Determination of cryogenic temperature loads for ﬁ nite-element model of LNG bunkering ship under LNG release accident

: The rising demand for lique ﬁ ed natural gas (LNG)-fueled ships requires the LNG bunkering facility that partially uses a ship-to-ship operation. The bunkering process of LNG fuel may have a greater risk due to LNG volatility. The cryogenic temperature of LNG poses a threat to the personnel and structural embrittlement to ships. Therefore, cryogenic spill protection optimization was introduced concerning the structural strength analysis using ﬁ nite element (FE) by utilizing cryogenic temperature loads provided by the computational ﬂ uid dynamics (CFD) model of an LNG release. This study aims to build a platform for transferring the temperature load pro ﬁ le from CFD to FE software accurately. The CFD model usually uses a structured Cartesian grid, and the FE method adopts an unstructured tetrahedral or hexahedral mesh. As a result, both con ﬁ gurations store results at di ﬀ erent positions, and it is not preferred for the load pro ﬁ le to be transferred directly. The error will be greater due to the variance of positions. Random Forest, a machine learning method, has been employed that uses a regression technique to deal with a continuous variable. An accurate load pro ﬁ le for the FE model can be obtained by adopting decision tree learning in Random Forest. The procedure for determining the temperature load pro ﬁ le is presented in this article.


Introduction
In order to control air pollutant emission, the International Maritime Organization has established several emission control area that restricts ships with excessive exhaust gas of SO X and NO X .To deal with the new regulation, either many ships are being converted to operate on liquefied natural gas (LNG) as well as 303 new LNG-fueled ships are being commissioned since 2020 [1].In consequence, the demand for LNG fuel increase to 3.01 million per year for the shipping sector use only [2].Besides this, the LNG supply facility will be required in the major port to serve those LNG-fueled ships.A ship-to-ship platform such as an LNG bunkering ship is preferable, that it only requires a few land acquisitions and stores large quantities of LNG fuel rather than the truck-to-ship operation [3].
The European Commission reported that since 1986, there have been a significant number of LNG release accidents involving the loading/unloading, storing, and distribution, which are the bunkering activities [4].The SAFEDOR risk model also included the LNG release during loading/ unloading as a generic accident category for ships carrying LNG, besides collision and grounding [5].The risks of this cryogenic release would impact both personnel and ship structures, such as cryogenic burn and steel embrittlement, respectively, since LNG is stored at −163°C [6].Direct contact of LNG flow to a structure can rapidly cool the steel below the embrittlement temperature.Consequently, it would interfere with safety measures, including early detection, isolation, and blowdown, which might not be able to overcome the cryogenic hazard completely [7].Further, the cryogenic flow could cause brittle cracks that ultimately cause the structure to collapse and escalate into a catastrophic disaster due to an initial event of LNG release [6,7].
Based on those risk identification, a consequence analysis which is a part of risk assessment would be useful that provides a comprehensive analysis by conducting either experiment or simulation of an accidental LNG release [6,7].The problem of LNG release simulation can be done by employing the turbulence flow model provided by the computational fluid dynamics (CFD) solver, i.e., Kameleon Fire Ex (KFX) and flame acceleration simulator [8][9][10].
To deal with the cryogenic flow hazard, the cryogenic thermal and structural response must be performed to deliver an optimized structural design [6].Lloyd Register published the cryogenic spill guidance that provides the cryogenic spill protection (CSP) procedure.Using CFD techniques, CSP requires identifying the most exposed area to a cryogenic hazard and predicts the cryogenic heat transfer to the structure in that area [7].Furthermore, the result of cryogenic heat transfer in CFD analysis can be applied as an input for thermal-stress analysis using finite element (FE) [6,7].By adopting this technique, the region of degraded material can be identified based on the cryogenic brittle fracture criterion.Thus, it would be useful to redesign the structure in case of brittle fracture escalation [7].
This study aims to build a platform for transferring the thermal data from CFD to FE software in order to support CSP assessment.The cryogenic gas leak model is based on an LNG bunkering ship's accidental release of LNG that was analyzed on KFX.The temperature in each coordinate point of the KFX grid was carried out as an input as well as the node information of the FE model, for Random Forest.R-squared and root mean square errors (RMSE) were employed to evaluate the Random Forest model.In addition, both temperatures in both KFX and FE models were compared to see the Random Forest accuracy.Finally, the temperature profile was obtained, which is compatible with the FE model's node position.This temperature profile is ready to use as input for further FE analysis.

Review of thermal load determination
The integration of load profiles derived from CFD into FE software for structural response analysis plays a crucial role in CSP assessment [6,7].However, this integration task is challenging, as CFD and FE models often employ different mesh or grid configurations.While some commercial packages offer partial solutions, they are not fully compatible or versatile.For instance, FAHTS, designed for heat transfer analysis, can read radiation and convection from KFX simulation results but requires additional software, such as USFOS [11], to address the structural response problem [12].Furthermore, the temperature profile cannot be exported to various FE software.Another limitation is that USFOS only supports FE models using beam elements for nonlinear structural response analysis.
To overcome these limitations, Kim et al. (2013) developed a platform called KFX2DYNA, specifically designed to map thermal loads from KFX to LS-DYNA for shell element problems [13].This platform employs an interpolation technique to transfer the thermal load, with interpolation occurring at LS-DYNA nodes based on the closest KFX monitoring points [12,13].Notably, popular FE software like ABAQUS also adopts interpolation for load transfer [14].Alternatively, adopting an ensemble learning method, such as Random Forest, holds promise for load transfer.By constructing multiple decision

Output of Load Profile
• LNG bunkering ship model • LNG release scenarios Input: • Grid points of KFX model and temperature profile trees in the training model, this technique can effectively address regression tasks, estimating the value of a target variable based on input variables [15].Figure 1 provides an overview of the framework used to map temperature loads from KFX to FE models.Temperature loads are obtained from LNG release simulations using KFX, focusing on the LNG bunkering ship as the target model.Various LNG release scenarios are considered, encompassing parameters such as leak diameter, position, flow rate, wind speed, wind direction, and ambient temperature.The KFX simulation results, specifically the steel temperature, are retrieved from the area of interest for Random Forest pre-processing.
In this study, the Random Forest technique is employed to integrate KFX grid points, FE node positions, and the steel temperature output from KFX simulations.The positions of grid points and nodes are treated as dependent variables, with their values depending on the corresponding temperature values, which serve as the independent variable.Decision trees in the Random Forest model are constructed using KFX grid points and temperature load data.The FE node positions are then used as input to predict the temperature load.To evaluate the accuracy of the predictions, the R-squared score is employed, which measures the deviation between the predicted temperatures and the temperatures obtained from KFX simulations, taking into account the shape of the data.Additionally, the RMSE is used to assess the error in the data values, providing further insights into the performance of the Random Forest regression model.These evaluation techniques are commonly employed for assessing the efficacy of Random Forest regression models.Furthermore, a direct comparison of the load profiles between the KFX and FE models is performed at specific coordinate points, allowing for a comprehensive evaluation of the load transfer process and the fidelity of the predicted temperature load in the FE model.

The past study of LNG release
KFX is a CFD program based on the finite-volume model that uses a structured Cartesian grid to solve the conservation equations for three-dimensional time-dependent turbulent flow [6,8,9,16].Several experimental data have been employed for validating the accuracy of the KFX code that focuses on the large-scale hydrocarbon release experiment [9,17,18].In this study, an accidental LNG release occurred on the deck of the LNG bunkering system that was released from a point on a pipeline.The release duration was limited to 15 s following the response time of the emergency shutdown valve that was installed on the LNG bunkering system [19].The detail of the LNG release scenario is given in Table 1.
Figure 2 exhibits the gas cloud dispersion after the KFX simulation has been conducted.The contour is presented based on the lower flammability of LNG, which is a 5% gas concentration of the overall gas mixture.The LNG gas cloud was flown to the ship's stern that directly hit an obstruction which is a fuel gas supply room.Thus, this fuel gas supply room is an area of interest where a potential brittle crack may occur.The wall of the fuel gas supply room was significantly exposed to the gas cloud that has a temperature of up to 174.08 K or −99.07°C [19].In this case, the gas release path was re-entrained after the gas cloud particles were reflected due to an existing nearby obstruction.The gas cloud dispersion decelerates because of the gas re-entrainment mechanism, which causes a gas cloud accumulation.

Load transfer process
This section addresses transferring the load profile from the CFD results to the FE model.The primary challenge stems from the disparity in mesh configurations between the two numerical models.To tackle this issue, a technique named Random Forest regression was employed, which offers a promising solution.

Pre-processing
In KFX, the result of various calculations is stored inside the control volume (CV) point such as fluid density and temperature, which is a scalar variable.The scalar variable is located in the middle of the CV, and the vector variable is stored at the CV's boundary [16].A non-uniform structured cartesian grid (NSCG) is adopted in KFX to solve the finitedifference problems [16].Grids can be controlled to have different sizes of CVs, and the finer CV is used in the area of interest.The simulation process can be optimized in terms of result accuracy and simulation time with this grid control [16].Figure 3 shows the NSCG configuration in KFX.
A different configuration is used in FE, which is adopting a non-uniform unstructured mesh.This mesh configuration can accommodate an arbitrary geometry [21].Load information, such as forces, moments, and temperatures, can be stored inside a node point in the FE model [22].Figure 4 exhibits an FE model of an LNG bunkering ship in ANSYS/ LS-DYNA.
Grid and node points provide the position information in the Cartesian system.Thus, the independent variable consists of the coordinate point in the X, Y, and Z axes.It is followed by temperature profiles as the dependent Figure 3: NSCG on KFX [16] with LNG bunkering ship model.

isometric portside starboard front
The contour set to be more than 5% gas concentration or >LFL variable.The steel temperature is the only independent variable that was retrieved from the KFX result.Here is an example of the dataset for building a random forest model that was retrieved from KFX, as shown in Table 2.This dataset is limited to ten instances from the actual 29,865 instances.

Random forest procedure
This study implemented all the algorithms required for constructing the Random Forest model using Python code.
The machine learning package "scikit-learn" was utilized to develop the algorithm [23].The Random Forest model leverages decision trees to make predictions of the dependent variables based on the provided independent variables.Additionally, the study applied a technique known as "bagging" (bootstrapping-aggregating) to the Random Forest model.Bootstrapping involves randomly sampling the dataset with replacement to determine the values used in executing the decision tree algorithm [24,25].Typically, 100 decision trees are employed to obtain precise results.The aggregation step involves selecting the majority of the data processed by the decision trees algorithm.In the case of regression problems, the decision tree results can be simply averaged to obtain the majority values [26].Figures 5  and 6 exhibit the procedure for utilizing the Random Forest and an example of the bootstrapping-aggregating process, respectively.
Upon acquiring the KFX results, the dataset is categorized into grid points and corresponding steel temperatures.To develop the Random Forest model, the dataset is partitioned into training and testing subsets, constituting 80 and 20% of the entire dataset, respectively.The training subset plays a crucial role in identifying and learning the underlying data patterns within the Random Forest model [27,28].Conversely, the testing subset is employed to assess the performance and progression of the Random Forest algorithm [27,29].It is essential for the testing subset to represent the  Obtain LS-dyna node and estimated steel temperature START FINISH (10).Get LS-DYNA load input   Determination of cryogenic temperature loads for finite element model  7 entire dataset adequately and possess sufficient data points to facilitate accurate predictions [27].The training and testing subsets are vital components in the model development and evaluation process.An extensive evaluation was conducted to assess the performance the Random Forest model by comparing the predicted values with the true values of the original dataset.Figure 7 presents the results of this evaluation, showcasing the plots alongside the corresponding R-squared score and root mean square errors.
Here, the RMSE and R-squared score can be expressed as follows: where n is the amount of the value, and x i is each value which is steel temperature in this case.Furthermore, RSS and TSS are the sum of squares of residuals and the total sum of squares, respectively.
The training and testing subsets demonstrate a high R-squared score, indicating a strong correlation between the predicted and true values.The RMSE values are relatively low, further affirming the accuracy of the predictions.Notably, the training subset, comprising 80% of the entire dataset, exhibits a better fit than the testing subset.Overall, the evaluation outcomes indicate favorable results.During the implementation stage, the ANSYS/LS-DYNA node points (X_real) were utilized as the dependent variable.This variable plays a crucial role in estimating the new steel temperature data.

Load profile validation
To ensure the credibility of the load profile when applied in the FE software, an additional evaluation was conducted.Specifically, a comparison was made between the steel temperature datasets obtained from KFX and the Random Forest model.The temperature contours for both datasets were prepared using the same range of contour colors and are presented in Figure 8.In terms of the temperature contour, both plots exhibit a similar shape, primarily located on the wall of the fuel gas supply room.However, it is worth noting that certain equipment details were omitted in the FE model to focus on the structural analysis of the ship.As a result, there are variations in the sizes of the independent variables between the two models.To validate the consistency of the steel temperatures, two points were selected for comparison, situated in almost identical positions along the wall of the fuel gas supply room.Table 3 provides detailed information about these selected points.
The comparison between the steel temperatures obtained from KFX and the FE load profiles demonstrates a high level of  Future studies will focus on conducting structural response analysis of the LNG bunkering ship, considering the effects of cryogenic temperature loads using FE simulations.
The proposed platform exhibits the potential of the Random Forest approach in integrating load profiles from different models, thereby contributing to the field of CSP assessment.By effectively combining CFD and FE data, the platform enables a comprehensive understanding of temperature load profiles for accurate risk assessment.This research provides valuable insights for the optimization of LNG bunkering operations, particularly in terms of safety considerations.The findings highlight the significance of considering cryogenic temperature loads and offer a practical and reliable tool for engineers and practitioners involved in the design and analysis of LNG bunkering structures.

Figure 1 :
Figure 1: The framework of temperature load transfer.

Figure 2 :
Figure 2: Gas cloud dispersion of LNG release simulation.

Figure 5 :
Figure 5: The framework of random forest.

Figure 7 :
Figure 7: Plots of true and estimated steel temperatures; training (a) and testing subsets (b).

Figure 8 :
Figure 8: The steel temperature plot of (a) KFX and (b) FE.

Table 2 :
Example of the input dataset Obtain:

Table 3 :
Comparison of steel temperature between KFX and FE load profiles , as the discrepancies in temperature values are negligible.This agreement further reinforces the credibility of the load profile when utilized in the FE software, confirming the accuracy and reliability of Random Forest model's predictions.This article presents a platform for integrating load profiles obtained from CFD and FE models to facilitate CSP assessment.The proposed approach involves utilizing a Random Forest regression model to construct the temperature load profile for the FE model.Key aspects of the study include conducting CFD-based gas dispersion analysis for an LNG bunkering ship model and retrieving steel temperature results from KFX, along with grid points and FE node positions.The obtained dataset serves as input for the Random Forest model, which demonstrates good agreement between the R-squared score and RMSE during the evaluation stage.The implementation stage involves utilizing ANSYS/LS-DYNA node points to generate a suitable load profile for FE input, resulting in minor discrepancies between steel temperatures from KFX and FE models.The Random Forest model is a valuable alternative to interpolation techniques, offering a wider range of variables and ensuring coverage of all destination nodes without relying solely on the steel temperature value at the nearest nodes. agreement