# ON THE ANALATICAL SOLUTIONS AND NUMERICAL VERIFICATIONS OF THE TWO-PHASE WATER FAUCET PROBLEM

## Abstract

The two-phase water faucet problem is one of the benchmark problems originally proposed by Ransom. The test consists of a vertical pipe, which is initially filled with a uniform column of liquid moving with an initial velocity and an annulus of gas sitting still. At the top boundary, liquid is supplied at the same velocity as the initial velocity, and the bottom of the pipe opens to the ambient. Due to the gravity effect, the liquid column accelerates and becomes thinner. With simplifications, such as massless gas phase and no wall and interfacial frictions, an analytical solution could be obtained for the transient liquid velocity and void fraction distribution. The test has been widely used for the purposes of code assessment, benchmark and numerical verifications. This exact solution was used in this work to verify the numerical accuracy of a high-resolution spatial discretization scheme. The high-resolution spatial discretization scheme is based on the commonly used staggered grid mesh, and slope limiter was introduced to achieve high resolutions in space. It was found that, at the steady state, an expected second-order spatial accuracy could not be achieved. A further investigation showed that this exact solution does not actually satisfy the commonlymore »

- Authors:

- Publication Date:

- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)

- OSTI Identifier:
- 1357894

- Report Number(s):
- INL/CON-14-33924

- DOE Contract Number:
- DE-AC07-05ID14517

- Resource Type:
- Conference

- Resource Relation:
- Conference: 16th International Topical Meeting on Nuclear Reactor Thermalhydraulics (NURETH-16), Chicago, Illinois, USA, August 30 through September 4, 2015

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; Exact Solutions; Numerical Verification; Two-Phase; Water Faucet

### Citation Formats

```
Zou, Ling, Zhao, Haihua, and Zhang, Hongbin.
```*ON THE ANALATICAL SOLUTIONS AND NUMERICAL VERIFICATIONS OF THE TWO-PHASE WATER FAUCET PROBLEM*. United States: N. p., 2015.
Web.

```
Zou, Ling, Zhao, Haihua, & Zhang, Hongbin.
```*ON THE ANALATICAL SOLUTIONS AND NUMERICAL VERIFICATIONS OF THE TWO-PHASE WATER FAUCET PROBLEM*. United States.

```
Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. Tue .
"ON THE ANALATICAL SOLUTIONS AND NUMERICAL VERIFICATIONS OF THE TWO-PHASE WATER FAUCET PROBLEM". United States. https://www.osti.gov/servlets/purl/1357894.
```

```
@article{osti_1357894,
```

title = {ON THE ANALATICAL SOLUTIONS AND NUMERICAL VERIFICATIONS OF THE TWO-PHASE WATER FAUCET PROBLEM},

author = {Zou, Ling and Zhao, Haihua and Zhang, Hongbin},

abstractNote = {The two-phase water faucet problem is one of the benchmark problems originally proposed by Ransom. The test consists of a vertical pipe, which is initially filled with a uniform column of liquid moving with an initial velocity and an annulus of gas sitting still. At the top boundary, liquid is supplied at the same velocity as the initial velocity, and the bottom of the pipe opens to the ambient. Due to the gravity effect, the liquid column accelerates and becomes thinner. With simplifications, such as massless gas phase and no wall and interfacial frictions, an analytical solution could be obtained for the transient liquid velocity and void fraction distribution. The test has been widely used for the purposes of code assessment, benchmark and numerical verifications. This exact solution was used in this work to verify the numerical accuracy of a high-resolution spatial discretization scheme. The high-resolution spatial discretization scheme is based on the commonly used staggered grid mesh, and slope limiter was introduced to achieve high resolutions in space. It was found that, at the steady state, an expected second-order spatial accuracy could not be achieved. A further investigation showed that this exact solution does not actually satisfy the commonly used two-fluid single pressure two-phase flow equations. More importantly, we have also found that a steady-state exact solution could be obtained for the water faucet problem. In this work, we have demonstrated the derivation of the steady-state exact solution for the water faucet problem. The exact solution was then used to verify a first-order and a high-resolution spatial discretization scheme, from which expected order of accuracy was achieved by doing mesh refinement.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Sep 01 00:00:00 EDT 2015},

month = {Tue Sep 01 00:00:00 EDT 2015}

}