Scaling the vorticity dynamics in the leading-edge vortices of revolving wings with two directional length scales

Nathaniel H. Werner; Junshi Wang; Haibo Dong; Azar Eslam Panah; Bo Cheng

doi:10.1063/5.0024213

Scaling the vorticity dynamics in the leading-edge vortices of revolving wings with two directional length scales

Physics of Fluids ◽

10.1063/5.0024213 ◽

2020 ◽

Vol 32 (12) ◽

pp. 121903

Author(s):

Nathaniel H. Werner ◽

Junshi Wang ◽

Haibo Dong ◽

Azar Eslam Panah ◽

Bo Cheng

Keyword(s):

Leading Edge ◽

Length Scales ◽

Vorticity Dynamics ◽

Leading Edge Vortices

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An Analytical Thermodynamic Approach to Friction of Rubber on Ice

Tire Science and Technology ◽

10.2346/1945-5852-40.2.124 ◽

2012 ◽

Vol 40 (2) ◽

pp. 124-150

Author(s):

Klaus Wiese ◽

Thiemo M. Kessel ◽

Reinhard Mundl ◽

Burkhard Wies

Keyword(s):

Coefficient Of Friction ◽

Liquid Layer ◽

Contact Area ◽

Leading Edge ◽

Viscous Friction ◽

Analytical Approximation ◽

Real Contact Area ◽

Length Scales ◽

Real Contact ◽

Ice Surface

ABSTRACT The presented investigation is motivated by the need for performance improvement in winter tires, based on the idea of innovative “functional” surfaces. Current tread design features focus on macroscopic length scales. The potential of microscopic surface effects for friction on wintery roads has not been considered extensively yet. We limit our considerations to length scales for which rubber is rough, in contrast to a perfectly smooth ice surface. Therefore we assume that the only source of frictional forces is the viscosity of a sheared intermediate thin liquid layer of melted ice. Rubber hysteresis and adhesion effects are considered to be negligible. The height of the liquid layer is driven by an equilibrium between the heat built up by viscous friction, energy consumption for phase transition between ice and water, and heat flow into the cold underlying ice. In addition, the microscopic “squeeze-out” phenomena of melted water resulting from rubber asperities are also taken into consideration. The size and microscopic real contact area of these asperities are derived from roughness parameters of the free rubber surface using Greenwood-Williamson contact theory and compared with the measured real contact area. The derived one-dimensional differential equation for the height of an averaged liquid layer is solved for stationary sliding by a piecewise analytical approximation. The frictional shear forces are deduced and integrated over the whole macroscopic contact area to result in a global coefficient of friction. The boundary condition at the leading edge of the contact area is prescribed by the height of a “quasi-liquid layer,” which already exists on the “free” ice surface. It turns out that this approach meets the measured coefficient of friction in the laboratory. More precisely, the calculated dependencies of the friction coefficient on ice temperature, sliding speed, and contact pressure are confirmed by measurements of a simple rubber block sample on artificial ice in the laboratory.

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