Presentación

We present here part of the work done in the project ‘Advanced Numerical Simulation and Performance Evaluation of WAM-V’ developed by CIMNE under a Navy Grant issued by ONRG. The project aimed at developing computational solvers:

• to study the dynamics of the deformable hulls and superstructure
• to analyze the hydrodynamic performance of the hulls paying special attention on spray generation

This presentation focuses on the work done in the development of the model for the evaluation of the spray generation.

• SL-PFEM is computationally efficient since it usually admits very large time steps - about 15 times the CFL condition - without a noticeable loss of accuracy (Idelsohn et al. 2016).
• However, this nice property is partially lost in the case of wave motion propagating on the water surface. This is due to the fact that pathlines and streamlines quickly diverge in those cases.

• Nevertheless, any of the analyzed cases can be run in nearly 24 hours, using an Intel Core™i7 - 3820 CPU (four cores).

A computational model for the evaluation of the spray generation of a Wave Adaptive Modular Vessel

J. García-Espinosa, E. Oñate, B. Serván-Camas, P. Nadukandi and P.A Becker

Introduction (I)

Motivation

Computational model

Final comments and conclusions

Modeling spray generation

Dr. A. Souto

The Wave Adaptive Modular Vessel (WAM-V, nickname "Spider Boat“) is an innovative class of watercraft developed by Marine Advanced Research.

• There is little room for hydro-dynamic shape optimization using inflatable hulls –tubular shape-, and the generation spray in the current WAM-V design is massive in certain conditions.

We have recently proposed a solution to overcome this limitation, by using solutions to the following explicit second-order system of equations -instead of the X-IVAS operator-:

Unlike in the X-IVAS scheme the solution of the above equation admits correction to the trajectories caused due to the updates in the particle velocities within a time-step (Nadukandi et al. 2006).

Q1: The authors motivate their analysis by indicating that spray generation may be a significant contribution to total resistance for this type of vessel. Do they know of any study that backs their statement? It would seem to this discusser that with such a blunt hull, pressure form drag or even wave generation would be far dominant.

A1: There is no question that in full load condition, standard drag components should be dominant. However, WAM-V concept is a very light craft -with a minimum draft- and therefore pressure components of the drag are smaller compared to a conventional vessel. Furthermore, the generation of spray is those conditions is very important, which suggests that this is a relevant source of energy dissipation in this case.

In the SL-PFEM model, the fluid data at any given time is available as discrete samples at the spatial locations occupied by the particles.

Each particle has an identity which is either air (label: +1) or water (label: -1).

For a given time-step, the particle identities are projected to the element nodes; then each node has a value between -1 and +1. Then, a continuous piecewise linear approximation of the otherwise discrete identity data is obtained on the background mesh. A reference for the water-air interface is constructed as the piecewise planar surface where the aforesaid approximate identity takes a value 0.

The Particle Finite Element Method (PFEM, Idelsohn et al., 2004) is a versatile framework for the analysis of fluid-structure interaction problems.

It combines Lagrangian particle-based techniques with the integral formulation of the Finite Element Method (FEM).

The latest developed within the framework of the PFEM carried out at CIMNE is the X-IVAS (eXplicit Integration along the Velocity and Acceleration Streamlines) scheme (Idelsohn et al., 2012, Becker, 2015 and Nadukandi et at., 2016).

It is a semi-implicit scheme built over a Semi-Lagrangian (SL) formulation of the PFEM.

Due to its characteristics, the SL-PFEM has been selected in this work as the platform to develop the model for evaluation of the spray generation.

• similar in design to a catamaran -twin hull-
• inflatable hulls -helps to absorb the high frequency wave loads-
• the superstructure is not rigidly attached to the hulls -it uses shock absorbers and ball joints to articulate the vessel-

• Apart from its abilities to 'surf the waves', WAM-V is a very light craft -with a minimum draft- and therefore pressure components of the drag are smaller compared to a conventional vessel.
• When the rest of the components of drag are significantly reduced, any other source of energy dissipation –such as the spray generation- becomes increasingly important.
• In addition, excessive spray generation can increase the difficulties associated with operating the ship in certain cases.

It has to be emphasized that this projection process implies a relevant loss of resolution; in this work the flow is actually solved with twenty particles per element (on average) but the isosurface is constructed only with the weighted values on the nodes of the linear elements. In the zones where the developed flow is highly complex, this isosurface should only be understood as a reference for the free surface -there may not be an actual free surface-.

In due course, situations may arise where we will find water particles on the air-side of the interface. These particles compose the spray

generated in the simulations.

Should the pockets of water particles be large enough

then it creates a situation where there are one

or more water-elements surrounded by

air-elements. These islands of water-elements

are seen as water splash in the simulations

which represent violent separation

and/or merger of the interface.

Application example

X-IVAS scheme

Those features allows WAM-V:

• to conform to the surface of the water while mitigating the stresses transmitted to the structure.

Consider the Eulerian description of the incompressible Navier-Stokes equations

Dr. A. Souto

• to travel efficiently with low wave resistance in rough seas, by surfing on top of the waves rather than cut through them.

The effective acceleration field in the fluid domain is obtained from the momentum balance equation of the flow

• Accurate modeling of the complex physics of the different phenomena involved in the spray generation was out of the scope of this phase of the work. We just aimed to evaluate the applicability of the SL-PFEM to qualitatively analyze the spray generation phenomenon.
• The particles in the proposed model are just tracers that carry with them only the intrinsic properties of the flow. In particular, they have no associated mass. Therefore, the model cannot evaluate the generated mass flow rate of spray, but just give qualitative indications on the development of the phenomenon.
• However, the developed model can give qualitative indications on the development and intensity of the generated spray. This information could be used to design and evaluate strategies to reduce the spray generation of the vessel.

Our future research plan considers to improve the physics of the model by incorporating the transport equations for the droplet size distribution in the semi-Lagrangian framework. This approach will imply consider new particles tracers that will transport properties characterizing the droplet size distribution. The solution of this enriched problem will allow computing quantities like the mass flow rate, or the number of droplets of certain size per unit volume.

As application example of the method, a 14 feet WAM-V has been analyzed in different conditions.

A computational domain of 9x3x2m has been generated around the hull. It is discretized by a mesh of more than 3,0 million three-node tetrahedral elements. On an average twenty particles per element were used in the simulations -approx. 60 million particles-.

The hull is considered rigid

and its motions are taken into

account by using an ALE

formulation.

A water wave motion has

been generated by imposing

the solution of a first-order Stokes wave in a narrow strip

of water at the inlet and on the walls of the outlet.

Q2: The algorithm for spray generation is not clear. How does a particle cross the free surface (a material surface) and adds up to the gas ones? Can they elaborate a bit on this?

A2: The blue isosurface drawn in the pictures corresponds to the piecewise planar surface where the projected identity of the particles on the nodes takes a value 0. It has to be emphasized that this projection process implies a relevant loss of resolution; the flow is actually solved with twenty particles per element (on average) but the isosurface is constructed only with the weighted values on the nodes of the linear elements. Therefore, in the zones where the developed flow is highly complex, this isosurface should only be understood as a reference for the free surface, since there is no real free surface; below the isosurface, we will find water with a relatively small proportion of air bubbles, and above it, we will find an increasing presence of air.

WAM-Vs are designed for either manned or unmanned operations and can be built in different lengths to match specific services.

Source: http://www.wam-v.com/

The fundamental principle of kinematics relates the Eulerian description of the flow with the Lagrangian description as follows

Introduction (II)

Acknowledgements

where X(λ,t), U(λ,t) are the fluid particle trajectory and velocity.

The authors would like to acknowledge the support given to this project by the Office of Naval Research Global with the Grant N62909-12-1-7101.

Dr. A. Souto

The basic idea of the X-IVAS scheme is to update the fluid particle position and velocity within a time-step using

A fluid-structure interaction solver to study the dynamics of the deformable hulls and superstructure has been implemented.

It combines a time-domain FEM seakeeping solver with a FEM structural solver -beams and membranes-.

The fluid-structure

coupling scheme used

is an iterative strong

algorithm based on the

Block Gauss-Seidel

method.

YZ plane views of the spray generated by the 14 ft WAM-V hull at -from above to below- 15, 20 and 25 knots.

Snapshots at time = 3.5 s, with a wave amplitude of 0.05 m and wave length of 1.5 m.

where

• uʰ and aʰ denote spatially continuous piecewise linear approximations of u and a on a background mesh
• The matrices A, C and the vectors b, d are spatially piecewise constant and depend on the time tⁿ

Q3: Finally, it should be feasible to estimate some mass flow rate of spray that is generated, thus leading to some quantitative difference between the different speeds in Figs 7-9. Even though they are different velocities, the amount of generated spray and its penetration in the gas phase seems similar in the three pictures.

A3: It should be noted that the particles in the proposed model are just tracers that carry with them only the intrinsic properties of the flow. In particular, they have no associated mass. Therefore, the model cannot evaluate the generated mass flow rate of spray, but just give qualitative indications on the development of the phenomenon.

Our current research plan to improve the physics of the model proposes to enrich the model by incorporating the transport equations for the droplet size distribution in the semi-Lagrangian framework. This approach will imply that the particles will transport properties characterizing the droplet size distribution. The solution of this enriched problem will allow computing quantities like the mass flow rate.

SL-PFEM model

Step 1: Lagrangian advection of the particles

Prof. S. Idelsohn

15 kn

Step 2: Project the estimate of the velocity (and other information associated with the particles) onto a background FE mesh*

* In this work, the projection used to calculate the implicit approximation, fʰ, of the variables, is based on weighting the samples of the function, f (at the particles), with the values of the FEM shape-function.

Other alternatives, like the Shepard method -based on inverse distance weighting- or least squares interpolation have been tested in this work. But no noticeable effect in the results has been identified.

J. García Espinosa

julio@cimne.upc.edu

Q: [...] It would be desirable, since this article is part of a research project, that certain experimental results give some agreements to the numerical results. For example, the maximum height of the drops or the density of the air-drops for different vessel speeds. Without some of these comparisons, the numerical results have no meaning.

A: [...] Regarding the need to validate the presented model, the authors completely agree on it. The SL-PFEM model has been extensively validated for multi-fluid flow applications (see references). But unfortunately, no experimental data regarding the spray generation of the WAM-V is available. At this point, we were only able to perform some qualitative comparisons based on videos and pictures of different tests carried out on the 33’ WAM-V.

On the other hand, as stated in the paper, the current model only allows a limited analysis of the spray phenomenon, since relevant aspects of the physics are not considered. Our future research lines propose to improve the model physics and then to focus in the quantitative analysis including the necessary validation against experimental data.

Step 3: Solve the remaining Stokes problem on the background mesh -using the FEM-

Using the backward Euler time integration, and the iterative monolithic approach inspired in the fractional step method (García-Espinosa and Oñate, 2003, García-Espinosa et al. 2008), the semi-discrete Stokes system to be solved is

25 kn

Step 4: Update (correct) the particle velocities