Untitled - Aerobib - Universidad Politécnica de Madrid

11.2. DIMENSIONLESS PARAMETERS OF AEROTHERMOCHEMISTRY 265
2) γ = c p0
c v0
. (11.17)
Keeping in mind that velocity a 0 of sound in the mixture, at pressure p 0 and
with density ρ 0 , is a 0 = √ γp 0 /ρ 0 , we can promptly see that P 2 may be written in the
form
being
P 2 = 1
γM0
2 , (11.18)
3) M 0 = v 0
a 0
, (11.19)
the Mach number of the flow, which will be used as a third characteristic dimensionless
parameter in lieu of P 2 .
The combination of P 3 and P 6 gives the following value
4) Pr = P 3
P 6
= µ 0c p0
λ 0
, (11.20)
which is the Prandtl number, fourth dimensionless parameter the substitutes P 6 .
Likewise, the combination of P 3 and P 8 gives
5) Sc = P 3
P 8
= µ 0
ρ 0 D 0
, (11.21)
which is the Schmidt number, fifth dimensionlees parameter in lieu of P 8 .
The aforegoing parameters are the same used in classical Aerothermodynamics
and the characteristic constants of the chemical reaction have no bearing on them. This
constants act through two other parameter, P 1 and P 5 . The first may be written
where
P 1 = v 0τ ch0
l 0
, (11.22)
τ ch0 = ρ 0
w 0
(11.23)
is a characteristic chemical time. The reciprocal of (11.22) is the first parameter of
Damköhler,
6) Da 1 = l 0
v 0 τ ch0
, (11.24)
and it is the sixth dimensionless parameter of the process.
Finally, P 5 is the second parameter of Damköhler
7) Da 2 = q
c p0 T 0
, (11.25)
this being the seventh dimensionless parameter of the process.