Numerical analysis of influencing factors on wave load for an amphibious aircraft

Numerical method of wave load for an amphibious aircraft is carried out in this paper, and its effectiveness is verified by comparing with towing tank model test. It shows that at the same wavelength and speed, the aircraft’s wave load is positively correlated with the change of wave height, but with the increase of wavelength, the difference shows a gradually decrease. And wave load is positively correlated with the speed, the greater the speed, the greater the wave load is. The wave load decreases with the increase of the wavelength. The peak load generally occurs in the short wave state of 1.2 times the length of the fuselage. With the increase of the wavelength, the aircraft load gradually decreases.


Introduction
In recent years, with the rapid development of mass storage of computer, numerical simulation plays an increasingly important role in study of the wave motion response characteristics of amphibious aircraft.Ma Zenghui used ALE (Arbitrary Lagrange-Euler) method to describe the computational fluid domain, used penalty function coupling method to describe the coupling between aircraft and water body, and studied the motion response of aircraft taking off and landing on different wave surfaces and the dynamic characteristics of fuselage bottom pressure [1].Chen and others systematically studied the landing performance of amphibious aircraft in waves using RANS equation combined with FVM and VOF methods [2].Li Xinying carried out numerical simulation research on seakeeping of the hull of an amphibious aircraft based on the sliding grid method, and compared with the model test results to verify the reliability of the method [3].
Based on the STAR-CCM software, this paper uses the Reynolds mean N-S equation and the SST k-w twoequation model to solve the unsteady flow field on the wave surface, the fluid volume fraction method (VOF) is used to capture the free surface, and comparison with the model test results is made to verify the reliability of the numerical simulation method.Based on this, this paper studies the influence of the parameters of taxiing speed, wavelength and wave height on the water skiing load, which has some reference value for the evaluation of the wave load of amphibious aircraft.

Numerical calculation method
2.1 Governing equations Continuity equation and momentum equation are universal equations for numerical solution of viscous fluid motion, and their basic form is: Where , 1 2 3 are pulsation values of velocity component, P is the mean value of pressure; Si is the generalized source type of momentum equation.Turbulence model should be introduced to enclose above equations.In this paper, the widely used SST k   two-equation model is adopted.

Boundary conditions and mesh generation
Because amphibious aircraft are symmetrical in structure, and the flow field around the aircraft is also symmetrical about the longitudinal section during navigation.In order to save calculation cost, this paper uses semi-model to carry out the numerical simulation.The computational domain is created by a cuboid with a size of 4λ×2L×2L in length, width and height, respectively, whereλ is wavelength, L H is the hull form length of the seaplane.
In order to capture the motion attitude of the aircraft as well as to reduce the computational cost, a trapezoidal grid layout is introduced to conduct different degrees of mesh transition and encryption for the entire computational domain.The area in front of the fuselage head consists of wave generating zone of 0.8λ and encounter zone of 0.2λ, area behind the rear part of the seaplane is composed of wake zone of 0.7λ, transition zone of 0.3λ, and absorbing zone of 1λ.Grid distribution of symmetry plane and the seaplane are shown in Figure 1 and figure 2, respectively.The k   shear stress transport (SST) turbulence model is adopted to solve the stress tensor based on the research of turbulence model effect in numerical wave simulation.The second-order upwind scheme is used to solve convection term, free surface of the wave is captured by the volume of fluid domain (VOF method, and the SIMPLE algorithm is applied to address the pressure-velocity coupling.

Validation of numerical method
In order to validate the accuracy of numerical method, simulation of typical wave state is made by using the STAR CCM+ commercial software package, and comparisons with towing tank model test are made.Figure 3 and Figure 4 shows comparison of gravity load in time and wave pattern, respectively.It can be seen that the time-history curve of gravity load obtained by numerical simulation is basically consistent with the model test result.
It can be seen in Figure 4 that the CFD method can well capture the cavitation near the fuselage step and the splash at the rear bilge line, but it is difficult to capture the large deformation of the free surface such as flap splash.This is because the numerical calculation is implemented based on grid technology.In the grid of the computational domain, each point has a fixed number of predefined adjacent points 4. The connection relationship with the adjacent points is used to solve the grid control equation and transfer the solution information to the entire computational domain.When the grid deformation becomes large to a certain extent, the connection relationship between the grids is difficult to maintain if no error is introduced, although the grid can be subdivided in the simulation.However, it will eventually lead to an increase in the accumulation of errors, which will make it impossible to capture such large-scale deformation.
In terms of numerical simulation accuracy, the numerical load simulation value is 1.78g, with a deviation -10.1% compared with the model test value of 1.98g, which is within the acceptable range of the engineering application of the numerical simulation of seaplane, indicating that the CFD method is feasible for the study of wave load for the seaplane.

Analysis of influencing factors of wave load
Calculations of conditions listed in Table 1 are performed to study the effect of wavelength, wave height and sailing velocity on gravity load of the seaplane.Figure 5 shows the variation curve of wave load at the center of gravity with speed at fixed wave height and different wavelengths.It can be seen that the load is gradually increasing with the increase of speed, but the impact of speed variation on load is significantly stronger in the transition stage than the navigation and taxiing stage, because during the transition stage, the taxiing area of the rear body is gradually reduced with the increase of speed, and this leads the seaplane into a single step taxiing stage [5].And change of speed has a significant impact on the aircraft attitude, there, the impact load generated by the collision force between the fuselage and wave surface changes obviously with speed.Figure 6 shows the wavelength effect on wave load performance.It can be seen that as the wavelength increases from 1.2L to 4.3L, the wave load generally shows an opposite feature against the wavelength.Maximum load of the aircraft at fixed speed and wave height occurs at the short wave length of 1.2 times the length of fuselage.This is because the aircraft has a phenomenon of wave hopping, that is, after the aircraft jumps off the water surface in a short wave state, it will not collide with the water surface until it has flown over 1-2 wave peaks, and the fuselage will suffer a large impact force, which caused a relatively large impact load.Figure 7 shows variation of load with wave height, it is obviously that the load is positively influenced by wave height.However, the impact of wave height variation on load in short wave state is significantly greater than that in the long wave state, so the aircraft should avoid taking off and landing in the short wave state.

Conclusions
In this study, numerical simulation method is used to carry out the numerical calculation of wave load for an amphibious aircraft, and the feasibility of the method is verified by comparing with the towing tank model test results.Based on the method, the effects of wavelength, wave height and velocity on wave load are studied, and the conclusions are as follows: (1) The load value and wave pattern obtained by numerical simulation are in good agreement with the experimental results.The calculation error is controlled at about 10%, which is within the allowable range of engineering application.
(2) Wave load of the aircraft increases with wave height and velocity.Higher sea conditions and high navigation speed will cause the aircraft to bear greater overload.
(3) Wave load is negatively correlated with wavelength.The maximum load occurs at the short wave of 1.2 times the length of the fuselage hull state.When the wavelength reaches to 4 times the length of the fuselage hull, the load gradient caused by the wave height and velocity gradually decreases.

Figure 1 .
Figure 1.Mesh generation of computational domain.

Figure 3 .Figure 4 .
Figure 3.Comparison of time-history curve of wave load between simulation and experimental result

Figure 6 .
Figure 6.Influence of wave length on wave load (wave height:0.04L)