Untitled - Aerobib - Universidad Politécnica de Madrid

266 CHAPTER 11. SIMILARITY IN COMBUSTION. APPLICATIONS
The interpretation of the meaning of Damköhler two parameters is simple. The
first is a measurement of the relationship between the mean mechanical time required
by a particle to travel the characteristic lenght l 0 at the characteristic velocity v 0 and
the time required by the chemical reaction of the mixture to take place. The second
parameter of Damköhler is a measure of the relationship between the heat produced
by unity of mixture when burning at constant pressure and the heat contained by the
same at characteristic temperature T 0 .
It should be noted that in the non-stationary processes a additional parameter
appears, Strouhal number, which originates from the time derivatives ∂/∂t of the
equations of motions. Likewise, if the mass forces are present as occurs in the phenomena
of free convection, then another dimensionless parameter appears, due to the
gravity terms of the equations, which originates the Froude number.
Finally, when the number of species and chemical reaction is increased, the
number of the Damköhler parameters (of both kinds time and heat) increases as well.
In technical literature we frequently find other parameter which are combinations
of the above mentioned. Por example, occasionally Prandtl number is substituted
by Peclet number, which is a product of the numbers of Reynolds and Prandtl
Pe = Pr · Re = ρ 0v 0 l 0 c p0
λ 0
. (11.26)
Likewise, the Schmidt number is replaced by the Lewis-Semenov number which is
obtained as follows
L = Pr
Sc = ρ 0D 0 c p0
, (11.27)
λ 0
used specially in combustion processes as seen in Chap. 6.
The advantage of utilizing the Peclet and Lewis-Semenov numbers in combustion
phenomena is based on the fact that the conductivity and diffusion coefficients
appear explicity in their expressions. Such coefficients are the ones of interest in these
processes in which the influence of the viscosity coefficient is negligible in many
cases, as said in Chap. 5.
We shall now see some practical applications of this theory.
11.3 Scaling of rockets
The problem of the scaling of rockets has a great practical interest since its solutions
would allow the prediction of the behavior of the rockets after tests made with reduced
scale models.