Measuring and testing – Frictional resistance – coefficient or characteristics – Lubricant testing
Reexamination Certificate
2000-04-10
2003-02-11
Fuller, Benjamin R. (Department: 2855)
Measuring and testing
Frictional resistance, coefficient or characteristics
Lubricant testing
Reexamination Certificate
active
06516652
ABSTRACT:
BACKGROUND OF INVENTION
Since M. O. Kramer reported successful experimental results in 1957, there have been repeated attempts to reduce frictional drag in turbulent fluid flow over a surface by applying a passive compliant coating. Experimental results in this area have been mixed. Most investigators have reported a drag increase, while only a few have claimed drag reduction for turbulent flow. A number of theoretical studies have characterized the stability of the laminar boundary layer over a deforming surface and other studies have characterized the reaction of a coating to a fluctuating load. However, no rigorous analytical technique has been previously reported that has been used to successfully design a drag-reducing coating for turbulent flow.
In the past, passive coatings were tested without specification and full characterization of critical physical parameters, such as the frequency dependent complex shear modulus, density, and thickness. In order to achieve and ensure drag reduction with a viscoelastic coating, a methodology is required for selecting appropriate material properties and for estimating anticipated drag reduction as a function of configuration and velocity.
Relevant background information for associated technical topics is available in the literature, and may be useful due to the technical complexity of this invention. A classical discussion of boundary layer theory, including formulation of Navier-Stokes and turbulent boundary layer equations, is provided in
Boundary
-
Layer Theory,
by Dr. Hermann Schlichting, published by McGraw Hill, New York, seventh edition, 1979. A discussion of structures and scales in turbulent flows can be found in
Turbulence,
1975, McGraw Hill, written by J. O. Hinze, and in “Coherent Motions in the Turbulent Boundary Layer,” in
Annual Review of Fluid Mechanics,
1991, volume 23, pp. 601-39, written by Steven K. Robinson. Background on Reynolds stress types of turbulence models is found in the chapter, “Turbulent Flows: Model Equations and Solution Methodology,” written by Tom Gatski, and included in the
Handbook of Computational Fluid Mechanics,
published by Academic Press in 1996. Equations in fluid and solid mechanics are often expressed in indicial, or tensor, notation, for compactness. Chapter 2 in the text
A First Course in Continuum Mechanics,
by Y. C. Fung, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1977, provides a brief introduction into tensor notation for mechanics equations. An introduction to finite difference methods, which are used to solve the system of momentum and continuity equations for a turbulent fluid, is provided in the text,
Computational Fluid Dynamics for Engineers,
written by Klaus Hoffman, and published in 1989 by the Engineering Education System i Austin, Texas. Descriptions of measured and mathematically modeled physical properties of polymers are found in the text,
Viscoelastic Properties of Polymers
by J. D. Ferry, Wiley, New York, 1980, 3
rd
edition. The article, “Loss Factor Height and Width Limits for Polymer Relaxation,” by Bruce Hartmann, Gilbert Lee, and John Lee, in the
Journal of the Acoustical Society of America
Vol. 95, No. 1, January 1994, discusses mathematical characterization of shear moduli for real viscoelastic, polymeric materials, including those approximated by the Havriliak-Negami approach.
Recently in the international literature (K. S. Choi, X. Yang, B. R. Clayton, E. J. Glover, M. Atlar, B. N. Semonev, and V. M. Kulik, “Turbulent Drag Reduction Using Compliant Surfaces,”
Proceedings of the Royal Society of London, A
(1997) 453, pp. 2229-2240). Choi et al. reported experimental measurements of up to 7% turbulent friction drag reduction for an axisymmetric body coated with a viscoelastic material. These experiments were performed in the United Kingdom, using coatings designed and fabricated in Russia at the Institute of Thermophysics, Russian Academy of Sciences, Novosibirsk, by a team headed by B .N. Semenov. The basic design approach was outlined in “On Conditions of Modelling and Choice of Viscoelastic Coatings for Drag Reduction,” in
Recent Developments in Turbulence Management,
K. S. Choi, ed., 1991, pp. 241-262, Dordrecht, Kluwer Publishers. The Novosibirsk design approach is semi-empirical in nature, and does not take into account the full characterization of the complex shear modulus of the viscoelastic material, namely, the relaxation time of the material. The Novosibirsk design approach does take into account frequency-dependent material properties. Furthermore, the Novosibirsk concept is valid only for a membrane-type coating, such as a film which coats a foam-rubber saturated with water or glycerine, and where only normal fluctuations of the surface are considered.
The structure of coatings intended for drag reduction has been addressed in the international literature, starting with the 1938 patent No. 669-897, “An Apparatus for the Reduction of Friction Drag,” issued in Germany to Max O. Kramer. Kramer later received a patent in 1964, U.S. Pat. No. 3,161,385, and in 1971, U.S. Pat. No. 3,585,953 for coatings to extend laminar flow in a boundary layer. Soviet inventor's certificates, such as “A Damping Covering,” USSR patent 1413286, Publication 20.01.1974,
Bulletin of the Inventions
14, by V. V. Babenko, L. F. Kozlov, and S. V. Pershin, “An Adjustable Damping Covering,” USSR patent 1597866, Publication 15.03.1978,
Bulletin of the Inventions
110, by V. V. Babenko, L. F. Kozlov, and V. I. Korobov, and “A Damping Covering for Solid Bodies,” USSR patent 1802672, Publication 07.02.1981,
Bulletin of the Inventions
15, by V. V. Babenko and N. F. Yurchenko, have also described the structure of drag-reducing coatings comprised of viscoelastic materials. These inventor's certificates identified the three-dimensional structure within a drag-reducing coating, but do not address the methodology for choosing appropriate parameters of the viscoelastic materials to be used in the manufacture of such coatings. Structural features include multiple layers of materials, longitudinal, rib-like inclusions of elastic, viscoelastic, or fluid materials, and heated elements. Viscoelastic coatings may be combined with other forms of structure, such as longitudinal riblets molded on or within the surface of the coating. As described in the international literature in publications such as “Secondary Flow Induced by Riblets,” written by D. B. Goldstein and T. C. Tuan, and published in the
Journal of Fluid Mechanics,
volume 363, May 25, 1998, pp. 115-152, two-dimensional, rigid riblets alone have been shown experimentally to reduce surface friction drag up to about 10%.
BRIEF SUMMARY OF THE INVENTION
The present invention enables the design of a passive viscoelastic coating for the reduction of turbulent friction drag. Coatings with material properties designed using the methodology described in this invention have reduced friction drag by greater than 10%. The methodology of the present invention permits, as a first object of the invention, the specification of the frequency dependent complex shear modulus, the density, and the thickness of an isotropic viscoelastic material which will reduce turbulent friction drag relative to specific flow conditions over a rigid surface. Quantitative levels of drag reduction can be estimated. Mathematical detail is provided for the cases of turbulent flow over a rigid flat plate as well as a viscoelastic flat plate, where the invention accounts for both normal and longitudinal oscillations of the surface. A second object of the invention is the specification of material properties for a coating composed of multiple layers of isotropic viscoelastic materials. A third object of the invention is the specification of material properties for a coating composed of an anisotropic material. A fourth object of the invention is the minimization of edge effects for coatings of finite length. A fifth object of the invention is the stabilization of longitudinal vortices through combination of viscoelastic coating design wit
May Carol L.
Voropayev Gennadiy A.
Arnold Bruce Y.
Arnold International
Cortana Corporation
Davis Octavia
Fuller Benjamin R.
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