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RESEARCH PAPERS: Forced Convection

# Numerical Simulation of Flow Field and Heat Transfer of Streamlined Cylinders in Cross Flow

[+] Author and Article Information
Zhihua Li, Susan C. Mantell

Department of Mechanical Engineering, University of Minnesota, 111 Church St., SE, Minneapolis, MN 55455

Jane H. Davidson

Department of Mechanical Engineering, University of Minnesota, 111 Church St., SE, Minneapolis, MN 55455jhd@me.umn.edu

J. Heat Transfer 128(6), 564-570 (Dec 23, 2005) (7 pages) doi:10.1115/1.2188463 History: Received March 08, 2005; Revised December 23, 2005

## Abstract

The drag and convective heat transfer coefficients along the outer surface of lenticular and elliptical tubes with minor-to-major axis ratios of 0.3, 0.5, and 0.8 were determined numerically for cross-flow Reynolds numbers from 500 to $104$. The two-dimensional, unsteady Navier-Stokes equations and energy equation were solved using the finite volume method. Laminar flow was assumed from the front stagnation point up to the point of separation. Turbulent flow in the wake was resolved using the shear stress transport $k-ω$ model. Local heat transfer, pressure and friction coefficients as well as the total drag coefficient and average Nusselt number are presented. The results for streamlined tubes are compared to published data for circular and elliptical cylinders. Drag of the elliptical and lenticular cylinders is similar and lower than a circular cylinder. Drag can be reduced by making the streamlined cylinders more slender. Drag is relatively insensitive to Reynolds number over the range studied. An elliptical cylinder with an axis ratio equal to 0.5 reduces pressure drop by 30–40% compared to that of a circular cylinder. The Nusselt numbers of lenticular and elliptical cylinders are comparable. The average Nusselt number of an elliptical or lenticular cylinder with axis ratio of 0.5 and 0.3 is 15–35% lower than that of a circular cylinder.

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## Figures

Figure 6

Comparison of numerical drag coefficient with experiment (7-8) for an elliptical cylinder with λo=0.5

Figure 7

Comparison of predicted local Nusselt number with experiment (12) and an empirical correlation (8) for an elliptical cylinder with λo=0.5 at ReD=3074

Figure 8

Comparison of predicted average Nusselt number with empirical correlations (8,12-13) for an elliptical cylinder with λo=0.5

Figure 1

Example of a “shaped” polymer tube. The outer surface of the tube is an ellipse. The inner flow passage is circular. The non-uniform wall is selected to minimize the conductive resistance across the wall and to prevent deformation and strain failure (5).

Figure 2

Streamlined outer profile of (a) elliptical, and (b) lenticular tubes. The outer surface of a lenticular cylinder is formed by two symmetrically intersected arcs, each given by (rcosα)2+(rsinα+Rl−ro)2=Rl2, where and λo is the length ratio of the minor to major axis of the outer surface. A value of λo=1 represents a circular cylinder. The cylinders become more slender as λo is decreased.

Figure 3

Computational domain and boundary conditions of flow and heat transfer

Figure 4

Triangular and quad meshes for flow over an individual elliptical cylinder

Figure 5

Comparison of predicted local friction coefficient with experiment (8) for an elliptical cylinder with λo=0.5 at ReD=3200

Figure 9

Friction, pressure and drag coefficient of an elliptical cylinder with λo=0.3

Figure 10

Comparison of drag coefficients of elliptical, lenticular and circular cylinders. The drag coefficient of a circular cylinder is calculated from correlation of (22).

Figure 11

Average Nusselt number of streamlined cylinders with λo=0.3, 0.5, and 0.8 at 500⩽ReD⩽104, (a) elliptical, (b) lenticular. The Nusselt number of the circular cylinder is calculated from correlations provided by (8).

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