3.1. Temporal Evolution of Global Bubble Shapes
In order to show the effect of the anisotropic beams on bubble shapes,
Figure 2,
Figure 3 and
Figure 4 show the transient evolution process of bubble morphology at three different initial bubble positions, i.e.,
γ = 1.65, 1.32, and 1.00. When the normalized parameter
γ is more than 1.65, the cases show almost no specific phenomenon, but instead show the buoyancy effect.
Figure 2 shows the front and side views of the transient evolution of the shape of the bubble near the C-1 and C-2 plates when
γ = 1.65. As shown in
Figure 2a, it can be observed from the front view that when the time was
t = 0–4.83 ms (the first bubble oscillation period), the bubble near the C-1 plate expanded and contracted as a sphere. When the time was
t = 3.00 ms, the bubble reached its maximum volume, and when the time was
t = 4.83 ms, the bubble shrunk to its minimum volume. It should be noted that during the first oscillation period, the center of the bubble moved obviously. When the time was
t = 5.25–10.50 ms, the bubble expanded and contracted many times. In this process, the center position of the bubble began to change and moved to the left (negative
x-axis direction). From the side view, it can be seen that the bubble expanded and contracted as a sphere during the whole observation period, and there was no obvious migration movement. In contrast, when the bubble oscillated near the C-2 plate, the front view showed that the bubble expanded, contracted, and collapsed in the first cycle with time
t = 0–4.83 ms. In this process, the bubble did not move obviously. When
t = 6.70–10.50 ms, the migration trajectory of the bubble was slightly upward to the left. The side view shows that when the time was
t = 0–4.83 ms, the bubble still expanded, contracted, and collapsed as a sphere in the first cycle. When
t = 6.70–10.50 ms, the bubble moved to the left and slightly upward.
Figure 3 shows the front and side views of the transient evolution of the bubble near the C-1 and C-2 plates when
γ = 1.32. Similarly, in the period of
t = 0–3.00 ms, the bubble oscillated from the C-1 plate and C-2 plate with a spherical expansion. The bubble kept in situ oscillation during
t = 4.50–4.83 ms, and its center position did not change. When the time was
t = 5.25–9.00 ms, the second cycle of expansion and collapse of the bubble began near the C-1 and C-2 plates. The difference was that, at the beginning of the second collapse cycle, the bubble near the C-1 plate migrated to the left and down in the front view, but moved directly downward in the side view. The bubble near the C-2 plate moved to the left and down in the front view, and also moved to the left and down in the side view.
Figure 4 shows the front and side views of the transient evolution of the bubble near the C-1 and C-2 plates when
γ = 1.00. In the front view of the C-1 plate, the bubble reached its maximum volume at
t = 1.50 ms, the bottom surface of the bubble contacted the wall structure, and the free end of the C-1 plate obviously moved downward. When the time was
t = 3.00–4.50 ms, due to the oscillation of the plate, the bubble gradually formed a mushroom shape. However, due to the larger displacement of the free end than that of the fixed end, the deformation of the right side of the bubble was larger than that of the left side. When the time was
t = 4.70–5.00 ms, the second cycle of the expansion process started from the lowest volume. In this process, the bubble split into two parts and the upper part of the sub bubble moved upward to the left, while the lower molecular bubble adhered to the surface of the structure wall, and the left side of the lower molecular bubble was higher than the right side. For the front view of the C-2 panel, although the fiber ply angle of the wall structure is different, the bubble collapse morphology was very similar to the bubble near the C-1 plate, so we will not repeat here. In the side view of C-1 plate, the bubble expansion, collapse, and rebound stages were very similar to those near the elastic boundary, resulting in a symmetrical mushroom shape. In addition, the mushroom-like bubble formed two sub-bubbles with a vertical wall structure and motion in opposite directions. In the side view of the C-2 plate, an asymmetric mushroom-like deformation on the right side was larger than that on the left side in the first oscillation period (
t = 0–4.5 ms). When the time was
t = 4.70–5.00 ms, the bubble split into two sub-vacuoles. The lower sub-bubble was attached to the surface of the structure wall, the upper terminal bubble was a point-like bubble, and migration occurred.
In order to clearly and intuitively describe the bubble morphology, the comparison of the front and side views of bubble collapse near the C-1 plate and the C-2 plate is given in
Figure 5 and
Figure 6, respectively. For the front view shown in
Figure 5, the bubble morphology and migration direction near the C-1 and C-2 plates were similar to each other. When
γ = 1.65, the bubble moved to the upper left; when
γ = 1.32, the bubble moved to the lower left; and when
γ = 1.00, the bubble split into two parts, and the upper molecular bubble moved to the upper left while the lower molecular bubble adhered to the surface of the structure wall. For the side view shown in
Figure 6, all the bubbles near the C-1 plate migrated along the direction of gravity, but the direction of bubble migration near the C-2 plate was deflected. The experimental results show that the bending effect of the C-1 plate makes the trajectory of the bubble deflect and migrate only in the front view, which makes a certain angle with the direction of gravity. In contrast, due to the bending-twisting coupling effect of the C-2 plate, the migration trajectory of the bubble makes an angle with the direction of gravity in the front view and the side view.
Figure 7 shows the comparison of bubble collapse times near the C-1 and C-2 plates. The normalized time of bubble collapse
τ∗ is defined as:
where
tB is the time from bubble inception to minimum volume, and
tOSC is defined as the Rayleigh oscillation time of the bubble. In order to compare this value with other typical wall collapse times, the bubble collapse time near a rigid wall reported by Brujan et al. [
23] and Best et al. [
24], and the bubble collapse time near a free surface reported by Hung and Hwangfu [
15], Tomita et al. [
17], Zhang et al. [
25], and Best et al. [
24] are also included in the figure. As shown in the figure, the bubble collapse time near the C-1 and C-2 plates is between the values for collapse near the rigid wall and near the free surface. At the same time, the collapse time of the bubble near the C-1 plate and the C-2 plate is slightly longer than one for different initial positions of the bubble. However, the collapse time of the bubble near C-1 and C-2 was consistent, which indicates that the coupling effect of bending and twisting of the C-1 plate does not affect the collapse time of the bubble.
3.2. Characterization Method of Curved Bubble Migration
In order to quantitatively describe the corresponding relationship between the bubble curve migration trajectory and the bending-twisting coupling effects of composite materials, the bending angle, twisting angle, and bubble trajectory parameters of the composite plate are shown in
Figure 8. The response process of the board was measured by an image-processing method. As shown in
Figure 8b, the bending angle of composite plate is defined as:
where
hL and
hR are the heights of the two ends of the long side of the composite plate from the bottom of the water tank. The trajectories of the bubble are mapped to a curve in the front view:
where
r1 is the linear distance mapped by the trajectory of bubble migration in the front view, and
αxz is the angle between the line
r1 and the direction of gravity. It is worth noting that both
r1 and
αxz are time dependent variables. Similarly, as shown in
Figure 8c, the twisting angle of composite plate is defined as:
where
uL and
uR are the height from the two ends of the short side of the composite plate to the bottom of the water tank. The mapping of the bubble migration trajectory in the side view can be defined as:
where
r2 is the linear distance mapped by the trajectory of bubble migration in the side view, and
αyz is the angle between the line
r2 and the direction of gravity.
In order to clearly understand the physical meaning of the variables
βxz,
r1, α, and
αzx, the physical meaning of the mapping trajectory (
r1,
αzx) between the bending angle
βxz and the bubble migration in the front view is given in
Figure 9. For
βxz, when
βxz > 0, the position of the left endpoint of the middle section of the long side of the composite material is higher than that of the right endpoint, indicating that the free end of the composite plate has risen; when
βxz < 0, the position of the right endpoint of the middle section of the long side of the composite material is higher than the left endpoint, indicating that the free end of the composite plate has sunk. Since
r1 and
αxz jointly determine the position of the bubble migration at a certain time, the physical relationship between them must be considered at the same time. The values of
r1 = 0 and
αzx = 0 indicate that the bubble oscillates at a fixed position and there is no migration. Under the condition of
r1 > 0, when
αxz is 0°, 90°, and 180° the bubble migrates downward, leftward, and upward, respectively; when 0 <
αxz <90°, the bubble migrates to the left and down; when 90°<
αxz < 180°, the bubble migrates to the upper left. Similarly,
Figure 10 gives the physical meaning of the mapping trajectory (
r2,
αyz) between the twisting angle (
βyz) of the composite and the bubble migration trajectory (
r2,
αyz) in the side view.
3.3. Effect of Bending-Twisting Coupling of Plate on Bubble Migration
Figure 11 shows the relationship between the bending effect of the C-1 plate at different initial positions of the bubble and the direction of bubble migration. When the initial position of the bubble is
γ = 1.65, the trajectory of the bubble and the deformation of the C-1 plate are observed and projected on the front view. When the time is
t = 0–4.83 ms, the length and deflection angle of the bubble trajectory are
r1 = 0 and
αzx = 0, respectively, which indicates that the bubble oscillates in situ during this period; meanwhile, the bending angle
βzx < 0° of the C-1 plate indicates that the free end of C-1 plate is in the process of subsidence, and the value decreases first and then increases. When the time is
t = 4.83–8.00 ms, values of
r1 > 0 and 90° <
αzx < 180° indicate that the bubble moves to the left and up; the bending angle (
βzx) of the C-1 plate is less than 0° at first, and then greater than 0° after
t = 6.0 ms, indicating that the free end of the C-1 plate changes from a sinking state to an upward state. The trajectory of the bubble and the deformation of the C-1 plate were observed quantitatively in the lateral view. It was found that the twisting angle of the C-1 plate always fluctuated up and down at
βyz = 0° during the whole process of motion. This shows that there was no twisting effect of the C-1 plate under the action of bubble collapse. When the time is
t = 0–5.5 ms, the length and deflection angle of the bubble trajectory are
r2 = 0 and
αyz = 0°, respectively, indicating that there is no migration of the bubble in this time period; when the time is
t = 5.5–8.0 ms, the
r2 > 0 and
αyz = 0° values of the bubble indicate that the direction of the bubble migration is vertically downwards.
When the initial position of the bubble is γ = 1.32, the trajectory of the bubble and the deformation of the C-1 plate are observed and projected on the front view. When the time is t = 0–4.83 ms, the length and deflection angle of the bubble trajectory are r1 = 0 and αzx = 0, respectively, which indicates that the bubble oscillates in situ in this time period; meanwhile, the bending angle βzx < 0° of the C-1 plate indicates that the free end of the C-1 plate is in the process of subsidence, and the value decreases first and then increases. When the time is t = 4.83–8.00 ms, values of r1 = 0 and αzx < 90° indicate that the bubble moves downward to the left; the bending angle (βzx) of the C-1 plate is less than 0° at first, and then greater than 0° after t = 6.0 ms, indicating that the free end of C-1 plate changes from a sinking state to an upward state. The trajectory of the bubble and the deformation of the C-1 plate are observed quantitatively in the lateral view. It was found that the trajectory of the bubble is the same as that of the C-1 plate in a twisting state; that is, the bubble moves vertically downward, and the plate has no twisting deformation. It was also found that the length and deflection angle (r1, αzx) of the bubble trajectory are divided into two branches when the time is 4.5 ms: one group has values of r1 > 0 and 90° < αzx < 180°; and the other group has values of r1 > 0 and αzx < 90°, which indicates that the bubble is divided into two parts. The former moves to the upper left, and the latter to the lower left.
For the side view projection of γ = 1.00, the value of βzx = 0° for the C-1 plate indicates no twisting deformation; the length and deflection angle (r2, αyz) of the bubble track are also divided into upper and lower parts. Through the above analysis, it can be seen that under the bending effect of the C-1 plate, the bubble does not move in the first period, and after collapse, its trajectory is no longer vertical up and down in the projection of the front view but instead it makes a certain angle with the direction of gravity; however, the trajectory of the bubble still moves vertically up and down under the projection of the side view.
Figure 12 shows the effect of the bending-twisting coupling effect on the bubble migration direction of the C-2 plate at different initial positions of the bubble. When the initial position of the bubble is
γ = 1.65, 1.32, and 1.00, it was found that the trajectory of the bubble and the deformation of the C-2 plate in the front view are very similar to those of the C-1 plate. The reason for this is that the migration path of the bubble on the front view projection is curved due to the bending deformation of the plate. Therefore, the front view of the C-2 plate will not be analyzed in detail. When the initial position of the bubble is
γ = 1.65, the trajectory of the bubble and the deformation of the C-2 plate are projected on the side view. The values of
r2 = 0 and
αyz = 0° indicate that there is no movement of bubble in this period; the twisting angle of
βzx < 0° for the C-2 plate is less than 0°, which indicates that the C-2 plate has obvious twisting deformation, and the left endpoint of the plate is higher than the right endpoint. When the time is
t = 4.50–8.00 ms, the length and deflection angle of the bubble trajectory are
r2 > 0 and 90° <
αyz < 180°, indicating that the bubble moves upward to the left; the twisting angle of the plate is
βzx > 0° after
t = 5.8 ms, indicating that the left endpoint of the bubble is lower than the right endpoint.
For the condition γ = 1.32, the twisting trend of the C-2 plate in the whole process is similar to that of the condition γ = 1.65: when the time is t = 0–4.8 ms, the bubble center remains unchanged; when the time is t = 4.8–8.0 ms, the length and deflection angle of the bubble trajectory are r2 > 0 and αyz < 90°, indicating that the bubble moves downward to the left.
For the condition of γ = 1.00, the motion of the bubble is more complex. In the first period (t = 0–4.5 ms), the bubble center remains unchanged; however, when t = 4.5–8.0 ms, the length and deflection angle (r1, αxz) of the bubble trajectory are divided into two branches, one group with values of r1 > 0 and 90° < αxz < 180° and the other group with values of r1 > 0 and αxz < 90°, indicating that the bubble is divided into two parts. The former moves to the upper left, and the latter to the lower left. At the same time, the twisting angle of the plate is the same as that of the working conditions for γ = 1.65 and 1.32.
In order to further study the difference between the bending-twisting coupling effect of the C-2 plate and the bending effect of the C-1 plate on the path of bubble migration,
Figure 13 shows the curve of the bubble migration path ratio (
Sd) near the C-1 and C-2 plate with the different initial positions of the bubble. The data show that the distance of bubble migration near the C-2 plate is more than that near the C-1 plate; this data was obtained by calculating the mapping trajectory of the bubble migration curve in the side view. As shown in the figure, when the initial distance of the bubble is
γ = 1.00, the distance ratio is
Sd = 5%; when the initial distance is increased to
γ = 1.32, the distance ratio increases to
Sd = 30%; and when
γ = 1.65, the distance ratio decreases to
Sd = 8%. After that, the distance ratio is almost zero. This is because when the bubble is close to the plate, the bubble adheres to the surface of the wall structure, and the bubble cannot move. However, when the initial distance is far away, the force exerted by the plate on the bubble is very small, and the bubble almost collapses in Rayleigh oscillation. It can be seen from the figure that when the bubble is between 1.00 <
γ < 1.75, the migration of the bubble will present a curve track due to the bending-twisting coupling effect of the anisotropic composite plate, which increases the distance for the bubble to reach the structural wall and significantly consumes the kinetic energy of the high-speed fluid generated by the collapse of the bubble, thus reducing the impact of the high-speed fluid on the structural wall.