The Airbus A 380, The Boeing 747 gigantic vehicles that are the largest passenger
airplanes on earth. The Bruj Khalifa, the tallest building ever built by humans.
New York City, the largest city in United States. All of them have one thing in common:
the size. Let’s say we are in the design phase and we want to analyze the aerodynamics of the
two airplanes, or how storms would Impact the Burj Khalifa once they are built, or we want to analyze
how the winds would affect the pollution in New York City. Let's find out how we can do that.
All the examples that we just introduced can be analyzed using a scaled model that can fit inside
an experimental testing facility such as a wind tunnel. In order to perform a consistent analysis,
we need to respect some requirements: the first is geometric similarity.
The real object and the model must have the same shape and be perfectly scaled
geometrically, meaning that the ratio of the corresponding lengths is always the same.
The second fundamental requirement is dynamic similarity, this implies that the
objects have to be geometrically similar and they must present similar flow
patterns meaning that the velocity field and forces acting on them must scale with geometry.
For example, the streamlines around the real body and the model will look the same
if we have dynamic similarity. The importance of dynamic similarity is
that the results obtained for the test model can be scaled and applied to the real system.
It is common to see applied these concepts in many research facilities
where scaled models are used to analyze the behavior of the real system.
Especially during the design phase of new vehicles
or large buildings, it is useful to predict if the design would meet the expected performance.
How can we make sure that the model and the real body are dynamically similar? The first step
is to non-dimensionalize the problem. This means that we're going to take our governing equations
and manipulate them to obtain their non dimensional form.
Any single solution of these equations will be equally valid for a multitude of similar problems.
The second step is to use dimensionless parameters. They will emerge naturally
from the non-dimensionalization of the governing equations. Those parameters
are used to ensure the dynamic similarity: indeed, two flows are dynamically similar
if all relevant dimensionless parameters are the same.
In the next lectures we're going to see how to approach these two steps and obtain
the non-dimensional form of the equations and a set of dimensionless parameters.