# The fluid close to the solid surface of

The term ‘boundary layer’ refers to a phenomenon where a
layer of fluid in the immediate vicinity of a bounding surface (the edge of a
boundary of flow, usually another medium or material) changes its behaviour due
to the effects of viscosity. This experiment was tasked with studying the
behaviour of the boundary layer across a flat plate with two different types of
surfaces, smooth and rough. Using an airflow bench, a flow can be created in a
controlled environment to mimic a situation where knowledge of the boundary
layer is crucial, for example air flowing over an aircraft’s wing, a craft’s
movement through water or oil flowing through a pipeline. Pressure readings
were taken within and beyond the boundary layer by a pitot tube. From these
pressure readings, critical information such as displacement thickness,
momentum thickness and shape factor can be calculated. This data for the smooth
and the rough side of the plate can be compared to determine how these factors
influence the boundary layer. The experiment was also used to analyse the
relationship between momentum thickness and skin friction coefficient, as well
as the power law. The results are generally in line with what would be expected
if calculated.

2. Introduction
Understanding of boundary layers in a fluid have a wide variety of
practical applications that affect even the most mundane things in our lives
that we take for granted, such as the water that we receive in our homes. The
boundary layer was first discovered in 1904 by Ludwig Prandtl.

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A boundary layer is a thin layer of viscous fluid close to
the solid surface of a wall in contact with a moving stream in which (within
its thickness ?) the flow velocity varies from zero at the wall (where the flow
“sticks” to the wall because of its viscosity) up to Ue at the
boundary, which approximately (within 1% error) corresponds to the free stream
velocity (Epifanov, 2011). To simplify, viscosity causes the fluid to stick to
the bounding layer, and thus the molecules in direct contact have their fluid
velocity decreased to zero. This causes disruption in the flow, and slows down
molecules that are in contact with the immobile molecules but not necessarily
the bounding layer. This creates a velocity gradient where the fluid gradually
speeds up until it reaches ‘free stream velocity’ which is the maximum speed of
the flow. The distance is takes to go from no velocity to free stream velocity
is known as the boundary layer. Viscosity is how determined a fluid is to
resist stress and being deformed, and is caused by friction between molecules. More
viscous fluids are often referred to as ‘thicker’; glue is ‘thicker’ and thus
more viscous than water. The chaos and disorder of a boundary layer’s flow can
be measured by its Reynold’s Number (Re). A smooth, layered flow is known as
laminar, and has a relatively low Re. Consequently, a flow characterised by
unsteady swirling flows in known as turbulent, and has a relatively high Re.

This experiment looked specifically at how the boundary
layer behaves when a flat plate is the bounding surface, when that surface is
both rough and smooth. Being aware of the details within boundary flow are very
important for many problems in aerodynamics, including wing stall, skin
friction drag and the heat transfer that occurs in high speed flight. For
example, a boundary layer gives an object an effective shape, which the
external flow reacts to as if it would to a physical surface. The boundary
layer can even separate itself from the body create an effective shape
different to that of the actual object, which occurs when the boundary layer
has very low energy. Flow separation is the cause for wing stall at high angle
of attack (NASA, 2015). Thus, controlling the boundary layer on an aircraft’s
wing is crucial to the aerospace industry. On a less extreme level, controlling
the transition from laminar to turbulent directly affects the lift generated
and how efficient an aircraft can be. Reducing turbulent flow reduces skin friction
drag and thus parasitic drag and would increase the efficiency of an aircraft
and increase its maximum cargo capacity/payload. Increasing efficiency and thus
using less fuel is paramount to the aviation industry, since it is estimated
that 32.3% of airline expenditure was on fuel in 2012 (Statista, 2018). Reducing
turbulent boundary layers are also of great importance in hydrodynamics, since
the laws governing air are very similar to those of water. The increased
globalisation of the world has resulted in us using products from all over the
world. The easiest way to transport these products is through cargo ships. Keeping
the surface as smooth as possible through polishing and removing adhesive sea
life all contribute to reducing drag, and thus costs and environmental impact. Aerodynamics
and hydrodynamics are sometimes referred to separately, the major difference
between them being that water is considered an incompressible fluid. They are
both disciplines of fluid dynamics.

The experiment tests these principles on a much smaller and
isolated level. This experiment allows data to be attained and analysed that
directly relates to real world applications; the development in turbulent air
flow, the classical characteristics of a boundary layer and the comparison of
the effect of surface finish on the boundary layer.

3. Experimental
Problem and Theory
The primary objectives of the experiment were to study the boundary
layer development in turbulent air flow on a flat plate and to calculate and
analysis the classical boundary layer characteristics on the smooth flat plate
by numerical integration. A velocity profile of the boundary layer, from the
bounding surface to the free stream velocity, can be calculated from the
changes in flow pressure. Pressure readings were obtained using a pitot tube
along the whole boundary layer and in the freestream. These readings can then
be used to obtain boundary layer thickness (), boundary layer
displacement thickness () and boundary layer
momentum thickness (). This can be done with the
following equations:

(3.1)   (3.2)                 (3.3)              (3.4)

In theory, the velocity should decrease as the pitot tube gets
nearer to the leading edge, up until the bounding surface where the velocity
will be nought. This is due to the air molecules in contact with the bounding
surface being stationary. The friction between molecules causes the next layer
of molecules to lose momentum and slow down, thus creating the velocity
thickness, the shape factor can be calculated. The shape factor determines the
nature of the flow; a higher shape factor means a lower Re:

(3.5)

A velocity profile can be created of the flow which would
allow quantification of the power law parameter n for the boundary layer, which will allow the nature of the flow
to be determined. Furthermore, observing the growth of the momentum thickness
along the plate gives an indication of how the skin friction coefficient also
develops along the plate:

(3.6)                                                                    (3.7)

4. Methodology
The experiment took place using an AF10 Airflow Bench. The airflow
bench created a stable freestream flow, induced vertically, from ceiling to
floor. A thin, flat plate was suspended inside the usable area of the bench,
also vertically, so that the air was flowing parallel to the plate. An AF14
pitot tube was attached to measure pressure. The plate could alternate between
four set positions (of which we used three) so data could be taken from various
distances from the leading edge without the need to tamper with the pitot tube.
The plate was initially in position 1 which was 265mm from the leading edge.
Firstly, a measurement is taken far from the plate so that the freestream
pressure can be known and used for reference. Then, the pitot tube was
gradually slid towards the plate until a change in pressure was noted. The
change in pressure signified the outer edge of the boundary layer. The pitot
tube was then stopped and the distance to the plate was calculated with a
micrometer. The measured distance was divided by ten, which gave us the length
of the increments we would use. Ten readings were then recorded at each
increment using a FC0510 micromanometer throughout the boundary layer until
reaching the leading edge. The process was repeated for positions 2 and 3 which
were 215mm and 165mm from the leading edge respectively. The whole sequence was
repeated for the rough side of the plate. All pressure measurements taken the
manometer were in units of  and thus require converting to SI units (). Ultimately, another
group’s results were used due to technical problems with the airflow bench.

The results were initially recorded on paper and then post
processed to create an Excel spreadsheet that would be easier to read and make
producing graphs easier. After converting the pressure values, equation 3.1 was
used to calculate the flow velocity using the pressure reading in the
freestream. It was then straightforward to find  using equation 3.2.

and  must be found using numerical integration. The
trapezium rule was deemed too inaccurate and thus they had to be found using Simpson’s
rule. The parameter n and the skin
friction coefficient were calculated using equations 3.6 and 3.7.