## 1 Introduction
### Background of Pipe Whip Tests  
The French CEA along with the FRAMATOME agency has carried out several dynamic tests on nuclear piping financed by the Electric Power Research Institute (EPRI). The experimental tests on pipe impacts were performed in the Cadarache Laboratory in France. The main objective of these tests was to determine the effect of impact on the surrounding structures and piping systems in the NPPs and to assess the safety of the related components and structures for the development of the power plants for future applications. The restraining system of the piping in the NPPs are known to be developed using a conservative approach and, hence, various structural parameters, like material non-linearity and large displacements, are often neglected in the restraint design methodology. An intricate restraint design would be expensive as well as redundant in certain cases. Therefore, studying the whipping behavior and the large displacements of NPP pipes during failure conditions would be beneficial in developing the restraint technology and assessing the surrounding structural damage [2]. The experimental tests proved to be expensive and complex owing to the intricacy of the operating conditions and the testing procedure. Due to this, several numerical methods and finite element models were developed over time to replicate the experimental tests. However, computational models are also sometimes computationally expensive and difficult to model with such operating conditions and demand coherence with the experimental models [3]. Several finite element codes have simulated the pipe whipping behavior by incorporating beam and shell elements with linear spring behavior using ABAQUS-EPGEN (Version 4.5), EUROPLEXUS-2005, and TEDEL (CEASEMT-V1) codes [2; 4; 5]. These codes use an explicit numerical algorithm to solve large deformations, fast dynamics, and strain rate-related problems. The pipe whipping behavior as simulated in the previous research using computational tools does not justify the effect of material non-linearity and the pipe response to fluidic forces in three-dimensional models incorporating the fluid-structure interaction method without compromising the computational time. Computational time and feasibility have become major concerns with the advancement of numerical models for fast dynamics problems. These explicit models can alternatively be conservative and redundant depending on the complexity of the analysis and loading conditions. Hence, simpler and more efficient finite element models are preferred over complicated models. Several attempts have been made to simplify the finite element models to achieve feasibility and solve complex explicit problems without compromising the accuracy. These developed numerical models are validated with the experimental results from time to time to evaluate their degree of acceptability [3; 5; 6; 7]. This research applies the functions of both finite volume method (FVM) and finite element method (FEM) to solve large displacement problems of pipe whipping phenomenon with a simplified modeling approach by using a coupled one-dimensional and three-dimensional (1D/3D) numerical model. The fluid-structure interaction (FSI) methodology of the Ansys Workbench software is applied in this research to predict the response of the pipe under transient loading conditions. The FSI methodology can be classified as one-way or two-way depending upon the coupling approaches integrated in the simulation. The one-way FSI approach uses the fluidic loads from the FVM simulation as the input load for the structural simulation whereas the two-way FSI approach includes the flow changes due to the structural deformations caused by the fluid forces from the FVM simulations, and the cycle continues. The two-way FSI approach is deemed to be computationally expensive, while the one-way FSI is conservative, as per the previously conducted research [8; 9].