MODELING AND SIMULATION OF HYDRODYNAMIC RAM FOR AIRCRAFT SURVIVABILITY
by Kangjie Yang, Young W. Kwon, Christopher Adams, and David Liu
Hydrodynamic Ram (HRAM) refers to the damage process due to high pressures generated when a kineticenergy projectile penetrates a
compartment or vessel containing a fluid [1]. The large internal fluid pressure acting on the walls of the fluid filled tank can result in severe structural damage. The study of HRAM effects on fuel tanks used on military aircraft is vital if the designs can withstand HRAM loads due to a hostile environment.
Many types of threats could result in HRAM damage to aircraft fuel tanks, including armorpiercing rounds from small arms fire or fragments from missile warhead detonations. Statistics from Operation Desert Storm indicated that 75% of aircraft losses were attributable to fuel system vulnerability, with HRAM being one of the primary kill mechanisms [2]. A ruptured aircraft fuel tank and its damaged surrounding structures would likely require a long downtime for depotlevel maintenance, as opposed to quick patch repairs of the entry wall panel. In other words, HRAM damage results in lower aircraft availability and higher cost of recovery. In some cases, HRAM could also lead to catastrophic attrition of the aircraft due to the cascading effect of fuel tank failure [3]. To design structures to withstand the HRAM loads, or to develop the HRAM mitigation techniques for existing aircraft, it is necessary to first predict the pressures distribution inside the tank at the different phases of the HRAM phenomenon.
The goal for HRAM research is to develop ways to eliminate the extensive damage to the entry and exit walls of the fuel tank immediately after being impacted by a projectile. The objective of the study described herein was to model and simulate HRAM using a finite element (FE) technique [4] to analyze the dynamic response of a tank structure and conduct parametric studies on factors affecting tank wall response during the initial phase of the HRAM event. The model will enable a better understanding of how various parameters affect the pressure waves generated in the fluid, as well as the dynamic response of the coupled structure. For the parametric studies conducted, the
emphasis was mainly on the structural exit wall response, where critical components or main structural members of the aircraft are typically located in close proximity.
REVIEW OF HRAM
In most nonexploding projectile impacts, in which the projectile penetrates and then traverses through a fluidfilled tank, the HRAM
phenomenon can be described in four distinct phases [2]:
 Shock Phase: the initial impact of the projectile into the entry wall of the fuel tank
 Drag Phase: the movement of the projectile through the fluid
 Cavitation Phase: the development of the cavity behind the projectile as it moves through the fluid and the subsequent cavity oscillation and collapse
 Exit Phase: the penetration of the projectile through the exit wall and tank (when there is sufficient energy remaining).
Each phase contributes to structural damage of the tank walls via a different mechanism, and the extent of damage depends on numerous factors, such as projectile shape and velocity, fluid level in the impacted tank, obliquity of impact, and the material of the fuel tank [5]. The high cost of performing experiments to understand HRAM phenomenon has led to extensive efforts in developing numerical techniques for computational simulation. Such efforts have been attempted for the past 30 years, with earlier efforts trying to simplify the phenomenon into a structural response problem, with boundary conditions representing the applied loads from the pressure field generated by ram effects. Subsequent efforts attempted to solve the nonlinear sets of hydrodynamic equations using numerical techniques by coupling the fluid and structure interaction.
MODELING PROCEDURES
The HRAM model consists of Lagrangian mesh for the tank and projectile and Eulerian mesh for the fluid inside the tank. The simulation of HRAM required an extremely fine Euler mesh and small sampling times to capture the propagation of shock waves in the fluid, thereby resulting in large files and long computational times. For a computational model simplification, a generic 200mm x 200mm x 200mm cubic tank impacted by a 10mmdiameter spherical projectile was developed. Subsequent parametric studies on the tank wall response and fluid pressures during the different phases of the HRAM event were presented with this simplified fluidfilled tank model. This simplified model is generally much smaller than a typical fuel tank in aircraft. However, regardless of the size and simplification, the present model shows all
the important HRAM characteristics.
The projectile impacting at the center of the tank’s entry wall was a 4g, 10mmdiameter, solid steel sphere. It was considered as a rigid material. One reason for selecting a projectile with a spherical surface was to prevent the tumbling of the projectile during the drag phase, which would have resulted in significant pressure fluctuations in the fluid causing erratic response to the coupled tank walls. The 200mm3 tank was discretized with 9,600 quadrilateral shell elements with four grid points, as shown in Figure 1. The element size was set to 5 mm and was assigned properties defined as an isotropic, elasticplastic material (the properties of which are provided later).
The fluid in the tank was discretized with threedimensional (3D) solid eightnode hexahedron Eulerian elements. A total of 64,000 Eulerian elements made up the box with 5mm element lengths. The fluid level and properties were varied for the different cases investigated. The mesh size for the Eulerian fluid elements was chosen to be similar to the Lagrangian tank shell elements, so the nodes are coincident to one another at the coupling surface. This condition is necessary for proper coupling of the Lagrangian and Eulerian elements to avoid unnecessary problems arising from the failure of the coupling surfaces.
As shown in Figure 2, two models were constructed for the purpose of this study. The first model (Model 1) was for the investigation of the shock phase of the HRAM, with the projectile outside the tank impacting the entry wall at a prescribed velocity. For this model, the displacement of the tank walls due to projectile impact and the subsequent ram pressure of the propagating hemispherical shock wave in the fluid from the impact point are of interest.
For the second model (Model 2), the projectile initial starting position is flush to the inner surface of the entry wall at the impact point, simulating the projectile’s position immediately after penetrating the entry wall. The initial velocit y of the projectile is less than 250 m/s due to retardation of the projectile by the entry wall. Model 2 is used to study the fluid pressures and tank wall response during the drag phase.
The initial loads and boundary conditions for the two models are tabulated in Table 1. An important aspect of fluid structure interaction problem is the coupling of the surfaces between the structure and fluid mesh.
Table 1 Loads and Boundary Conditions
Loads and Boundary
Conditions 
Description 
Displacement 
Model 1: Bottom surface of tank is fixed
Model 2: Bottom surface of tank is fixed 
Projectile Initial Velocity 
Model 1: 300 m/s
Model 2: 250 m/s 
Contact 
Model 1: Masterslave surface contact between projectile and tank
Model 2: Adaptive masterslave contact between projectile and tank 
Coupling (between fluid and projectile)  Model 1: Nil
Model 2: General coupling 
Coupling (between fluid and tank)  Model 1: Arbitrary LagrangianEulerian (ALE) coupling
Model 2: ALE coupling 
For Model 2, the projectile was coupled to the fluid by the general coupling technique while the fluid and tank surfaces were coupled
together using the Arbitrary LagrangianEulerian (ALE) coupling technique. In MSC Dytran, the general coupling mode allows the motion of a structure through a fixed Eulerian mesh, such as the movement of the projectile through the fluid. The Lagrangian structure, which is the projectile in this case, acts as a moving flow boundary for the fluid in the Eulerian domain while the fluid in turn acts as a pressure load boundary on the projectile.
For the ALE coupling technique used to define the interaction between the tank and fluid, the Eulerian mesh is now allowed to move and follow the motion of the Lagrangian mesh at the interface, since the nodes between the two meshes are now physically coupled together. When the tank walls start to displace, the fluid Euler mesh also moves together. Due to the motion of the Euler mesh, a compressive force is exerted on the adjacent fluid element. The compressed fluid element in turn exerts a pressure load back on the structural tank wall elements [6].
Tracer elements were defined at various locations within the model to collect data required for timehistory plots of the tank wall displacement, velocity and stresses, and the fluid pressures for analysis. Locations of the tracer elements are illustrated in Figure 3. There were nine tank shell elements across the entry, left, and exit walls, and there were three fluid hex element tracers.
For ease of comparison and analysis, the graphs plotted were obtained from the middle node and element of each wall, labeled No. 1, 5, and 7 for the tank structure and Fluid 2 for the fluid pressures output. The material properties and constitutive models for baseline Model 1 and 2 are summarized in Table 2.
Table 2 Summary of Material Properties and
Constitutive Model
Property  Tank  Fluid 
Density (kg/m3)  2,700  1,000 
Elastic Modulus (GPa)  70  N.A. 
Bulk Modulus (GPa)  N.A.  2.2 
Von Mises Yield
Strength (GPa) 
20  N.A. 
Mass (kg)  N.A.  N.A. 
Thickness (mm)  2.0  N.A. 
Poisson Ratio  0.33  N.A. 
RESULTS AND DISCUSSION
Even though a typical HRAM event consists of four phases, it was decided this study would analyze the impact phase separately using Model 1, as the failure process of projectile penetration and the subsequent material failure are still not well modeled at present. To avoid the unclear nature and the possible ambiguity in the results, it was determined that the modeling of projectile penetration into and out of the tank be omitted from the simulation. Data collected to plot the time history for the tank wall’s displacement, velocity, and effective stress were taken from the nodes and elements output at the center of each wall. The gauges corresponded to shell element gauge no. 1, 5, and 7 (as shown in Figure 3). Similarly, the fluid pressures generated during the shock and drag phase were plotted using data collected from fluid gauge no. 2.
Baseline Model 1
The baseline Model 1 simulation was set up for a 100%waterfilled tank impacted without penetration at the center of the entry wall by a spherical rigid projectile with an initial velocity of 300 m/s. Even though this is a hypothetical situation, because the projectile would likely penetrate the entry wall in an actual experiment, this simulation provided some insight to the tank wall behavior during the initial shock phase of the HRAM event. The event was simulated for 1 ms with a sampling rate of 20 μs for data collection. For comparison purposes, the following discussion compares Model 1 to an empty tank impacted under the same conditions.
Entry wall Xdisplacement and Xvelocity plots are shown in Figures 4 and 5, respectively. The Xdirection corresponds to the major component of the entry wall, as the direction of projectile velocity impacting the entry wall is in the positive Xdirection.
It was observed the peak displacement of the entry wall for the 100%filled baseline Model 1 is higher at around 9 mm as compared to 7 mm for the empty tank. An interesting phenomenon observed for Model 1 was the entry wall displacing in the negative Xdirection at around 0.06 ms after impact, indicating the entry wall bulging outward. The Xcomponent velocity timehistory plot shown in Figure 5 indicates a much larger peak value of around 210 m/s in the negative X direction right after projectile impact. This result corresponds to the time when the entry wall starts to bulge. The subsequent velocity of the entry wall after deforming outward was lower compared to the empty tank. The effective entry wall stress (i.e., the von Mises stress) reached a 11% higher peak value for Model 1 but over a shorter duration of time than the empty tank.
The exit wall response to HRAM is of main interest in this study as it is an area on the aircraft where main structural components and loadbearing members are likely to be located. Graphs for exit wall response were plotted from data collected from the center node of the exit wall panel. The Xdisplacement plot in Figure 6 shows a peak displacement of around 2 mm experienced by the exit wall at the end of the simulation, a value which is much higher than was experienced by the empty tank. The exit wall for Model 1 started deforming earlier at approximately 0.13 ms. This is approximately the time where the initial shock wave due to projectile impact at the entry wall impinged onto the exit wall, causing it to displace. The presence of fluid in the tank actually resulted in a much smaller velocity and effective stress at the exit wall. Peak stress at the center of the exit wall registered a much lower value of approximately 100 MPa, as compared to 500 MPa for the empty tank.
Besides the propagation of shock wave through the aluminum tank structure, a hemispherical shock wave was observed to propagate in the fluid toward the exit wall. This ram pressure generated by the impact of the projectile in the shock phase was recorded by the three fluid tracer elements, whose locations are shown in Figure 3.
Data for the ram pressure collected by the fluid element pressure tracer are plotted in Figure 7 (with the inset figure showing the fluid gauge locations). The graph showed a peak pressure of 7 MPa, as recorded by fluid gauge 1, which is located nearest to the impact point. This ram pressure was found to weaken significantly as it propagated through the fluid medium, reducing to a magnitude of 0.9 MPa near the exit wall, as recorded by fluid gauge 3. As the shock wave moved across the fluid toward the exit wall, its energy was dissipated across a larger volume of fluid, thereby resulting in a drastic reduction in ram pressure. The rapid weakening of the initial shock wave due to geometric expansion about the impact point and its short duration indicated the left and exit walls of the tank are unlikely to experience significant pressures from the impact shock wave.
The simulation for baseline Model 2 was set up for a 2mmthick 100%waterfilled tank, with the initial position of the spherical projectile centered and flushed to the inner surface of the entry wall and given an initial velocity of 250 m/s. Model 2 was developed to assist in understanding the structural response of the tank walls during the drag and cavitation phase of HRAM. All displacement, velocity, and effective stress values plotted were obtained from the center node or element of the tank walls. Because the collapse of the cavity would most likely occur at a much later time, the cavitation collapse pressure and its subsequent effect on the tank walls were omitted from this study. Instead, the effects on tank walls due to the drag phase pressure and the formation of the cavity in the fluid were the main interest.
The exit wall response graphs were plotted from the start of simulation up to 1.5 ms, just before the projectile impacted the exit wall. The exit wall started to move and deform at approximately 0.13 ms into the simulation due to the initial shock wave impinging onto the exit wall. At approximately 1 ms into the simulation, the rate of displacement of the exit wall registered an increase, as observed from the steeper gradient of the displacement timehistory plot of the exit wall. Correspondingly, there was a sharp increase in the exit wall X velocity after 1 ms, as illustrated in Figure 8. This increase is due to the projectile approaching the exit wall and the highpressure region in front of the projectile during the drag phase, exerting a greater pressure on and prestressing the exit wall before projectile impact.
The prestressing of the exit wall before the projectile impact is further illustrated in Figure 9. Likewise for the exit wall velocity, the effective stress has the peak value after 1 ms, when the projectile approached the exit wall. The exit wall registered a peak velocit y of 7 m/s and a peak stress of approximately 94 MPa prior to projectile impact.
Figure 10 shows the drag phase fluid pressure recorded by fluid gauge 2, located in the middle of the tank near the shotline. A peak pressure of approximately 5 MPa was registered as the projectile approached fluid gauge 2 at around 0.5 ms. The drag phase pressure rise was gradual and occurred over a longer period of time, as compared to the initial shock phase pressure. As the projectile moved past fluid gauge
2, the pressure recorded went to 0, indicating the formation of a cavity behind the projectile path. The cavitation phase of HRAM, which includes the oscillation and the subsequent collapse of the cavity, is not part of this study, as it would occur after the simulation had ended.
An interesting parameter that the numerical simulation provided for drag phase analysis was the cavity evolution when the projectile traverses the fluid towards the exit wall. The Model 2 simulation fringe plot of material fraction in the fluid Euler mesh obtained at a 0.4ms interval is shown in Figure 11. The maximum cavity diameter measured from the fringe plot at 2 ms was found to be approximately 60 mm. The bulging of the entry and exit wall was also observed.
Parametric Studies Conducted for Model 1 and Model 2
Parametric studies were conducted on Model 1 and 2 to understand how different factors could affect the exit wall response. For Model 2, even though the simulation end time was set at 2 ms, peak values that were tabulated were chosen from the start of simulation until the point before the projectile impacted the exit wall.
The fluid level was varied for Model 1 and 2 to study the effects of free surface on the shockwave propagation and the resultant exit wall response. With the rest of the parameters and impact conditions kept constant, the fluid level was varied for 80% and 60% fluid levels. This variation was made possible by adjusting the initial condition of the fluid elements filling the tank.
The exit wall response and fluid pressures for Model 1 and Model 2 are tabulated in Table 3 and Table 4, respectively. For Model 1, it was observed the lower fluid levels resulted in a lower exit wall displacement but higher velocity and stress. The shock phase ram pressure was also reduced significantly from 1.61 MPa in the fully filled tank to a mere 0.45 MPa in the 60%filled tank. This was due to the presence of free surface distorting the hemispherical formation of the shock wave at the impact point.
Table 3 Model 1 Exit Wall Response to Varying Fluid Levels
Parameters 
Percent– Filled Level 
Maximum Displacement (m) 
Peak Stress (MPa) 
Shock Phase Ram Pressure From Fluid Guage 2 (MPa) 
Peak Velocity (m/s) 
Fluid Level Variation 
100  0.002035  104.802  1.61365  12.7263 
80  0.002027  170.765  1.3469  19.1264  
60  0.001714  240.244  0.45185  19.2642 
Table 4 Model 2 Exit Wall Response to Varying Fluid Levels
Parameters 
Percent– Filled Level 
Maximum Displacement (m) 
Peak Stress (MPa) 
Peak Fluid Drag Pressure From Fluid Gauge 2 (MPa) 
Peak Velocity (m/s) 
Fluid Level Variation 
100  0.00471648  94.074  4.64315  6.85024 
80  0.00398923  102.79  4.27619  6.23109  
60  0.00274174  109.94  3.0948  4.98805 
The reduction of exit wall displacement is more evident in Model 2 from 4.7 mm for the fully filled tank to 2.7 mm for the 60%filled tank. The peak stress at the exit wall for the three different fluid levels shows a lesser variation as compared to Model 1. Peak drag phase pressure was also observed to be higher for a 100%filled tank at 4.63 MPa compared to 3.09 MPa for a 60%filled level.
Projectile mass was varied from 2 g to 6 g. Results are tabulated in Tables 5 and 6. Model 1 results showed projectile mass having a strong effect on the exit wall response during the initial shock phase. Peak displacement, stress, velocity, and ram pressures were all found to increase significantly. By increasing the mass from 4 g to 6 g, the peak stress recorded a considerable increase from 105 MPa to 172 MPa.
However, for Model 2, the variation in projectile mass on exit wall response was not proportional to the mass. The peak fluid drag pressure was also found to be of similar magnitude for the 4g and 6g projectile. Nevertheless, some correlation was observed for the peak stress and velocity at the exit wall for Model 2, where a higher projectile mass resulted in a higher peak stress and velocity.
The initial velocity of the projectile was also varied from 100 m/s to 500 m/s. The results for Model 1 and 2 exit wall response are tabulated in Tables 7 and 8, respectively. Model 1 results indicated a strong influence of projectile velocity on the exit wall response and fluid ram pressures. A projectile impacting the tank at a higher velocity of 500 m/s resulted in a drastic increase in peak stress and velocity at the exit wall. The ram pressure from projectile impact saw an increase from 1.61 MPa for the baseline Model to 2.39 MPa for a 500m/s projectile.
It was evident the exit wall response and fluid pressure were even more sensitive to projectile velocity for Model 2. With an increase in velocity from 250 m/s to 500 m/s, the displacement of the exit wall saw an increase from 4.72 mm to 5.89 mm. Similarly, as shown in Figure 12, drag phase pressure doubled due to the projectile velocit y increasing from 250 m/s to 500 m/s.
The elastic modulus of the tank material was varied from 40 GPa to 70 GPa, while keeping the rest of the parameters constant. Examination of the data presented in Table 9 revealed no particular trend for displacement and velocity for the different elastic modulus. However, there was a noticeable trend for both displacement and velocity for the variation in elastic modulus shown in Table 10.
The Xdisplacement plot for the exit wall showed the 100 GPa tank had a larger displacement initially but was eventually overtaken by tanks with lower modulus, as seen in Figure 13. This is an interesting phenomenon, which warrants further investigation. Values for peak stress and shock phase ram pressure for Model 1 did see a correlation, with the stiffer tank with modulus of 100 GPa experiencing a higher stress and larger ram pressure at 143 MPa and 2.03 MPa, respectively.
Table 5 Model 1 Exit Wall Response to Varying Projectile Mass
Parameters 
Mass (g) 
Maximum Displacement (m) 
Peak Stress (MPa) 
Shock Phase Ram Pressure From Fluid Guage 2 (MPa) 
Peak Velocity (m/s) 
Projectile Mass 
2  0.00128098  70.5868  1.0475  7.32631 
4  0.00203513  104.802  1.61365  12.7263  
6  0.00243127  172.462  2.02303  16.4221 
Table 6 Model 2 Exit Wall Response to Varying Projectile Mass
Parameters 
Mass 
Maximum Displacement (m) 
Peak Stress (MPa) 
Peak Fluid Drag Pressure From Fluid Gauge 2 (MPa) 
Peak Velocity (m/s) 
Projectile Mass 
2  0.00295588  68.2312  2.68013  4.07203 
4  0.00471648  125.866  4.64315  8.3379  
6  0.00478961  170.508  4.52462  13.4958 
Table 7 Model 1 Exit Wall Response to Varying Projectile Initial Velocity
Parameters 
Projectile Velocity (m/s) 
Maximum Displacement (m) 
Peak Stress (MPa) 
Shock phase Ram Pressure From Fluid Gauge 2 (MPa) 
Peak Velocity (m/s) 
Projectile Velocity 
100  0.000660054  29.5669  0.46631  2.78716 
300  0.00203509  104.802  1.61365  12.7263  
500  0.00255664  406.831  2.39176  34.2576 
Table 8 Model 2 Exit Wall Response to Varying Projectile Initial Velocity

Moving to Model 2, the effect of varying Young’s modulus was minimal for the exit wall displacement and velocity. However, the correlations for peak stress and drag phase pressures were more apparent, with the stiffer tank experiencing a larger stress but smaller drag pressures.
The next parametric study conducted on Model 1 and 2 was the variation in the density of the tank’s material. With the baseline Model 1 and 2 having the density of 2,700 kg/m3, material density was changed to 1,500 kg/m3 and 4,500 kg/m3 to evaluate its effect on the structural response at the exit wall. The results obtained are summarized in Tables 11 and 12.
Data from Table 11 indicated no discernible effect of material density on displacement and stress. It was observed that the baseline Model 1 has the highest displacement and stress, but the difference in value for the different material density was small. Some correlations were observed for shock ram pressure and velocity, with the denser material at 4,500 kg/m3 having a smaller ram pressure of 1.09 MPa and peak velocity of 10.7 m/s. For Model 2, the simulation model found that varying material density has almost negligible effects on the exit wall displacement. Peak stress and velocity also see small changes even though density was varied from 1,500 kg/m3 to 4,500 kg/m3.
For the final investigative choice, the density of the fluid was varied from 800 kg/m3 to 1,200 kg/m3, with the baseline Model 1 and 2 having the density of water at 1,000 kg/m3. Results for this study are tabulated in Tables 13 and 14.
The effect of fluid density on the shock phase of the HRAM for Model 1 saw no consistent trend at the exit wall, especially for stress, velocity, and ram pressure. Even though displacement of the exit wall for lower fluid density seemed to be higher, the difference is perceived to be small. Results for shock phase ram pressure were also inconsistent, with the more dense and less dense fluids both having a smaller ram pressure than the baseline Model 1.
As for the drag phase analysis for Model 2, varying fluid density was observed to have little effect on the exit wall displacement. However, the less dense fluid allowed the projectile to reach the exit wall earlier. With lower fluid density of 800 kg/m3, the projectile reached the exit wall after 1.4 ms, approximately 0.5 ms faster than the denser fluid with a density of 1,200 kg/m3.
CONCLUSIONS
HRAM is a complex phenomenon that is still not well understood. However, computational models can now provide an alternative to experimental testing in the understanding of HRAM by coupling the tank mesh to fluid mesh to simulate the fluid structure interaction. In particular, FE Models 1 and 2 provided some insights into the dynamic response of the tank structure and fluid pressures at the early phases of the HRAM phenomenon.
For the studies conducted with Models 1 and 2, the examination and analysis of the data collected revealed the following observations.
 The initial shock wave pressure upon projectile impact is unlikely to have detrimental effects on the exit wall of tank due to its rapid extinction in the fluid.
 The presence of free surface with lower filling levels reduced both the initial shock pressure and subsequent drag phase pressures.
 The projectile mass has a strong effect on the exit wall response during the shock phase, but once the projectile penetrates the entry wall, the drag phase was not correlated to different projectile masses.
 The velocity of the projectile had the largest influence on the exit wall response and fluid pressures, as the kinetic energy of the projectile is proportional to the square of its velocity. Therefore, when projectile velocity was increased to 500 m/s, all data collected for analysis observed a huge increase, especially during the drag phase.
 The tank material with a higher Young’s modulus resulted in a larger shock pressure but smaller drag phase pressures.
 Effective stress experienced by the exit wall was significantly greater for the stiffer tank.
 Varying tank material density had little effect on the exit wall response during the drag phase.
 Increasing the density of fluid in the tank resulted in higher drag phase pressures.
 As expected, the projectile was observed to reach the exit wall at a later time with increased fluid density.
Table 9 Model 1 Exit Wall Response for Varying Tank Material Modulus
Parameters 
Elastic Modulus (GPa) 
Maximum Displacement (m) 
Peak Stress (MPa) 
Shock Phase Ram Pressure From Fluid Gauge 2 (MPa) 
Peak Velocity (m/s) 
Tank Material Modulus 
40  0.00180311  72.9672  1.04987  11.6687 
70  0.00203509  104.802  1.61365  12.7263  
100  0.00181285  142.944  2.0287  9.30065 
Table 10 Model 2 Exit Wall Response for Varying Tank Material Modulus
Parameters 
Elastic Modulus (GPa) 
Maximum Displacement (m) 
Peak Stress (MPa) 
Peak Fluid Drag Pressure From Fluid Gauge 2 (MPa) 
Peak Velocity (m/s) 
Tank Material Modulus 
40  0.00502539  73.4471  5.35703  9.39117 
70  0.00471648  125.866  4.64315  8.3379  
100  0.00435498  152.739  3.00561  7.25874 
Table 11 Model 1 Exit Wall Response for Varying Tank Material Density
Parameters 
Density (kg/m3) 
Maximum Displacement (m) 
Peak Stress (MPa) 
Shock Phase Ram Pressure From Fluid Gauge 2 (MPa) 
Peak Velocity (m/s) 
Tank Material Density 
1,500  0.00187647  93.5504  2.08677  13.448 
2,700  0.00203509  104.802  1.61365  12.7263  
4,500  0.00151676  98.4064  1.08979  10.6776 
Table 12 Model 2 Exit Wall Response for Varying Tank Material Density
Parameters 
Density (kg/m3) 
Maximum Displacement (m) 
Peak Stress (MPa) 
Peak Fluid Drag Pressure From Fluid Gauge 2 (MPa) 
Peak Velocity (m/s) 
Tank Material Density 
1,500  0.00466953  124.526  4.70424  9.52921 
2,700  0.00471648  125.866  4.64315  8.3379  
4,500  0.00465953  109.789  5.27148  7.03468 
Table 13 Model 1 Exit Wall Response to Varying Fluid Density
Parameters 
Density (kg/m3) 
Maximum Displacement (m) 
Peak Stress (MPa) 
Shock Phase Ram Pressure From Fluid Gauge 2 (MPa) 
Peak Velocity (m/s) 
Fluid Density 
800  0.00208119  126.662  1.16409  14.1915 
1,000  0.00203512  104.802  1.61365  12.7263  
1,200  0.00178056  105.41  1.5171  14.2918 
Table 14 Model 2 Exit Wall Response to Varying Fluid Density

ABOUT THE AUTHORS
Mr. Kangjie (Roy) Yang is a mechanical engineer at Singapore Technologies (ST) Aerospace Limited, where he supports the Engineering and Development Centre’s (EDC’s) work on military projects and the Republic of Singapore’s Air Force fleet of aircraft. He holds a degree in mechanical engineering (majoring in aeronautical engineering) from Nanyang Technological University and is pursuing postgraduate studies at the National University of Singapore and Naval Postgraduate School.
Dr. Young W. Kwon is a Distinguished Professor in the Mechanical and Aeronautical Engineering Department of the Naval Postgraduate School. His research interests include multiscale and multiphysics computational techniques for material behaviors, composite materials, fracture and damage mechanics, nanotechnology, and biomechanics. He has authored or coauthored more than 300 technical publications, including textbooks on FE methods using MATLAB and multiphysics and multiscale modeling. He is an ASME fellow and is the Technical Editor of the ASME Journal of Pressure Vessel Technology as well as the Journal of Materials Sciences and Applications. He holds a Ph.D. from Rice University.
Mr. Christopher Adams is the Director of the Center for Survivability and Lethality at the Naval Postgraduate School, where he currently teaches combat survivability. He is a former Associate Dean of the Graduate School of Engineering and Applied Sciences, as well as a former thesis student of Distinguished Professor Emeritus Robert Ball. He also accumulated more than 20 years of operational flight experience in F14s and EA6Bs, serving multiple tours in Iraq and Afghanistan. Mr. Adams holds a B.S. degree in aerospace engineering from Boston University and an M.S. degree in aerospace engineering from the Naval Postgraduate School.
Maj. Dave Liu is an assistant professor of Aeronautical and Astronautical Engineering at the Air Force Institute of Technology (AFIT), leading the school’s aircraft combat survivability education and research program. Prior to this experience, he was deployed as a member of the Joint Combat Assessment Team in Afghanistan, where he collected aircraft combat damage data for U.S. and coalition air assets.
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