# Numerical Study on the Characteristic of Temperature Drop of Crude Oil in a Model Oil Tanker Subjected to Oscillating Motion

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## Abstract

**:**

## 1. Introduction

## 2. Physical and Mathematical Model

#### 2.1. Physical Model

- (1)
- The liquid oil does not evaporate, and the total volume does not change with temperature and time.
- (2)
- The oil tanker is only subjected to rotational motion.
- (3)
- The change of density with temperature is described by the Boussinesq approximation in the momentum equation, while the change of other physical properties with temperature is not considered, i.e., only the average value in the range of temperature change is used.
- (4)
- There is no phase change in the crude oil during temperature drop.

#### 2.2. Mathematical Model

#### 2.2.1. Governing Equations

^{3}·s); and ${S}_{aq}$ is the source term and is zero in this research, kg/(m

^{3}·s). The volume fraction equation is not solved for the primary phase; the primary-phase volume fraction is computed by $\sum _{q=1}^{n}{\alpha}_{q}}=1$.

^{2}/s; and ${S}_{h}$ is the defined volume source term, W/m

^{2}.

^{3}). ${G}_{b}$ is the generation of turbulence kinetic energy brought by buoyancy, kg/(m·s

^{3}). ${C}_{1}$, ${C}_{2}$, ${C}_{1\epsilon}$ and ${C}_{3\epsilon}$ are constants. ${\sigma}_{k}$ and ${\sigma}_{\epsilon}$ are the turbulent Prandtl numbers for $k$ and $\epsilon $, respectively.

^{2}/s; ${S}_{\varphi}$ is the source term of $\varphi $; and $\partial V$ indicates the boundary of control volume $V$.

#### 2.2.2. Boundary Conditions

^{2}·K), and that of air is 20–100 W/(m

^{2}·K). In this paper, the forced heat transfer coefficient of water is 1250 W/(m

^{2}·K), and that of air is 50 W/(m

^{2}·K). In conclusion, the detailed information about the boundary conditions is provided in Table 1.

## 3. Numerical Method

## 4. Results and Discussion

^{8}.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Instantaneous phase distribution in Case 2: (

**a**) t = 1 s; (

**b**) t = 18 s; (

**c**) t = 42 s; and (

**d**) t = 59 s.

**Figure 8.**Instantaneous steam function in Case 1: (

**a**) t = 60 s; (

**b**) t = 660 s; (

**c**) t = 1020 s; and (

**d**) t = 2106 s.

**Figure 9.**Instantaneous steam function in Case 3: (

**a**) t = 264 s (moving to the left); (

**b**) t = 660 s (moving to the left); (

**c**) t = 990 s (moving to the right); and (

**d**) t = 2112 s (moving to the right).

**Figure 10.**Instantaneous boundary Nusselt number in Case 1: (

**a**) t = 60 s; (

**b**) t = 660 s; (

**c**) t = 1020 s; and (

**d**) t = 2106 s.

**Figure 11.**Instantaneous boundary Nusselt number in Case 3: (

**a**) t = 264 s (moving to the left); (

**b**) t = 660 s (moving to the left); (

**c**) t = 990 s (moving to the right); and (

**d**) t = 2112 s (moving to the right).

**Figure 12.**Instantaneous temperature fields in Case 1 (non-osculating condition): (

**a**) t = 1 s; (

**b**) t = 20 min; (

**c**) t = 40 min; and (

**d**) t = 60 min.

**Figure 13.**Instantaneous temperature fields in Case 3: (

**a**) t = 60 s (The tanker is rotating to the left); (

**b**) t = 682 s (The tanker is rotating to the left); (

**c**) t = 992 s (The tanker is rotating to the right); and (

**d**) t = 2108 s (The tanker is rotating to the right).

Boundaries | Convective Heat Transfer Coefficient | Fluid Temperature |
---|---|---|

$X=-20\text{}\mathrm{cm}$, $Y\ge 15\text{}\mathrm{cm}$ | ${h}_{f}=50\text{}\mathrm{W}/\left({\mathrm{m}}^{2}\xb7\mathrm{K}\right)$ | ${T}_{f}=293.15\text{}\mathrm{K}$ |

$X=20\text{}\mathrm{cm}$, $Y\ge 15\text{}\mathrm{cm}$ | ${h}_{f}=50\text{}\mathrm{W}/\left({\mathrm{m}}^{2}\xb7\mathrm{K}\right)$ | ${T}_{f}=293.15\text{}\mathrm{K}$ |

$X=-20\text{}\mathrm{cm}$, $Y\le 15\text{}\mathrm{cm}$ | ${h}_{f}=1250\text{}\mathrm{W}/\left({\mathrm{m}}^{2}\xb7\mathrm{K}\right)$ | ${T}_{f}=290.4\text{}\mathrm{K}$ |

$X=20\text{}\mathrm{cm}$, $Y\le 15\text{}\mathrm{cm}$ | ${h}_{f}=1250\text{}\mathrm{W}/\left({\mathrm{m}}^{2}\xb7\mathrm{K}\right)$ | ${T}_{f}=290.4\text{}\mathrm{K}$ |

$-20\text{}\mathrm{cm}\le X\le 20\text{}\mathrm{cm}$, $Y=0\text{}\mathrm{cm}$ | ${h}_{f}=1250\text{}\mathrm{W}/\left({\mathrm{m}}^{2}\xb7\mathrm{K}\right)$ | ${T}_{f}=290.4\text{}\mathrm{K}$ |

Materials | Density (kg/m^{3}) | Thermal Conductivity (W/m·°C) | Specific Heat Capacity (J/kg·°C) | Dynamic Viscosity (Pa·s) | Volume Expansion Coefficient (1/°C) |
---|---|---|---|---|---|

crude oil | 850 | 0.14 | 2000 | 0.004 | 1.0 × 10^{−5} |

air | 1.225 | 0.0242 | 1006.43 | 1.7894 × 10^{−5} | 0.00272 |

Case | Time Cycle of Oscillation | Amplitude of Oscillation |
---|---|---|

Case 1 | ∞ | 0 |

Case 2 | 10 s | $18.2\text{}\xb0$ |

Case 3 | 20 s | $18.2\text{}\xb0$ |

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**MDPI and ACS Style**

Yu, G.; Yang, Q.; Dai, B.; Fu, Z.; Lin, D.
Numerical Study on the Characteristic of Temperature Drop of Crude Oil in a Model Oil Tanker Subjected to Oscillating Motion. *Energies* **2018**, *11*, 1229.
https://doi.org/10.3390/en11051229

**AMA Style**

Yu G, Yang Q, Dai B, Fu Z, Lin D.
Numerical Study on the Characteristic of Temperature Drop of Crude Oil in a Model Oil Tanker Subjected to Oscillating Motion. *Energies*. 2018; 11(5):1229.
https://doi.org/10.3390/en11051229

**Chicago/Turabian Style**

Yu, Guojun, Qiuli Yang, Bing Dai, Zaiguo Fu, and Duanlin Lin.
2018. "Numerical Study on the Characteristic of Temperature Drop of Crude Oil in a Model Oil Tanker Subjected to Oscillating Motion" *Energies* 11, no. 5: 1229.
https://doi.org/10.3390/en11051229