### Abstract

Three-dimensional numerical simulations in a square duct were conducted to investigate entrance lengths of normal fluid and superfluid flows in a thermal counterflow of superfluid
^{4}
He. The two fluids were coarse-grained by using the Hall–Vinen–Bekharevich–Khalatnikov (HVBK) model and were coupled through mutual friction. We solved the HVBK equations by parameterizing the coefficient of the mutual friction to consider the vortex line density. A uniform mutual friction parameter was assumed in the streamwise direction. Our simulation showed that the entrance length of the normal fluid from a hot end becomes shorter than that of a single normal fluid due to the mutual friction with the parabolically developed superfluid flow near the hot end. As the mutual friction increases, the entrance length decreases. Same as that, the entrance length of the superfluid from a cold end is affected by the strength of the mutual friction due to the parabolically developed normal fluid flow near the cold end. Aside from the entrance effect, the realized condition of a tail-flattened flow is discussed by parameterizing the superfluid turbulent eddy viscosity and the mutual friction.

Original language | English |
---|---|

Journal | Journal of Low Temperature Physics |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Fingerprint

### Keywords

- Entrance length
- HVBK model
- Mutual friction
- Superfluid
- Thermal counterflow
- Two-fluid model

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Materials Science(all)
- Condensed Matter Physics

### Cite this

**
Numerical Study on Entrance Length in Thermal Counterflow of Superfluid
^{4}
He
.** / Kobayashi, Hiromichi; Yui, Satoshi; Tsubota, Makoto.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Numerical Study on Entrance Length in Thermal Counterflow of Superfluid 4 He

AU - Kobayashi, Hiromichi

AU - Yui, Satoshi

AU - Tsubota, Makoto

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Three-dimensional numerical simulations in a square duct were conducted to investigate entrance lengths of normal fluid and superfluid flows in a thermal counterflow of superfluid 4 He. The two fluids were coarse-grained by using the Hall–Vinen–Bekharevich–Khalatnikov (HVBK) model and were coupled through mutual friction. We solved the HVBK equations by parameterizing the coefficient of the mutual friction to consider the vortex line density. A uniform mutual friction parameter was assumed in the streamwise direction. Our simulation showed that the entrance length of the normal fluid from a hot end becomes shorter than that of a single normal fluid due to the mutual friction with the parabolically developed superfluid flow near the hot end. As the mutual friction increases, the entrance length decreases. Same as that, the entrance length of the superfluid from a cold end is affected by the strength of the mutual friction due to the parabolically developed normal fluid flow near the cold end. Aside from the entrance effect, the realized condition of a tail-flattened flow is discussed by parameterizing the superfluid turbulent eddy viscosity and the mutual friction.

AB - Three-dimensional numerical simulations in a square duct were conducted to investigate entrance lengths of normal fluid and superfluid flows in a thermal counterflow of superfluid 4 He. The two fluids were coarse-grained by using the Hall–Vinen–Bekharevich–Khalatnikov (HVBK) model and were coupled through mutual friction. We solved the HVBK equations by parameterizing the coefficient of the mutual friction to consider the vortex line density. A uniform mutual friction parameter was assumed in the streamwise direction. Our simulation showed that the entrance length of the normal fluid from a hot end becomes shorter than that of a single normal fluid due to the mutual friction with the parabolically developed superfluid flow near the hot end. As the mutual friction increases, the entrance length decreases. Same as that, the entrance length of the superfluid from a cold end is affected by the strength of the mutual friction due to the parabolically developed normal fluid flow near the cold end. Aside from the entrance effect, the realized condition of a tail-flattened flow is discussed by parameterizing the superfluid turbulent eddy viscosity and the mutual friction.

KW - Entrance length

KW - HVBK model

KW - Mutual friction

KW - Superfluid

KW - Thermal counterflow

KW - Two-fluid model

UR - http://www.scopus.com/inward/record.url?scp=85062613671&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062613671&partnerID=8YFLogxK

U2 - 10.1007/s10909-019-02169-8

DO - 10.1007/s10909-019-02169-8

M3 - Article

AN - SCOPUS:85062613671

JO - Journal of Low Temperature Physics

JF - Journal of Low Temperature Physics

SN - 0022-2291

ER -