TIO N B -B
4.2 Dynamic Large-Scale Model Autoinjector
4.2.3 Results: Syringe Acceleration and Pressurization
4.2.3.5 Case 10
Test cases 10 to 15 are performed with the reversed outer projectile: the impact of the projectile occurs on the syringe wall rather than on the buffer. Several tests were performed in this configuration. As indicated at the beginning of this section, damping material in the form of two stacked O-rings is introduced between the projectile and the syringe wall. The impact of the projectile on the damping material accelerates the syringe. The acceleration, in turn, creates a pressure and stress transient.
Case 10 is for a syringe terminated with a flat wall, filled with water, but with no buffer sealing the syringe. This is equivalent to having an air gap which is infinite in size. Although it may not be obvious at first, this configuration without a buffer is the simplest configuration possible for this type of transient event. The effect of adding the buffer and reducing the air gap size is discussed later.
-15 -10 -5 0 5 10 15 -1
0 1 2 3 4 5
Figure 4.34: Velocity of the syringe for case 10 of the dynamic, large-scale model autoinjector experiments (test LS-0322).
The velocity of the syringe is shown in Figure 4.34. The impact of the projectile on the syringe wall occurs at -11.5 ms, promptly accelerating the syringe. The magnitude of the syringe acceleration is approximately 3,000 m/s2. Note that the projectile rebounds on the O-rings, and it does not impact a second time on the syringe wall in the time period of interest.
The large syringe acceleration is followed by a weak deceleration, indicated with a red-dashed curve inFigure 4.34. This is again the result of a cavitation event in the syringe. The magnitude of the deceleration is approximately 121 m/s2, close to the expected magnitude of 141 m/s2. The positive acceleration of the syringe around 0 ms is the result of a substantial pressure increase at the bottom of the syringe, creating a large force on the tip of the syringe. This pressure increase occurs when the first cavitation event ends, and this is what triggers the data acquisition system.
This cycle is repeated a few times.
Figure 4.35 is a plot of the pressure measured at the bottom of the syringe. The pressure history supports the observations reported above. The syringe acceleration begins at -11.5 ms (label 1), resulting in a pressure decrease. As explained in Section 2.2.2, the acceleration of the syringe creates tension waves which reduce
139
-15 -10 -5 0 5 10 15 20 25 30
0 2 4 6 8 10
-0.5 0 0.5 1
0 5 10
Figure 4.35: Pressure at the bottom wall for case 10 of the dynamic, large-scale model autoinjector experiments (test LS-0322).
the liquid pressure to vapor pressure, and cavitation occurs. The tension waves originate in the vicinity of the tip, and propagate toward the free surface located at the top end of the syringe. There, the tension waves reflect as compression waves.
The role of the tension and compression waves is to accelerate the liquid forward.
The first cavitation event lasts until 0 ms, ending with a substantial pressure increase (label 1) up to 8.0 MPa. The pressure increase is created by the collapse of a large cavity or bubble in the syringe. This is confirmed later with images obtained from tests performed with a clear syringe.
Figure 4.35indicates this cycle (i.e., cavitation event followed by a pressure increase) is repeated several times. The peak pressure created at the end of each cavitation event decreases in amplitude from cycle to cycle due to dissipation in the system.
The duration of each cavitation event (i.e., the time lapse between successive peaks) also becomes shorter, indicating a faster propagation of pressure waves in the bubbly liquid during the cavitation event. This, in turn, indicates the average void fraction decreases from one cycle to another (Brennen, 1995).
The pressure signals from Figures 4.35 can be compared with the pressure signal from Figure 3.13 (0 to 2.5 ms) obtained with the in situ methods. Both signals
exhibit similar features. In both cases the transient events begin with a pressure decrease from ambient conditions to vapor pressure. This is followed by multiple pressure peaks created by cycles of cavitation. The peak magnitude of pressure is similar (8 to 9 MPa), and the amplitude of the pressure peaks caused by the successive collapses of cavities decreases monotonically from cycle to cycle. The time scales for both tests are different, however, because the syringes used in both setups have different size; the syringe used in the large-scale model autoinjector is approximately 6 times larger. The similarities noted suggest the physics at play is similar in the autoinjector device and the dynamic, large-scale model autoinjector.
Returning to the results for test case 10, the duration of the first cavitation event is 11.5 ms. A simple model which provides an estimate for the expected duration of this cavitation event was developed. The model assumes the syringe and the liquid column inside the syringe move independently as two rigid bodies. This approximation is justified because the pressure waves and stress waves can complete multiple axial round trips in 11.5 ms. The model assumes the syringe is impulsively accelerated to a velocityu0, which corresponds to the velocity of the syringe after the impact event. A cavity immediately starts forming between the liquid column and the syringe: the syringe is moving, but the liquid column is still stationary.
The pressure inside the cavity is vapor pressure, creating a net force oriented in the negativezdirection applied on the syringe. The equation of motion for the syringe is:
us(t)=u0− (P0−Pvap)Ait ms
. (4.6)
This equation indicates the syringe experiences a linear deceleration as a result of the low pressure which subsists inside the cavity forming between the syringe and the liquid water. Equivalently, the low pressure in the cavity creates a net force oriented in the positive z direction applied on the water column. The equation of motion for the liquid column is:
ul(t)= (P0−Pvap)t ρlLl
. (4.7)
The difference in velocity∆u(t)between the syringe and the liquid column dictates the growth and collapse of the cavity. The velocity difference is:
∆u(t)=us(t) −ul(t)= u0− (P0−Pvap)t Ai
ms + 1 ρlLl
, (4.8)
141 and the volume of the cavity is:
Vcav(t)= Ai
∫ t 0
∆u(t0)dt0=u0t Ai− Ai(P0−Pvap)t2 2
Ai
ms + 1 ρlLl
. (4.9) The collapse time is obtained whenVcav = 0. The nontrivial solution ofVcav = 0 fromEquation 4.9is:
tcollapse= 2u0msρlLl
(P0−Pvap) (AiLlρl +ms) . (4.10) Evaluating with numbers that are representative of the experiments (u0= 3 m/s, ρl = 1,000 kg/m3, Ll= 0.286 m,P0= 101,325 Pa,Pvap= 2,300 Pa, and Ai= 1.14× 10−3m3) yieldstcollapse= 12.1 ms, in very reasonable agreement with the measured value of 11.5 ms.
The hoop and axial strains for case 10 are shown inFigure 4.36. The hoop strains confirm the pressure pulse forms at the bottom wall (label 2) and propagates upward at the Korteweg speed, toward the free surface. A precursor wave also forms in the syringe wall, visible from the detectable hoop deformation occurring prior to the arrival of the pressure pulse (i.e., strains to the left of the oblique line indicating the Korteweg speed). The pressure pulse reflects on the free surface (label 3) as a tension wave. The reflected tension wave, upon reflection on the bottom wall, initiates the second cavitation event (label 4).
The peak magnitude of the hoop strains is approximately 212 µ. The quasi-static, thin shell theory (Equation 3.2) is used to estimate the magnitude of the pressure pulse needed to create a 212µhoop strain. A value of 2.1 MPa is obtained, and this is not in agreement with the measured peak pressure of 8.0 MPa. In other words, an 8.0 MPa pressure pulse is expected to create hoop strains that are significantly larger than 212µ. The zoomed-in view of the pressure pulse shown in the top-right corner ofFigure 4.35 provides an explanation for this. Although the pressure does reach a peak value of 8.0 MPa, the pressure does not remain this large for an extended period of time: the pressure is greater than 2.5 MPa for only 6µs.
There are three reasons why the short pulse is not visible in the hoop strains: 1) the frequency response of the strain gauges and signal conditioners is not large enough to capture such short pulses; 2) the sharp pressure pulse attenuates as it travels away from the end of the tube; 3) inertial effects in the syringe wall are important, and the wall of the tube can’t respond this fast to a pressure pulse. The transit time of the waves for a round trip through the thickness of the tube is 4.2 µs, comparable to
-1 0 1 2 3 0.1
0.2 0.3
0 200 100 300 400
(a) Hoop strains
-1 0 1 2 3
0.1 0.2 0.3
0 -100
200
-200 100
(b) Axial strains
Figure 4.36: Hoop and axial strains for case 10 of the dynamic, large-scale model autoinjector experiments (test LS-0322).
143 the 6µs duration of the pressure pulse, and the natural period of motion in the hoop direction is 75 µs (seeEquation 4.12discussed below), longer than the duration of the pulse. The pressure however remains around 2.0 MPa for an extended period of time, close to 0.5 ms, creating the measurable 212 µ.
The peak magnitude of the axial strains is 121 µ in tension, and -96 µ in com- pression. The axial strains result from both the Poisson effect and the pressure force applied on the tip. The pressure force applied on the tip tends to create a tensile axial stress in the syringe walls, while the Poisson effect tends to create a compressive stress. The two effects are competing, resulting in complex interactions. The axial strains confirm there is a detectable precursor wave traveling in the syringe wall, ahead of the pressure pulse and to the left of the oblique line indicating the Korteweg speed. The precursor wave creates a tensile axial strain of 49 µ.
A quasi-static thin shell approximation is used to estimate the magnitude of the tensile stress wave created by the pressure force applied in the tip, and, in turn, the magnitude of the precursor axial strain:
z = PRi2
(Ro2−Ri2)E . (4.11)
This quasi-static estimate is adequate as long as the rise time of the pressure P is small compared to the natural period of oscillationTof the tube in the hoop direction (Shepherd and Inaba, 2010):
T = π(Ri+ R0) s
ρs(1−ν2)
E , (4.12)
equal to approximately 75 µs for the aluminum syringe. The expected value ofz
for a 2 MPa pressure applied on the tip is 44 µ, close to the measured magnitude of 49 µ. Note that the stress wave in the syringe wall reverberates multiple times, creating oscillatory axial strain signals over a long period of time. Note that the axial transit time for a round trip of the stress wave in the axial direction is approximately 125 µs.
A repeat test was performed with a clear, polycarbonate syringe, referenced as test case 10b. The pressure in the syringe is shown in Figure 4.37, and it is similar to what was obtained for case 10. Figure 4.38is a sequence of images of the cavitation event inside the syringe, in the vicinity of the tip. The time stamp above each frame can be used to position the frames on the pressure plot fromFigure 4.37.
-15 -10 -5 0 5 10 15 20 25 30 0
1 2 3 4 5 6 7 8
-0.5 0 0.5 1 1.5 0
2 4 6 8
Figure 4.37: Pressure at the bottom wall for case 10b of the dynamic, large-scale model autoinjector experiments.
Initially (-16.0 ms), no cavitation is observed. The syringe is stationary, and the pressure inside corresponds to ambient pressure. The impact of the projectile on the syringe wall occurs at around -15.0 ms, causing the syringe to rapidly accelerate.
The tension waves created by the acceleration of the wall and the tip reduce the pressure to vapor pressure, promptly initiating cavitation. A distributed cavitation event occurs away from the tip, where multiple relatively small bubbles form and collapse from -14.9 ms to -11.7 ms. There is a column separation event at the very bottom of the syringe.
The column separation event begins with the formation of multiple small bubbles attached to the flat wall at -14.9 ms. From -13.8 ms to -11.7 ms, the bubbles grow and coalesce to form a single cavity which occupies the entire cross section of the syringe. This is followed by the vertical growth of the cavity until -7.3 ms, and the collapse of the cavity. Complete collapse occurs at 0.0 ms, an event which creates a substantial pressure increase in the tip. This is followed by a second cavitation event, the beginning of which is visible in the last two frames, from 1.3 ms to 2.1 ms.
The duration of the first cavitation event for test 10b is 15.0 ms, longer than the 11.5 ms duration measured for test 10 with the aluminum syringe. The difference
145
Figure 4.38: Sequence of images showing the cavitation event at the bottom of the syringe for test 10b of the dynamic, large-scale model autoinjector experiments (test LS-0382).
is explained by the lower mass of the polycarbonate syringe – 0.36 kg for the polycarbonate syringe and 0.81 kg for the aluminum syringe – which results in the syringe being accelerated to a larger velocity after the impact of the projectile on the syringe wall. The velocity of the syringe after impact is 4.3 m/s for case 10b, compared to 3.3 m/s for case 10.
Adding a buffer at the top of the syringe affects the results significantly. Qualitatively, the measured signals all look alike, but the peak magnitude of the pressure and strains are changed. Figure 4.39is a plot of the peak pressure as a function of initial air gap size. In general, increasing the air gap size results in a larger peak pressure. This trend is investigated further using case 11.
0 5 10 15 1
2 3 4 5 6 7 8 9
Figure 4.39: Peak pressure in the syringe tip as a function of initial air gap size. The outer projectile impacts on the syringe wall. This is for the dynamic, large-scale model autoinjector test setup with a flat tip.
Figure 4.39also indicates there is substantial vertical scatter in the measured peak pressure, both for the aluminum and the polycarbonate syringes. The polycarbonate syringe is used to investigate this further. Results suggest that variability in the position of the bubble with respect to the pressure transducer in the final stage of the collapse is the key factor in determining the peak magnitude of the pressure pulse. A bubble that collapses close to the transducer creates a larger measured pressure than a bubble collapsing far away from the transducer. This is because the magnitude of the pressure waves forming upon bubble collapse decays rapidly. Neglecting the effect of the wall, the decay is expected to be in 1/r, wherer is the distance from the center of the collapsing bubble (Brennen, 1995;Franc and Michel, 2005).
Figure 4.40contains sequences of images of the final stage of bubble collapse for two different test cases. Figure 4.40ais for test case 10b, discussed above. Figure 4.40bis for test case 10c, which is another repeat test with the same experimental conditions.
Figure 4.40aindicates that the final bubble collapse occurs right above the pressure transducer in test case 10b. This results in a peak pressure of 6.0 MPa. It is even possible to observe two successive collapses of the bubble, in agreement with the
147
(a) Test case 10b (test LS-0382)
(b) Test case 10c (test LS-0388)
Figure 4.40: Final stage of bubble collapse for tests cases 10b and 10c performed without a buffer. This is for the dynamic, large-scale model autoinjector.
pressure trace shown inFigure 4.37. The first collapse occurs at 0.0 µs, resulting in a peak pressure of 3.1 MPa. The bubble rebounds, and collapses again 54 µs later.
The second collapse results in a peak pressure of 6.0 MPa.
Figure 4.40bindicates that the final stage of bubble collapse is different for test 10c.
The collapse occurs in the front of the tube, away from the tip of the transducer, and no bubble rebound is observed. The pressure history for this test case is not shown, but the peak pressure is only 3.0 MPa, half the peak pressure measured for test 10b.