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Water impact and hydrodynamic loads

A. Iafrati

Large hydrodynamic loads and highly localized pressure distributions are experienced when the ship is moving in heavy sea state. Accurate estimates are needed for structural safety, either on the large scale due to large bending moments and on the small scale because of the high pressure peaks. Beside the structural integrity, the loads associated to the vertical motion are also important for personnel safety and comfort on board. For lifeboats, the high accelerations undergone during the water impact can be very high, well beyond the acceptable limits for the human body.

The description of the water entry problem is rather complicated due to the singularity of the flow at the intersection between the free surface and the body contour. As usual in free boundary problems, the nonlinearity arises from the fact that the free surface position is unknown and has to be determined as a part of the solution. Moreover, if the body has some degree of freedom or in those cases in which the structural deformations are relevant, the fully coupled problem has to be considered. The complexity of the problem is such that numerical approaches are not always able to provide accurate predictions of loads and pressures, and sometime combined theoretical and numerical tools need to be adopted. Although the intense research activity done in the field in the last ten years, there are still many unresolved issues that need a further investigation.

Numerical modelling of water entry flows and related loads
Numerical solvers have been developed, which can provide accurate estimates of the flow and of the resulting pressure distribution. The numerical solver is developed for two-dimensional and axisymmetric problems and provide the time-dependent solution either in the constant entry velocity case o in free-fall motion. The model is based on the potential flow approximation, with fully nonlinear boundary conditions (i.e. enforced at the actual free surface position, accounting for quadratic terms). A careful validation versus other theoretical or experimental solution has been carried out. Further issues are currently under consideration which involve the flow separation from smoothly curved solid contours, full three dimensional problems and hydroelastic coupling.

Water entry of a cone with 10 degrees deadrise angle: free surface profilesWater entry of a cone with 10 degrees deadrise angle: free surface profiles

Water entry of a cone with 10 degrees deadrise angle: pressure distributionWater entry of a cone with 10 degrees deadrise angle: pressure distribution









Asymptotic estimates of the impacting loads
The loads generated during the water entry process are impulsive and characterized by large spatial gradients. Although for many problems time domain numerical solvers provide accurate predictions, there are some specific conditions which cannot be easily handled by the time domain tools. In these cases theoretical analyzes, based on the matched asymptotic methods, can be used in combination with numerical approaches to overcome the limitations. This is for instance the case of the impact of bodies originally floating on the free surface in which the flow in the initial condition is singular and the highest loads are generated in the early stage of the entry process. In this case the problem was formulated in terms of a small time expansion procedure together with a matched asymptotic expansion. The outer solution was derived analytically whereas the inner solution was derived by a fully nonlinear numerical method. The method provided asymptotic estimates of the solution, which well describe both pressure distribution and impacting loads in a initial stage. For some problems, the loads are expressed in terms of a series expansion, coefficients of which are given analytically. For other cases the coefficients are given in quadratures. Such kind of analyzes have been applied to two-dimensional or to some axisymmetric problems only, whereas full three-dimensional problems have to be studied yet, although strip theory can be used for shapes with large aspect ratios.

Water landing of re-entry space vehicles
With the purpose of evaluating the dynamics of the water entry process at landing, experimental activities have been done for two different unmanned space vehicles. The first set of experiments were done for the CIRA USV vehicle. This vehicle arrives vertically at the free surface and penetrate deeply into the water. In the next stage the vehicles is pushed up by buoyancy forces and exit completely out of the water surface. During the exit phase, the vehicle turn toward back and impacts the water surface with the wings. Accelerations were measured at the nose and at the COG, wherease the velocities of some points of the geometry were extracted by image analysis of the movies.

A much wider and complete experimental campaign was performed for the IXV (Intermediate eXperimental Vehicles) of the ESA ( For this case the entry conditions were agreed with Thales Alenia Space Italia ( with the aim of analyzing the accelerations induced at the different attitudes. The effect of the wind was also considered. To this purpose the model was mounted onto the carriage and launched at a horizontal speed of 5 m/s. In this case measurements involved the pressures at several points on the skin and the triaxial accelerations at the nose, at the back and at the COG. The flaps were instrumented in order to extract the total forces acting during the entry phase. The six DOF motion was recorded by a IMU platform. In order to avoid the spurious effects induced by the umbilical cable, an on board acquisition system developed at CNR-INSEAN was employed.

IXV - Experimental tests of water landing in wind conditionsIXV - Experimental tests of water landing in wind conditions