348
P. Liu
Determination of length scale λ L . Set the model propeller diameter D m ,
which is determined according to
π D 2
m
4 /A = 0.2 − 0.3, where A is the crosssectional area of the wind tunnel test section. For wind tunnel cross-sectional
area A = 1.52 = 2.25 m 2 , the diameter of the propeller of the scaled model
is D m = 0.8 m. Prototype diameter D p = 4.0 m. Length scale is λ L = 5.
(1) Design the model according to the Ma number and Sh number criteria
The design set λ L = 5.0, D m = D p /λ L = 4.0/5.0 = 0.8 m, according to
Mach number similarity criterion, obtain that
V p
a p
=
V m
a m
, a p ≈ a m , λ V = 1
Obtained by the Strouhal number similarity criterion
D p f p
V p
=
D m f m
V m
,
V m
D m n m
=
V p
D p n p
,
λ V
λ L λ n
= 1, λ n =
1
λ L
= 1/5
Accordingly, the similar parameters of the model obtained and prototype
are given in Table 5.1.
(2) Design the model according to the Re number and Sh number criteria
The design set λ L = 5.0 ,according to Reynolds number similarity criterion,
obtain that
λ V λ L
λ ν
= 1, λ ν ≈ 1, λ V = 1/λ L = 1/5
Obtained by the Strouhal number similarity criterion
λ V
λ L λ n
= 1, λ n =
λ V
λ L
=
1
λ 2
L
= 1/25
Table 5.1 Related variables prototype and model values (Ma criterion)
Name
Prototype value
Model value
Scale
Propeller diameter D(m)
4.0
0.800
5
Propeller rotate speed n (rpm)
1075
5375
1/5
Standard takeoff speed V 0 (km/h)
258.0
258.0
1.0