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Technical Brief

# Radial Stagnation Flow on a Twisting Cylinder

[+] Author and Article Information
Patrick Weidman

Department of Mechanical Engineering,
Boulder, CO 80309-0427

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 4, 2019; final manuscript received April 3, 2019; published online May 8, 2019. Editor: Francine Battaglia.

J. Fluids Eng 141(11), 114502 (May 08, 2019) (3 pages) Paper No: FE-19-1086; doi: 10.1115/1.4043425 History: Received February 04, 2019; Revised April 03, 2019

## Abstract

The problem of stagnation-point flow impinging radially on a linearly twisting cylinder is considered. This advances previous work on the motion outside a cylinder undergoing linear torsional motion. The problem is governed by a Reynolds number R and a dimensionless torsion rate σ. Numerical calculations are carried out using the ODEINT program, and convergence of the shooting method is obtained using the MNEWT program. The radial and azimuthal wall shear stresses are found over a range of R and σ, and radial and azimuthal velocity profiles at $σ={0,1,2}$ are presented for various values of R. The interesting feature is that the axial wall shear stress parameter $f″(1)$ is a very weak function of σ while the azimuthal wall shear stress parameter $g′(1)$ is a strong function of σ although both stress parameters are a strong function of R.

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## References

Sprague, M. , and Weidman, P. D. , 2011, “ Three-Dimensional Flow Induced by the Torsional Motion of a Cylinder,” Fluid Dyn. Res., 43, pp. 1–12.
Wang, C. Y. , 1974, “ Axisymmetric Stagnation Flow on a Cylinder,” Q. Appl. Math., 32(2), pp. 207–213.
Drazin, P. , and Riley, N. , 2006, The Navier-Stokes Equations: A Classification of Flows and Exact Solutions (London Mathematical Society Lecture Note Series 334), Cambridge University Press, Cambridge, UK.
Turner, M. , and Weidman, P. D. , 2019, “ The Boundary Layer Flow Induced Above the Torsional Motion of a Disk,” Phys. Fluids (under review).
Press, W. , Flannery, B. , Teukolsky, S. , and Vetterling, W. , 1989, Numerical Recipes, Cambridge University Press, Cambridge, UK.

## Figures

Fig. 1

Variation of the axial wall stress parameter f″(1) as a function of σ for R = {0.2, 0.5, 1.0, 2.0, 5.0, 10.0}. The solid diamonds at σ = 0 replicate the results of Wang [2].

Fig. 2

Variation of the azimuthal wall stress parameter g′(1) as a function of σ for R = {0.2, 0.5, 1.0, 2.0, 5.0, 10.0}

Fig. 3

Axial velocity profiles f′(η) for R = {0.2, 0.5, 1.0, 2.0, 5.0, 10.0} at σ = 0 with the arrow pointing in the direction of increasing R. The solid dots are the computations of Wang [2] at R = {0.2, 1.0, 10.0}.

Fig. 4

Axial velocity profiles f′(η) for R = {0.2, 0.5, 1.0, 2.0, 5.0, 10.0} at σ = 1 with the arrow pointing in the direction of increasing R

Fig. 5

Azimuthal velocity profiles g(η) for R = {0.2, 0.5, 1.0, 2.0, 5.0, 10.0} at σ = 1 with the arrow pointing in the direction of increasing R

Fig. 6

Axial velocity profiles f′(η) for R = {0.2, 0.5, 1.0, 2.0, 5.0, 10.0} at σ = 2 with the arrow pointing in the direction of increasing R

Fig. 7

Azimuthal velocity profiles g(η) for R = {0.2, 0.5, 1.0, 2.0, 5.0, 10.0} at σ = 2 with the arrow pointing in the direction of increasing R

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