where
A b Area of grain (cm
2 ).
In Eq. (9.27), the burning rate of grain is
r ¼ a t p
n
c
ð9:28Þ
According to the principle of gas flow continuity, the weight flow through the
nozzle should be equal to the weight flow out of the grain. After sorting out, it
can be obtained,
p c ¼ d
a 1
A t
A b
A 0
1
1Àn
ð9:29Þ
Set n ¼ 0:5, substituting K ¼ d
a 1
A t
, it is obtained
p c ¼ k
2 A b
A 0
2
ð9:30Þ
(4) Functional relationship between gas pressure and characteristic diameter
From the simplification of the above equation, it is obtained
p c ¼ k
2 d b
d 0
4
ð9:31Þ
where
d b Grain diameter (cm);
d 0 Nozzle throat diameter (cm).
(5) Functional relationship between gas pressure change rate and relative change
rate of characteristic diameter
Equation
a ¼
1 À
Dd b
d b
1 À
Dd 0
d 0
! 4
À1
ð9:32Þ
where
a
Gas pressure change rate;
Dd b Variation of grain diameter (cm);
Dd 0 Variation of nozzle diameter (cm).
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9 High-Temperature and High-Speed Gas Turbine Pump …