ABSTRACT

                         The study of hydrodynamic impact between a body in motion and a free water surface finds applications, in aeronautical fields, in splashdown and ditching problems. The effect of this impact is often prominent in the design phase of the project and, therefore, the importance of studying the event with more accuracy than in the past is imperative. Usually the study of the phenomenon is dealt with experiments, empirical laws, and lately, with finite element simulations. These simulations are performed by means of special codes that allow the fluid-structure coupling; these codes have their origin in Lagrangian finite element programs developed for crash analysis improved with possibility of interfacing with Eulerian spatial description, typical of fluids. Critical points in this type of modeling are the fluid-structure interaction algorithms, constitutive modeling of the fluid and time efficiency of the computation. This study describes an effort that focuses on the development of a crash modeling and simulation approach utilizing a non-linear explicit finite-element code (LSDYNA 960) to demonstrate the potential for Helicopter Water Impact analysis in the development of crash design criteria and concepts. Initially, the Water Model shall be developed and validated using default Lagrangian techniques. Subsequently, more accurate Arbitrary Lagrangian Eulerian analyses will be conducted to obtain finer results for the Ball Impact scenario and Helicopter Impact. Finally, the response of an occupant for the above helicopter crash test is analyzed using the MADYMO code, utilizing accelerations obtained from the LSDYNA output. Lumbar load, the most crucial mode of injury in these types of crashes will be investigated and discussed.

   INTRODUCTION

                    The in-flight behavior of aircraft can be predicted with an optimum degree of precision, the same cannot be said for the phenomenological behavior that takes place at impact. Analysis of the crash behavior of aircraft structures into water is a complex process due to the material and geometric non-linearity of the structural response. Large deflections and rotations in the deformed structure, regions of intense curvature (wrinkling), material strain rate effects, and interference and contact between structural components during a crash are some of the difficulties encountered in modeling the crash response of aircraft structures. The structural response and failure modes in crash impact conditions are not easy to predict using static analytical techniques. Initially, the under floor structure absorbs energy by crushing, but the amount of energy absorbed is dependent upon the surface impacted. Water can displace and provide a reasonably uniform loading on the base of the structure, but a rigid surface results in more direct loading of the frame members. Moreover, the water behavior to allow a reliable prediction of reactive forces against various geometries of the impact head when subjected to a dynamic loading simulation involves great deal of complexity. The functional relationships and behavioral characteristics of water are much more complicated than for other common engineering materials, thus making generalized behavior conditions extremely difficult to determine with reliable accuracy.  

The development of the water model is one of the most important issues to be taken care of in this water impact simulation. When an aircraft impacts the water, it hits with a thud wherein the acceleration ‘g’ values are found even greater than hard surface impacts. After the initial impact it slowly sinks down and then finally depending upon the buoyant force system, it either settles down or comes to the surface and floats. It is thus necessary to develop a water model that represents this behavior as accurately as possible.

Multi-Material Eulerian technique (ALE) [4] shall be utilized to gather data.  In the Multi-Material Eulerian formulation the material flows through a mesh that is completely fixed in space and each element is allowed to contain a mixture of different materials. The method completely avoids element distortions and it can, through a Eulerian-Lagrangian coupling algorithm, be combined with a Lagrangian description of motion for parts of the model. By translating, rotating and deforming the multi-material mesh in a controlled way, the mass flux between elements can be minimized and the mesh size can be kept smaller than in a Eulerian model.

            There are a couple of numerical problems associated with the Eulerian formulation too. There are dissipation and dispersion problems associated with the flux of mass between elements. In addition, many elements might be needed for the Eulerian mesh to enclose the whole space where the material will be located during the simulated event. The new Eulerian-Lagrangian coupling algorithm was implemented in the 950 version of LSDYNA. It is penalty-based and it is defined to preserve the total energy of the system. The old constraint based methods consume some kinetic energy, which is a problem in many impact applications. 

 WATER MODELING

              Water is modeled using MAT_ELASTIC_ *, which is an isotropic elastic material and is available for beam, shell, and solid elements in LSDYNA. A specialization of this material allows the modeling of fluids. The FLUID option is valid for solid elements only. The standard input deck requires: Material Identification, Mass Density, Young’s Modulus, Poisson’s Ratio, Bulk Modulus, Tensor viscosity coefficient and Cavitation Pressure. For the Fluid option the Bulk Modulus (K) has to be defined as Young’s Modulus and Poisson’s Ratio are ignored. With the fluid option fluid-like behavior is obtained where the Bulk Modulus, K, and pressure rate, p, are given by:

                                                               K   =    E  /  3 (1 – 2 n)

 p  = - K Ô_ii                                                                                            

and the Shear Modulus is set to zero. A tensor viscosity is used which acts only for the deviatoric stresses, S_ijⁿ⁺¹, given in terms of the damping coefficient as:

                                                                   S_ijⁿ⁺¹ = VC . DL . a . r . Ô_ij               

Where DL, is a characteristic element length, ‘a’ is the fluid bulk sound speed, r is the fluid density, and Ô_ij is the deviatoric strain rate. In this elastic material, co-rotational rate of the deviatoric Cauchy stress tensor is computed as:

Where G and K are the elastic shear and bulk moduli, respectively, and V is the relative volume, i.e., the ratio of the current volume to the initial volume. The axial and bending damping factors are used to damp down numerical noise. The update of the force resultants, F_i , and moment resultants, M_i , includes the damping factors:

                                                                                       F_i =  F_iⁿ + { 1 + D A }D F_i^{n+1/2    /}    

                                                                                       M_i =  M_iⁿ + { 1 + D B }D M_i^{n+1/2    /}                   

The input properties for this model are:

Density: Density of Water is 0.001 kgs/cm³ @  3.98 °C  

 Bulk Modulus: The Bulk modulus for a material refers to the ratio of pressure induced to the decrease in volume. This is the inverse of compressibility. For most practical purposes water may be considered as incompressible, but actually it is about 100 times as compressible as steel.   Bulk Modulus = K for Water = 292,000 P(force)si @ temperature 32 °F and pressure 15 p(force)si . Converting to standard units of Kg/cm/sec; K = 2.06e+07 Kg/cm.sec²

Viscosity Coefficient: As explained in section 2.5, it is a function of (characteristic element length DL, ‘a’ the Fluid bulk sound speed, r is the fluid density, and Ô_ij the deviatoric strain rate and deviatoric stresses).

S_ijⁿ⁺¹ = VC . DL . a . r . Ô_ij

VC . DL . a . r = Absolute Viscosity (Dynamic Viscosity)

Absolute Viscosity @ 32 °F = 1.792 cp = 0.01792e-03 kg/(cm.s)  [9,10]

‘a’ (Fluid bulk sound speed) =  ( K/r)^1/2 = (2.06e+07/0.001)^1/2 = 143527 cm/s

Hence, V.C = 1.248e-07 / DL  (DL depends upon the model in consideration)

Cavitation Pressure: Cavitation is defined as the process of formation of the vapor phase of a liquid when it is subjected to reduced pressures at constant ambient temperature. A liquid is said to cavitate when vapor bubbles are observed to form and grow as a consequence of pressure reduction. When the phase transition is a result of pressure change by hydrodynamic means, a two-phase flow composed of a liquid and its vapor is called a cavitating flow. From a purely physical-chemical point of view, of course, no distinction need be made between boiling and cavitation. Hence, Saturation pressure can be taken as the cavitation pressure. Saturation Pressure of Water @ 32 °F = 6.564 mill bars = 0.00669 Kg/cm²

VALIDATION OF WATER MODELS

 Two balls of different sizes and weights but same material were dropped into a glass flask filled with water. The impact scenario was captured using a High Speed Camera. The apparatus used in the trials is listed in the Table 1. All the physical characteristics, dimensions and weights have been specified.

Figure 1. shows the flask with water in it and the balls used in the experiment. Ball-I was initially impacted with the water. This was repeated three times to make sure that what we record as the physical test data is legitimate. There was no release mechanism used to drop the balls for the experiments. Balls were released by hand, but it was made sure that there were no additional velocities induced to the ball in any direction. Similarly, three drop tests were done with the second ball too. The whole show was recorded as a movie in a VHS professional videocassette. Also, the data was recorded onto the disc of the High Speed Camera. Figure 2. shows one of the still frames. Subsequently, the data was transferred to a compact disc, which was analyzed to study the kinematics of the ball when impacting water. This was done using customized software called High Speed Video Player (HSV95).

Three data sets were taken with each ball. Test data (distance time history during the time of impact) from test2 (ball 2) was considered for validation. The position of the ball was tracked using a position prediction method. HSV is not automated software where the kinematics of the moving bodies is given in a user-friendly format. Visual approximation is required to find out the coordinates of the ball at every frame.

Hence, this is really a crude method to find the distance v/s time figures. The background color and the lighting are the key parameters that affect that approximation. Moreover, since the camera was run at 500 frames/sec, only 3-4 valid data points could be obtained which can be compared with the impact data obtained from the Simulation (Impact is for 6 milliseconds). Attempt has been made to take the best approximation (experimental data) by repeating the exercise. 

  EULERIAN SIMULATIONS OF WATER IMPACT

               We have conducted initial approximate analyses (lagrangian) to verify the validity of the models, which now can be used for the eulerian analyses. The purpose to conduct those analyses was really to collect a fairly accurate data that matches with the published data. This section elaborately covers the eulerian simulations carried out to study the exact kinematics of a simple ball model (similar to those used in the previous lagrangian analyses) and a finally a full-scale helicopter model, while impacting water.

Simulation (ALE – Pure Eulerian Ball Impact on a constrained water model)

               The water and air were defined with ALE solid elements with multi-material characteristics. The number of cycles between advections was chosen as 1 (Van Leer Advection). Smoothing has been turned OFF. Part group (air and water both) is the slave and ball is the master entity. Ball is a lagrangian solid and the slave part set is an Eulerian fluid. To define contact a penalty coupling with a factor of 0.5 was used. Quadrature rule – slaves have been coupled to solids at nodes only. Coupling is in the normal direction only (compression only). To save on computational effort the lagrangian solid has been coupled with the material with highest density (water). Start time for coupling is 0 seconds and the end time is 1+e28 seconds.

The Ball was modeled as a lagrangian solid with shell elements. The dimensions of the ball are same that as used in lagrangian simulations, but the mesh is different. Each curve has 10 as mesh seed and the total number of 4-Node Belytschko-Tsay quad elements with shell thickness 0.1 centimeters is 600. 1 point was chosen for through the shell integration. The ball is a rigid body (Material type 20).  Table 2. shows the material properties used for the ball and other parameters used for the simulation.