抄録
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.
| 元の言語 | English |
|---|---|
| ホスト出版物のタイトル | 42nd AIAA Fluid Dynamics Conference and Exhibit 2012 |
| 出版物ステータス | Published - 2012 |
| イベント | 42nd AIAA Fluid Dynamics Conference and Exhibit 2012 - New Orleans, LA 継続期間: 2012 6 25 → 2012 6 28 |
Other
| Other | 42nd AIAA Fluid Dynamics Conference and Exhibit 2012 |
|---|---|
| 市 | New Orleans, LA |
| 期間 | 12/6/25 → 12/6/28 |
Fingerprint
ASJC Scopus subject areas
- Fluid Flow and Transfer Processes
- Energy Engineering and Power Technology
- Aerospace Engineering
- Mechanical Engineering
これを引用
Weakly-stochastic Navier-Stokes equation and shocktube experiments : Revealing the Reynolds' mystery in pipe flows. / Naitoh, Ken; Ryu, Korai; Matsushita, Shunsuke; Tanaka, Shinichi; Kurihara, Mitsuaki; Marui, Mikiya.
42nd AIAA Fluid Dynamics Conference and Exhibit 2012. 2012.研究成果: Conference contribution
}
TY - GEN
T1 - Weakly-stochastic Navier-Stokes equation and shocktube experiments
T2 - Revealing the Reynolds' mystery in pipe flows
AU - Naitoh, Ken
AU - Ryu, Korai
AU - Matsushita, Shunsuke
AU - Tanaka, Shinichi
AU - Kurihara, Mitsuaki
AU - Marui, Mikiya
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84881222857&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84881222857&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84881222857
SN - 9781600869334
BT - 42nd AIAA Fluid Dynamics Conference and Exhibit 2012
ER -