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On the pressure and stress singularities induced by steady flows of incompressible viscous fluids

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Abstract

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier–Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence–divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.

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References

  1. Sinclair G.B.: Stress singularities in classical elasticity—II: Asymptotic identification. Appl. Mech. Rev. 57, 385–439 (2004)

    Article  Google Scholar 

  2. Kondrat’ev V.A.: Asymptotic solution of the Navier–Stokes equations near the angular point of the boundary. J. Appl. Math. Mech. 31, 125–129 (1967)

    Article  MathSciNet  Google Scholar 

  3. Blum H., Rannacher R.: On the boundary value problem of the biharmonic operator on domains with angular corners. Math. Meth. Appl. Sci. 2, 556–581 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  4. Rayleigh L.: In Scientific Papers VI 18–21. Cambridge University Press, Cambridge (1920)

    Google Scholar 

  5. Dean W.R., Montagnon P.E.: On the steady motion of viscous liquid in a corner. Proc. Camb. Phil. Soc. 45, 389–394 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  6. Moffatt H.K.: Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18 (1964)

    Article  MATH  Google Scholar 

  7. Liu C.H., Joseph D.D.: Stokes flow in wedge-shaped trenches. J. Fluid Mech. 80, 443–463 (1977)

    Article  MATH  Google Scholar 

  8. Moffatt, H.K.: The asymptotic behavior of solutions of the Navier–Stokes equations near sharp corners. In: Proceedings of Symposium on Approximation Methods for Navier–Stokes Problems, Paderborn, Germany, 371–380. Springer Verlag, Berlin (1979)

  9. Milikan R.A.: Coefficients of slip in gases and the law of reflection of molecules from the surfaces of solids and liquids. Phys. Rev. 21, 217–238 (1923)

    Article  Google Scholar 

  10. Williams M.L.: Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19, 526–528 (1952)

    Google Scholar 

  11. Seweryn A., Molski K.: Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions. Eng. Fract. Mech. 55, 529–556 (1996)

    Article  Google Scholar 

  12. Taylor, G.I.: On scraping of viscous fluid from a plane surface. In: The Scientific Papers of Sir Geoffrey Ingram Taylor IV, pp. 410–413. Cambridge University Press Cambridge (1971)

  13. Dempsey J.P., Sinclair G.B.: On the stress singularities in the plane elasticity of the composite wedge. J. Elast. 9, 373–391 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sinclair, G.B., Beisheim, J.R., Sezer, S.: Practical convergence–divergence checks for stresses from FEA. In: Proceedings of 2006 International ANSYS Conf., Pittsburgh, Pennsylvania, on CD-ROM (2006)

  15. http://www.fluent.com/software/fluent/index.htm

  16. Zak A.R.: Stresses in the vicinity of boundary discontinuities in bodies of revolution. J. Appl. Mech. 31, 150–152 (1964)

    Google Scholar 

  17. Aksentian O.K.: Singularities of the stress-strain state of a plate in the neighborhood of an edge. J. Appl. Math. Mech. 31, 193–202 (1967)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA

    G. B. Sinclair

  2. Department of Aerospace Engineering, Iowa State University, Ames, IA, 50011, USA

    X. Chi & T. I-P. Shih

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  1. G. B. Sinclair
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  2. X. Chi
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  3. T. I-P. Shih
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Correspondence to T. I-P. Shih.

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Sinclair, G.B., Chi, X. & Shih, T.IP. On the pressure and stress singularities induced by steady flows of incompressible viscous fluids. Acta Mech Sin 25, 451–462 (2009). https://doi.org/10.1007/s10409-009-0278-y

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  • DOI: https://doi.org/10.1007/s10409-009-0278-y

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