The Dynamic Response Analysis Method of Steel Containment in Floating Nuclear Power Plant

Abstract

During the operation of the floating nuclear power plant, if the floating nuclear power plant is anchored near the shore for power generation, it may be impacted by runaway ships. If the impact causes damage to the tank of the floating nuclear power plant and water inflow, and even damage to the containment structure, it will seriously threaten the structural safety of the floating nuclear power plant and even threaten nuclear safety. This paper uses the explicit dynamics method to establish two models of dry/wet impact. It assumes that the 5000T container ship will laterally impact the reactor compartment of the floating nuclear power plant at a speed of 2 m/s, and the effects of the fluid domain (water and air domain) are ignored/counted in the calculation process. Then, comparing the effects of the above two models of dry/wet impact on the calculation duration, the damage and water ingress state of the floating nuclear power plant, the stress of the steel containment (including support). Studies have shown that if the relevant personnel do not need to understand the effect of water intrusion into the damaged cabin, the influence of water and air domain on the impact simulation results can be ignored, and the dry model can be directly used for calculation.

1 Introduction

Ship impact refers to the accident that ships contact and cause damage at sea or in navigable waters connected with the sea. It often leads to disastrous consequences, such as casualties, sinking of ships, and even environmental pollution. There are many reasons for ship impact accidents, and researchers in many countries are trying to find ways to avoid ship impact accidents [1]. At present, due to the influence of human factors, ship impact accidents cannot be completely eliminated. For floating nuclear power plants, it is more important to study the dynamic response of impact. Once a ship collides with a floating nuclear power plant, it will not only cause serious economic losses, but also cause more terrible harm to the environment that is difficult to evaluate [2, 3].

There are three main methods for impact analysis of ship structures: experimental method, simplified analytical method and numerical simulation method. The test method includes actual accident investigation and real ship or ship model impact test. The results obtained by it are very intuitive and have self-evident guiding significance for the theoretical method [4, 5]. However, it often costs a lot of money. The accuracy of the simplified analytical method is relatively low. It simplifies a lot of ships in impact. Using the analytical method and some empirical data, it establishes the semi analytical/semi empirical mechanical equations of the hull or local ship structures to evaluate the impact characteristics of the hull. The advantage of numerical simulation method is that it can reproduce the real ship impact scene virtually. With the help of some finite element analysis software, various physical quantities in the process of ship impact can be output as results [6].

With the continuous upgrading and development of computer software and hardware technology and the increasing progress and maturity of finite element technology, explicit finite element numerical simulation technology has gradually received attention in the research of ship impact, and the research of ship structure impact based on full coupling technology has become gradually feasible. This paper mainly uses ANSYS-APDL software to establish the impact model, and uses the nonlinear explicit dynamics analysis software ANSYS workbench LS-DYNA to solve the analysis. Based on the comparison of dry/wet calculation results, the applicability of the two impact models is studied.

2 Modeling and Theoretical Basis

2.1 ANSYS APDL Model Parameter Settings

Container ships and floating nuclear power plants are modeled by 4-node shell181 shell element and beam188 beam element in classic ANSYS (after importing work bench LS-DYNA, it is automatically converted to LS-DYNA applicable element types: shell163 and beam161). The plate thickness is divided into 15, 18, 20, 22, 24, 26, 28, 30, etc. The grids at the bulbous bow of the container ship and the impact part on the port side of the floating nuclear power plant are densified (Figs. 1 and 2).

Fig. 1.

Finite element model of container ship.

Fig. 2.

Finite element model of floating nuclear power plant.

After the model is processed in classical ANSYS, three CBD files of stern containment, floating nuclear power plant (excluding stern containment) and container ship are written respectively, and then imported into workbench LS-DYNA module for pre impact model processing.

2.2 Contact Algorithms and Contact Types

The contact impact algorithm in LS-DYNA usually has the following methods:

• (1) Dynamic constraint method

As the contact algorithm first used in dyna program, the basic principle of dynamic constraint method is: before calculating and running each time step ∆T, retrieve those slave nodes that currently have no penetration with the master surface, and retrieve whether these slave nodes have penetration with the master surface at this time step. If there is penetration, reduce the time step ∆T. under the reduced time step, the slave node just contacts the main surface but does not penetrate the main surface. However, when the mesh division of the master surface is fine, some nodes on the master surface can penetrate the slave surface without constraints, which has a great impact on the accuracy of the calculation results. This algorithm will not be applicable. To sum up, this algorithm has certain limitations and is relatively complex, so it is only used for fixed connection and fixed connection disconnection contact at present.

• (2) Distributive parameter method

The basic principle is: distribute half of the mass of each slave unit being contacted to the main surface being contacted, and distribute positive pressure at the same time. Then, the principal surface acceleration is corrected. Finally, the acceleration and velocity constraints are imposed on the slave node to ensure that the slave node does not slide and avoid rebound.

• (3) Penalty function method

This method is widely used in numerical calculation. The basic principle is: in each time step, check whether the slave node passes through the main surface. If not, do not deal with it. On the contrary, a larger surface is introduced between the slave node and the penetrated surface. The size of this contact surface is related to the penetration depth and the stiffness of the main surface, also known as the penalty function value. Its physical meaning is that a spring is placed between the two to limit the penetration, as shown in the following figure. The so-called symmetric penalty function method means that the program processes all master nodes according to the above steps, using the same algorithm as the slave nodes (Fig. 3).

Fig. 3.

Penalty function method.

The magnitude of contact force is expressed by this formula: In the above formula: k is contact interface stiffness, is penetration.

Because the symmetrical penalty function method is adopted, the calculation of this method is simple, the hourglass phenomenon in the impact process is not obvious, and there is no noise impact. The energy conservation in the system is accurate, symmetrical and the momentum conservation is accurate, and the impact conditions and release conditions are not required. If obvious penetration occurs in the calculation process, it can be adjusted by enlarging the penalty function value or reducing the time step.

Among the three algorithms, the dynamic constraint method is mainly applicable to the fixed interface, the distributed parameter method is mainly used for the sliding interface, and the symmetric penalty function method is the most commonly used method. The following problems in contact analysis should be paid attention to: first, in terms of data, try to make the material data accurate, because the accuracy of most nonlinear dynamic problems is related to the mass density of the input data; Second, in terms of units, the definition of material properties is to coordinate units, which will cause abnormal response and even calculation problems; Third, in terms of contact, the calculation efficiency varies greatly with different contact types. It is best to use automatic contact types and be particularly cautious about complex problems; Fourth, multiple contacts should be defined in the definition process.

Contact problem is state nonlinear, and is a highly nonlinear behavior, which requires more computer resources. There are two major difficulties in simulating contact problems with finite elements: the user usually does not know the contact area until the problem is solved. Moreover, it is difficult to estimate the time when their contact surfaces are separated. Changes in the two contact surface materials, loads, boundaries, and other conditions will also change the analysis of the contact problem. In LS-DYNA, contact is not simulated by elements that are in contact with each other, but by contact surfaces that may be in contact. By setting the contact type and parameters, the contact-impact interface algorithm is used to solve the problem. Common contact types are single-surface contact, node-to-surface contact, and surface-to-surface contact.

2.3 Workbench LS-DYNA Model Preprocessing

Since the displacement of the container ship is 5000t and the ship type has been determined, the draft of the container ship is set to 8 m in this simulation. In addition, in order to reduce the simulation time, the distance between the container ship and the floating nuclear power plant is adjusted to about 0.1 m, and the impact position is the port side in the middle of the stern bunker. The three-dimensional and finite element models are shown in the following (Figs. 4, 5 and 6):

Fig. 4.

Three dimensional model of impact between two ships.

Fig. 5.

Finite element model of two ship impact.

Fig. 6.

Local finite element mesh refinement model of two ship impact.

Define the material properties. The material of the floating nuclear power plant (except the stern containment) is defined as nonlinear structural steel, Poisson’s ratio is set to 0.3, elastic modulus is set to 2.06 × 10¹¹Pa, tangent modulus is set to 1.45 × 10⁹Pa, and yield strength is set to 3.55 × 10⁸Pa. In order to make the floating nuclear power plant have the possibility of damage, it is necessary to add a plastic strain failure criterion, and its maximum equivalent plastic failure criterion is set to 0.0035, according to the young’s modulus.

Connection relationship settings. The single surface only type suitable for the beam shell hybrid model in the body interaction is adopted, and the constraint for forming contact algorithm with high accuracy is adopted for the flexible constraint algorithm. In addition, the contact and connection between the stern containment and the floating nuclear power plant are realized by using body to body fixed, and the coupling point is set as flexible coupling (Fig. 7).

Fig. 7.

Connection between containment and floating nuclear power plant.

Loads, boundary conditions and analysis settings of workbench LS-DYNA. Fix the bow and stern surfaces of the floating nuclear power plant rigidly, as shown in Figs. 8 and 9. Set the end time to 3.5 s, and the calculation accuracy is double precision. Set the speed of the container ship to 2 m/s and the direction to −y, and conduct body tracking for the container ship, the floating nuclear power plant and its containment, so as to check the contact force later. In addition, it can provide data for subsequent fatigue analysis and ultimate bearing capacity analysis.

Fig. 8.

Rigid fixed surface 1.

Fig. 9.

Rigid fixed surface 2.

3 Comparison of Simulation Results

3.1 Equivalent Stress During Impact

For dry impact, the time history curve of the maximum equivalent stress of the whole ship is shown in Fig. 10. The maximum equivalent stress is 360 MPa, which occurs in 0.471 s, as shown in Fig. 11. The degree of damage is shown in Fig. 12. The simulation results show that the damage range of the hull outer plate is small, and the deformation of the bulkheads is small and undamaged.

Fig. 10.

The time history curve of the maximum equivalent stress of the whole ship

Fig. 11.

Equivalent stress cloud diagram of the whole ship at 0.471 s

Fig. 12.

Damage diagram of the whole ship at 0.471 s

For dry impact, the maximum equivalent stress of the containment is 331.7 MPa, which occurs at 0.319 s as shown in Fig. 13.

Fig. 13.

Equivalent stress cloud diagram of containment at 0.319 s

For wet impact, the maximum equivalent stress of the whole ship is about 360 MPa, which occurs at 0.48 s, as shown in Fig. 14. The degree of damage is shown in Fig. 15. Figure 16 shows the details of the water ingress of the damaged tank. The maximum equivalent stress of the containment is 304.3MPa, which occurs at 0.320 s, as shown in Fig. 17.

Fig. 14.

Equivalent stress cloud diagram of the whole ship at 0.48 s

Fig. 15.

Damage diagram of the whole ship at 0.48 s

Fig. 16.

The water ingress of the damaged tank.

Fig. 17.

Equivalent stress cloud diagram of containment at 0.320 s

3.2 Force Analysis of Supports During Impact

For dry impact, the time history curve of the horizontal force on the containment support is shown in Fig. 18–20. The maximum translational force of the containment support in the X direction is $1.04 \times 10^{6} N$, which occurs in 0.655 s; The maximum translational force in the Y direction is $4.09 \times 10^{6} N$, which occurs in 0.384 s; The maximum translational force in the Z direction is $2.25 \times 10^{6} N$, which occurs in 0.453 s.

Fig. 18.

The time history curve of the horizontal force on the bearing in the X direction

Fig. 19.

The time history curve of the horizontal force on the bearing in the X direction

Fig. 20.

The time history curve of the horizontal force on the bearing in the Z direction

For wet impact, the maximum translational force of the containment support in the X direction is $1.03 \times 10^{6} N$, which occurs in 0.659 s; The maximum translational force in the Y direction is $4.09 \times 10^{6} N$, which occurs in 0.388 s; The maximum translational force in the Z direction is $2.25 \times 10^{6} N$, which occurs in 0.456 s.

For dry impact, the time history curve of the rotating force on the containment support is shown in Fig. 21–23. The maximum rotation force of the containment support around the X direction is $2.10 \times 10^{7} N \cdot m$, which occurs in 2.753 s; The maximum rotation force around the Y direction is $7.78 \times 10^{6} N \cdot m$, which occurs in 0.396 s; The maximum rotation force around the Z direction is $1.11 \times 10^{7} N \cdot m$, which occurs in 0.384 s.

Fig. 21.

The time history curve of the rotating force on the bearing in the X direction

Fig. 22.

The time history curve of the rotating force on the bearing in the Y direction

Fig. 23.

The time history curve of the rotating force on the bearing in the Y direction

For wet impact, the maximum rotation force of the containment support around the X direction is $2.09 \times 10^{7} N \cdot m$, which occurs in 2.807 s; The maximum rotation force around the Y direction is $7.78 \times 10^{6} N \cdot m$, which occurs in 0.409 s; The maximum rotation force around the Z direction is $1.11 \times 10^{7} N \cdot m$, which occurs in 0.384 s.

4 Conclusion

The simulation time of wet impact is 2.5 times that of dry impact, and the equivalent stress of the whole ship, the equivalent stress of the containment, the damage degree of the hull and the force of the support are not much different. So, if the relevant personnel do not need to understand the effect of water intrusion into the damaged cabin, the influence of air and water on the impact simulation results can be ignored, and the dry mode can be directly used for calculation.