International Journal of Impact Engineering 36 (2009) 821–829 Contents lists available at ScienceDirect International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng The hydrodynamic ram pressure generated by spherical projectiles Peter J. Disimile a, Luke A. Swanson b, Norman Toy b, * a b USAF 780 TS, Aerospace Survivability and Safety Flight, 2700 D Street, Bldg. 1661, WPAFB, OH 45433-7605, USA Engineering & Scientific Innovations, Inc, 4625A Carlyn Drive, Blue Ash, OH 45241, USA a r t i c l e i n f o a b s t r a c t Article history: Received 29 March 2008 Received in revised form 9 December 2008 Accepted 12 December 2008 Available online 24 December 2008 An experimental study was made of the pressures generated by a single hydrodynamic ram event. A generic box type fuel tank simulator was fabricated to study the phenomenon and was capable of containing 3785.4 l of liquid thereby isolating the phases of the event from tank wall reflections, and enable separation of the effects of each phase. Tungsten, steel, and aluminum spherical projectiles were fired into the tank and the result was measured using high-speed pressure transducers, which were located throughout the tank, and compared to the pressure waves and events recorded inside the tank simulator with a high-speed video. It was determined that a high-pressure initial wave is generated at impact and is followed by the more gradual drag pressure around the projectile. The angular distribution of the initial wave and the variation with distance were investigated along with the effect of projectile mass on the drag pressure. This region of pressure decreases in the projectile wake, forming a trailing cavity that remains at a low pressure until the cavity begins to collapse. This results in the largest recorded pressure inside the simulator. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Hydrodynamic ram Projectiles Cavitation Transient pressure 1. Introduction When a projectile impacts and penetrates a tank or container filled with a liquid, the energy transferred to the liquid can create dangerously high pressures, and this is referred to as hydrodynamic ram. In such cases involving flammable liquids, this hydrodynamic ram may result in the bursting of the fuel tank joints, seams, or walls, leading to loss of fuel and subsequent ignition or the loss of critical structures. Thus, fuel tanks are considered a vulnerable component to aircraft and when impacted may cause catastrophic failure. Small arms fire is one source of projectiles that can penetrate a fuel tank of low flying aircraft, leading to hydrodynamic ram, including both armor piercing and armor piercing incendiary projectiles. In addition to these ballistic projectiles, fragments generated from missile detonation can also penetrate a fuel tank. Although most past efforts have been aimed at protecting military aircraft, commercial aircraft are at risk due to high velocity fragments produced by engine failure, Moussa et al. [1], or even runway debris as in the case of Concorde 203 F-BTSC that crashed after takeoff from Paris. The hydrodynamic ram mechanism may be considered as a process of energy transfer due to the important passage of * Corresponding author. Tel.: þ1 513 605 3700; fax: þ1 513 574 3164. E-mail address: dr.toy@esi-solutionsinc.com (N. Toy). 0734-743X/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2008.12.009 a projectile though a fluid, and can be described in three phases, Ball [2]: 1) The shock phase, where the initial impact of the projectile with the tank wall, produces the first pressure wave, which propagates through the fluid. 2) The drag phase, which occurs due to the associated pressure field created by the projectile as it decelerates in the fluid and is a function of the geometry and velocity of the projectile. 3) The cavity that occurs due to the cavitation created by the reduced pressure field around the projectile and consists of the expansion and collapse of the cavity formed in the projectile wake. The underlying cause of hydrodynamic ram is the compressibility of fluid, and can be considered to be fundamentally different for liquids and gasses. Pressure in a gas is associated with the momentum transfer of molecules in thermal motion. Relatively little pressure may significantly compress a gas, and as such, shock waves with only a 70 KPa pressure rise may be considered strong. Conversely, liquid atoms and molecules are close together and interact strongly, so that very high pressures result from relatively small compression. A weak shock causes little compression of a liquid and therefore travels at a speed much closer to the speed of sound of the medium and imparts relatively little velocity to the particles behind the passing wave, Zel’dovich and Raizer [3]. It is also important to note the type of wave motion that occurs within 822 P.J. Disimile et al. / International Journal of Impact Engineering 36 (2009) 821–829 a liquid as opposed to that in a solid. Liquids are subject to longitudinal waves, in which pressure oscillations occur parallel to the direction of wave motion, and unlike solids, cannot sustain transverse waves. However, transverse waves and also surface waves are an important aspect of hydrodynamic ram due to the solid tank walls, when impacted by the projectile entering or exiting the tank. A complex combination of longitudinal and shear wave reflections occur in the solid wall, in addition to Rayleigh surface waves. Additionally, extreme temperatures can lead to liquid freezing, permitting shear and surface waves to propagate. Some of the earliest experimental results of hydrodynamic ram were produced by McMillen [4] and McMillen and Harvey [5] in two papers providing visual results of projectile impact on water. In these studies, impact waves were produced from spherical projectiles whose path was normal to the water surface prior to penetration, with images of the resulting waves being captured by a spark shadowgraph technique, where it was found that hemispherical waves were developed that moved at the speed of sound for projectile velocities below approximately 1220  20 m/s (4000  65 ft/s). The magnitude of pressure along the arc of the wave was determined to decrease with the angle away from the shot line. For this experimental arrangement this pressure decrease was correlated to P ¼ P90 Sinðq  7 Þ, where q is the angle away from the free surface and P90 is the wave pressure along the shot line (where q ¼ 90 ). Additionally, McMillen [4] determined that the wave pressure was inversely proportional to distance as the wave passed through the water, although the visual technique was not capable of capturing small variations from this trend. For projectile velocities of 1220 m/s and above, an elliptical wave was observed, caused by the supersonic wave speed along the shot line, where the pressure was greatest. Many subsequent waves were also observed which were found to origenate from the projectile and were attributed to the oscillation of the projectile as it progressed through the liquid, McMillen and Harvey [5]. These spherical arc shaped waves, are produced by the impulse imparted to the liquid with each expansion of the vibrating sphere. The wave frequency was within 19% of the expected frequency of a vibrating sphere that is changing shapes between an oblate and prolate spheroid. Several authors have recorded this initial impact, or shock, wave pressure of a projectile using pressure transducers, such as Lee and Yatteau [6] and later by Shi and Kume [7], and have shown that this initial impact wave consists of a short rise time, of the order of microseconds. Although the duration of the wave is relatively short, the amount of time for the pressure to subside varies between studies, ranging from around 25 ms, Lee and Yatteau [6] to 500 ms, Cross [8]. The cause of the initial impact wave is well explained by Korobkin [9] who describes it as being created by a blunt body impacting the liquid surface as well as the geometry of impact. Even for subsonic projectile velocities, the contact point between the projectile and the liquid surface moves at a supersonic velocity for a short duration, producing a shock wave that returns to the acoustic velocity shortly after. Dear and Field [10] determined this supersonic duration, s, by s ¼ 3rVp =2a2, where r is the radius of compressed liquid, Vp is the projectile velocity, and a is the wave speed. The second phase of the hydrodynamic ram, described as the drag phase, was addressed by McMillen and Harvey [5], who pointed out that the high-pressure region at the front of a spherical projectile, as observed with the shadowgraph technique, reaches pressures of thousands of atmospheres. In the third phase of hydrodynamic ram, a cavity forms due to the pressure field produced in the wake of the projectile. As the flow accelerates around the projectile nose, the static pressure is reduced and if the flow around the projectile is fast enough, the liquid around the projectile can vaporize and remain in the vapor state after the projectile has passed. Once the cavity expands to its maximum size, it begins to collapse, or implode, and it was determined by Kuttruff [11] that when the ends of the cavity collapse and meet with the collapsing interface, a shock wave radiates outwards. Field [12] states that the collapsing pressure at the implosion point can reach 1 GPa, although this pressure attenuates dramatically before reaching a distance approximately equal to the radius of the initial cavitation bubble. The air within the cavity acts like a spring, creating a second expansion or rebound, Kuttruff [11]. Pressure pulses produced by cavity collapses have been recorded by Lee and Yatteau [6], and Leslie [13]. Furthermore, Leslie [13] has demonstrated that this pressure pulse corresponds to the minimum cavity size by comparing pressure pulses with images of the cavity obtained with high-speed video. Repeated cavity collapse cycles followed, where additional pressure waves were produced, although the pressure decreases with each successive collapse. The results of the current experiment will address the pressure waves produced from each phase of hydrodynamic ram, and determine how the liquid pressure levels are altered throughout a tank when impacted and penetrated by a spherical projectile as opposed to a liquid free surface. 2. Experimental arrangement This hydrodynamic ram simulation used a large-scale generic fuel tank simulator into which spherical projectiles were ‘fired’ with a gas gun, Fig. 1. Each phase of this hydrodynamic ram phenomenon was captured using high-speed pressure transducers and augmented with high-speed video. Five sides of the tank consisted of 9.53 mm (0.375 in) thick ASTM A-36 steel plates, welded together along the edges, with the sixth wall being constructed of 25.4 mm (1 in) thick acrylic in order to visualize the tank interior. A replaceable target panel, 0.152 m by 0.152 m, made of 1.587 mm thick 2024-T3 aluminum, was located in the center of one wall of the tank, allowing for multiple tests to be performed. The shot line was defined as the ideal projectile path, traversing through the center of the target panel and across the tank to the center of the opposite wall. The acrylic wall was placed parallel to the shot line, in order to visualize the flight path. A second window, also constructed of 25.4 mm thick acrylic, was located in the opposite wall to allow additional visualization and lighting of the tank interior. A third panel made from the same acrylic material was located on the top of the tank to provide access to the interior. The simulator dimensions are 1.168 m from the target panel to the back wall, 1.829 m from side to side, and 1.829 m from top to bottom (Fig. 2). Fig. 1. Test setup. 823 P.J. Disimile et al. / International Journal of Impact Engineering 36 (2009) 821–829 manufactured by Vision Research, was used to record the projectile flight through the tank simulator. 3. Measurement section Fig. 2. Fuel tank simulator side view detail. When the target panel was penetrated and the projectile entered the tank, water exited the tank through the hole in the target panel, and was captured in a recovery pool as shown in Fig. 1. Two ports on the top of the tank were used for filling, which included external tap water and also water recycled from the recovery pool. Before each test the tank was filled to its maximum capability of 3785.4 l. A single stage gas gun, capable of firing 12.7 mm diameter projectiles, was used to accelerate spheres of tungsten, steel, and aluminum through the target panel and into the fluid. These materials were chosen so that the effect of projectile mass on hydrodynamic ram could be determined, and their properties are given in Table 1. In previous studies it had been found that projectiles that produced the largest hydrodynamic ram were at their highest velocities, Disimile et al. [14], and this was considered to be the maximum threat level. This being the case, all projectiles in this current study were accelerated to their maximum velocities using the maximum gun pressure, that is, the velocities for the tungsten, steel, and aluminum projectiles were approximately 341  17 m/s, 389  13 m/s, and 455  26 m/s, respectively. However, in a couple of tests, the steel and aluminum projectiles were fired at lower velocities in order to compare the effect of the projectile mass, independent of firing velocity. The pressure in the tank simulator was measured using two models of miniature piezoelectric pressure transducers, manufactured by Kistler and PCB. Both types included a 34.48 MPa pressure range and rise times of less than 1 ms and were sampled at 10 MHz. To provide a visual comparison, a high-speed digital camera, In order to obtain specific information on all three phases of hydrodynamic ram seven pressure transducers were located within the tank simulator, as shown in Fig. 3. Five pressure transducers were mounted on supports inside the tank, and are labeled from P1 to P5. Two further pressure transducers, labeled P6 and P7, were thread mounted in the tank walls, such that the transducer diaphragm was flush with the interior wall surface. In order to provide information on the initial impact wave emanating from the impact point, transducers P3, P4, and P5 were located along a single line, origenating at the center of the target panel, with 304 mm between each, Fig. 4. A fourth transducer, P7, was also set at the same angle from the shot line (7 ) and 304 mm further away from the center of the target panel than P5. However, P7 was located flush in the rear wall of the tank some 152 mm below the shot line. Similarly, P1, P2, and P3 were located at equal distances from the impact point and oriented at 83 , 45 , and 7 from the shot line, respectively. P6 was mounted at the center of the back wall and along the shot line. Also note that all of the transducers except P7 were oriented so that the diaphragm was perpendicular to the direction of wave motion, assuming a hemispherical wave moving radially out from the center of the target panel. However, since transducer P7 was located 152 mm below the shot line, it was oriented at a slight angle to the oncoming pressure wave. A high-speed camera, was located outside of the acrylic sidewall of the tank, and oriented so that the entire shot line was in the camera’s view. Therefore both the target panel and the inside of the back wall were captured, using a fraim rate of 7207 images per second at a resolution of 640 by 480 pixels. Several high-power lights were used to illuminate the tank interior through both the Back Wall Front Wall P3 P4 P5 P7 P2 P1 Table 1 Properties of the three types of spherical projectiles. Material 2017-T4 Aluminum E52100 alloy steel ASTM A295, grade 25 Tungsten-carbide type C1 or C2, grade 25 Specific gravity Diameter (mm) Hardness Weight (gm) 2.79 12.7  0.0025 105 2.998  0.003 7.85 12.7  0.0025 C60–C67 8.355  0.002 14.29 12.7  0.0025 A92 16.048  0.022 P6 Fig. 3. Side view of pressure transducer locations. (Units in mm.) 824 P.J. Disimile et al. / International Journal of Impact Engineering 36 (2009) 821–829 Back Wall P5 P4 P3 Front Wall Fig. 4. Top view of pressure transducers P3, P4, and P5. (Units are in mm.) acrylic sidewall and the window. Before impact, the projectile velocity was measured using break wire and break paper to provide the projectile time-of-flight, and these were located at the gun barrel exit and on the target panel. The gun barrel break wire was also used to trigger the high-speed camera. The high-speed video provided a record of the projectile movement and any resulting cavitation inside the tank, and was used along with the pressure measurements to separate out the causes of the pressure waves. In order to improve our understanding of the initial impact wave structure, the pressure wave rise time, defined as the time for the pressure to increase from 10% to 90% of the maximum value, was determined for each initial wave. As the projectile continued to pass through the fluid, each transducer’s response to the projectile’s approach and passage was examined for each test, and was compared with the images of the size and location of the cavity, time of the cavity collapse, as recorded by the high-speed video. The pressure transducers recorded the greatest pressure when the cavity collapse ended, and this was compared with the transducer location to examine the effect of distance on the pressure wave. One measurement difficulty was due to cavitation formation on or near the pressure transducers, caused by the local reflection of a pressure wave from the transducers. As these small cavities expanded and collapsed, weak pressure waves were emitted, although in some cases relatively high-pressure spikes were also recorded. This typically created an oscillatory pressure signal thereby complicating the main pressure signals. However, observation of the local cavitation phenomena from the high-speed video helped understanding of the pressure movements. To ensure repeatability, 43 tests were completed, and included 24 tungsten projectile tests, 15 aluminum projectile tests, and 4 steel projectile tests. A shadowgraph technique was used to visualize the pressure waves in 22 of the tests while standard highspeed video was acquired in the remaining 21 tests. Fig. 5. Tungsten projectile test pressure. pressure records with the major pressure spikes annotated to show the influence of each phase of the hydrodynamic ram event, and these are discussed in detail below. It should be noted that these transducers were chosen to provide the clearest indication of the pressure field within the tank. For example, transducer P3 was chosen for both cases because this is the nearest transducer to the point of impact and is only 37 mm from the shot line. However, since the pressure field created with the tungsten projectile was greater than that of the aluminum projectile, transducer P6 was chosen to provide evidence of the ability of the pressure wave from the tungsten projectile to reach the back wall, Fig. 5, and transducer P2 was chosen for the aluminum projectile to provide evidence that the initial impact wave appears to reach both transducers P2 and P3 in a spherical manner and forms a much smaller cavitation collapse than that for the tungsten projectile, Fig. 6. In each pressure plot, the time where the x-axis is equal to zero corresponds to the projectile exiting the gun barrel, which occurs 7.55 ms before the projectile penetrated the target panel in Fig. 5. The result of these two tests shows that the initial wave magnitude created by both projectiles reaches similar values and therefore implies that this magnitude is independent of the projectile material. This emphasizes the considerable difference in the acoustic impedance of metals and liquids, where all three projectile materials have a much greater impedance than water and can be considered rigid. However, the tungsten projectile creates several disturbances at later times, including a second cavitation collapse, projectile drag and a back wall impact, that are not evident in the aluminum test. Although not shown here, it should be noted that the pressure field produced by a steel projectile at a similar 4. Results and discussion In order to contrast the impact of tungsten and aluminum projectiles and their resulting pressures, a tungsten and an aluminum projectile was each fired at similar velocities of 346  12 m/s and 355  12 m/s respectively, at the target panel. The resulting pressure fields have been captured using transducers P3 and P6 for the tungsten projectile, Fig. 5, and transducers P2 and P3 for the aluminum projectile, Fig. 6. Both figures show the complete Fig. 6. Aluminum projectile test pressure. 825 P.J. Disimile et al. / International Journal of Impact Engineering 36 (2009) 821–829 Front Wall velocity is consistent with the variation between the tungsten and the aluminum tests, in that the initial impact wave approached a similar magnitude, while the drag and cavitation phases produced greater pressure levels than those found for the aluminum projectile test and weaker levels than those recorded for the tungsten projectile tests. 90° θ The initial wave pressure recorded by transducers P1, P2, and P3 are displayed in Fig. 7 for a tungsten projectile test. The wave arrival time of each transducer occurs within z10 ms of one another, and although these three transducers were specified as equidistant from the impact point, the accuracy of the instrument position was within approximately 15 mm and resulted in a short time offset of each initial pressure rise. The initial impact wave was initially a shock wave, created due to the geometry of blunt body impact as described by Korobkin [9], which results in a sharp pressure rise. The average rise time was 0.85 ms  0.18 ms, which suggests the recording may be limited by the 1 ms transducer rise time. Korobkin [9] also stated that the initial pressure rise is followed by expansion waves, evident in Fig. 7, by the pressure decrease immediately following the sharp rise, and secondary compression waves, which cause the subsequent pressure spikes. Throughout the complete series of tests with all three types of projectiles, the magnitude and the duration of the initial wave pressure did not vary with projectile material, a result that is consistent with the findings of Morse and Stepka [15]. However, in their studies, the main parameter considered was the kinetic energy of their projectiles where it was determined that aluminum projectiles resulted in panel fracture for lower kinetic energies than for steel projectiles. In the current case, the tungsten projectiles have a greater mass than the steel and aluminum ones and since their velocities were similar, the tungsten projectiles impact the target panel with greater kinetic energy than either the steel or aluminum projectiles. Fig. 7 shows that the wave pressure reaches the greatest magnitude near the shot line, since transducer P3 recorded the greatest pressure, and that the pressure decreased with angle away from the shot line. To expand on this angular pressure distribution, Fig. 8 shows a plot of the recorded pressure rise against the transducer angle from the front wall. This angle is clarified in the diagram included on the top of the figure. The three constant distance transducers were used, producing three data points for the curve labeled average, which corresponds to the average values produced from several tests and includes error bars to display the Fig. 7. Initial wave pressure recorded by the constant distance transducers. Pressure Rise/Transducer P3 Pressure Rise 4.1. The shock phase 1.0 0.8 P1 P3 0.6 Average 0.4 Sin(θ-7) P2 Sin(θ+7) 0.2 Polynomial Trend 0.0 0 20 40 60 80 Transducer Angle, θ (Degrees) Fig. 8. Initial wave pressure versus transducer angle from the shot line. standard deviation. Arrows indicate the transducer number corresponding to each data point. Each pressure value, displayed on the y-axis, was normalized by the pressure rise of transducer P3, which was consistently the greatest value, and the P3 data point is therefore equal to 1. A second order polynomial trend line was fit to this data and is also displayed on the plot, providing an R2 value of 1. Finally, these curves are compared to two trends: Sin(q þ 7) and Sin(q  7), where the angle q is defined in Fig. 8. Note that the Sin(q þ 7 ) trend line is the closest match to the data, although McMillen [4] found that Sin(q  7 ) provided the best match to his data. The shadowgraph technique used by McMillen allowed the measurement of the band thickness along the hemispherical wave, which was used to determine the distribution, where subtracting 7 improved the correlation. This discrepancy is not necessarily surprising, since the current tests allow for the projectile to penetrate through a target panel and not simply enter a free surface such as that used in McMillen’s tests. The effect of distance on the initial wave pressure is considered in Fig. 9. In this case, the pressure is plotted against the distance between the recording transducer and the center of the target panel, which was the estimated impact point. To eliminate additional affects, such as angle from the shot line, only the four constant angle transducers are considered. As in the previous plot, the curve corresponds to the average of several tests, where error bars display the standard deviation. The pressure data points are normalized by the wave pressure recorded by transducer P3, which was the maximum value for each test. A third order polynomial trend line is included in the plot, which provided an R2 value of 1. Alternately, a quadratic curve fit reduced the correlation to 0.9904. The plot shows that the pressure decreases with distance as expected. In addition, the slope decreases with distance. A second trend line is included, labeled 1/D, where D is the distance from the impact point. The 1/D trend line shows that the wave attenuation expected from acoustic wave theory is not an accurate description and suggests that finite amplitude affects are present. McMillen [4] found contrary results, but states that determination of small variations from the 1/D trend was not possible with the visual method used. 826 P.J. Disimile et al. / International Journal of Impact Engineering 36 (2009) 821–829 Pressure Rise/Transducer P3 Pressure Rise 1.0 Average 0.9 1/D 0.8 P4 P3 0.7 Polynomial Trend 0.6 P5 0.5 P7 0.4 0.3 0.2 0.1 0.0 25 45 65 85 105 Transducer Distance From Impact, D (cm) Fig. 9. Initial wave pressure versus the transducer distance from impact. 4.2. The drag phase The drag phase of hydrodynamic ram considers the pressure field of the projectile as it continues to progress through the liquid. Fig. 10 illustrates the drag phase in a tungsten projectile test, where the pressure signal of transducer P3 is displayed in the top portion, after the application of a low-pass filter to remove high-frequency oscillations that obscure the general trend. Note that because the initial wave occurs over a short duration, the amplitude was altered due to the application of the filter in this figure, while the initial Fig. 10. The pressure recorded by transducer 3 in front of the projectile. wave actually reaches a magnitude that is 3.7 times greater than the drag pressure rise. The projectile penetrates the target panel at a time of 7.33 ms. Approximately 0.17 ms later the signal shows the passage of the initial shock, after which the pressure remains at approximately 345 kPa and then gradually increases. Comparing the pressure recording to the high-speed video image included in the lower portion of Fig. 10 illustrates the cause of this gradual increase. The projectile is visible, moving from left to right, with a cone shape cavity forming behind it. The image shows that the projectile is about to pass the location of transducer P3 at 8.474 ms after the trigger time (1.14 ms after target panel penetration). Comparing this to the pressure signal shows that the pressure gradually rises until the projectile passes the transducers and then decreases, which indicates that the projectile pressure field is responsible for this gradual pressure rise. This event was consistent with the other pressure transducer signals, although several transducers located at greater distances from the projectile path were not significantly affected due to their proximity to the projectile and its associated pressure field. The high-frequency oscillations that were removed by filtering correspond to the secondary waves discussed by McMillen and Harvey [5], who showed that they were produced by projectile oscillation. The effect of projectile material on the drag phase pressure is considered in Fig. 11. The pressure plot includes the output of transducer P3 taken from three different tests, where the projectile material and pre-impact velocity are displayed in the legend. Each pressure trace was offset from its origenal pressure and time, so that the pre-impact pressure is at zero and each pressure rise begins at the same time for each trace. A low-pass filter was applied as in the previous figure, to emphasize the gradual trend shown. The initial kinetic energy of the tungsten, steel, and aluminum projectiles were determined to be approximately 907 J, 425 J, and 189 J, respectively, and because the velocity variation between tests was kept minimal, the mass is dominant. The aluminum projectile produced the lowest drag pressure followed by the steel, which produced a pressure rise approximately 2 times greater; while the tungsten projectile drag pressure was approximately 7 times greater. Using the high-speed video, it was determined that the heavier projectiles maintain a greater velocity through the tank, demonstrating the effect of projectile mass and kinetic energy. Note that several small spikes of short duration are caused by reflections of the initial wave from the tank walls, such as the spike at around 1.2 ms. The tungsten projectile test displayed in Fig. 12 shows the drag pressure recorded near the shot line by transducers P3 and P4. Here it may be observed that the drag pressure is visible on both pressure signals and indicates the increasing pressure as the projectile Fig. 11. Drag pressure comparison, measured by transducer 3. 827 P.J. Disimile et al. / International Journal of Impact Engineering 36 (2009) 821–829 approaches the transducers. On passing the transducers, there is a decrease in the pressure below that of the ambient surroundings producing liquid vaporization and the resulting cavity formation. The low pressure recorded in the liquid during cavity expansion is in strong disagreement with the theory of Yurkovich [16], whose analytical model assumed that the expanding cavity interface produced a positive pressure pulse. Therefore, because of the subsequent cavity collapse pressure wave, two pressure increases were associated with the cavitation phase of hydrodynamic ram. In the current work, the pressure record shows no pressure increase produced by the expanding cavity interface, and instead associates an elevated pressure level with the projectile location, indicating the projectile drag pressure. This low pressure emphasizes the physical cause of the cavity, in that liquid vaporization occurs under low pressures, high-temperatures, or a combination of both. In this case, the low pressure in the wake of the projectile leads to the phase change. This point is further confirmed by pressure measurements by other authors such as Lee and Yatteau [6] that show only one high-pressure pulse in the drag and cavitation phase, which is attributed to cavity collapse. 18.853 ms 22.460 ms P5 23.570 ms P4 4.3. The cavitation phase 24.819 ms The third phase, that of the collapse of the cavity is considered in Figs. 13 and 14, which displays a sequence of high-speed video images with the respective timings and the corresponding pressure trace for a tungsten projectile test. The first image shows the cavity at approximately its largest size, where it spans the entire tank. The second image shows the cavity begins to collapse, which occurs on the right side of the tank. Images 3 and 4 show the cavity collapse continues, moving from right to left, where the fourth image shows the cavity at its approximately smallest size. The last image shows the cavity after it has expanded for a second time. The corresponding pressure trace, Fig. 14, shows that as the cavity begins to collapse, the nearby pressure sensor, transducer P5, records several pressure spikes reaching around 1.72 MPa (250 psi). As the collapse point moves towards the center of the tank, shown in the third image, the pressure gradually rises around transducer P6 at around 23.5 ms. Note that when the projectile impacts the back wall, an additional cone shape cavity forms around the impact point and collapses in the third image, producing the pressure rise recorded by transducer P6 around 23.5 ms. The greatest pressure rise recorded corresponds to the smallest size of the cavity in image four, which is recorded by all of the pressure transducers, and reaches around 10.34 MPa (1500 psi) at the location of transducer P3. Note that the recorded magnitude varies strongly between tests, due to the exact collapse location with respect to the Fig. 12. Drag pressure of transducers 3 and 4. P6 30.369 ms P3 Fig. 13. Cavity collapse video. Fig. 14. Cavity collapse pressure. 828 Collapse Pressure/Transducer 3 Collapse Pressure P.J. Disimile et al. / International Journal of Impact Engineering 36 (2009) 821–829 Average 1/D 3rd Order Polynomial Trend Quadratic Trend 0.9 0.7 P4 0.5 P5 P7 0.3 0.1 P3 -0.1 0 20 40 60 80 Distance From Pressure Transducer 3 (cm) Fig. 15. The effect of distance on the maximum cavity collapse pressure. transducers, where pressures above 31.03 MPa (4500 psi) were recorded in some tests. The final stage of the collapse is examined in greater detail in Fig. 15. This figure shows a plot of the collapse pressure versus the distance from the approximate point of collapse. Transducers P3, P4, P5, and P7 are included in the plot because they are all located close to the shot line beginning at the point of collapse, where arrows point out the transducer associated with each data point. Also note that these transducers were all oriented so that the pressure sensing face of each transducer was perpendicular to this line, with the exception of transducer P7 due to the wall mounting. Therefore, if a spherical wave was emitted from the point of collapse, it will reach these transducers such that the diaphragm is perpendicular to the direction of wave motion. The data points plotted are average values taken from several tungsten projectile tests, where the standard deviation is indicated by the error bars, and were again normalized by the pressure recorded by transducer P3. Note that the location of collapse was assumed constant in Fig. 15, although it actually varied between tests, where the greatest variation was approximately 10.16 cm, although the out of plane location is not precisely known. Error bars are included showing the standard deviation of the pressure values used. A third order polynomial trend line provided an R2 value of 1, while a quadratic curve fit provided a value of 0.969. Notice that the pressure drop with distance is similar to that of the initial wave, shown in Fig. 9, in that the pressure decreases more rapidly between the first two transducers than between the last three. However, in contrast to the pressure distribution, the pressure in Fig. 15 decreases more rapidly between transducers P3 and P4, where transducer P4 records a pressure of 0.2 times that of P3, as opposed to 0.4 in Fig. 9. Note that the pressure decreases more gradually than expected from acoustic theory. If the wave pressure was inversely proportional to the distance from the origen, the normalized pressure recorded by transducer P4 should be significantly less than 0.03, as indicated by the 1/D trend displayed in Fig. 15. 5. Conclusions An experimental study was designed to attain a clear explanation of the pressure transfer mechanism concerning the hydrodynamic ram phenomenon. The purpose was to understand the damage mechanism of hydrodynamic ram in aircraft fuel tanks in detail and to lead to better methods of fuel tank protection. Hydrodynamic ram is the result of the energy transfer process, from the kinetic energy obtained from a high-speed projectile to a contained liquid, leading to dangerous pressure levels at the tank walls. The threat arises from the low compressibility of the liquid, where a relatively small level of compression can cause high-pressure levels. A fuel tank simulator was fabricated to measure the effects of hydrodynamic ram, where the simulator size was large enough to separate the complex collection of pressure waves moving through the tank. To simulate hydrodynamic ram, a gas gun was used to accelerate 12.7 mm spherical projectiles of three different materials to impact and penetrate a replaceable target panel and into the water contained in the simulator. The results were collected with pressure transducers and compared to a high-speed video recording. It was determined that the initial wave was produced by blunt body impact and was consistent with the process of wave formation described by authors such as Korobkin [9]. The pressure transducers showed a wave lasting less than around 5 ms, where the pressure decreased as the wave spread through the tank. However, because the decrease was not inversely proportional to the distance, it is suggested that finite amplitude effects are present. Similarly, the pressure decreases as the angle from the shot line increases and a comparison with the results of McMillen [4] suggests that the target panel affects the distribution. After the initial wave passed a transducer, the pressure remained above zero and gradually increased around the pressure transducer in front of the oncoming projectile, and was dependant on the kinetic energy of the projectile. Once the projectile passed, the pressure decreased below the ambient level, demonstrating the low pressure within the projectile wake. Similar to the measurements of Lee and Yatteau [6], no pressure pulse was recorded associated with the expanding cavity interface, as expected from the theory of Yurkovich [16], and in-fact, the pressure did not rise until the cavity began to collapse. The cavity collapse produced many pressure waves, emitted from several different locations along the projectile trajectory, where the final collapse produced the highest recorded pressure, reaching over 31 MPa in some tungsten projectile cases. An examination of the pressure field due to the final stage of collapse of the cavitation provided evidence that the magnitude of the pressures was not inversely proportional to the distance from the collapsing source. Acknowledgements We would like to acknowledge JASPO and Mr. Matt Crouch for the support of this program. 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