3.1. Mach Number, Static Pressure, and Velocity Friction Fields
The results are described referring to the Supplementary Material
, which are compounded by five videos that show the Mach number, the static pressure, and the friction velocity. The time interval between each frame is 0.01 s. The Mach number is shown in the Video S1
(xy plane) and Video S2
(xz plane), the static pressure along the plane xy is the Video S3
, while the plane xz is the Video S4
. The friction velocity is shown in Video S5
. Only the more significant frames of these videos are shown in the paper.
At 0.01 s of the beginning, due to the very high expansion ratio, the incoming air accelerates in the duct sonically and then supersonically in the vacuum vessel: a high Mach number flow bubble is observed just at the exit of the penetration line. Then, the jet slows down due to friction with the surrounding air at rest (Figure 3
The duct is pressurised with respect to the vessel, and a shock wave, which separates the jet from air at rest in the Tokamak starts to propagate inside it (Figure 4
). The friction velocity is very high in the duct, due to the high speed, but also on the walls in the surroundings of the connection between the penetration line and vessel (Figure 5
). An increase in the Mach number and pressure inside the duct is observed with the increase of time. At 0.02 s, the flow is slightly supersonic already inside the duct, because of the pressure increase at the inlet and the subsequent propagation downstream of the disturbance: the flow accelerates up to supersonic speed in the duct and continues its expansion inside the vessel.
The jet has travelled for approximately one-third of the distance between the duct connection to the vessel and the opposite wall. A low-pressure zone (about 60 Pa, less than the initial value of it) is observed in the region where the jet expands, while a recompression bubble forms downstream the jet. What is seen is that the incoming air forms an over expanded jet, which is subsequently recompressed. A bubble of air at pressure higher than that of the rest of the vessel forms and precedes the propagation of the jet. The friction speed increases as the jet is getting faster, and the surface of the walls that are exposed to the movement of the air gets bigger.
After only 0.03 s, the jet reaches the middle of the space between the duct-vessel connection and the opposite wall, while the high-pressure bubble touches it. The zone where the friction velocity is high gets larger and larger.
After 0.04 s, the jet has almost reached the wall, as well as the recompression bubble. The region where the friction speed is high continues to enlarge, as the jet expands and fills the vacuum vessel. It can be noticed that its maximum value does not differ appreciably from the one at 0.02 s and 0.03 s.
At 0.05 s, the recompression bubble, which precedes the front of the jet, has reached the wall (Figure 6
). The jet has, in the region just downstream of the connection between the duct and the vessel, and just before the recompression bubble, a lower pressure than that in the undisturbed part of the Tokamak (100 Pa): overexpansion still occurs. As shown by the contour lines, the flow is reaching the rear part of the Tokamak, but the highest values of the friction speed are still in the duct and in the region of the connection between it and the vessel, due to the high speed of the flow. It can also be noticed that a high friction speed zone on the part of the wall where the jet impingement occurs appears: this means that after 0.05 s, appreciable resuspension on that part of the internal blanket has to be expected.
The front of the jet has reached the wall and a stagnation point forms at 0.06 s. In the Mach field, a slight asymmetry of the flow is noticed: the stream of air deviates in the y-positive direction when the jet comes into contact with the wall. This instability is due to the fact that the jet is getting compressed in its frontal zone, so it tends to deviate and to divide into non-perfectly identical streams, although all of the initial and boundary conditions are symmetrical. An increase of pressure is noticed around the stagnation point and the overexpansion zone at the front of the jet is squeezing because the jet tends to move forward while the wall blocks it.
At 0.07 s, the jet breaks into two streams on the xz plane. An acceleration of it occurs just after the stagnation point, as there is room for the jet to move and continue expanding. As the jet impinges the wall, the frontal overexpansion region breaks on the xz plane and moves downstream: the two jets that are resulting from the division of the incoming original stream accelerate, as seen in Figure 7
, and therefore the pressure drops under the one of the air at rest. Figure 8
shows how greatly the high friction speed zone has grown on the wall. Due to the impingement of the high-speed jet and of the two streams that form after the impact on the wall, shear stresses are very high and affect a large part of the walls.
At 0.08 s, there is an increase of the Mach number, due to the rise of the total pressure at the inlet and therefore of the expansion ratio, the displacement downstream on the xz plane of the acceleration (and low speed zones) and the enlargement of the high friction speed region around the impingement point.
The frames at 0.09 s show the same trends for all of the properties mentioned above. The friction speed pattern shows low values around the stagnation point, because the speed is low, then a steep increase due to the acceleration of the flow, and finally a fast decrease to very low values as the flow is supersonic and has not reached yet all of the points of the vacuum vessel.
The same trends are confirmed also at 0.1 s: a deeper penetration of the jet inside the vacuum chamber, an acceleration of the flow due to the high expansion ratio and an enlargement of the high friction speed zone.
After 0.2 s, it can be seen that the flow inside the duct is highly supersonic (roughly Mach 3) and that the flow is reaching the rear part of the vessel. The flow divides into two streams also on the xy plane and starts moving towards the duct-vessel connection: two toroidal counter-rotating vortices form at the margins of the jet and are filling the vessel.
The frames from 0.2 s to 2.0 s show a progressive increase of the Mach number inside the duct, as well as a deep penetration of the incoming air into the vacuum vessel. Instant by instant, a larger and larger surface of the walls is subject to interaction with the blowing flow, and therefore to friction (Figure 8
and Figure 9
). The Mach number grows up to values up to 6, value for which the static temperature drops from 293.15 K (initial temperature in the vessel and total temperature at the inlet during all of the transient) to 36 K. Of course, when temperature gets so low, the real behaviour of the fluid deviates from the one of a perfect gas and condensation phenomena may occur. However, as these extreme values of the Mach number and temperature are reached only in a very small region (the duct), and that in the vessel the Mach number reaches maximum values of about 3, it can be said that the perfect gases state equation is valid on the overall domain, and, what is more important, inside the Tokamak, which is what this investigation is focused on.