# Numerical Validation of the Two-Way Fluid-Structure Interaction Method for Non-Linear Structural Analysis under Fire Conditions

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## Abstract

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## 1. Introduction

## 2. Numerical Approach

#### 2.1. Heat Transfer from Fires

#### 2.2. Adiabatic Surface Temperature

#### 2.3. FTMI Method

#### 2.4. Numerical Approach for Two-Way FSI

- CFD simulation by $\mathsf{\Delta}t$ using the FDS
- Heat transfer analysis and non-linear FEM according to the CFD simulation results
- CFD simulation until the second $\mathsf{\Delta}t$, and updating the geometry with the previous non-linear FEM
- Repetition of the CFD simulation with the updated geometry and FEM until completion of the fire scenario

- Case I: 4000 s
- Case II: 2000 s
- Case III: 1000 s
- Case IV: 500 s
- Case V: 250 s

## 3. Validation Study

#### 3.1. Material Properties

#### 3.2. FDS Simulation of Propane Burner Fire

#### 3.2.1. FDS Model Geometry and Computational Mesh

#### 3.2.2. FDS Results and Discussion

#### 3.3. Thermal Analysis

## 4. Results and Discussion

## 5. Conclusions

- One-way FSI tended to overestimate the structural consequences of exposing an H-beam to propane burner fire compared with the experimental results.
- One-way FSI may result in the overestimation of the fire safety design requirements for ships and offshore structures.
- For an H-beam under a propane burner fire, a $\mathsf{\Delta}t$ of 500 s was appropriate for two-way FSI. This use of this $\mathsf{\Delta}t$ also led to a similar structural behavior prediction as that obtained by using a smaller $\mathsf{\Delta}t$ (250 s), both of which were similar to the experimental results.
- As the structural consequences increased over time, the differences between the one-way and two-way FSI methods became more significant. This was a result of the one-way FSI being unable to readjust the fire load characteristics, due to changes in the time-variant geometry.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Abbreviation | |

FSI | Fluid-Structure Interaction |

FDS | Fire Dynamic Simulator |

FEM | Finite Element Method |

CFD | Computational Fluid Dynamics |

CoV | Coefficient of Variation |

Symbols | |

${q}^{\u2033}{}_{tot}$ | Total heat flux [W/m^{2}] |

${q}^{\u2033}{}_{rad}$ | Radiative heat flux [W/m^{2}] |

${q}^{\u2033}{}_{conv}$ | Convective heat flux [W/m^{2}] |

$\epsilon $ | Emissivity |

${e}^{\u2033}{}_{r,abs}$ | Radiative energy absorbed by the surfaces [J] |

$\sigma $ | Stefan–Boltzmann constant |

${T}_{g}$ | Gas temperature [°C] |

${T}_{s}$ | Multiplied by the convective heat transfer coefficient [°C] |

$h$ | Convective heat transfer coefficient [W/(m^{2} K)] |

${T}_{AST}$ | Adiabatic surface temperature [°C] |

$\mathsf{\Delta}t$ | Increment time [s] |

${E}_{20}$ | Elastic modulus of steel at room temperature [GPa] |

${E}_{T}$ | Elastic modulus of steel at elevated temperature [GPa] |

${f}_{y20}$ | Yield strengths of steel at room temperature [MPa] |

${f}_{yT}$ | Yield strengths of steel at elevated temperature [MPa] |

${\alpha}_{s}$ | Expansion coefficient [1/K] |

${D}^{*}$ | Diameter of a plume [m] |

$\dot{Q}$ | Heat release rate [W] |

${\rho}_{\infty}$ | Ambient density [ kg/m^{3}] |

${c}_{p}$ | Specific heat of air at constant pressure [kJ/kg·K] |

$dx$ | Length of a grid cell [m] |

${R}^{*}$ | Spatial resolution |

${\theta}_{m}$ | Surface temperature of the steel member [°C] |

${k}_{sh}$ | Correction factor for the shadow effect |

${A}_{m}/V$ | Section factor for the unprotected steel member [m^{−1}] |

${c}_{a}$ | Specific heat of steel [kJ/kg·K] |

${\rho}_{a}$ | Mass density of steel [kg/m^{3}] |

${h}_{net}$ | Net heat flux [W/m^{2}] |

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**Figure 1.**Sanchi oil tanker (

**left**), Piper Alpha (

**middle**) and U.S.S. Bonhomme Richard (

**right**) accidents.

**Figure 2.**Extent of the concept of the mapping procedure between the finite element method (FEM) and a computational fluid dynamics (CFD) method. FDS: Fire Dynamics Simulator; T

_{AST}: adiabatic surface temperature; h: convective heat transfer coefficient; APDL: ANSYS Parametric Design Language.

**Figure 3.**Differences between the schemes of the one-way and two-way fluid-structure interaction methods for determining the non-linear structural response to fire. $\mathsf{\Delta}t$: time increment.

**Figure 4.**Analytical logic of the two-way fluid-structure interaction for determining the non-linear structural response to fire. FDS: Fire Dynamics Simulator; FTMI: Fire-Thermochemical Interface; APDL: ANSYS Parametric Design Language.

**Figure 10.**Extent of the Fire Dynamics Simulator model geometry (

**left**) and the grid composition (

**right**).

**Figure 11.**Experimental and computational fluid dynamics scenes of flame movement. FDS: Fire Dynamics Simulator.

**Figure 23.**Deflection at 4000 s and maximum deflection versus time increments ($\mathsf{\Delta}t$) at VD-1.

**Figure 24.**Deflection at 4000 s and maximum deflection versus time increments ($\mathsf{\Delta}t$) at VD-2.

**Figure 25.**Deflection at 4000 s and maximum deflection versus time increments ($\mathsf{\Delta}t$) at VD-3.

**Figure 26.**Statistical analysis results of two-way FSI for deflection versus time increments ($\mathsf{\Delta}t$) at VD-1.

**Figure 27.**Statistical analysis of two-way FSI for deflection versus time increments ($\mathsf{\Delta}t$) at VD-2.

**Figure 28.**Statistical analysis of two-way FSI for deflection versus time increments ($\mathsf{\Delta}t$) at VD-3.

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**MDPI and ACS Style**

Woo, D.; Seo, J.K. Numerical Validation of the Two-Way Fluid-Structure Interaction Method for Non-Linear Structural Analysis under Fire Conditions. *J. Mar. Sci. Eng.* **2021**, *9*, 400.
https://doi.org/10.3390/jmse9040400

**AMA Style**

Woo D, Seo JK. Numerical Validation of the Two-Way Fluid-Structure Interaction Method for Non-Linear Structural Analysis under Fire Conditions. *Journal of Marine Science and Engineering*. 2021; 9(4):400.
https://doi.org/10.3390/jmse9040400

**Chicago/Turabian Style**

Woo, Donghan, and Jung Kwan Seo. 2021. "Numerical Validation of the Two-Way Fluid-Structure Interaction Method for Non-Linear Structural Analysis under Fire Conditions" *Journal of Marine Science and Engineering* 9, no. 4: 400.
https://doi.org/10.3390/jmse9040400