Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

178 Compressible high-speed gas ¯ow
area 1 assumed to vary as 58
…x ÿ 2:5†2
a ˆ 1:0 ‡
12:5
for 0 4 x 4 5 …6:20†
The speed of sound is constant as the ¯ow is isothermal and various conditions at
in¯ow and out¯ow limits were imposed as shown in Fig. 6.3. In all problems
2.0
1.5
ρ 1.0
0.5
0
0 1.0 2.0
x
3.0 4.0
(a) Subsonic inflow and outflow
2.0
1.5
ρ 1.0
0.5
0
0 1.0 2.0
x
3.0 4.0
(b) Supersonic inflow and outflow
2.0
1.5
ρ 1.0
0.5
0
0 1.0 2.0
x
3.0 4.0
2.0
1.5
u 1.0
0.5
0
0 1.0 2.0
x
3.0 4.0
2.0
1.5
u 1.0
0.5
(c) Supersonic inflow–subbsonic outflow with shock
Exact
C L = 2.0
C L = 1.0
0
0 1.0 2.0
x
3.0 4.0
2.0
1.5
u 1.0
0.5
0
0 1.0 2.0
x
3.0 4.0
u' 0.75 a/2 0.5
u
0.0 5.0
2
C1 C1 Fig. 6.3 Isothermal ¯ow through a nozzle. 1 Forty elements of equal size used.