction of laminar to turbulent transition is identified as the main reason for the misprediction of flow forces with common statistical turbulence models. It is demonstrated that improvements are possible with available transition models. Although no grid independence in spatial direction could be achieved, the results indicate that 3D calculations may abolish remaining deviations between calculated and measured force coefficients. (Most of the data contained within this paper have been presented at the 2005 ASME PVPD Conference in Denver, Colorado. Although the title of the paper has not been changed, some newer results have been added.)

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## Figures

Figure 1

Calculated (2D) drag coefficients compared with experimental data. Triangles: SST turbulence model; squares: Wilcox98 k-ω model. Lines without label are envelopes of experimental data from literature.

Figure 2

Calculated (2D) lift coefficients compared with experimental and theoretical data from literature. Triangles: SST turbulence model; squares: Wilcox98 k-ω model.

Figure 3

Calculated (2D) drag coefficients for the Wilcox98 k-ω model extended by the laminar to turbulent transition model of Wilcox. Filled squares: no transition model; filled triangles: transition model with default constants; open squares: transition model with constant α0* set to 3.5 times its default value.

Figure 4

Calculated (2D) drag coefficients for empirical transition onset models applied in the framework of the “γ-ReΘ model, CFX-V-1.0 ”. Filled diamonds: experimental data of West and Apelt (17) at the same freestream turbulence level as in the calculations; filled triangles: Langtry–Menter empirical correlation; filled squares: Abu Ghannam and Shaw empirical correlation; open triangles: Langtry–Menter empirical correlation on a grid refined by a factor of 2 in both directions; open squares: Langtry–Menter correlation with a grid refined by 4 in both directions.

Figure 5

Calculated (2D) drag coefficient (top), lift coefficient (middle), and Strouhal number (bottom) with transition onset momentum Reynolds number set to a high constant value. Filled diamonds: experimental data (17) at the same freestream turbulence level as in the calculations; filled triangles: coarse grid; filled squares: grid refined by 2.0 in both directions; open triangles: grid refined by 4.0 in both directions.

Figure 6

Calculated (2D) drag coefficient (top), lift coefficient (middle), and Strouhal number (bottom) for the Langtry–Menter empirical transition onset correlation applied in the framework of the “γ-ReΘ model, CFX-V-1.0 ” with intermittency limited to values between 0.0 and 1.0. Filled diamonds: experimental data (17) at the same freestream turbulence level as in the calculations; filled triangles: coarse grid; filled squares: grid refined by 2.0 in both directions.

Figure 7

Calculated (3D) time series of drag coefficient at a Reynolds number of 2500 with the Wilcox98 model for transitional flows (constant α0* set to 3.5 times its default value)

Figure 8

Calculated (3D) time series of lift coefficients at a Reynolds number of 2500 with the Wilcox98 model for transitional flows (constant α0* set to 3.5 times its default value). First row: two cells per diameter in the z-direction; second row: four cells per diameter in the z-direction; third row: eight cells per diameter in the z-direction.

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