blastFoam + soilds4foam | Coupled FSI Computations for Close-In UNDEX
Accurate prediction of underwater explosion (UNDEX) damage against surface and subsurface vessels and structures is an important aspect of naval weapon system engineering, maritime lethality assessment, and protective design. The physical properties of water make this a challenging problem, as deformation of the target modifies the pressure in the surrounding fluid, changing the explosive loading. Consequently, it is necessary to couple the fluid/explosive modeling with the structure simulation. Thus, the underwater damage prediction problem is complex, extremely non-linear and target deformation can alter the effective load imposed by a weapon.
The following short article describes such a coupled analysis leveraging the opensource blastFoam and solids4foam solvers, and compares with simulation outputs and experimental data generated by the U.S. Navy.
Read the full article with images here: https://bit.ly/3loXBhY
Overview
The damage imparted to deformable underwater targets is difficult to predict due to the requirement to adequately model the physical properties of water, and in particular cavitation. Targets that deform create an additional volume that must be filled by the surrounding water, reducing the local pressure, and unloading the structure. However, close-in explosions add the complication of the shock-bubble interaction to fluid-structure interaction. In the close-in case, the primary shock reflects off the target and interacts with the explosion bubble, creating an expansion that travels towards the target, reducing the pressure between the bubble and target. This expansion reflects off the target, driving surface pressures even lower.
A consequence of the formation of low-pressure regions in the flow field is the creation of cavitation zones that, when surrounded by high-pressure fluid, collapse to generate a secondary shock that can reload the target. The bubble-shock interaction mechanism is operative even with a rigid target. However, target flexibility augments the pressure reduction by inducing wall motion and ultimately expanding the cavitation zone. To capture this behavior for close-in explosions requires a coupled fluid and structure analysis.
Objective
The objective of this effort was to leverage the blastFoam and solids4foam solvers to simulate the influence of shock-bubble interaction and the subsequent cavitation collapse on fluid-structure interaction for explosive tests using water-filled aluminum cylinders. Subsequent comparison of the calculations with experimental measurements provided an opportunity to validate the numerical approach.
The opensource blastFoam code has been developed by Synthetik Applied Technologies and is currently maintained and enhanced with funding from the U.S. Department of Defense (Heylmun et al., 2019). The solids4foam solver is an opensource toolbox for solid mechanics and fluid-solid interaction simulations (Cardiff et al., 2018). Results presented in this article describe the predicted flow field evolution within the cylinder and the agreement between computed and measured cylinder deflection. An important feature of this comparison is determining the efficacy of the selected equation of state for water and its ability to adequately consider cavitation.
Description of the Experiment
Development of an underwater damage predictive capability requires the development and validation of coupled high-fidelity physics-based codes. For this effort, validation data was obtained from a series of experiments that place an explosive inside a water filled cylinder (Chambers, et al., 1998). These tests acquired transient pressure data in the water, and transient deformation data on the cylinder mid-line. Although this experimental arrangement is simpler and smaller in scale than a ship or submarine, it exhibits target-shock loading and subsequent cavitation unloading that typifies underwater explosion-target interaction. Furthermore, its small size allows it to be conducted in a laboratory under ideal conditions, facilitating accurate data measurement. It is reasonable to assume that accurately simulating these small-scale tests is a prerequisite to successfully predicting explosion damage to vessels.
The experimental arrangement consists of a 9” water filled aluminum (Al 5086) cylinder with a 4” outer diameter and a 0.25” wall thickness. This cylinder contains approximately 3.0 g of PETN explosive plus detonator, located at the cylinder center, along the midline. The deformation history of the cylinder outer wall and surface pressure near the inner wall are measured following the charge detonation. This test provides wall velocity and pressure histories that can be used to verify the cavitation collapse and reloading phenomena described previously.
Description of the Simulation
Material Model for Water (including Cavitation)
A modified form of the Tillotson equation of state, devised to better fit high-pressure water data, was employed to model water for these simulations. The model uses a simple pressure floor cavitation simulation whereby pressure is prevented from dropping below a prescribed cavitation level however, the sound speed is calculated in the normal fashion.
The assigned value of the cavitation pressure corresponds to 0.05 bars. However, this value has little impact on the solution as long as it is selected to be positive and much less than 1 bar. Bulk cavitation regions are viewed as consisting of bubbly water, rather than a gaseous or void region. Here rapid volume expansion with a small change in pressure is permitted via growth in the number and size of the bubbles without placing the water in tension. The bulk cavitation model defined by the lower pressure limit of the cavitation pressure fulfills the basic requirement for cavitation simulation: it allows water at low pressure to significantly expand without going into tension. However, it introduces other characteristics that are not realistic. In particular, prescription of a uniform pressure throughout a variable density cavitation region implies a sound speed of zero and changes the form of the equations from hyperbolic to parabolic. To be compatible with most numerical methods, a positive sound speed is required everywhere throughout the flow field. The present approach is to compute sound speed without consideration of the cavitation limit.
Material Model for Aluminum (Al 5086) Cylinders
The aluminum cylinder was simulated using a simple Power Law Isotropic Elastic-Plastic model. This material behavior is elastic-plastic with non-linear isotropic strain hardening given by a power law expression. This model is not currently rate dependent.
Similar Simulation Efforts
As well as experimental data, comparisons are presented herein against previous simulation efforts conducted by Wardlaw et al., (1998 and 2000). Their work included the coupling of the GEMINI, DYSMAS, and DYNA_N codes to the same water filled cylinder experiments. The DYSMAS code was developed by the IABG Corporation and maintained and enhanced in collaboration with the Warhead Performance and Lethality Division, Indian Head. The GEMINI code is a product of the US Navy’s work at Indian Head, and DYNA_N is the Navy version of the DYNA code - an explicit finite element code for problems where high-rate dynamic or stress wave propagation effects are important.
Comparison of Experiment Data and Numerical Simulation Outputs
The flow at 30 μs shows the reflected shock from the cylinder as it intersects the bubble for the first time. A cavitation region has formed at the wall because of wall motion and a second cavitation region is starting to form behind the reflected expansion. These regions merge at 40 μs to form a large zone, surrounded by high pressure fluid, that collapses at 90 μs, generating a collapse shock that reloads the cylinder.
The surface pressures exhibit a pressure pulse at about 90 μs, which is coincident with the predicted cavitation collapse event. This supports the conclusion that the observed change in wall velocity and surface pressure at this time is a consequence of cavitation collapse. Furthermore, it lends credence to the proposition that coupled codes, using a simple cavitation model, are capable of capturing such a phenomenon.
References:
1. J. Heylmun, P. Vonk, P., and T. Brewer, "blastFoam: An OpenFOAM Solver for Compressible Multi-Fluid Flow with Application to High-Explosive Detonation." Synthetik Applied Technologies, LLC., 2019.
2. P. Cardiff, A Karac, P. De Jaeger, H. Jasak, J. Nagy, A. Ivanković, Ž. Tuković, “An open-source finite volume toolbox for solid mechanics and fluid-solid interaction simulations.” arXiv:1808.10736v2, 2018, available at https://arxiv.org/abs/1808.10736
3. Chambers, G., Sandusky H., Zerrilli, F., Rye K., Tussing R., "Pressure Measurements on a Deforming Surface in Response to an Underwater Explosion", CP429, Shock Compression of Condensed Matter, Ed. Schmidt, Dandekar, Forbes, the American Institute of Physics, 1998.
4. A. Wardlaw, M. Jr., L. Reid, and Alan, “Coupled Hydrocode Prediction of Underwater Explosion Damage:,” Defense Technical Information Center, Fort Belvoir, VA, Jan. 1998. doi: 10.21236/ADA363434.
5. A. B. Wardlaw Jr. and J. A. Luton, “Fluid-Structure Interaction Mechanisms for Close-In Explosions,” Shock and Vibration, vol. 7, no. 5, pp. 265–275, 2000, doi: 10.1155/2000/141934.
Videos:
About blastFoam:
blastFoam is an opensource solver for multi-component compressible flow with application to high-explosive detonation, explosive safety and airblast.
The solver is based on the OpenFOAM® framework and provides solutions to highly compressible systems including single and multi-phase compressible flow, and single- and multi-velocity systems.
blastFoam provides implementations of the essential numerical methods (e.g. 2nd and 3rd order schemes), equations of state (e.g. ideal gas, stiffened gas, Jones-Wilkins-Lee, etc.), run-time selectable flux schemes (e.g. HLL, HLLC, AUSM+, Kurganov/Tadmor) and high-order explicit time integration (e.g. 2nd, 3rd, and 4th order).
blastFoam provides activation and explosive burn models to simulate the initiation and expansion of energetic materials, as well as afterburn models to simulate under-oxygenated explosives that exhibit delayed energy release.
Synthetik's opensource CFD airblast code based on the OpenFOAM framework is available on GitHub: https://github.com/synthetik-technologies/blastfoam
blastFoam is developed by Synthetik Applied Technologies:
https://www.synthetik-technologies.com/
About solids4foam:
solids4foam is a toolbox for OpenFOAM with capabilities for solid mechanics and fluid solid interactions
The solver is developed by Philip Cardiff and Zeljko Tukovic, with contributions from many others, in particular Danial Khazaei.
solids4foam is available here:
https://bitbucket.org/philip_cardiff/solids4foam-release/src/master/
Acknowledgments:
We would like to thank Dr. Philip Cardiff (Lecturer/Assistant Professor, School of Mechanical and Materials Engineering, University College Dublin) for his support and guidance with solids4foam.
Disclaimer:
This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software via www.openfoam.com, and owner of the OPENFOAM and OpenCFD trade marks.