# Computational Study of Wet Steam Flow to Optimize Steam Ejector Efficiency for Potential Fire Suppression Application

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## Abstract

**:**

## 1. Introduction

- The simulation will take advantage of a wet steam model to investigate the condensation effect on the flow behavior and steam ejector performance.
- The numerical model will be validated against experimental data and the results will also be compared with the ideal gas model.
- Different wall functions and turbulences models will be tested to determine the most optimized model in terms of prediction accuracy.
- A series of simulations with different wetness operating conditions will be performed to investigate the relationship between the wetness of working flows and pump efficiency.

## 2. Mathematical Model

#### 2.1. Wet Steam Modeling

_{v}) is the vapor density and (β) is the liquid-phase mass fraction. And in Equation (3), the internal energy (E) and the specific enthalpy (h) are given by:

_{d}is the average droplet volume, which is calculated by the average droplet radius (${\overline{r}}_{d}$) using the volume formula of a circle.

#### 2.2. Wet Steam Equation of State

_{1}=0.0015, a

_{2}= −0.000942, and a

_{3}= −0.0004882.

_{0}= 0.8978, α = 11.16, a = 1.772, and b = 1.5 × 10

^{−6}.

_{v}), specific enthalpy (h

_{v}), and specific entropy (s

_{v}), which is applied for calculating the state of vapor, are also given below.

_{0}, h

_{0}, s

_{0}are the standard state isobaric specific heat capacity, enthalpy, entropy respectively.

## 3. Modeling Setup and Boundary Conditions

## 4. Validation of the Numerical Model

## 5. Results and Discussion

#### 5.1. Turbulence Model and Wall Functions for Steam Ejector Modeling

#### 5.2. Wetness Influences of Inlets on Entrainment Ratio

## 6. Conclusions

- Based on the ideal gas model, the realizable k−ε turbulence model with enhanced wall functions showed a better performance of simulating the working process of the steam ejector.
- Compared with the ideal gas model, the wet steam model showed a better agreement against the experimental data, especially in the mixing chamber section with approximately 23% improvement.
- The spontaneous condensation happened in the nozzle and during the mixing chamber, the condensation effect had an influence on the entrainment ratio.
- By reducing the wetness of the secondary fluid or improving the wetness of the primary fluid, the condensation effect lasted longer and improved the entrainment ratio, which means the performance of the steam ejector is enhanced.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

B, C | virial coefficients (m^{3}/kg, m^{6}/kg^{2}) |

Cp, Cp_{0} | isobaric heat capacity, standard state heat capacity (J/kg·K) |

E_{m} | entrainment ratio |

h, h_{0}, h_{l}, h_{v}, h_{lv} | specific enthalpy, standard state enthalpy, liquid specific enthalpy, vapor specific enthalpy, specific enthalpy between phases (J/kg) |

I | nucleation rate (1/s) |

K_{b} | Boltzmann constant (J/mol·K) |

k | turbulent kinetic energy (m^{2}/s^{2}) |

M | molecular mass (kg) |

$P$ | pressure (Pa) |

${P}_{b}$ | back pressure (Pa) |

${P}_{b}^{*}$ | critical back pressure (Pa) |

${P}_{b}^{r}$ | reversing back pressure (Pa) |

${P}_{sat}$ | saturation pressure |

q_{c} | evaporation coefficient |

R | gas-law constant (J/mol·k) |

$\overline{r}$ | droplet average radius (m) |

${r}_{*}$ | critical droplet radius (m) |

S | super saturation ratio |

s, s_{0,} s_{v} | specific entropy, standard state entropy, vapor specific entropy (J/kg·mol·K) |

T | thermal temperature (K) |

T_{0} | droplet temperature (K) |

t | time (s) |

u | velocity (m/s) |

V_{d} | average droplet volume (m^{3}) |

α_{v} | volume fraction |

β | mass fraction |

γ | specific heat capacities ratio |

Γ | mass generation rate (kg/s) |

ε | turbulent energy dissipation rate (m^{2}/s^{3}) |

η | droplet number density (1/m^{3}) |

θ | non-isothermal correction factor |

μ, μ_{t} | dynamic viscosity, turbulent viscosity (Pa·s) |

ν | kinetic viscosity (m^{2}/s), |

ρ, ρ_{l}, ρ_{v} | mixture density, liquid density, vapor density (kg/m^{3}) |

σ | droplet surface tension (N/m) |

E | internal energy |

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**Figure 1.**Configuration of a typical steam ejector and flow characteristic along the axis of the steam ejector.

**Figure 2.**Characteristic curve of a steam ejector at a fixed temperature [10].

**Figure 3.**(

**a**) Enthalpy-entropy diagram of the working process in the nozzle of the steam ejector. (

**b**) Main view of the ejector refrigeration system (

**c**) Steam ejector. (

**d**) Three-dimensional isometric side view of the system.

**Figure 6.**Comparison of static pressure distribution along the ejector wall between wet steam model and experimental data.

**Figure 7.**Static pressure distribution along ejector wall between ideal gas model and wet steam model against the experimental data.

**Figure 8.**Axial static pressure distribution of different turbulence models against the experimental data.

**Figure 10.**Axial static temperature distribution of different wetness of inlet flows based on the wet steam model.

**Table 1.**Detailed dimensions for the inlet and outlet diameter sizes, lengths of the components for the steam ejector.

Geometry | Value |
---|---|

Diameter of Nozzle inlet | 7.75 mm |

Diameter of Nozzle outlet | 8 mm |

Diameter of Mixing chamber inlet | 24 mm |

Diameter of Mixing throat | 19 mm |

Length of Nozzle | 60 mm |

Length of Mixing chamber | 130 mm |

Length of Throat | 95 mm |

Length of Diffuse | 180 mm |

Expanded angle of nozzle | 10° |

Nozzle exit position | 0 mm |

Inlet Fluid | Temperature (K) | Pressure (Pa) |
---|---|---|

Primary fluid | 393.15 | 200,000 |

Secondary fluid | 283.15 | 1200 |

Case Number | Wetness of Primary Flow (Inlet 1) | Wetness of Secondary Flow (Inlet 2) |
---|---|---|

Case 1 | 0 | 0 |

Case 2 | 0 | 0.1 |

Case 3 | 0.1 | 0 |

Case 4 | 0.1 | 0.1 |

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## Share and Cite

**MDPI and ACS Style**

Li, A.; Yuen, A.C.Y.; Chen, T.B.Y.; Wang, C.; Liu, H.; Cao, R.; Yang, W.; Yeoh, G.H.; Timchenko, V.
Computational Study of Wet Steam Flow to Optimize Steam Ejector Efficiency for Potential Fire Suppression Application. *Appl. Sci.* **2019**, *9*, 1486.
https://doi.org/10.3390/app9071486

**AMA Style**

Li A, Yuen ACY, Chen TBY, Wang C, Liu H, Cao R, Yang W, Yeoh GH, Timchenko V.
Computational Study of Wet Steam Flow to Optimize Steam Ejector Efficiency for Potential Fire Suppression Application. *Applied Sciences*. 2019; 9(7):1486.
https://doi.org/10.3390/app9071486

**Chicago/Turabian Style**

Li, Ao, Anthony Chun Yin Yuen, Timothy Bo Yuan Chen, Cheng Wang, Hengrui Liu, Ruifeng Cao, Wei Yang, Guan Heng Yeoh, and Victoria Timchenko.
2019. "Computational Study of Wet Steam Flow to Optimize Steam Ejector Efficiency for Potential Fire Suppression Application" *Applied Sciences* 9, no. 7: 1486.
https://doi.org/10.3390/app9071486