Comprehensive Research Paper: Wind Tunnel Testing and Fluid Dynamics

This research paper provides a comprehensive overview of wind tunnel testing, focusing on the principles of fluid dynamics and aerodynamics. It begins by classifying fluid flow regimes, including hypersonic, supersonic, sonic, transonic, and subsonic flows. The paper then delves into the fundamental forces of pressure, thrust, lift, and drag, explaining their calculation and significance. Bernoulli's principle is discussed in relation to lift generation, followed by an explanation of velocity measurement using a Pitot tube. The Magnus effect is also examined, detailing its impact on rotating spheres in fluid flow. The paper concludes by emphasizing the importance of wind tunnel testing in education and product development, particularly in improving efficiency and preventing structural failures. Desklib offers a platform for students to access this and similar research papers, along with a wealth of study resources.

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RESEARCH PAPER ON WIND TUNNEL TESTING
A Research Paper on Wind Tunnel By
Student’s Name
Name of the Professor
Institutional Affiliation
City/State
Year/Month/Day

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INTRODUCTION
The wind tunnel can be defined as a system that can be used to produce a rapid
air stream through a section of testing in which a series of objects or an object is
located. The major reasons for carrying out such tests are to evaluate the structural
and/or aerodynamic effect of the object under consideration through simulating travel
through wind or air on a structure. Wind tunnels are normally used in testing buildings,
bridge structures, ground vehicles, wind sections, and aircraft, all in small scale.
Classification of Fluid Flow Regimes
Math number (M) can be defined as a quantity with no dimension representing the ratio
of the speed of sound to the flow velocity past a boundary.
Math Number, M = u
c , where c is the speed of sound in the medium and u is the local
velocity relative to the boundaries. Math number, M can range from 0 to , however,ꝏ
this broad range can be grouped into numerous flow regimes. These regimes include
hypersonic flow, supersonic flow, sonic flow, transonic flow, and subsonic flow.
Hypersonic flow: This is when the flow math number is greater than 5 as per the thumb
rule (Childress, 2009).
Supersonic flow: This is when the flow Math number is greater than everywhere in the
domain. This flow is not pre-warned because the speed of the fluid is greater than the
speed of sound.
Sonic flow: This is when the flow Math number is equivalent to one.
Transonic flow: This is when the flow Math number is between the range 0.8 and 1.2.
Highly unstable and mixed supersonic and subsonic flows are the major characteristics
of this regime (Gülçat, 2015).
Subsonic flow: This is when the flow Math number is in the range of 0 to 0.8 or below 1,
i.e., the fluid velocity is lower than the acoustic speed. However, flow Math number
varies while passing through a duct or over an object.

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Drag, Lift, Thrust, and Pressure
Pressure
Pressure is the amount of force applied perpendicularly to the object surface per unit
area. Mathematically, pressure, P can be expressed as:
P = F
A ; Where F is the magnitude of the normal force A is the contact surface area. The
most important variables when calculating pressure are the Force and Area of the
surface in contact (Jakobsen, 2014).
Thrust
Thrust can be defined as the force applied to a surface in a direction normal or
perpendicular to the surface. Thrust, T can be mathematically expressed as:
T = v dm
dt where v denotes the speed of the exhaust measured relative to the rocket
and dm
dt is mass flow rate or the rate of variation of mass relative to time. The most
important variables when calculating thrust are the velocity, mass, and time of surface in
contact.
Lift
Lift is a force that conventionally acts in an upward direction so as to counter the
gravitational force, however, the lift force can also act in a given direction at a right
angle to the flow. In the case of an aeroplane, lift, L can be calculated as:
L = ½ vꝭ 2SCL
Where; CL is the lift coefficient, S is the wing area, v is the velocity, is the air density,ꝭ
and L is the lift force. The most important variables when calculating lift are the area of
the surface, the velocity of the fluid, fluid density, and lift coefficient (Ledoux, 2017).
Drag

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This is a force acting opposite with respect to the relative motion of an object relative to
the surrounding fluid. Drag force can be calculated as:
FD = ½ vꝭ 2CDA; Where A is the area of cross-section, CD is the drag coefficient, v is the
velocity of the object with respect to the fluid, is the fluid density, and Fꝭ D is the drag
force. The most important variables when calculating drag are the area of the surface,
the velocity of fluid, fluid density, and drag coefficient (Palmer, 2011).
Bernoulli’s Principle in the Theory of Lift Generation
The generation of lift is normally explained in terms of Bernoulli's Principle which
states that for an incompressible, steady, and non-viscous fluid, the sum of kinetic,
potential energies, and pressure per unit volume at any point is constant. When
potential energy is ignored because of altitude, the Bernoulli’s Principles states that
when the velocity of a fluid increases, there is a decrease in pressure by an equal
quantity to maintain the overall energy (Pillai, 2010). From the Bernoulli's Principle, the
passing air over the wing’s top or aerofoil must propagate faster and further compare to
a similar air propagating the shorter distance below the wind in the same moment but
the energy related with air must be constant at every moment. The results of this is that
the above air the aerofoil has lesser pressure compared to the air beneath the wing and
this variation in pressure results in the generation of lift (Rathore, 2010).
The principle of Velocity Measurement by Pitot tube
The pitot tube is an adaptable and reliable measuring device for fluid velocity.
The pitot tube is used in airspeed sensor in the nose or wing of an aircraft, but the
device can be used to measure the velocity of any fluid moving.
Figure 1: Pitot tube (Vennard, 2013)

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The pitot tube works by the measuring the difference between pressure due to the
momentum or velocity and the static pressure of the flowing fluid of the fluid molecules.
The static pressure, Pstat, can be defined as the pressure without considering the motion
and is determined by inserting an open-tube probe into the fluid so that the opening is
parallel to the flow direction. The total pressure (stagnation) which is the pressure due
to fluid momentum can be determined by inserting an open-tube probe facing upstream
directly. In case both the probes are joined to two sections of diverse pressure gauge as
shown below, the gauge reading is the pressure difference and is known as velocity
head (Vennard, 2013).
ΔP = velocity head = Ptot – Pstat …………………………………………….. (i)
Work per unit mass can be determined by:
W = (Ptot – Pstat)/ ………………………………………………………….. (ii)ꝭ
Since the only form of storable energy that varies in equation (i) is kinetic energy, then:
(Ptot – Pstat)/ P = -(ke) = (Vs2)/2 - (Vtot2)/2 …………………………………… (iii)
Where ½ v2 is the kinetic energy per unit mass and Vs is the velocity of the undisturbed
flowing gas. Vtot = 0 since it is the velocity at the stagnation point. Hence, the velocity of
moving fluid is:
Vs = {2 * ((Ptot – Pstat)/ )ꝭ 1/2 or ………………………………………………... (iv)
Vs = {2 * ΔPp/}1/2 …………………………………………………………….. (v)

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Magnus Effect
Magnus effect or force is observed when a rotating sphere in uniform flow
experiences a lift which causes the object to drift across the flow direction. The rotation
of a sphere that is rigid will result in the surrounding fluid to be entrained. When the
sphere is positioned in a uniform flow, this will result in higher angular velocity on one
side of the sphere, and lower angular velocity on the other section of the sphere. This
provides an asymmetrical pressure distribution around the object (Wight, 2012). This
will result in a lift on the sphere that moves the sphere towards the area of higher local
angular velocity as shown in the figure below:
Figure 3: Magnus lift force on a rotating sphere (Wight, 2012)
Magnus force, FM can be expressed as:
FM = ½ CL vꝭ 2A; Where CL is the coefficient of lift, A is the characteristic area, v is
velocity magnitude, and is fluid densityꝭ
Conclusion
A wind tunnel is also an important tool in education for studying aerodynamics
and fluid dynamics. The investigation of the aerodynamic behaviour of a product can be
used in improving the efficiency and prevention of disastrous failure. Such as
experiments of wind tunnels on cars can minimize consumption of fuel by reducing drag
or aerodynamics of bridge can be performed so as to evaluate the wind forces that will
be exerted on it.

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Reference
Childress, S., 2009. An Introduction to Theoretical Fluid Mechanics. London: American Mathematical Soc.
Gülçat, Ü., 2015. Fundamentals of Modern Unsteady Aerodynamics. Michigan: Springer.
Jakobsen, H., 2014. Chemical Reactor Modeling: Multiphase Reactive Flows. London: Springer Science &
Business Media.
Ledoux, M., 2017. Fluid Mechanics. Colorado: John Wiley & Sons.
Palmer, G., 2011. Physics for Game Programmers. Sydney: Apress.
Pillai, N., 2010. Principles Of Fluid Mechanics And Fluid Machines. Berlin: Universities Press.
Rathore, M., 2010. Thermal Engineering. New York: Tata McGraw-Hill Education.
Vennard, J., 2013. Elementary Fluid Mechanics. Melbourne: Read Books Limited.
Wight, G., 2012. Fundamentals of Air Sampling. California: CRC Press.
Zohuri, B., 2017. Thermal-Hydraulic Analysis of Nuclear Reactors. Perth: Springer.