Weakly-stochastic Navier-Stokes equation and shocktube experiments: Revealing the Reynolds' mystery in pipe flows

Ken Naitoh, Korai Ryu, Shunsuke Matsushita, Shinichi Tanaka, Mitsuaki Kurihara, Mikiya Marui

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)

Abstract

Although Reynolds showed the transition to turbulence in pipe flow 100 years ago, instability theories based on deterministic continuum mechanics and numerical simulations based on the deterministic Navier-Stokes equation cannot indicate the transition point in closed pipe flow. Our previous computations (Naitoh, 2007, 2008, 2009, 2010) in a straight and closed pipe using the random number generator have showed the transition in space without applying any stability theories and turbulence models, which suggests the possibility of a stochastic Navier-Stokes equation. The most important point of our approach is a theoretical and philosophical method proposed for determining the stochasticity level, which is deeply related to boundary condition. In this paper, computational analyses performed for the stochastic Navier-Stokes equation with grid systems having high and low resolutions quantitatively reveal the mysterious relation between inlet disturbance and the transition point to turbulence for pipe flows, while consideringsurface roughness of solid walls. Independence of the transition point on grid size implies that stochasticity is dominant rather than numerical discretization. Moreover, a laminarization phenomenon in a straight pipe, including puffs and slugs, are also captured. Finally, we will also show shocktube experiments, which qualitatively clarify the influence of inlet-outlet disturbances on the transition points.

Original languageEnglish
Title of host publication42nd AIAA Fluid Dynamics Conference and Exhibit 2012
Publication statusPublished - 2012 Dec 1
Event42nd AIAA Fluid Dynamics Conference and Exhibit 2012 - New Orleans, LA, United States
Duration: 2012 Jun 252012 Jun 28

Publication series

Name42nd AIAA Fluid Dynamics Conference and Exhibit 2012

Conference

Conference42nd AIAA Fluid Dynamics Conference and Exhibit 2012
CountryUnited States
CityNew Orleans, LA
Period12/6/2512/6/28

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ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Energy Engineering and Power Technology
  • Aerospace Engineering
  • Mechanical Engineering

Cite this

Naitoh, K., Ryu, K., Matsushita, S., Tanaka, S., Kurihara, M., & Marui, M. (2012). Weakly-stochastic Navier-Stokes equation and shocktube experiments: Revealing the Reynolds' mystery in pipe flows. In 42nd AIAA Fluid Dynamics Conference and Exhibit 2012 (42nd AIAA Fluid Dynamics Conference and Exhibit 2012).