Page 41 - Aerodynamics for Engineering Students

24 Aerodynamics for Engineering Students
From the figures given above, the Reynolds number VDp/p may be calculated for each case.
These are found to be
Case (A) Re = 5.52 x lo7 Case (D) Re = 7.75 x lo6
Case (B) Re = 1.84 x lo7 Case (E) Re = 5.55 x lo7
Case (C) Re = 5.56 x lo7 Case (F) Re = 1.11 x lo8

It is seen that the values of Re for cases (C) and (E) are very close to that for the full-size
aircraft. Cases (A), (C) and (E) are therefore dynamically similar, and the flow patterns in these
three cases will be geometrically similar. In addition, the ratios of the local velocity to the free
stream velocity at any point on the three bodies will be the same for these three cases. Hence,
from Bernoulli's equation, the pressure coeficients will similarly be the same in these three
cases, and thus the forces on the bodies will be simply and directly related. Cases (B) and @)
have Reynolds numbers considerably less than (A), and are, therefore, said to represent a
'smaller aerodynamic scale'. The flows around these models, and the forces acting on them,
will not be simply or directly related to the force or flow pattern on the full-size aircraft. In case
(F) the value of Re is larger than that of any other case, and it has the largest aerodynamic scale
of the six.
Example 1.2 An aeroplane approaches to land at a speed of 40 m s-l at sea level. A 1/5th
scale model is tested under dynamically similar conditions in a Compressed Air Tunnel (CAT)
working at 10 atmospheres pressure and 15°C. It is found that the load on the tailplane is
subject to impulsive fluctuations at a frequency of 20 cycles per second, owing to eddies being
shed from the wing-fuselage junction. If the natural frequency of flexural vibration of the
tailplane is 8.5 cycles per second, could this represent a dangerous condition?
For dynamic similarity, the Reynolds numbers must be equal. Since the temperature of
the atmosphere equals that in the tunnel, 15 "C, the value of p is the same in both model and
full-scale cases. Thus, for similarity

vfdfpf = Vm4nfi
In this case, then, since
Vf =mms-'
1
40x 1 x 1 = v, x-x 1o=2vm
5
giving

Now Eqn (1.38) covers this case of eddy shedding, and is

nd
- = g(Re)
V
For dynamic similarity

Therefore

giving nf = 8 cycles per second