TIO N B -B
4.2 Dynamic Large-Scale Model Autoinjector
4.2.4 Results and Discussion: Syringe Deceleration
4.2.4.1 Case 13
the conical tip is as much as 6 times larger than the pressure with a flat tip. Visual observations suggest the geometry of the conical tip forces the bubble to collapse very close to the tip of the cone, where the transducer is located.
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Figure 4.49: Velocity of the syringe for case 13 of the dynamic, large-scale model autoinjector experiments (test LS-0296).
rebounds on the decelerator. The magnitude of the deceleration is approximately 10,000 m/s2. The liquid contained inside the syringe experiences a regime 1 or impulsive type of deceleration (seeChapter 2), andEquation 2.5is used to estimate the peak pressure. The change in velocity ∆uof the syringe is 2.9 m/s, and this is expected to create a pressure pulse with a peak magnitude of 4.4 MPa.
The rapid deceleration of the syringe is followed by a deceleration of much lesser magnitude, indicated with a red-dashed line inFigure 4.49. This occurs between 61 and 65 ms, and again between 66 and 70 ms. The magnitude of the deceleration is 140 m/s2. As before, the cavitation events are responsible for those weak decelera- tions. We recall that the expected magnitude of the deceleration is 141 m/s2, close to the measured value of 140 m/s2.
Figure 4.51is a plot of the pressure in the syringe tip. A few labels are positioned on the plot to identify key features. Label 1 identifies the beginning of the syringe deceleration, creating a compressive pressure pulse in the liquid. The peak pressure resulting from the deceleration is 4.4 MPa, equal to the value predicted using acoustic theory. The pressure pulse predicted using LS-DYNA is also shown, and it is in reasonable accord with the measurements if the acceleration and velocity change
Figure 4.50: Sequence of images showing the motion of the projectile, the buffer and the syringe for case 13 of the dynamic, large-scale model autoinjector experiments (test LS-0296).
are selected to be approximately the same as in the experiments. All the simulation results shown in this subsection are for a 12,000 m/s2deceleration, and a change in velocity of 3 m/s.
The compression wave forms in the tip of the syringe and propagates in the liquid toward the buffer. The wave reflects as a tensile wave on the air-water interface located below the buffer. The reflected wave propagates toward the syringe tip and reflects as a tensile wave on the flat wall, promptly initiating distributed cavitation.
Label 3 identifies the beginning of the first distributed cavitation event. The pressure is constant and approximately equal to vapor pressure throughout the cavitation event. The tensile wave continues to propagate in the water, reflects at the top end of the syringe on the air-water interface as a compression wave, and propagates toward the bottom of the syringe. Label 4 identifies the end of the first cavitation event, marked by a rapid increase in pressure due to the return of the compression wave and the collapse of cavitation bubbles.
This cycle is repeated several times, but the magnitude of the pressure pulse and the severity of the cavitation event decreases between each cycle. The decrease in severity of the cavitation event is inferred from the shortening of the time interval
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LS-DYNA
Figure 4.51: Pressure at the bottom wall for case 13 of the dynamic, large-scale model autoinjector experiments (test LS-0296).
between two successive pressure peaks, indicating an increase in the average wave speed. This, in turn, is directly correlated with a decrease of the average void fraction within the liquid column during the cavitation event (Brennen, 1995).
The hoop and axial strains on the outer surface of the syringe barrel are shown in Figure 4.52. The oblique, dashed lines in Figure 4.52 have a slope which corresponds to the Korteweg speed. The strains result from the combined effect of the hoop stress created by the pressure pulse traveling in the liquid, and the axial stress wave traveling in the syringe wall, created by the contact force between the syringe and the decelerator. The pressure and stress waves travel at different speeds and repeatedly reflect from the ends to create the rather complex strain distributions shown in FigureFigure 4.52. The boundary conditions on the water column are also different from the boundary conditions on the syringe wall. To obtain some insight as to the wave mechanics, a simplified model of the fixture and boundary conditions is considered.
The simplified schematic from Figure 4.53 illustrates the wave mechanics in the water and the syringe walls under the simplifying assumption of no radial stress waves. The schematic is in a moving frame attached to the syringe. The boundary
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LS-DYNA
(a) Hoop strains
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Figure 4.52: Hoop and axial strains for case 13 of the dynamic, large-scale model autoinjector experiments (test LS-0296).
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Figure 4.53: Schematic of the wave mechanics in the syringe wall and the liquid column during and after the syringe deceleration for case 13.
condition at the bottom of the syringe barrel changes over time. During the syringe deceleration, there is a contact between the decelerator and the syringe wall, resulting in the partial transmission and reflection of stress waves upon reaching the interface.
The first reflection of the stress wave at the bottom wall results in no sign change of the axial stress wave. Later on there is a loss of contact between the syringe and the decelerator, and the boundary becomes stress free. The subsequent reflections of the axial stress wave on that boundary result in a sign change. Note that the boundary condition on the top end of the syringe barrel is always a stress free end, and the stress waves always changes sign upon reflection there.
The wave mechanics in the liquid is similar to what is explained in Section 4.1.
The pressure pulse does not change sign upon reflection in the tip. The pressure pulse changes sign when it reflects on the interface between the air gap and the liquid. When no air gap is present, the reflection of the pressure pulse occurs on the moving surface of the buffer; this type of reflection on a moving boundary has been explained inSection 4.2.3.
The pressure and stress waves reverberate multiple times in the system. There is constructive and destructive interference between the multiple waves. The shaded area corresponds to a region where cavitation occurs.
The hoop strains (see Figure 4.52a) primarily result from the hoop stress created by the pressure pulse forming during the rapid deceleration of the syringe (label 1). The hoop strain wave primarily travels at the Korteweg speed, but there is also a precursor wave traveling faster. Close to the top end of the tube, positive hoop strains are observed to the left of the oblique line that indicates the Korteweg speed.
This is because the compressive axial stress wave, which travels in the syringe wall at approximately 5,500 m/s, creates hoop strains through the Poisson effect.
The largest hoop strains are observed close to the bottom end of the syringe. There the maximum hoop strains are approximately 150µ. The hoop strains at the top end of the tube are close to zero, a consequence of the stress free boundary condition.
Label 3 indicates the beginning of a cavitation event, visible in the form of a plateau in the hoop strains. When the cavitation event ends (label 4), the pressure pulse propagating in the liquid becomes visible again, creating a positive hoop strain signal which travels at the Korteweg speed.
The LS-DYNA simulation predicts the hoop strains with reasonable accuracy. It is also possible to estimate the expected maximum hoop strains using a quasi-static thin shell theory (Equation 3.2). A 4.4 MPa pressure wave is expected to create a 194µ hoop strain. The predicted value is of the same order as the measured value (150 µ).
Figure 4.52bis a plot of the axial strains. The axial strains are primarily created by the axial stress wave forming during the rapid deceleration of the syringe (label 1).
The peak magnitude of the axial strains is approximately -220 µ, in compression, close to the tip the syringe. The axial strains close to the top end are negligible, a consequence of the stress free boundary condition. The axial strain wave is observed to travel faster than the Korteweg speed, as expected.
163 The LS-DYNA simulation predicts the axial strains with reasonable accuracy. It is also possible to estimate the magnitude of the axial stress wave usingEquation 2.19.
Assuming a deceleration of 10,000 m/s2, the axial stress wave is σz = -16 MPa.
Under a uniaxial stress assumption, this is expected to create -235µof axial strain, close to the measured value of -220µ.
A repeat test, referenced as test 13b, was performed with the clear, polycarbonate syringe. A sequence of images is shown in Figure 4.54. The buffer is shown at the top, and the flat wall of the syringe tip is shown at the bottom. Before the deceleration, the air gap and the interface between the air and the water are not well defined. Before a test the interface between the water and air is sharp and horizontal, but the transient events created by the acceleration and pressurization of the syringe result in a mixture region.3 This has not been taken into account in the numerical simulations, where a well defined air gap is assumed. This also indicates that assuming the deceleration event isentirelydecoupled from the acceleration and the pressurization events is, in fact, a simplifying assumption.
The wave speed in the mixture region can be significantly different than the wave speed in pure liquid water or air. The relatively good match between the experimental and numerical results however suggests that this has negligible effects on the results.
Figure 4.54indicates the cavitation event can be classified as distributed cavitation.
Cavitation is confined to the bottom half of the syringe. The collapse of the cavitation bubbles occurs from top to bottom, resulting from the slow propagation of the compressive pressure pulse in the bubbly liquid.