2.3 Reynolds Number Effect and Laminar to Turbulent Transition
33
Fig. 2.4 Turbulator or transition trigger for the boundary layer
micro-vortices which destabilise the boundary layer. Figure 2.4 shows a saw-tooth
transition trip placed on an aerofoil model.
2.4 Dynamics Similarity and Dimensionless Parameters
In addition to the Mach and Reynolds numbers, other dimensionless parameters must
be respected during wind tunnel test, the most common being:
– The Prandtl number to simulate thermal conduction: Pr =
μC p
κ
, C p being the
specific heat at constant pressure and κ the thermal conductivity.
– The Lewis number, to reproduce the diffusion phenomena of species: Le =
κ
ρ D j C p
, D j being the diffusion coefficient of species j.
– Knudsen number which measures the ratio between the average molecular free
path λ in the gas and a characteristic dimension L of the vehicle: K n =
λ
L
. This
number defines the rarefaction effects encountered at very high altitude flights,
during atmospheric re-entry (see Sect. 1.2).
– For periodic or unsteady phenomena, the Strouhal number is introduced: St =
f V
L
where f is a characteristic frequency. This number represents the ratio between
the time taken by a fluid particle to travel the reference length and the period of
the phenomenon.
– The Froude number, Fr =
V ∞
√
Lg
whose square is a measure of the ratio between
the dynamic pressure terms and the gravitational forces within the fluid. A large
Froude number implies that the action of gravity is negligible as a first approximation. This number plays an important role in hydrodynamics, particularly in
air-water interface problems involving a light fluid (air) and a heavy fluid (water).
Since air is much lighter, most of the time the effect of gravity is neglected in problems involving air, except in modelling the Earth’s atmosphere or if the weight of
the displaced air is comparable to aerodynamic forces, which may be the case for
airships. In general, in aerodynamics, the weight of the displaced air is ignored.
33
Fig. 2.4 Turbulator or transition trigger for the boundary layer
micro-vortices which destabilise the boundary layer. Figure 2.4 shows a saw-tooth
transition trip placed on an aerofoil model.
2.4 Dynamics Similarity and Dimensionless Parameters
In addition to the Mach and Reynolds numbers, other dimensionless parameters must
be respected during wind tunnel test, the most common being:
– The Prandtl number to simulate thermal conduction: Pr =
μC p
κ
, C p being the
specific heat at constant pressure and κ the thermal conductivity.
– The Lewis number, to reproduce the diffusion phenomena of species: Le =
κ
ρ D j C p
, D j being the diffusion coefficient of species j.
– Knudsen number which measures the ratio between the average molecular free
path λ in the gas and a characteristic dimension L of the vehicle: K n =
λ
L
. This
number defines the rarefaction effects encountered at very high altitude flights,
during atmospheric re-entry (see Sect. 1.2).
– For periodic or unsteady phenomena, the Strouhal number is introduced: St =
f V
L
where f is a characteristic frequency. This number represents the ratio between
the time taken by a fluid particle to travel the reference length and the period of
the phenomenon.
– The Froude number, Fr =
V ∞
√
Lg
whose square is a measure of the ratio between
the dynamic pressure terms and the gravitational forces within the fluid. A large
Froude number implies that the action of gravity is negligible as a first approximation. This number plays an important role in hydrodynamics, particularly in
air-water interface problems involving a light fluid (air) and a heavy fluid (water).
Since air is much lighter, most of the time the effect of gravity is neglected in problems involving air, except in modelling the Earth’s atmosphere or if the weight of
the displaced air is comparable to aerodynamic forces, which may be the case for
airships. In general, in aerodynamics, the weight of the displaced air is ignored.