MAE 315-Lab 4 Fluids Writeup
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Transcript of MAE 315-Lab 4 Fluids Writeup
MAE 315 Mechanical and
Aerospace Lab 4:
Fluid Mechanics
Alexander SpiridakisProf. GlauserDue: 5/30/2014
1
Table of Contents
I. Abstract................................................................................................................................... 2
II. Introduction.......................................................................................................................... 3Basic Concepts...................................................................................................................................... 3Force Balance and Calibration.........................................................................................................7Pitot-static Tube................................................................................................................................... 8Boundary Layer and Reynold’s Number....................................................................................10Formation of Wakes......................................................................................................................... 14Airfoil Theory.................................................................................................................................... 192-D v. 3-D Objects............................................................................................................................. 24Von Karman Vortex Shedding – Unsteady Aerodynamics.....................................................25
III. Procedure.......................................................................................................................... 28Week 1................................................................................................................................................. 28
Equipment..........................................................................................................................................................28Part 1: Force Balance and Calibration.....................................................................................................28Part 2: Boundary Layer.................................................................................................................................30Part 3: Wake......................................................................................................................................................30
Week 2................................................................................................................................................. 31Equipment..........................................................................................................................................................31Part 1: Freestream Velocity.........................................................................................................................32Part 2: Airfoil....................................................................................................................................................32Part 3: Cylinders..............................................................................................................................................32Part 4: Vortex Shedding................................................................................................................................33
IV. Results and Discussion.................................................................................................... 34Week 1................................................................................................................................................. 34
Part 1: Force Balance and Calibration.....................................................................................................34Part 2: Boundary Layer Test........................................................................................................................36Part 3: Wake Test............................................................................................................................................38
Week 2................................................................................................................................................. 41Part 1: Airfoil Test..........................................................................................................................................41Part 2: Cylinder Drag Test...........................................................................................................................43Part 3: Vortex Shedding................................................................................................................................44
V. Conclusion........................................................................................................................... 49
VI. References.......................................................................................................................... 50
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I. Abstract
Fluid mechanics is a vital concept within the field of engineering because it plays
key roles in both theoretical understanding of concepts and design application. The
applications of fluid mechanics can be seen in everyday engineering systems, from
showers and kitchen sinks to airplanes and almost anything involving aerodynamics.
This lab was a glance into the vast field of fluid mechanics. The two main devices
used to collect the data were a wind tunnel and a force balance. The wind tunnel was used
to explore fluid phenomena such as drag and lift on an airfoil. The vortex shedding
portion in this lab was unique in the sense that unsymmetrical flow patterns and data
from unsteady aerodynamics was recorded. Boundary layer and wake data were recorded
around a pitot-static tube and cylinder respectively, which demonstrated how flows
behave very close to a surface and how flows appear in the wake of an object. Lift, drag,
and moment data from the force balance was primarily used as a reference for the data
taken in the wind tunnel portion. Reynolds numbers were recorded for every section of
the lab where possible, which helped indicate similarities in flow patterns.
The focal point of this experiment was fluid mechanics: studying how flows form
around objects given certain dimensions and the forces that consequently develop as a
result of these flows. The goal was to gain an understanding of how flows work and
apply a theoretical understanding to real world situations. Data from one section to the
next demonstrated how drastically different flows can be, given objects and flow speed.
Overall, this lab provided valuable insight as to how engineers can use fluid mechanics to
understand and design systems that incorporate flows.
3
II. Introduction
In the realm of physics, fluid describes any gas or liquid that conforms to the
shape of its container.i Fluid mechanics, the study of gases and liquids at rest and in
motion, is applied to almost every form of mechanical engineering. Not only is this so,
but the concepts of fluid mechanics apply to a multitude of systems, both in nature and
manufactured systems, that are important in everyday life: Fluid mechanics is involved in
every person’s cardiovascular systems, in the brakes and around spoilers on cars, in
airplane flight, and in virtually any hydraulic powered equipment.
Two main subcategories fall under the scope of fluid mechanics: fluid statics,
often called hydrostatics, the study of fluids at rest, and fluid dynamics, the study of
fluids that flow or are in motion. For example, fluid dynamics explains how the airflow
above and below the wings of an airplane allows it to lift off the ground.
Basic Concepts
Before diving into the theory of fluid mechanics, it is best to understand how
fluids work in terms of forces.ii A fluid is fundamentally defined as a substance that
deforms continuously when acted on by a shearing stress. Flow is understood to be
continuous deformation under a given shear stress. Some important fluid properties
include density, r, specific weight, , dynamic viscosity, , kinematic viscosity, ,
along with pressure, temperature, and velocity. Fluids differ from solids in this sense:
applying a shearing stress to a solid would initially cause minor deformation, but a solid
will not continuously deform and return to its original shape.iii The effects of forces on a
fluid and fluid flow were examined a great detail in this lab.
4
The term fluid in classical fluid mechanics is used almost interchangeably in
describing a liquid or a gas.iv When analyzing flows in fluid dynamics, usually some
basic assumptions are made to make analysis simpler. For example, in this lab, the flow is
assumed to be inviscid or nonviscous, so friction is negligible and there are no shearing
stresses within the moving fluid, irrotational, so the fluid particles do not rotate while in
motion, and lastly time independent and steady because the wind tunnel used was
designed to minimize turbulence in the test section.
Steady flow implies that the velocity at a given point in space does not change
with time.v In other words, each particle in the flow field that passes through a given
point will have the same velocity every other particle that has already passed that point.
For steady flow, each particle in a flow slides along its path, and its velocity vector is
everywhere tangent to its path. These tangent velocity vectors through the flow field are
called streamlines. Figure 1.1 below shows an example of particle streamlines flowing
above and below an airfoil.
Figure 1.1vi
5
The equations and laws of fluid mechanics are an adaptation for Newton’s Laws
of Motion to a medium treated as “continuous” mass as opposed to having discrete
particles.vii That being said, the Newtonian principles remain the same, but the equations
become more complex because of additional variables, such as those stated above, that
need to be taken into account. The law of conservation of mass is described by Equation
1 below known as the continuity equation and the law of conservation of momentum is
described by Equation 2.
∂∂ t
∫Vol
ρdV +∮A
ρ U⃗∗d A⃗=0
Equation 1
∂∂ t
∫Vol
ρ U⃗ dV +∮A
U⃗ ρ U⃗∗d⃗ A=F⃗
Equation 2
By combining the continuity and momentum equations with the viscous forces of
the fluid the Navier-Stokes Equations are derived viii:
δ u⃗δt
+( u⃗∗∆ ) u⃗=gh−1ρ∇P+ν∇2 u⃗
Equation 3
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In the 3 above equations, p is pressure, ρ is density of the fluid, g is gravity, u or
(U) is the flow velocity, and h is the height.
The Navier-Stokes equations are directionally dependent and provide a complete
mathematical description of the flow of incompressible Newtonian fluids.ix
Unfortunately, because these are nonlinear, second-order, partial differential equations,
there are currently no mathematical methods available to obtain solutions with all
variables at play. However, with making assumptions about the flow being considered,
such as the assumptions used in this lab as stated above (incompressible, steady, and
inviscid), the Navier-Stokes equations can be reduced to Bernoulli’s equation along a
streamline as shown in Equation 4 below.
p+ 12
ρ U 2+ρgz=Const .
Equation 4
Bernoulli’s general form in Equation 4 can be manipulated to relate two points of a flow
that exist along the same streamline:
p1+12
ρ U 12+ ρg z1=p2+
12
ρ U 22+ρg z2
Equation 5
In the 2 above equations, p is pressure, ρ is density of the fluid, g is gravity, u or
(U) is the flow velocity, and z is the height.
7
Further simplification of Equation 5 can be made in any case where gravity can
analytically be neglected as a result of height variation of a flow being small. The terms
involving variable “z” drop out thus allowing each term in Bernoulli’s Equation to
represent a particular pressure:
Static Pressure: Ps=p
Dynamic Pressure: PDym=12
ρ U∞2
Total Pressure: Ptotal=P s+12
ρU ∞2
Force Balance and Calibration
When an object is present in a flow field, shear forces and moments act on that
object as a result of the fluid flow. One effective and simple way to measure these forces
and moments is through the use of a force balance. A force balance utilizes one load cell
for each directional component of force and moment.viii When a force or moment is
applied to an object mounted on a force balance, a strain is created within the respective
load cell. A strain gage in the load cell measures that strain and returns the reading as a
voltage. Since the voltage returned is directly proportional to the force in each direction,
the forces and moments and acting on the object can be extrapolated from these readings.
Figure 1.3 below shows how a force balance can be configured to obtain values of lift
and drag forces specifically using weights.
8
Figure 1.3 viii
Some calibration is required to ensure the force balance obtains accurate results.
The load cells become less accurate with time: results obtained by the load cells will
begin to “drift” from the actual values. This “drift” simply causes results to slightly
deviate from their true values over time, creating a factor of error. Calibration must be
done to avoid this error and maintain the integrity of the results obtained. In order to see
the “drift” in each component of the force or moment one force component or moment
must be calibrated at a time.viii The measured voltage or force must be plotted versus the
known weight. The plot will show the voltage for the known forces and moments and
will also give the trend of the voltage versus force. Since voltage is proportional to force
the calibration curve will be linear. Any data collected from here and forward should be
“zeroed” using the calibration. Since using a force balance is usually the starting base
point for most experiments, it is important that the results obtained be accurate.
Pitot-static Tube
Pitot-static tubes are measuring devices used to find total and static pressures as
shown in the Bernoulli equations. Each of these pressure-measuring devices is essentially
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a hollowed out tube, angled at 90 degrees from one end to the other, with a hole tap at
each end. An example of a pitot-static tube can be seen in Figure 1.2 below.
Figure 1.2 viii
The hole tap parallel to the flow creates a stagnation point, bringing the fluid
velocity to zero. This allows for the measurement of maximum or total pressure along
streamlines in the flow that pass parallel to the hole. The other hole perpendicular to the
flow simply measured ambient or static pressure. The ambient pressure is used as a
reference and can be put into Bernoulli’s equation along with the total pressure to yield
dynamic pressure. Velocity can be obtained knowing dynamic pressure as shown below:
PDym=Pt−Ps
Equation 6
U=√ 2(PDym)ρ
10
Equation 7
Boundary Layer and Reynold’s Number
The boundary layer is the layer of fluid adjacent or immediately next to the
surface of the object it is flowing over. As a fluid moves past an object, the fluid
molecules right next to the surface stick to the surface. The molecules just above the
surface are slowed down in their collisions with the molecules sticking to the surface.
These molecules in turn slow down the flow just above them. The farther the flow
molecules from the surface, the fewer the collisions they experience.x The molecules
directly in contact with the surface have a velocity at zero. These layers create a thin
surface where, on the side in contact with the object, the flow velocity is zero, and on the
other side, the velocity is the flow’s freestream velocity. This is otherwise referred to as
the “no slip” condition. Figure 1.4 below depicts a velocity profile moving through a
pipe. The surface being considered is the bottom portion of the pipe where it is evident
that the velocity of the profile is zero.
11
Figure 1.4 xi
The boundary area is that of viscous flow, which is subject to friction from the
surface of the object and heat transfer from the object. Therefore boundary layers are
ruled by there own set of equations derived from the Navier-Stokes equations because
previous assumptions made concerning the relating flow wouldn’t apply.
Fluid behavior at the boundary layer can be either laminar or turbulent. The
difference between laminar and turbulent flow is best represented in Figure 1.5 below.
Laminar and turbulent behavior are typically characterized by the Reynold’s number of
the flow. The Reynold’s number is a dimensionless characteristic of any given flow. It is
a ratio of inertia force to viscous force and is characterized by Equation 8 below.
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Figure 1.5 xii
ℜ= ρUlμ
=ULν
Equation 8
Where p is pressure, ρ is density of the fluid, l is the characteristic length, u or (U)
is the velocity, μ is the dynamic viscosity, and υ is the kinematic viscosity.
At low Reynold’s numbers, the boundary flow behavior is laminar. Any
Reynold’s number around 2(10^3) begins to deviate from laminar flow, transitioning into
turbulent flow. This transition stage is one where flow behavior is most unpredictable. As
a result of this unpredictable flow behavior, it is difficult for engineers to design and
work in this transition range. Any Reynold’s number above the transition range indicates
fully turbulent flow, where streamline velocity is unsteady. The relationship between the
Reynold’s number and the flow can be seen in the Moody Chart below. It is worth noting
that the exact behavior of the boundary layer flow is a function of the Reynold’s number
and roughness of the surface that the flow is passing over.
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Figure 1.6: Moody Chart
The details of the flow within the boundary layer are very important for many
problems in aerodynamics, including the stall of a wing, the skin friction drag on a
rocket, and the heat transfer that occurs in high speed flight.x The phenomenon of flow
separation at the boundary layer causes airplane wings to stall at high angles of attack.
Further study of the boundary layer shows that these effects create friction drag.
Frictional drag is associated with drag over blunt bodies and is described in greater detail
in the drag section. Figure 1.7 below shows the boundary layer effects on an airfoil. The
velocity profile becomes larger as airflow moves across the wing, starting from the
leading edge, and the flow changes from laminar to turbulent.
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Figure 1.7 viii
Formation of Wakes
As was discussed briefly in the last section, there is a phenomenon where, as flow
passes over a bluff body, the boundary layer is observed to separate from the surface and
forms a wake behind the body. Visible wakes develop behind speeding boats in water.
Wakes also propagate behind airplane wings as a plane rolls down the runway for
takeoff. Again, various parameters determine whether or not the flow behavior before, at
the boundary layer, and in the wake are laminar or turbulent. Below is a depiction of a
wake forming behind a cylinder.
15
Figure 1.8: Turbulent Wake behind cylinder viii
In front of the cylinder exists a high-pressure stagnation point, and a low-pressure
wake forms behind the object as a result of the boundary layer separating the flow from
the object surface. Directly behind the bluff body, the static pressure drops but with a
distance of roughly 10 cylinder diameters behind the bluff body, the wake static pressure
returns to the static pressure as in the freestream flow. Additionally, a momentum
deficiency can be seen when examining the flow as a loss in velocity within the wake of
the bluff object. Mathematically, the deficiency is the difference in the mass flux from in
front to behind the body and can be determined using the equations for conservation of
mass and momentum.
As previously established, boundary layer separation is the main cause of the
wake behind the flow of a bluff body, and the behavior of the wake flow is heavily
determined by the Reynold’s number and roughness of the surface. Figure 1.9 below
shows how flows in the wake region can be laminar or turbulent depending on the
Reynold’s number, the location at which the boundary layer separates for each bluff
body, and where the effects of the fluid viscosity are important. Generally, as the
Reynold’s number is increased, the area of the wake of the cylinder where viscous effects
are important becomes smaller. It is known that shear stresses are produced as a result of
16
fluid viscosity and velocity gradient, so it makes sense that viscous effects are confined to
wake and boundary layer regions. xiii
Figure 1.9
Drag is an incredibly important area of study in fluids, mainly applied to
aerodynamics and study of flight. A bluff body in a flow usually experiences two
components of drag: frictional drag and pressure drag. Frictional drag stems from the
friction between the surface and flowing fluid over it. Frictional drag, as mentioned, is
related to the boundary layer and is heavily dependent upon Reynold’s number. Pressure
drag, related to a wake, is observed to be less sensitive to Reynold’s number. To further
compare, frictional drag is most important in flows where there is no boundary layer
17
separation and is related to surface area of the object in contact with the flow whereas
pressure drag is important in separated flows and is related to the cross-sectional area of
the body.xiv Interestingly enough, bodies that are dominated by frictional drag are
commonly called streamlined bodies, and bodies dominated by pressure drag are referred
to as bluff bodies. Figure 1.10 shows the difference in drag coefficients for streamlined
bodies, on the bottom, to bluff bodies on top. For thoroughness, in this lab, the flow
around both cylinders and airfoils were examined.
Figure 1.10 xiv
Drag is formally defined as a net force in the direction of flow due to the pressure
and shear forces on the surface of the object. Interestingly enough, most of the
information of drag on objects has been accumulated through numerous experiments with
18
wind tunnels, water tunnels, and other ingenious devices where drag can be measured on
scale models.xv The formulas used to quantitatively calculate friction and pressure drag
individually differ. Equation 9 below shows the generalized formula used to calculate
drag:
D= ρLu12∫
0
w
(1−u2
u1)dy
Equation 9
Where, D is the drag force, ρ is density of the fluid, u or (U) is the flow velocity,
and L is the chord length.
Directly proportional to drag is what is known as the coefficient of drag. This is a
dimensionless parameter that is a function of other dimensionless parameters, such as
Reynold’s number, Mach number, Froude number, and relative roughness of the object
surface. Again, refer to Figure 1.10 to observe the relation between coefficient of drag
and Reynold’s number for a cylinder and airfoil. For a given shape, the formula for the
coefficient of drag is defined below:
Cd=D
12
ρ U∞2 S
Equation 10
19
Where, Cd is the coefficient of drag, D is the drag force, ρ is density of the fluid,
u or (U) is the freestream, flow velocity, and S is the area of the contact surface.
To further relate the ideas of wake formation and drag on a bluff body, Figure
1.11 below shows the wake of a cylinder. The effects of drag on the velocity profile can
be seen from the change as the flow moves from left to right.
Figure 1.11 viii
Airfoil Theory
Study of flow around an airfoil is crucial in understanding the concepts of lift and
drag. An airfoil is simply in the shape of a wing or a blade, as can be seen in Figure 1.11,
and produces aerodynamic forces when within a flow.
20
Figure 1.11: Cross-section of airfoil viii
The three aerodynamic forces created as a result of flow are lift force, drag force, and
moment. The lift is a force that exists normal to the direction of the freestream velocity
and creates “lift” or upward movement. The drag force opposes freestream direction. The
pitching moment develops as a result of the magnitude and lines of action of the lift and
drag forces.
First, it is critical to understand how these forces relate back to fundamental
principles in fluids. As fluid flows over the unique shape of an airfoil, a boundary layer
forms on the surface. At an angle of attack of zero degrees, the boundary layer around a
symmetric airfoil is equal on both sides.viii If the airfoil has a non-zero angle of attack, a
different boundary layer forms on top than on the bottom. When analyzing the flow
outside the boundary layer, viscous effects can be disregarded, so Navier-Stokes
equations can be simplified to Bernoulli’s. Figure 1.12 below shows that velocity profile
over a non-symmetrical airfoil or with a nonzero angle of attack is greater on the top than
it is on the bottom.
21
Figure 1.12
In Bernoulli’s equation lies the proof that the velocity below the wing is lower than the
velocity of the fluid above the wing, so the pressure below the wing is higher than the
pressure above the wing. The effects of velocity on pressure in this case are
predominantly proportional to dynamic pressure in Bernoulli’s for flows with large
Reynold’s numbers. Thus, it is shown that the pressure below the wing is higher than the
pressure above the wing. This pressure difference induces lift on the wing, and, in the
case of an airplane, allows it to fly. xvi Below, Figure 1.13 shows the possible streamline
for Bernoulli analysis on the airfoil.
Figure 1.13
The pressure difference causes the net forces of drag and lift and, consequently,
moment as mentioned above. Drag in the case of an airfoil is different than that of a
cylinder because, as referenced above, an airfoil is not bluff but rather a streamlined
body. Even so, pressure drag is a major source of drag on the airfoil, resulting from the
component of pressure difference, which is parallel to the freestream. The pressure drag
22
exponentially increases as lift increases. As with a bluff body, the airfoil will cause a
momentum deficit in flow, but unlike a bluff body, the drag caused by this momentum
deficit is small compared to the pressure drag. The formulas for drag and drag coefficient
are in Equations 9 and 10 above.
Lift force and coefficient of lift are best categorized by the two equations below.
Equation 11 shows the dimensionless parameter for lift per unit area or coefficient of lift.
Equation 12 stems from the theory that the lift produced by a symmetric airfoil is directly
related to its angle of attack.
CL=L
12
ρU ∞2 S
Equation 11
CL=2 πα
Equation 12
In the 2 above equations CL is the coefficient of lift, ρ is density of the fluid, u or
(U) is the freestream flow velocity, and S is the area of the surface.
Figure 1.14 below shows the relation of lift and drag forces to angle of attack.
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Figure 1.14
As angle of attack of the airfoil is increased, the boundary later stays attached to
the surface of the airfoil until a certain critical angle is reached. At this point, the
boundary later on the top of the airfoil begins to separate from the trailing edge of the
airfoil. If the angle gets too large, the boundary layer on the upper surface separates, the
flow over the wing develops a wide, turbulent wake region, the lift decreases, and drag
decreases creating a condition called a stall, also mentioned in the above section.xvii
Viscous effects and shear stresses contribute little to normal flow, but a stall is a special
condition where these play a role. In aircraft, stalling can be extremely detrimental to
flight and requires immediate action before the aircraft looses all lift.
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Lastly, the forces produce a moment or “pitching” moment about the airfoil with
the coefficient of moment formula described below. At the leading edge of the airfoil, the
moment has a negative slope as lift increases. There is a point on the airfoil where the
moment is zero, regardless of the magnitude of lift. This point is considered the mean
aerodynamic center.viii
CM= M12
ρ U∞2 Sx
Equation 13
Where M is the moment, ρ is density of the fluid, u or (U) is the freestream flow
velocity, x is chord length, and S is the area of the surface.
This pitching moment only occurs when an aerodynamic force, such as those
discussed above, is applied at the aerodynamic center of the airfoil. The aerodynamic
center is not quite the center of pressure on the airfoil but rather a point for which the
coefficient of the pitching moment remains nearly constant regardless of angle of attack.
2-D v. 3-D Objects
From what has been discussed about flow and drag, it is apparent that behavior of
flow is heavily dependent on the surface features of the object in contact with it. In the
wind tunnel test section of this experiment, the object in the flow could be considered
either two or three-dimensional.viii If the object spans the entire test section, the object is
considered to have infinite span from the perspective of the incoming flow. The flow
does not wrap around the edges of the object but only passes from above and below.
25
Therefore, the object is approximated as two-dimensional. An object that does not span
the entire width of the test section is considered three-dimensional
Figure 1.15: Two-dimensional body (left), three-dimensional body (right)
An object in two-dimensional flow has less drag than one in three-dimensional
flow. This is because a three-dimensional object has boundary layer separation on the
top, bottom, and sides, whereas a two-dimensional object would only experience that
separation on the top and on the bottom. As evidenced by Equation 10 for coefficient of
drag, the increased boundary layer separation and surface area will lead to increased
pressure drag. Lastly, additional energy in lost at the tips of the three-dimensional object
because of trailing vortices.viii
Von Karman Vortex Shedding – Unsteady Aerodynamics
Up until now, most topics discussed in this introduction have been explained in
terms of steady, inviscid, and irrotational flow behavior. These assumptions allow for the
26
Navier-Stokes equations to be simplified into Bernoulli’s. In reality, even everyday
phenomena are far more complicated to explain.
A Von Karman vortex street is a repeating pattern of swirling vortices caused by
unsteady separation of flow over bluff bodies.viii Depending on the Reynold’s number and
body parameters of the object, vortices can be continuously shed off the edges of the
body. Eventually, viscosity of the flow or fluid will drain the energy of the vortices and
cause them to die down with distance. Figure 1.16 below shows vortex shedding around
a cylinder.
Figure 1.16 viii
When a vortex is shed, it “changes the game” entirely when looking at normal
pressure distribution. The vortices shed can create lateral forces on the body in the flow.
The forces can cause the body to vibrate, and if the frequency of vibration is close to that
of the object’s natural frequency, resonance will occur. Resonance is a phenomenon that
can be destructive to many engineering systems and must be treated with care.
27
When considering a long cylinder, the frequency of vortex shedding can be found
by Equation 14 (which holds true for Reynold’s numbers from 250 to 2*10^5
magnitude):
f ∗dU∞
=0.198(1−19.7ℜ )
Equation 14
The dimensionless parameter to the left ( f ∗dU ∞
) is known as the Strouhal number.
This is a measure of the ratio of inertial forces due to unsteadiness of the flow to inertial
changes due to changes in velocity from point to point in the flow field.
28
III. Procedure
The following procedure for this lab was split over the course of two weeks. All
parts were performed by a group of about 10 engineering students.
Week 1
Equipment
Closed loop wind tunnel
Pitot-static tube
Aerolab Pyramidal Force Balance
o 3 load cells
NACA 0012 airfoil
Daytronic System 10 DataPac
Pressure Systems 9010 Optomux
3x 2” O.D. Cylinder
Pitot tube rake
Thermometer
Labview
Part 1: Force Balance and Calibration
1. Calibrating Lift
a. The carriage chord was run through three pulleys and connected to the
middle hole on the force balance.
b. A starting 5-pound weight was put on the carriage.
c. Labview was run to collect lift data from the weight.
29
d. The carriage weight was increased by 5 pound increments each trial.
e. Labview was run to collect data from each trial.
f. The trials continued until a carriage weight of 25 pounds was reached.
g. All measurements were saved and the weights were unloaded from the
carriage.
1. Calibrating Drag
a. A new Labview file was opened.
b. The carriage chord was removed from the middle hole and run through the
end hole on the force balance.
c. The 5-pound weight was loaded onto the carriage.
d. Labview was run to collect the drag data.
e. The carriage weight was increased from 5 pounds to 25 pounds in 5-pound
increments.
f. Labview was run to collect calibration data from each trial until 25 pounds
was reached.
2. Calibrating Moment
a. A new Labview file was opened.
b. The carriage, along with weights, was removed and placed aside.
c. A one-pound weight attached to string was strung around the first notch of
the top metal cylinder.
d. The distance was measured outward from the center of the cylinder.
e. Labview was run to collect the data.
30
f. The weight was moved to the next notch and the distance from the center
of the cylinder was noted.
g. Steps d-f were repeated until the last notch on the opposite side was
reached.
Part 2: Boundary Layer
The wind tunnel was run at 15 Hz for Part 2.
1. The access window to the wind tunnel was opened.
2. A pitot-static tube was placed in the first hole in the middle of the test section,
approximately 30 cm from the wall.
3. The pitot-static tube was aligned parallel to the freestream flow.
4. The pitot-static tube was moved toward the floor in 5 cm increments.
5. When the pitot static tube reached 5 cm off the wall, it was then moved toward
the floor in 0.5 cm increments.
6. The pressure was measured at each location and temperature was noted. (total of
10 times)
7. The pitot-static tube was moved to the second hole downstream and steps 3-6
were repeated with the tube in it’s new location.
Part 3: Wake
1. Wind tunnel was opened
2. The distance between each tap on the rake was measured.
3. The rake was the placed inside the wind tunnel, initially without the presence of
the cylinder.
31
4. Wind tunnel was turned on and run at 25 Hz.
5. Labview was run 20 times. With each time, pressure measurements were read and
recorded.
6. Cylinder was then mounted 6 diameters ahead of the rake in the wind tunnel.
7. The wind tunnel was then turned on and run again with the cylinder.
8. Labview was run again to record pressure data in a new file. (20 times to get the
average)
Week 2
Equipment
Closed loop wind tunnel
Pitot-static tube
Aerolab Pyramidal Force Balance
o 3 load cells
NACA 0012 airfoil
Daytronic System 10 DataPac
Pressure Systems 9010 Optomux
5x 4.8cm O.D. Cylinder
o Lengths: 10.5”, 18”, 20”, 22”, and 24” (convert to SI units)
Pitot tube rake
Thermometer
Labview 6i
Accelerometer
32
2x High Frequency Pressure Transducer
Part 1: Freestream Velocity
1. Pitot tube was placed upstream of the model. The angle of the pitot tube was
adjusted to be parallel to the freestream flow to achieve maximum dynamic
pressure.
2. Dynamic pressure was recorded 20 times for the average
Part 2: Airfoil
1. Airfoil was placed on top of the force balance in the wind tunnel.
2. The wind tunnel was turned on running at 30 Hz.
3. The angle of the airfoil was adjusted until the lift was equal to zero. In other
words, the degree of attack was zero.
4. Airfoil angle was then adjusted to -6 degrees. From here, lift, drag, and pitching
moment data were recorded via Labview.
5. The angle of attack was then increased by 2 degrees. (20 increments on the dial)
6. This was repeated until an angle of attack of 18 degrees was reached.
7. Wind tunnel speed was increased to 45 Hz (with a new Labview file)
8. Steps 4-6 were repeated.
9. The airfoil chord length and depth were measured.
Part 3: Cylinders
1. 20 measurements of dynamic pressure of upstream model were taken.
2. The length and outside diameter of each of the three cylinders were measured.
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3. The first cylinder, labeled number 1, was inserted into the wind tunnel.
4. The cylinder was placed perpendicular to the flow.
5. Wind tunnel was turned on at 30 Hz.
6. The drag produced from the cylinder was measured and recorded via LabView.
7. Steps 4-6 were repeated for each cylinder and mount alone, using new LabView
files for each.
Part 4: Vortex Shedding
1. The length and diameter of the cylinder were measured.
2. 24” long cylinder with accelerometer was secured into the first hole in the bottom
of the test section.
3. Wind tunnel speed was turned on to 35 Hz.
4. The dynamic pressure was measured 20 times to obtain the average.
5. The sampling frequency was set to 7500 Hz and 10240 sample time.
6. Accelerometer data was collected via LabView.
7. The wind tunnel speed was then increased to 40 Hz.
8. Steps 4-6 were repeated.
9. The old cylinder was removed and a cylinder with pressure transducers was now
placed in the wind tunnel.
10. The dynamic pressure was measured, again, 20 times.
11. Pressure data was recorded for several seconds.
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IV. Results and Discussion
Given the wide range of topics encompassed by this study, both theoretical and
practical, the lab work was split up into two weeks. During the first week, work was done
on force balance and calibration, experiments with the pitot-static tube, observing
boundary layers, and wakes caused by flow around cylinders. The second week included
studying flow around an airfoil, vortex shedding, and flows around 2-D and 3-D objects.
The results of each of these trials are published and discussed below. All data presented is
in SI units.
Week 1
Part 1: Force Balance and Calibration
This part was in essence the simplest part of the lab to collect data from, yet very
important. A force balance with attached to known weights was used to calibrate the load
cells in the sensors. As discussed in the introduction, this was done to prevent “drift” and
to ensure that the integrity of the results obtained further in this lab not be compromised
by error due to drift.
Using the force balance, Labview, and the setup described in the procedure,
results were calibrated for lift force, drag, force and moment. Figure 1.1.1 in this section
shows each plot where lift, drag, and moment are respectively are plotted against the
voltage readings from the load cells. It stands to reason that when no weight is applied,
there should be no force reading.
The drift for the moment data was the farther than the drift seen in the lift and
drag data. A line of best fit was taken through the data points and the y-intercept was
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recorded for each. The data was linear, as expected, therefore each line of best fit was in
the format of y=m*x+b. All data was effectively “zeroed” using the y-intercept
information for lift, drag, and moment.
Figure 1.1.1
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Part 2: Boundary Layer Test
The wind tunnel and a pitot-static tube were used to emulate boundary layer
flow conditions in this section. The wind tunnel was run at a speed of 15 Hz, once
with the pitot-static tube in a location upstream relative to the flow and another
where the tube was downstream. At each location, the tube was first placed about
25 cm above the ground, and then lowered incrementally, and the wind tunnel was
run each time the tube was lowered. At every height, the tube collected pressure
readings which were taken and converted into velocities using Bernoulli’s
equations. Moving the tube closer and closer to the flat surface of the wind tunnel
showed the change in the velocity profile of the fluid near the boundary layer of the
flow. Figure 1.2.1 has the results of both the upstream and downstream velocity
data.
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Figure 1.2.1
The results of Figure 1.2.1 show the upstream and downstream trends in velocity
from a tube height of about 25 cm above the ground to about 0 cm. The data obtained is
in accordance with the boundary layer theory discussed in the introduction. Starting with
the similarities, the freestream flow velocity of both profiles remained consistent for a
tube height of about 1 to 25 cm with upstream flow at around 12.6 m/s and downstream
flow at about 13.7 m/s. The flow down the center of the wind tunnel notably displays
steady-state qualities. Observing the upstream profile, at about 0.5 cm from the flat
surface, there was a drop in velocity. Velocity continued to decrease in large increments,
indicating that the flow was experiencing the viscous effects of the boundary layer. The
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same velocity drop happened with the downstream velocity profile at around a height of 1
cm off the wind tunnel floor.
At a small distance off the ground, both of the flows began experiencing viscous
effects and exhibiting turbulent behavior. The drop off in velocity confirms that the flows
encountered the “no-slip” condition when at the boundary layer.
The relatively quick drop in velocity over a small distance in the upstream profile
demonstrated how thin the boundary layer was. The downstream velocity profile
experienced a slower decrease at a greater height from the surface. This indicates that the
boundary layer downstream was thicker than the one upstream. This reinforces the theory
behind boundary layers: fluid viscosity and turbulent behavior had a slightly greater
effect downstream than the effect seen upstream.
Part 3: Wake Test
In this section, a cylinder was placed in the wind tunnel to examine the effect
a bluff body would have on a flow. This portion was run twice: once at 30 Hz and
once at 45 Hz. For each speed, the tunnel was run once without the cylinder to
obtain the accurate freestream velocity of the flow at every other tap in the rake
tube. Figure 1.3.1 below shows the velocity data collected at 30 and 45 Hz, both with
and without the presence of the cylinder. Table 1.3.1 has the quantitative results for
this section.
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Figure 1.3.1
The flow without the cylinder was consistent for the most part as expected. The
spike in the blue lines in Figure 1.3.1 must be attributed to error. It is possible that one of
the taps on the rake tube was bent or not reading accurately. Nevertheless, the flow acted
as expected with the presence of the cylinder.
The flow passing at the far ends of the cylinder hitting the first and last pins on
the rake tube had the same velocity as the freestream. Since the cylinder spanned the
entire width of the test section, it is considered a two-dimensional flow. Moving more
towards the center, there was a noticeable decrease in velocity. This is in accordance with
the theory discussed above: the flow hitting the front of the cylinder creates a stagnation
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point. The wake directly behind that point contains turbulent fluid motion. As a result of
more fluid particles colliding in turbulent flow, velocity is decreased.
Using the given parameters for this section, the drag and coefficient of drag were
calculated along with the momentum deficit and Reynold’s numbers. As discussed in the
introduction, the presence of a bluff body, such as a cylinder, produces a momentum
deficit. The results were exactly as expected with the momentum deficit calculated as the
area between the two curves. The drag force and coefficient of drag were calculated using
the Equations 9 and 10 in the introduction, and the numbers made sense given the
freestream velocity.
Table 1.3.1
30 Hz 45 Hz
Momentum Deficit 17.747 28.165
Drag Force (N) 40.916 ± 4.93 98.043 ± 12.44
Coefficient of Drag 1.45 ± 0.18 1.49 ± 0.18
Reynold’s Number 1.074*10^5 ± 2.70*10^3 1.644*10^5 ± 4.18*10^3
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Week 2
Part 1: Airfoil Test
The purpose of this section was to examine properties of a flow over an airfoil.
The angle of attack of the airfoil was changed from -6 to 18 degrees in 2-degree
increments. The data was taken at 30 Hz and again at 45 Hz. Lift, drag, moment and
their corresponding coefficients were calculated and analyzed in this section.
Strings were attached to the front of the airfoil to indicate stalling or to help
visualize when the boundary layer begins to separate from the airfoil.
Figure 2.1.2
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From the above graphs, it is easy the see the trends between each coefficient and
the angle of attack. The coefficient of lift was observed to increase with increasing angle
of attack. At about 17 degrees, the plot shows the coefficient of lift drops and then levels
out, indicating a stall. At this same angle, the drag force on the airfoil increased. This is
the point where the tufts (strings) visibly separated from the airfoil. At this point, viscous
effects became prevalent as the boundary layer further separated from the airfoil. The
logistics of a stall are discussed more in depth in the introduction.
Table 2.1.1
30 Hz 45 Hz
Slope of coefficient of lift v. angle of attack
1.604 1.679
Reynold’s Number 3.00*10^5 ± 3.113*10^4 4.469*10^5 ± 4.634*10^4
Table 2.1.1 displays some of the quantitative data collected in this section. The
ideal or theoretical value for the slope of the coefficient of lift v. angle of attack is about
6.28. The results obtained in this section do not match up exactly with the ideal number.
Some of this discrepancy could be attributed to error in conducting the experiment or in
the collection of the data. The main difference is that the airfoil that was used during this
section was not “thin” and therefore would not produce the same amount of lift as the
airfoil being considered in the theoretical calculation. The slope values and Reynold’s
numbers along with the graphs obtained from this section do in fact confirm the
theoretical fluid principles concerning airfoils.
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The Reynold’s number directly affects the coefficients of drag and lift, as
discussed in detail in the introduction. With decreasing Reynold’s number drag increases
and lift decreases. The results obtained in this section are in accordance with this theory.
Part 2: Cylinder Drag Test
Different cylinders were used in this portion of the experiment to examine
how aspects of drag changed with varying lengths. Table 2.2.1 below shows the
coefficients of drag and Reynold’s numbers measured for each cylinder. Differences
were also examined in the flow with both two-dimensional flow and three-
dimensional flow occurring for different cylinder lengths.
Table 2.2.1
Cylinder 1 Cylinder 2 Cylinder 3 Cylinder 4 Cylinder 5
Length (m) 0.603 0.559 0.508 0.457 0.267
Coefficient of Drag
0.7035 ± 0.0871
0.6344 ± 0.0785
0.6070 ± 0.0751
0.6150 ± 0.0761
0.5205 ± 0.0644
Reynold’s Number
9.971*10^4 ±1.2*10^4
9.975*10^4 ±1.2*10^4
9.978*10^4 ±1.2*10^4
9.982*10^4 ±1.2*10^4
9.986*10^4 ±1.2*10^4
Though the lengths do not differ much, there is still a noticeable change in each
drag coefficient. As cylinder length decreases, the coefficients of drag also decrease.
Considering the formula for drag, area (or characteristic length) directly factors in. It
makes sense that the Cylinder 5, the one with the least area in contact with the flow, has
the lowest coefficient of drag. Since the Reynold’s number is inversely proportional to
the coefficient of drag, it increases as coefficient of drag decrease. All of the empirical
44
results found here validate the preexisting theory. Comparison with other data found on
the web further validates these results.
The cylinder that was used in the wake test spanned the length of the entire test
section and, therefore, was characterized as two-dimensional flow. The cylinders used in
this section did not span the length of the test section. In addition to going above and
below the cylinders, the airflow also passed from the sides. As a result, the cylinders in
the three-dimensional flow experienced more drag.
Part 3: Vortex Shedding
The final part of this two-week experiment was done for the purpose of
generating and observing unsteady flow. This section was run twice: once at 35 Hz
and a second time at 40 Hz. Data was collected for both runs off of a pressure
transducer and an accelerometer. The results in Table 2.3.1 below shows all of the
quantitative data collected in this section.
Table 2.3.1
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Vortex shedding frequency was calculated twice: once with the use of the
empirical formula given in the introduction and once by using the maximum point on the
frequency domain plots shown below. A fast Fourier transform was used to take the plots
from the accelerometer and pressure transducer data and converted them to the frequency
domain. The measured values from the accelerometer and transducer data were relatively
similar for each given run. The empirical results were off by a small factor. The
discrepancy in these values could be attributed to uncertainty in measurement.
Looking at Figures 2.3.1. and 2.3.2 below, the accelerometer data indicates that
the cylinder vibrated most violently at a wind tunnel speed of 35 Hz. The noise from the
time domain data had greater amplitude in the 35 Hz run than the 40 Hz trial. The
frequency domain data also pointed to a larger spike in the 35 Hz run. The magnitude of
the vibrations were most likely caused by how close the vortex shedding frequency was
to the cylinder’s natural frequency. In other words, the most violent vibrations did not
occur at the faster wind speed because, even though velocity was greater, the vibrations
46
from the vortices were at a frequency farther from the cylinder’s natural frequency. This
is in accordance with the theory discussed in the introduction: if the frequencies produced
by vortex shedding are close to the natural frequencies of the object in the flow, the
object can reach resonance.
Vortex shedding frequency can be deduced using empirical methods, pressure
data, and accelerometer data. The accelerometer data provides the most direct
experimental way to find frequency. Using Fourier analysis, data in the pressure data in
the time domain can be converted into frequency data. Empirically, vortex-shedding
frequency is related to freestream velocity and Reynold’s number of a flow. The results
of this last section are all in accordance with fluid theory.
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V. Conclusion
The work done in this lab merely scratched the surface of the complex and
intricate field of fluid mechanics. The simple ideas explored here develop into profound
applications of fluids in engineering. The first portion of the lab demonstrated how
important calibration was to lessen error in calculation. The boundary layer portion of
this test was relatively simple to conduct but has profound theory backing the actual
experiment. Parameters such as the Reynold’s and Strouhal numbers play a vital role in
flow. Laminar and turbulent flow were first introduced when examining boundary layer
separation. The concepts governing boundary layer separation were directly related to
studying the behavior of wakes. Understanding how an object in a flow creates drag
force, lift force, moments, and their respective coefficients was undoubtedly one of the
most important lessons to be learned. That understanding was then used to analyze flow
around an airfoil. Studying the airfoil alone and how angle of attack affected the forces
present as a result of airflow led to a slightly better understanding of how immensely
large objects such as planes can lift off the ground. Vortex shedding was the last thing
examined in this lab because it involved an examination of unsteady flow: notably a
difficult area to understand even in the field of fluids.
Fluid mechanics is a discipline based on both complex physical laws and
seemingly impossible math. The subject incorporates an endless number of theories and
ideas that are interrelated to analyze flows. The intricacy of flows go well and beyond the
scope of what was examined in this lab. All else aside, without knowledge and
application of fluid mechanics, many of the engineering marvels in the world today
simply would not exist.
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