the nozzle outlet speed, so as to achieve the optimal characteristic ratio and achieve
high efficiency. But in doing so, it is necessary to use working fluids with low
enthalpy, such as compressed air. For the same working time and the same power
output, the weight and size of the whole device will increase a lot, so it is not advisable.
Another way to reduce the loss of residual kinetic energy is to adopt a
double-ring wheel structure in turbines. At this time, the exhaust of the first row of
moving blades passes through the steering blades and then enters the second row of
blades to work, so the residual kinetic energy can be fully recovered. If a preliminary estimate is made for this example, the effective power of 2:7 kW h can be
obtained from the second row of blades. Its speed is still 6000 r=min, and the total
power can reach 7:7 kW. It seems to be more profitable than increasing the speed,
but the complex structure of the double-ring wheel makes it more difficult to
process the impeller and more demanding to install it. Moreover, it is obvious that
the weight of the rotor must be almost doubled and the axial size of the plate
doubled, which is unfavorable to the axial bearing capacity of the cantilever rotor.
When the rotor is balanced, it is possible to make double-sided balancing (dynamic
balancing). In addition, the structure of the shell is more complex, the corresponding weight and size are increased, so the cost is not small.
9.4.3 Graphical Analysis Method for Stress of Small Gas
Turbine Disk for Missile
The gas turbine of missile uses the gas produced by retarded propellant as the
working medium. Because of the high temperature and pressure
(p 0 ¼ 4:0 $ 5:0 MPa; t 0 ! 1200
C), the gas has a high enthalpy value, i.e., the
available work of working medium per unit weight. In order to make the turbine
work at the optimum efficiency point, it is necessary to adopt a high rotational speed
of the disk. Obviously, it is necessary to estimate the stress of the disk in the
preliminary design.
Firstly, the simple impeller with equal thickness is analyzed and the force
equilibrium equation is established. For small gas turbine disks for missiles, the
axial thickness is relatively thin, so they can be treated as plane stress. A unit body
is arbitrarily intercepted from an equal thickness plate (Fig. 9.48). Its range is
surrounded by dr, d/, and unit length dz ¼ 1. Obviously, the centrifugal force
produced by its own mass is as follows
rx
2 dm ¼ rx
2
qrd/dr ¼ qx
2 r
2 d/dr
where
q Material density;
x Disk angular velocity.
144
9 High-Temperature and High-Speed Gas Turbine Pump …
high efficiency. But in doing so, it is necessary to use working fluids with low
enthalpy, such as compressed air. For the same working time and the same power
output, the weight and size of the whole device will increase a lot, so it is not advisable.
Another way to reduce the loss of residual kinetic energy is to adopt a
double-ring wheel structure in turbines. At this time, the exhaust of the first row of
moving blades passes through the steering blades and then enters the second row of
blades to work, so the residual kinetic energy can be fully recovered. If a preliminary estimate is made for this example, the effective power of 2:7 kW h can be
obtained from the second row of blades. Its speed is still 6000 r=min, and the total
power can reach 7:7 kW. It seems to be more profitable than increasing the speed,
but the complex structure of the double-ring wheel makes it more difficult to
process the impeller and more demanding to install it. Moreover, it is obvious that
the weight of the rotor must be almost doubled and the axial size of the plate
doubled, which is unfavorable to the axial bearing capacity of the cantilever rotor.
When the rotor is balanced, it is possible to make double-sided balancing (dynamic
balancing). In addition, the structure of the shell is more complex, the corresponding weight and size are increased, so the cost is not small.
9.4.3 Graphical Analysis Method for Stress of Small Gas
Turbine Disk for Missile
The gas turbine of missile uses the gas produced by retarded propellant as the
working medium. Because of the high temperature and pressure
(p 0 ¼ 4:0 $ 5:0 MPa; t 0 ! 1200
C), the gas has a high enthalpy value, i.e., the
available work of working medium per unit weight. In order to make the turbine
work at the optimum efficiency point, it is necessary to adopt a high rotational speed
of the disk. Obviously, it is necessary to estimate the stress of the disk in the
preliminary design.
Firstly, the simple impeller with equal thickness is analyzed and the force
equilibrium equation is established. For small gas turbine disks for missiles, the
axial thickness is relatively thin, so they can be treated as plane stress. A unit body
is arbitrarily intercepted from an equal thickness plate (Fig. 9.48). Its range is
surrounded by dr, d/, and unit length dz ¼ 1. Obviously, the centrifugal force
produced by its own mass is as follows
rx
2 dm ¼ rx
2
qrd/dr ¼ qx
2 r
2 d/dr
where
q Material density;
x Disk angular velocity.
144
9 High-Temperature and High-Speed Gas Turbine Pump …