5 Experimental Fluid Mechanics
347
For compressible flows, in addition to the similarity criteria described
above, Mach number similarity criterion, which characterizes compressibility,
will be derived, i.e.
Ma p = Ma m ,
V p
a p
=
V m
a m
,
λ V
λ a
= 1
where a is the sound wave speed.
2. Application of similarity criteria
Theoretically, in the fluid mechanics model test, the single-value conditions
between the prototype flow field and the model flow field are similar, and
the number of similarity criteria with the same name is equal. Guaranteeing
the similarity of single-valued conditions including geometric similarity is an
important premise of model experiment, which is related to factors such as
model design, model attitude, parameter distribution in flow field, model
support form, and other factors. In the fluid mechanics experiment, there are
more than a dozen similarity criteria, and five are often used. According to
the similarity theory, the corresponding similarity criteria should be simulated
simultaneously in the experiment to achieve “completely similar”. However,
this complete similarity is actually difficult to achieve, and generally can only
be “partially similar.” Fortunately, the physical meanings of various similarity criteria are different. In a specific case, not all similarity criteria are
equally important. In other words, for a particular experiment, some similarity criteria must be simulated, and some similarity criteria can be ignored.
To do this correctly, the physical meaning of each similarity criterion and its
impact on similar flows should be understood. For example, to simulate a
periodic non-stationary flow of an incompressible fluid, except for geometry
and motion, the dynamic similarity must satisfy the Strouhal number similarity criterion. In order to simulate the resistance problem of the pipeline
flow, the Reynolds number similarity criterion must be satisfied. For the flow
problem of gravity, the Froude number similarity criterion must be satisfied.
For compressible flow, the Mach number similarity criterion is needed.
Set a propeller diameter D p = 4 m, propeller speed n = 1075 rpm, standard takeoff speed V p = 258 km/h, static takeoff pulls force T = 4300 kg,
try to design the propeller wind tunnel scaled model according to different
similarity criteria.
347
For compressible flows, in addition to the similarity criteria described
above, Mach number similarity criterion, which characterizes compressibility,
will be derived, i.e.
Ma p = Ma m ,
V p
a p
=
V m
a m
,
λ V
λ a
= 1
where a is the sound wave speed.
2. Application of similarity criteria
Theoretically, in the fluid mechanics model test, the single-value conditions
between the prototype flow field and the model flow field are similar, and
the number of similarity criteria with the same name is equal. Guaranteeing
the similarity of single-valued conditions including geometric similarity is an
important premise of model experiment, which is related to factors such as
model design, model attitude, parameter distribution in flow field, model
support form, and other factors. In the fluid mechanics experiment, there are
more than a dozen similarity criteria, and five are often used. According to
the similarity theory, the corresponding similarity criteria should be simulated
simultaneously in the experiment to achieve “completely similar”. However,
this complete similarity is actually difficult to achieve, and generally can only
be “partially similar.” Fortunately, the physical meanings of various similarity criteria are different. In a specific case, not all similarity criteria are
equally important. In other words, for a particular experiment, some similarity criteria must be simulated, and some similarity criteria can be ignored.
To do this correctly, the physical meaning of each similarity criterion and its
impact on similar flows should be understood. For example, to simulate a
periodic non-stationary flow of an incompressible fluid, except for geometry
and motion, the dynamic similarity must satisfy the Strouhal number similarity criterion. In order to simulate the resistance problem of the pipeline
flow, the Reynolds number similarity criterion must be satisfied. For the flow
problem of gravity, the Froude number similarity criterion must be satisfied.
For compressible flow, the Mach number similarity criterion is needed.
Set a propeller diameter D p = 4 m, propeller speed n = 1075 rpm, standard takeoff speed V p = 258 km/h, static takeoff pulls force T = 4300 kg,
try to design the propeller wind tunnel scaled model according to different
similarity criteria.