Supersonic Flow (Mo > 1, в = yjM^ — 1)

Pressure Distribution and Flow Features

The pressure coefficients are given by the Ackeret formulae

C = 7 (л (1 – 6 7 +6 ?) – a)

C – = – в (A (1 – 67 +677) – a)

The plot of – C + and – C – versus x for this airfoil at a = 0 is seen in Fig. 15.27. See sketch of the flow at a = 0 (shocks, characteristic lines, expansion shocks), Fig. 15.28.

Static Equilibrium About an Axis

Подпись:2a 1

Cm,1 (a) = iCm, o) a=0 – ^ + 7 Cl(a)

Supersonic Flow (Mo > 1, в = yjM^ — 1)Fig. 15.27 Pressure coefficients on the thin cambered plate at zero incidence

Fig. 15.28 Flow field past the thin cambered plate at zero incidence

, . 4 c, x dx 4 A 1 2

Подпись:(‘Cm, o a_0 = d'(x) = (1 – 6£ + 6£2)£d£ = 0

a=0 в 0 c c в 0

Hence the moment about the mid-chord reduces to

2a 1 4a

Cm, 1 (a) = — + 2 – = 0

Any value of a satisfies the equilibrium requirement. The equilibrium is neutral.

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