124
P. Liu
Substituting into the continuous equation to get
(Ma
2
− 1)
dV
V
=
d A
A
It can be seen from the above formula:
(1) for subsonic (including low velocity) flow, if the pipe section shrinks,
the flow velocity increases, and the area expansion flow velocity
decreases;
(2) for supersonic (including low-speed) flow, if the cross section of the
pipe shrinks, the flow rate will decrease, and the flow rate of area
expansion will increase;
(3) the change rule of velocity and cross-sectional area of supersonic
section is opposite to subsonic speed, because the contribution of
density change to the continuous equation is different at supersonic
speed and subsonic speed. The change in density in subsonic is slower
than that in velocity, while that in supersonic is faster than that in
velocity.
It can be seen that for a one-dimensional isentropic pipe flow, if the
airflow is to be continuously accelerated from subsonic speed to supersonic
speed along the pipe axis, that is, to keep dV > 0 all the time, the pipe
should be contracted first and then expanded, with the minimum section
in the middle, that is, the throat. This shape of the pipe is called a Laval
pipe or nozzle, and the contraction type and Laval nozzle are shown in
Fig. 2.59. Figure 2.60 shows the supersonic jet flow in the tail nozzle of
the engine.
2. Broadcast interface and Mach wave of disturbance wave
When the object is moving in the still air, the influence range and the
influence way of different moving speeds on the air are different. The
so-called disturbance refers to the change in the speed, density, pressure,
Fig. 2.59 Retractable and Laval Nozzles
P. Liu
Substituting into the continuous equation to get
(Ma
2
− 1)
dV
V
=
d A
A
It can be seen from the above formula:
(1) for subsonic (including low velocity) flow, if the pipe section shrinks,
the flow velocity increases, and the area expansion flow velocity
decreases;
(2) for supersonic (including low-speed) flow, if the cross section of the
pipe shrinks, the flow rate will decrease, and the flow rate of area
expansion will increase;
(3) the change rule of velocity and cross-sectional area of supersonic
section is opposite to subsonic speed, because the contribution of
density change to the continuous equation is different at supersonic
speed and subsonic speed. The change in density in subsonic is slower
than that in velocity, while that in supersonic is faster than that in
velocity.
It can be seen that for a one-dimensional isentropic pipe flow, if the
airflow is to be continuously accelerated from subsonic speed to supersonic
speed along the pipe axis, that is, to keep dV > 0 all the time, the pipe
should be contracted first and then expanded, with the minimum section
in the middle, that is, the throat. This shape of the pipe is called a Laval
pipe or nozzle, and the contraction type and Laval nozzle are shown in
Fig. 2.59. Figure 2.60 shows the supersonic jet flow in the tail nozzle of
the engine.
2. Broadcast interface and Mach wave of disturbance wave
When the object is moving in the still air, the influence range and the
influence way of different moving speeds on the air are different. The
so-called disturbance refers to the change in the speed, density, pressure,
Fig. 2.59 Retractable and Laval Nozzles