9.3.2.2 Case Analysis
Example 1 Checking Gas Pressure p c
It is known that: grain parameters pressure index n ¼ 0:5, unit weight
d ¼ 1:52 g=cm
3 ), ambient temperature T ¼ À40
C, low-temperature burning rate
coefficient a t ¼ 0:88151 g mm/s
MPa , gas temperature T ¼ 1605:6 K, gas flow coefficient A 1 ¼ 7:7888 Â 10
À3
=s, grain diameter d b ¼ 7:7 cm, nozzle diameter
d 0 ¼ 0:23 cm.
Solution p c ¼ 3:57 MPa can be obtained by directly substituting known conditions
into formula (9.31) and k. Compared with the expected design requirement of
p c
½ ¼ 3:5 MPa, the error is þ 2%.
Example 2 Checking Gas Pressure Change Rate a
It is known that grain diameter tolerance d
0
ÀDd b
¼ 7:7
0
À0:01 cm, nozzle diameter
tolerance d
þ Dd 0
0
¼ 0:23
þ 0:003
0
cm.
Solution a ¼ À5:528% can be obtained by directly substituting known conditions
into formula (9.35). It satisfies the experience value a
½ ¼ Æ8% which is usually
allowed in design.
Explanation: 1. Burning pressure change rate depends on the tolerance of characteristic diameter, i.e., manufacturing accuracy, especially nozzle diameter tolerance.
Because of its small absolute value, it is more important than grain diameter tolerance. In engineering, Dd b is guaranteed by the manufacturing accuracy of grain
mold and the shrinkage rate of grain, Dd 0 is guaranteed by the manufacturing
accuracy of nozzle machinery and the high-temperature performance of nozzle
material.
2. Because the gas nozzle works above 1300
C, in order to ensure that the
nozzle aperture is not eroded or corroded by high-temperature gas, the special alloy
with high-temperature coal gas erosion and ablation resistance and corrosion
resistance, no deformation or low deformation must be selected. Engineering
practice has proved that Copper–Titanium alloy TZM is the preferred material and
its performance is superior to that of stainless steel 1Cr18NiTiA and heat-resistant
alloy GH36.
9.3.2.3 Related Discussion
(1) Effect of ambient temperature
The characteristics of gas generator are affected by ambient temperature, which
can be adjusted by setting a gas regulating valve. It is assumed that the ambient
temperature of the grain is constant in the preceding text. In fact, the ambient
temperature of tactical surface-to-air missiles varies greatly, usually from
130
9 High-Temperature and High-Speed Gas Turbine Pump …
Example 1 Checking Gas Pressure p c
It is known that: grain parameters pressure index n ¼ 0:5, unit weight
d ¼ 1:52 g=cm
3 ), ambient temperature T ¼ À40
C, low-temperature burning rate
coefficient a t ¼ 0:88151 g mm/s
MPa , gas temperature T ¼ 1605:6 K, gas flow coefficient A 1 ¼ 7:7888 Â 10
À3
=s, grain diameter d b ¼ 7:7 cm, nozzle diameter
d 0 ¼ 0:23 cm.
Solution p c ¼ 3:57 MPa can be obtained by directly substituting known conditions
into formula (9.31) and k. Compared with the expected design requirement of
p c
½ ¼ 3:5 MPa, the error is þ 2%.
Example 2 Checking Gas Pressure Change Rate a
It is known that grain diameter tolerance d
0
ÀDd b
¼ 7:7
0
À0:01 cm, nozzle diameter
tolerance d
þ Dd 0
0
¼ 0:23
þ 0:003
0
cm.
Solution a ¼ À5:528% can be obtained by directly substituting known conditions
into formula (9.35). It satisfies the experience value a
½ ¼ Æ8% which is usually
allowed in design.
Explanation: 1. Burning pressure change rate depends on the tolerance of characteristic diameter, i.e., manufacturing accuracy, especially nozzle diameter tolerance.
Because of its small absolute value, it is more important than grain diameter tolerance. In engineering, Dd b is guaranteed by the manufacturing accuracy of grain
mold and the shrinkage rate of grain, Dd 0 is guaranteed by the manufacturing
accuracy of nozzle machinery and the high-temperature performance of nozzle
material.
2. Because the gas nozzle works above 1300
C, in order to ensure that the
nozzle aperture is not eroded or corroded by high-temperature gas, the special alloy
with high-temperature coal gas erosion and ablation resistance and corrosion
resistance, no deformation or low deformation must be selected. Engineering
practice has proved that Copper–Titanium alloy TZM is the preferred material and
its performance is superior to that of stainless steel 1Cr18NiTiA and heat-resistant
alloy GH36.
9.3.2.3 Related Discussion
(1) Effect of ambient temperature
The characteristics of gas generator are affected by ambient temperature, which
can be adjusted by setting a gas regulating valve. It is assumed that the ambient
temperature of the grain is constant in the preceding text. In fact, the ambient
temperature of tactical surface-to-air missiles varies greatly, usually from
130
9 High-Temperature and High-Speed Gas Turbine Pump …