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INTRODUCTION
The basic aim of aerodynamics is to obtain the flow quantities
(especially, pressure
distribution and skin friction) about a body immersed in fluid.
Very often, the interest is
limited only to obtain the overall forces and moments acting on
the body.
There are two main ways these quantities can be found;
theoretically and experimentally.
Both the procedures have their relative advantages and
disadvantages and have acted and
are going to act as supplementary to each other in foreseeable
future
The limitation of theoretical methods basically stems from the
fact that the governing
equation of real fluid about a body the Navier-Stokes equation
can not, in general, be
solved theoretically. The theoretical methods are usually based
on some simplified form
of this equation. With the assumption of inviscid (infinite
Reynolds Number) and
incompressible (zero Mach number) flow, i.e., the ideal flow,
the Navier Stokes equation
can simplified to Laplaces equation. The solution of this ideal
flow, because of the above
simplification, differs from the experimental results. Efforts
are then made to employ
some corrections due to the effects of viscosity and
compressibility.
Even with simplification of inviscid incompressible flow, it is
not easy to solve the
problem. For a few simple configurations, exact analytic
solutions exist (Chap. 5).
Configurations of arbitrary shape are not amenable to analytic
methods and demand
numerical solution. In the early days, a variety of approximate
numerical methods were
developed. Examples are the different variants of linearised
theory by Munk, Weber etc.
for aerofoil problems, Prandtls lifting line theory, Multhopps
lifting surface theory,
Jones slender wing theory etc. for wing problems. With the
advent of high speed digital
computers, more sophisticated exact numerical methods (Panel
method) have been
developed. A variety of computer based theoretical schemes are
also developed for
effecting the corrections due to viscosity and compressibility
to these solutions.
Alternatively, attempts have been made to develop Euler as well
as Navier-Stokes codes
with or without turbulence modeling.
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It is almost certainly the case that however sophisticated these
theoretical methods may
eventually become the engineer will always wish to validate his
design, prior to
manufacture, by means of physical experiment. In this respect,
in aircraft industry, the
wind-tunnel experimentation will always play the superior role
of the two.
Wind-tunnel testing, like the theoretical calculations, has its
own deficiencies and
difficulties. Broadly speaking these are : the high capital and
running cost associated with
a wind tunnel, the expenses, elapsed time and skill needed in
manufacturing accurate
scale models, the difficulty in obtaining the adequate data
(forces, pressure distribution
etc.), the difficulty of interrogating this data.
Students of aeronautical engineering are well aware of the fact
that the forces and
moments etc. experienced in flight on an aircraft depends
primarily on two non-
dimensional parameters : Reynolds number and Mach number.
Reynolds number
expresses the relative contributions of inertia and friction
forces in the motion of the
fluid. The Mach number is the ratio of the flight speed and the
speed of sound. In general
it can be stated that only a full scale model operating at full
scale speed can give a totally
correct simulation of a real aircraft in flight. However,
because of power conservation
problem (specially for high-speed flow) the wind-tunnel model is
generally constructed at
a much smaller scale than the real aircraft. This in itself
presents numerous difficulties
associated with the acquisition of sufficiently detailed data on
such a small model.
However a more serious problem arises in simultaneously
recreating the Mach number
and Reynolds number experienced in flight.
If the working medium and its temperature are the same in the
wind-tunnel as in full-
scale flight in the atmosphere, then proper matching of the Mach
numbers requires the air
speeds to be the same in both cases. If this is not achieved,
then at Mach numbers of
interest of most aircrafts, the effects of compressibility will
be different between the
wind-tunnel and flight.
On the other hand, if the speeds are kept same for Mach number
simulation, the Reynolds
number in the wind-tunnel will be reduced (proportional to the
geometric scale of model)
relative to the real aircraft. Clearly, if the wind-tunnel speed
is increased to approach
full-scale Reynolds number then the Mach number will be
incorrectly simulated.
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Now many vital phenomena depend strongly on the Reynolds number
and these include :
development of boundary layer, transition from laminar to
turbulent boundary layer,
separation of boundary layer, vortex formation at high angle of
attack etc. If the Reynolds
number is not matched properly, viscosity will be incorrectly
simulated.
Numerous technological approaches have been proposed to overcome
such difficulties.
One of these consists of modifying the properties of working
medium and in particular
working at very low temperature or at high pressure. These
approaches, in turn, present
other difficulties. However, since the present study is
restricted to low speed regime
where compressibility effects are negligible, matching of both
parameters is not
necessary and simulation of Reynolds number alone is
sufficient.
The other difficulties associated with wind tunnel testing arise
from the fact that the flow
conditions inside the tunnel are not exactly the same as those
in the free air. Primarily, the
air in the tunnel is considered to be more turbulent than the
free air this turbulence being
produced in the tunnel by propeller, vibrations of the tunnel
walls etc. This consequently
increases the effective Reynolds number of the tunnel (Section
3.5). Excessive turbulence
makes the test data unreliable and difficult to interpret.
Secondly, the wind-tunnel model experiences spurious constraint
effects due to wind-
tunnel walls (chapter 10 and 11) which will be absent in free
air. These extraneous forces
must be calculated and subtracted out. These forces arise from
two sources. Due to
formation and growth of boundary layer in the test section, the
effective area is
progressively reduced resulting in increase of velocity and
decrease of static pressure
downstream. This variation of static pressure produces a drag
force known as horizontal
buoyancy. Again, the presence of a model in the test section
reduces the area through
which air flows. This blockage caused by the model and its wake
effectively increases
the average air speed in the vicinity of the model than they
would be in free air, thereby
increasing all forces and moments at a given angle of
attack.
Thirdly, the model in a tunnel is usually installed by some
supports which in turn affect
the flow. The effect of this supports (the so-called Tare and
Interference effects,
section 6.4) need to be calculated carefully and eliminated from
observed values.
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The procedure involved in wind-tunnel testing may now be
summarized. The prerequisite
of any experimental work is the calibration and evaluation of
the tunnel (Chapter 3)
itself. The wind-tunnel must be pre-calibrated to give the
velocity of air flow during any
testing (since it is not practical to measure the velocity by
pitot-static tube while the
model is in tunnel). The flow characteristics of the tunnel must
be ascertained by
measuring the variation of velocity (static pressure) in the
test section, flow angularity
and the turbulence level of the tunnel.
Wind-tunnel testing, then, involves model making, installation
of model in the tunnel and
measuring forces, moments, pressure distribution etc. the forces
and moments may be
obtained by any of the three methods :
a) Measuring the actual forces and moments with wind-tunnel
balance
b) Measuring the effects that the model has on the airstream by
wake survey (profile
drag, section 12.2)
c) Measuring the pressure distribution over the model by means
of orifices
connected to manometer and integrating the pressure distribution
over the model
surface.
The data acquired is then to be corrected for the tunnel
boundary and support effects.
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Chapter 1
WIND-TUNNEL
1.1 Introduction : The wind-tunnel is one of the most important
facilities available for experimental work in
aerodynamics. Its purpose is to provide a region of controlled
airflow into which models
can be inserted. This region is termed the working section or
test section. For aeronautical
work, the flow in the test section should ideally be perfectly
uniform in speed, direction
and vorticity. Such perfection can never be achieved in practice
and the quality of a wind-
tunnel is related to the closeness to which the airflow in the
test section approaches the
ideal.
1.2 Wind Tunnel Classification : Wind-tunnels are usually
classified according to the three main criteria :
i) the type of test section
ii) the type of return circuit
iii) the speed of flow in the test section
1.2.1 The type of test section:
The cross sectional form of a test section may be square,
rectangle, octagonal, circular or
elliptic. Again, it can be closed or open. A closed test section
is one which is completely
enclosed within solid walls, the airflow therefore being
constrained by these walls. An
open test section is one which is not enclosed within solid
walls (Fig. 1.1). Because the
flow is not constrained, it usually tends to expand, partly due
to pressure difference and
partly due to mixing between the air in the test section and
that outside. To allow for this
expansion, the downstream part of the tunnel is
bell-mouthed.
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Figure 1.1 Open test section
Comparing these two types of test section, the closed type has
the following advantages :
a) greater efficiency (i.e. reduced power losses)
b) better control of air flow
c) no loss of air
d) less noise
On the other hand, the open type of test section allows easier
access to the model and
easier visual study of the flow.
1.2.2 The type of return circuit
A wind tunnel may either be open-circuit or closed-circuit
tunnel. The open circuit tunnel
which is open at the both ends has no guided return of the air
(Fig. 1.2). After the air
leaves the tunnel it circulates by devious paths back to
intake.
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Figure 1.2 Open circuit tunnel
The closed circuit tunnel has, as the name implies, a continuous
path for the air (Fig. 1.3).
The whole circuit, except possibly the test section, is
enclosed.
1.2.3 The speed of flow in the test section:
Five categories of speed are usually recognized :
a) low speed (up to about 60 or 70 m/s)
b) high speed subsonic (but Mach number less than 0.9)
c) transonic (Mach number between 0.9 and 1.2)
d) supersonic (Mach number between 1.2 and 5)
e) hypersonic (Mach number greater than 5)
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Figure 1.3 Close circuit tunnel
The first two categories, low speed and high speed subsonic, are
often taken together as
subsonic tunnels.
1.3 Types of Wind Tunnel :
1.3.1 Subsonic Wind Tunnel :
The simplest kind of subsonic tunnel consists of a tube, open at
both ends, along which
the air is propelled. The propulsion is usually provided by a
fan downstream of the test
section (a fan upstream would create excessive turbulence in the
working section. Fig. 1.2
represents a tunnel of this type.
The following description relates to Fig. 1.2. The mouth is
shaped to guide the air
smoothly into the tunnel; flow separation here would give
excessive turbulence and non-
uniformity in velocity in the test section.
To make the flow parallel and more uniform in speed and top give
a little time for
turbulence to decay, the mouth is followed by a settling
chamber. The settling chamber
usually includes a honeycomb and wire-mesh screens.
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A honeycomb is a coarse mesh made of thin, broad plates set
edgewise to the flow. It has
two purposes. First, it helps to guide the air to flow parallel
to the tunnel axis. Second, if
there are any large eddies in the incoming flow, the honeycomb
cuts them into smaller
ones which can decay more rapidly than would the original larger
ones.
The mesh-screens are fitted to reduce non-uniformities in flow
speeds. A typical
installation might have one or two. The effects of screens on
dynamic pressure variation
in the test section is shown in Fig. 1.4. The screen also serves
to reduce the turbulence
level of the tunnel.
Figure 1.4 Effect of screen
The contraction followed by the settling chamber improves the
quality of flow in the test
section. The air flows from the mouth of the tunnel at low speed
into a comparatively
short settling chamber with a honeycomb and mesh screens. It is
then accelerated rapidly
in the contraction. The contraction reduces turbulence and also
non-uniformities in flow
speed and direction.
The test section is followed by a divergent duct, the diffuser.
The divergence results in a
corresponding reduction in the flow speed, which has two
principle effects. Firstly, it
enables an increased fan efficiency to be achieved. Secondly,
the reduction in dynamic
pressure leads to reduced power losses at the exit from the
tunnel in the laboratory.
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Leaving the diffuser, the air enters the laboratory, along which
it flows slowly back to the
mouth of the tunnel.
A typical tunnel will have a working section of about 1 meter
square and an overall
length of some 5 to 7 meters. The speed in the test section,
will be controllable, upto
about 30 m/s.
1.3.2 Transonic Tunnel:
The main special feature of a transonic wind-tunnel is its test
section. In this, test section
walls are neither open nor closed but a combination of both. The
walls usually have
perforation or streamwise slots. The reason is as follows :
If, as an Fig. 1.5 an aerofoil is being tested in a transonic
flow, shock waves occur. If the
walls were solid these shockwaves would be reflected from them
and would impinge on
the model. The flow over the model would therefore be very
different from that in free
flight and the test would be invalid.
If the test section were open, there would be a boundary between
the jet and the
surrounding atmosphere; the shock (compression) waves would be
reflected from this
boundary as expansion (rarefaction) waves. These would impinge
on the model, so again
the test would be invalidated.
Figure 1.5 Reflection of shock wave
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If the walls are perforated or slotted (i.e., the test section
is partly opened and partly
closed), the reflections are mixtures of compression waves and
rarefaction waves and so,
depending on the degree of perforation, these tend to cancel
each other out. The flow
over the model therefore approximates more closely to that in
free flight.
1.3.3 Supersonic Wind Tunnel:
The simplest form of supersonic wind-tunnel is the blow-down
type (Fig. 1.6). It consists
of a convergent-divergent duct whose upstream end is connected
to a tank filled with
compressed air. The downstream end is usually open to the
atmosphere. The air in the
tank then discharges through the duct. This means, of course,
that the pressure in the tank
fall continuously, and therefore a reducing valve is fitted to
maintain a constant pressure
at the inlet of the duct. The duration of each test run is
necessarily limited with this type
of tunnel.
The blow-down type of tunnel is relatively cheap. In particular,
a relatively low-powered
pump can be used to pressurize the tank taking, of course, a
correspondingly long time to
do so. The power expanded in driving the tunnel during a test Is
many times greater than
the power of the pump.
The test section of this type of tunnel is followed by a
convergent-divergent duct. It can
be shown that if the pressure ratio between the two ends of a
convergent-divergent duct
exceeds 1.892, the flow is sonic (M=1) at the throat and
supersonic downstream. A plane
downstream of the throat can therefore be used as a test section
in which the flow is
supersonic.
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Figure 1.6 Supersonic wind tunnel
The Mach number at the test section will depend only on the
cross-sectional areas at the
throat and the test section.
32
.
651
+=
MMA
A ST (1.1)
This shows that the test section Mach number is determined
solely by the shape of the
tunnel (provided the pressure ratio is sufficient to maintain
supersonic flow through the
test section). Because of this supersonic tunnels frequently
consist of a basic frame to
which various liners can be fitted. Each liner gives a unique
area ratio and therefore a
unique Mach number in the test section. The shapes of some
different liners for various
Mach number are illustrated in Fig. 1.7.
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Figure 1.7 Shapes of liners
1.3.4 Hypersonic Wind Tunnel :
The main special feature of hypersonic wind tunnel is that
provision must be made for
preheating the air before entering the tunnel.
By suitable design of lines i.e. providing the large area ratio
AT*S/ A* for generating high
Mach number, the Mach number in the test section of a supersonic
wind-tunnel may be
increased to hypersonic regime. But another consequence of
expanding air to high speed,
namely its change in temperature, becomes limiting criterion.
The equation for the
temperature ratio along a streamline originating in a region
where the flow is at rest with
temperature T0 and terminating where the temperature is T is
given by
5
12
0 MTT
+= (1.2)
For M = 10, this equation gives T =T0/21. Now if T0 be the
absolute temperature 228k
then the wind temperature in the test section will be 13.5K.
This is well below the
temperature where air becomes liquid. Thus a limiting Mach
number in the test section
would be one at which air remains gaseous.
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The obvious choice for increasing this limiting Mach number is
not preheat the air to be
used in the tunnel to such an extent that the very low
temperature in the test section is not
realized. Another choice is to use a gas which has very much
lower condensation
temperature than air, e.g. helium. The majority of hypersonic
tunnels, however use the
preheating method. The preheating of air may be done by heating
the reservoir air or
alternatively to allow the air to pass through a heat exchanger
as it leaves the reservoir to
enter the working section.
Apart from these wind tunnels, other types of wind tunnels are
also designed and
fabricated. The effort to simulate both Mach number and Reynolds
number of free flight
in wind-tunnel has resulted in development of two types of
tunnels :
1. Full Scale Tunnel
2. Compressed Air Tunnel
1.3.5 Full Scale Tunnel :
The Full Scale Tunnel is capable of testing actual aircrafts of
moderate size under near
flight condition. The wind tunnel, developed at Langley Field,
U.S.A., attains wind
velocities up to 53m/s with an open jet 18m wide and 9m high.
Apart from providing a
total simulation of Mach number and Reynolds number, such wind
tunnels also serve a
useful purpose in giving a correlation between flight and small
model tests.
1.3.6 Compressed Air Tunnel :
The use of high pressure and therefore a high density in the
test section can help to
achieve full scale Reynolds number with relatively small and low
speeds. Some tunnels
are therefore completely enclosed in a large tank which can be
pumped up to several
times atmospheric pressures. Such tunnels are termed compressed
air tunnels.
It is worth mentioning that high pressure is no cure-all for
getting a high Reynolds
number since model strength may be a limiting factor.
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1.3.7 Other Tunnels :
There are also other types of tunnels built for various
purposes. Some of these tunnels
are:
Smoke tunnel : For flow visualization
Spin Tunnel : For studying spin recovery
Low Turbulence tunnel : For testing at high Reynolds number
Stability Tunnel : For studying dynamic stability
Gust Tunnel : For studying effects of gust on models
V/STOL : For studying V/STOL configurations
Ice Tunnel : For studying formation and removal of ice on
models
subjected to icing condition.
Automobile Wind Tunnel : For testing full scale automobiles.
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Chapter 2
WIND TUNNEL INSTRUMENTATION 2.1 Introduction Instrumentation
plays an important role in wind tunnel testing. The accuracy of
experimental results depends not only on the quality of the
tunnel but also on the
performance of he measuring equipments.
The quantities which are frequently measured in wind tunnel
testing are generally
pressure distribution and over all forces and moments acting on
a model. Velocity, in
general, can be calculated from the pressure and hence need not
be measured. However,
in some cases velocity itself (for example, fluctuating velocity
components in turbulent
flow) may be of importance and need to be measured. Also,
measurement of skin friction
may be necessary in some experiments.
Measuring instruments may, broadly, be classified as two types:
mechanical and
electronic. Examples of mechanical type of instruments are the
liquid-level manometers
for pressure measurement and wind-tunnel mechanical balances for
measurement of
overall forces and moments. Such instruments lack the first
response, capability of
measuring high and low values and amenability to automation
required for unsteady or
short-duration high speed tunnel.
All these limitations may be overcome in electronic
instrumentation system. An
electronic system usually consist of:
a) pick-up or transducer
b) signal conditioner
c) data acquisition system
The pick-up or transducer receives the physical quantity
(pressure/force) under
measurement and delivers a proportional electrical signal to the
signal conditioner. Here
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the signal is amplified, filtered or otherwise modified to a
format acceptable to the data
acquisition system. The data acquisition system may be a simple
indicating meter, an
oscilloscope or a chart recorder for visual display.
Alternatively, it may be a magnetic
tape recorder for temporary or permanent storage of data or a
digital computer for data
manipulation or process control.
2.2 Pick-up or Transducer:
A transducer may be defined as a device which provides an
electrical output signal for a
physical quantity (pressure/force), whether or not auxiliary
energy is required. Many
other physical parameters (such as heat, light, intensity,
humidity) may also be converted
into electrical energy by means of transducers. Transducers used
in wind tunnel testing
may be classified according to the electrical principles
involved, as follows:
1) Variable resistance transducer (resistance strain gauge)
2) Variable capacitance transducer
3) Variable reluctance transducer
4) Piezoelectric transducer
Of all these transducers, resistance strain gauge, because of
its unique set of operational
characteristics, has dominated in transducer field for the past
twenty years.
2.2.1 Variable Resistance Transducer:
The strain gauge is an example of variable resistance transducer
that converts a physical
quantity into a change of resistance. A strain gauge is a thin,
wafer-like device that can be
attached (bonded) to a variety of materials. Metallic strain
gauges are manufactured from
small diameter resistance wire such as constantan, or etched
from thin foil sheets (Fig.
2.1). For simultaneous measurement of strain in more than one
direction, two-element or
three-element rosettes are used. The resistance of the wire or
metal foil changes with
length as the material to which the gauge is attached undergoes
tension or compression.
In a gauge diaphragm pressure transducer, strain gauges are
directly bonded on the
diaphragm while in a sting balance used for force measurement,
strain gauges are bonded
on he sting (Fig. 2.2). While the load is applied, the
resistances of the strain gauges
increase or decrease, depending on nature of stress (tensile or
compression). The
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sensitivity of a strain gauge is described in terms of
characteristics called the gauge
factor, G, defined as the unit change in resistance per unit
change in length
Or, G = (R/R) / (L/L) (2.1)
where G = Gauge factor
R = Gauge resistance
R = change in gauge resistance
L = normal length (unstressed condition)
L = change in length.
The term L/L is the strain , so that equation (2.1) may be
written as
G = (R/R) / (2.2)
Where = strain in the lateral direction.
Figure 2.1 Strain gauges (a: wire, b: foil)
The resistance R of a wire of length L can be calculated by
using the expression for the
resistance of conductor of uniform cross-section.
2
4d
Larea
lengthR
== (2.3)
Where = specific resistance of conductor material
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19
L = length of the conductor
=d diameter of the conductor
Figure 2.2 Sting balance
Tension on the conductor causes an increase L in its length and
a decrease d in its
diameter. The resistance of the conductor then changes to
( )( )( )
( )( ) ( )ddd
LLLdd
LLRR
2141.
4. 22
+=
+=+ (2.4)
Equation (2.4) may be simplified by using Poissons ratio, ,
defined as a ratio of strain
in lateral direction to strain in axial direction.
Therefore,
( ) ( )LLdd = (2.5) Substituting equation (2.5) in equation
(2.4) gives
( )
( ))21(
14 2 LL
LLd
LRR
+
=+
( )( )LLLLR 211 ++= ( )( )LLR 211 ++= [neglecting higher order
term] The gauge factor can now be obtained as
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20
( ) ( ) ( ) 21/ +== LLRRG (2.6) Poissons ratio for most metals
vary from 0.25 to 0.5 and the gauge factor is then of the
order of 1.5 to 2.0. For strain-gauge application, a high
sensitivity is very desirable. A
large gauge factor means a relatively large resistance change
which can be more easily
measured than a small resistance change. Semi-conductor gauges
are now developed,
which have gauge factor of the order of 120.
The semi-conductor strain gauges are however neither so
practical nor so widely used as
the conventional metallic gauges in general purpose, high
accuracy transducers. It is
worth nothing that semi-conductor gauges were originally
considered advantageous
because of their high output. This has less importance today
because the same
semiconductor technology which created the type of gauge has
also created smaller and
less expensive amplifiers high gain for use with conventional
strain gauges.
Conventional metallic strain gauges are generally of four types
: Constantan, Karma,
Isoelastic and platinum-tungsten. Constantan, a copper nickel
alloy, of gauge factor 2.0 is
the most popular alloy for transducer gauges. It possesses an
exceptional linearity over a
wide strain range and is readily manufactured. It is also easily
solderable. Its primary
limitation in precision applications is a slow irreversible
drift in grid resistance when
exposed to temperature above 75 C. Because the drift rate
increases exponentially with
temperature, Constantan is not recommended for transducers
operating continuously at
high temperature.
Karma (gauge factor 2.1) is a nickel-chromium alloy used in a
variety of modified forms
for strain sensing. Like Constantan it displays extremely good
linearity over a wide strain
range. It has greater resistivity than Constantan making higher
grid resistance feasible. A
major advantage is its improved resistive stability,
particularly at high temperature.
Isoelastic alloy offers exceptionally good fatigue life and a
gauge factor 3.1, about 50%
higher than Constantan or Karma alloys. It has limited use in
transducers because of its
poor zero stability with temperature variation. Because of its
good fatigue life, it is
normally used for dynamic measurements.
Platinum-tungsten alloys, like Isoelastic, find their primary
use in dynamic transducer
applications. With a gauge factor approximately two times
greater than Constantan and
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Karma, and with very good fatigue life, platinum-tungsten gauges
are used almost
exclusively in fatiguerated dynamic transducers.
2.2.1.1 The Wheatstone Bridge principle :
The change in resistance due to applied load can be converted
into a change in voltage by
the Wheatstone bridge circuit. Two types of Wheatstone bridge
circuits are possible :
summing circuit and differencing circuit. Generally, in wind
tunnel testing,
differencing circuit is used for measuring moment.
2.2.1.2 Summing Circuit :
In the summing circuit, resistance undergoing tension and
compression are connected in
opposite sides of the Wheatstone bridge. Four unstressed strain
gauges R1, R2, R3, R4 are
connected to form a Wheatstone bridge in summing circuit is
shown in Fig. 2.3.
The current passing through the resistance R1 and R3 is I13
where
31
13 RRVI+
= (2.7)
Similarly, the current passing through resistances R4 and R2 is
I42 where
24
42 RRVI+
= (2.8)
Figure 2.3 Summing circuit
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22
The voltage at A is therefore,
131
113 .RRRVVRIVVA +
==
The voltage at B is,
424
442 .RRRVVRIVVB +
==
The voltage across A and B is,
+
+
=== 421
131
RRR
VVRRR
VVVVVV BAAB
+
+
=31
1
4
4
2 RRR
RRV
( )( )42312143
RRRRRRRRV++
=
or, ( )( )42312143
RRRRRRRRVV++
= (2.9)
Now, the output voltage V will be exactly zero, if
(1) 02143 = RRRR or, 2
4
3
1
RR
RR
=
or, (2) RRRRR ==== 4321 (say)
no matter what the input voltage V may be.
If any of the resistance changes due to applied load, the output
voltage V will change.
Provision may be made to change only one resistance (quarter
active bridge) or two
resistance (half active bridge) or three resistance
(three-quarter bridge) or all four
resistances (fully-active bridge).
For the fully active bridge (Fig. 2.2), the output voltage due
to applied load is calculated
in a simple manner. The resistance R1 and R2 are subjected to
compression and will
therefore have a decrease in resistance value while resistance
R4 and R3 will have a
increase in resistance.
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23
The changed values of the resistances may be written as
RRRRRRRRR
+=
=
=
3
2
1
RRR += 4 (2.10)
RR , are the changes in resistances due to changes in strain at
positions 1 and 2 (Fig.
2.2).
Substituting the values in equation (9) yields
( )( ) ( )RRRRRRRRRRRRRRRR
VV
++++++
=
)())((
( )224
22RRRRRRR
+=
( )r
RRR4
2 +=
R
RR2
+=
(2.11)
If the strain gauges are bounded very close to each other, it
can be assumed
RRR ==
and the equation (2.11) is reduced to
244
RRR
VV
=
or, RR
VV
= (2.12)
The equation shows a linear relationship. However, for
quarter-bridge and half bridge a
non linearity appears in the expression for output voltage. For
example, if only R4 is
active (quarter-bridge) and the other three resistance are
passive (not bonded on the
sting), the expression for output voltage is
( )RRR
VV
+
=4
(2.13)
For a half-bridge (taking only R4 and R3 active)
-
24
( )RRR
VV
+
=2
(neglecting higher order terms) (2.14)
Similarly, for a three-quarter bridge (taking R4, R3 and R2
)
( )RRR
VV
+
=4
3 (2.15)
Because of the linearity in relationship, fully-active bridge is
usually used in
measurement techniques. It also has another advantage compared
to others i.e. the
temperature compensation effect. In a fully active bridge, all
resistances have same
temperature (neglecting the thermal e.m.f. effect) while in
other bridges, the temperature
of active gauges may be different from those of the passive
gauges which will cause a
change in resistance values resulting in further
non-linearities.
2.2.1.3 Differencing Circuit :
The arrangement of resistance in the Wheatstone bridge in
differencing circuit is shown
in Fig. 2.4. Using the similar procedure, the output voltage V
in this circuit is obtained
as
Figure 2.4 Differencing circuit
-
25
( )( )34213142
RRRRRRRR
VV
++
=
= ( )( ) ( )( )( )RRRRRRRRRRRRRR
++++
2.2(
( )( )224
2RRR
RRR+
=
( )242
RRRR
= [neglecting ( )2RR + with respect to 4R2]
R
RR2
=
(2.16)
If the strain gauges are pasted close to each other, the output
voltage will be virtually zero
since R will be almost equal to R.
2.2.2 Variable Capacitance Transducer :
The capacitance of parallel-plate capacitor is given by
)(.. 0 faradsd
AkC =
Where A = area of each plate (m2)
=d distance between the plates (m)
0 = 9.85 10 -12 (F/m)
=k dielectric constant
Since the capacitance is inversely proportional to the spacing
of the parallel plates, d, any
variation in d causes a corresponding variation in the
capacitance. This principle is
applied in the variable capacitance pressure transducer (Fig.
2.5). A pressure, applied to a
diaphragm that functions as one plate of a simple capacitor
changes the distance between
the diaphragm and the static plate. The resulting change in
capacitance can be measured
with an AC bridge but it is usually measured with an oscillator
circuit. The transducer, as
a part of the oscillatory circuit, causes a change in the
frequency of the oscillator. This
change in frequency is a measure of the magnitude of the
pressure applied.
-
26
Figure 2.5 Variable capacitance transducer
2.2.3 Variable Reluctance Transducer :
Such transducers employ magnetic diaphragms as sensing element
(Fig. 2.6). When a
differential pressure deflects the magnetic diaphragm, the air
gaps (initially about 0.025
mm) also changes differentially and so does the reluctance. The
two coils are connected
on a two-active arm bridge so that an output proportional to
pressure is obtained.
Figure 2.6 Variable reluctance transducer
-
27
Another type of variable reluctance transducer is based on
linear variable differential
transformer (LVDT). The LVDT is a three-coil device with a
movable magnetic core
(Fig. 2.7). Two outer coils are connected in opposition so that
induced voltages are 180
out of phase with each other. When the armature is centered,
these voltages are equal in
magnitude giving zero output. The pressure activates the
diaphragm and when it moves
the magnetic fluxes are unbalanced to produce an output
proportional to the pressure
applied.
Figure 2.7 Linear variable differential transducer
2.2.4 Piezoelectric Transducer:
The Greek word piezo means to squeeze. The piezoelectric effect
is appropriately
described as generating electricity by squeezing crystals. This
type of sensor is self-
generating, that is, it does not require external electrical
power as do the variable
resistance or variable reluctance sensors.
A piezoelectric transducer is illustrated schematically in Fig.
2.8. The sensitivity can be
enhanced at the expense of resonant frequency by stacking a
series of elements together
with the appropriate electrical connection.
-
28
Figure 2.8 Schematic diagram of piezoelectric transducer
A variety of piezoelectric materials are used, with quartz being
most popular. Although
piezo-electric transducers may be used for near static pressure
measurements, they are
more frequently employed for transient measurement.
2.3 Signal Conditioner: Signal originating from the transducer
is fed to the signal conditioner in which it is
transformed into a form acceptable to the data acquisition
system. Broadly speaking, the
signal conditioner provides circuitry for amplification, noise
suppression, filtering,
excitation, zeroing, ranging, calibration and impedance
matching. Because the operating
principles of the different transducers are different, a variety
of signal conditioners have
been developed. The different types of signal conditioner for
different transducers are
outlined below.
2.3.1 Signal conditioner for Variable Resistance Transducer
:
The signal conditioner usually provides supporting circuitry for
resistance strain gauge
transducer. Usually, the equipment is able to accept
quarter-bridge, half-bridge and full-
bridge by providing appropriate dummy gauges. The circuitry
usually provides excitation
power, balancing circuits, calibration elements, signal
amplification etc.
2.3.1.1 Excitation Supply :
Normally DC excitation is used for resistance strain gauge
transducer. Although AC
excitation can be used, the disadvantages outweigh the
advantages. The accuracy of an
AC system is not as good as that of DC system. Also the noise
rejection near the carrier
frequency is poor. Earlier DC amplifier circuit was based on the
chopper principle in
-
29
which the DC is first converted to AC and then amplified and
later converted to DC.
Such a DC amplifier is fairly expensive. However, with the
advent IC chips, DC
amplifiers are no longer more costly than AC system.
However, the DC power supplied must have high stability. To
achieve this, the power
supply should be isolated from all other common lines and from
the AC power line. In
the other words, it should have a very low coupling to the power
line and to the ground.
2.3.1.2 Bridge Balance :
The Wheatstone bridge circuit should ideally have zero voltage
output under no load
condition, equation (2.9). However, because of normal gauge-to
gauge resistance
variations and additional resistance changes during gauge
installation, the bridge circuit is
usually in a resistively unbalanced state when first connected.
It is advantageous to have
a balancing network to nullify any residual signal.
Figure 2.9 Parallel balance network
The most common arrangement uses a shunt on one side of the
bridge as shown in Fig.
2.9, the fixed resistor in the potentiometer wiper lead being
used to omit the loading
effect on the active arms of the bridge.
If all the resistance strain gauges are of exact equal values,
the voltage at A and B will be
0.5 V and the output V will be zero. In this hypothetical case,
the potentiometer wiper
-
30
lead will be at the center (position C) and the voltage there
will also be 0.5 V and
therefore there will be no current through R4.
However, if due to any of reasons mentioned above, the output V
is not zero, the voltage
at A is then either higher or lower than the voltage at B. in
either case, bridge can be
balanced by moving the wiper lead downward (C2) or upward (C1)
respectively.
The range of he balance network is given by
44R
RVV
= if R4>>R
where V is the maximum out-of balance (zero offset) that can be
nullified. The range
can be extended by decreasing the value of R4. However, R4 can
not be decreased
indefinitely because it will then have loading effect on the
power supply. Usually, to limit
the loading effect, R4 is many times higher than R (of the order
of 75 k to 100 k ).
2.3.1.3 Shunt Calibration :
Usually, in all signal conditioners, shunt resistors are
provided across the arms connected
to balance network. The shunt resistor, when connected, can
usually accommodate a
0.4% change of resistance of the arm shunted. This actually
amounts to simulating 2000
strain on the arm shunted as shown in Fig. 2.10. From equation
(2.2), = (R/R)/G. For
R = 120 , G = 2.0, R = 0.48, becomes 0.002 or 2000.
-
31
Figure 2.10 Shunt calibration
2.3.1.4 Signal Amplification :
Signal amplification is the major function of a signal
conditioner. Usually, the output
voltage V (equations 2.12, 2.16) of a wheatstone bridge circuits
is of the order of
microvolts since the change in resistance is usually of the
order of 10 5 to 10 6 ohms.
Such a weak signal may not be accepted by the data indicator or
recording system
(although microvoltmeters are now available) and therefore the
signal originating from
transducer need to be amplified.
Signal requirements for amplifier are quite stringent. These
include impedance matching
with the data indicator or recording device, high
signal-to-noise ratio (SNR), low drift
(change in output voltage with time is called drift) etc.
With low impedance devices such as resistance strain gauges, no
special problems arise
in the operational mode. A fairly conventional voltage amplifier
with an input impedance
of 100k or greater in suitable for use with the data indicator
system (such as DVM) or
-
32
C.R.O. For bridge circuits in which neither output terminal is
grounded, a differential
amplifier is needed. Such amplifiers offer good common mode
rejection characteristics.
The philosophy underlying noise cancellation is outlined in Fig.
2.11.
Figure 2.11 Noise cancellation by amplifier common-mode
rejection
If the common mode rejection ratio is of the order of 105, the
noise that appears at the
output terminal is largely eliminated. Such transducers have the
ability to handle direct
coupled signals, the D.C. drift being less than 10V/hour after
allowing one hour warm-
up. Low drift rates are fairly difficult to achieve and the cost
of D.C. amplifier with this
sort of performance is comparatively high.
2.3.2 Signal Conditioner for Variable Capacitance Transducer
:
A number of signal conditioner is available based on the
following schemes
i) D.C. polarization as the input circuit for an amplifier.
ii) An A.C. bridge circuit for use with and amplitude modulation
system.
iii) A frequency modulating oscillator circuit.
iv) A pulse modulating circuit.
The D.C. polarization circuit, the simplest of these, is
described here. It is effected by the
circuit shown in Fig. 2.12. in which C represents the
capacitance of the transducer
together with that of the connecting cable and any stray
parallel capacitance. The
polarizing voltage V is usually a few hundred volts. If it is
assumed that the capacitance
C can be represented by a constant portion C0 plus a
sinusoidally varying part C1 sinwt,
then
-
33
C = C0 + C1 sinwt
If C1
-
34
amplified by an A.C. amplifier and demodulated. It is then
filtered to remove any ripple
from the carrier wave.
Figure 2.13 Carrier wave amplifier system
2.3.4 Signal Conditioner for Piezo-electric Transducer :
Piezo-electric transducers are self-generating; they do not
require an external source of
energy. However, using them poses some special problem. In order
to measure the charge
separation which occurs when the piezo-electric material is
mechanically strained, a
measured circuit must be connected to it. The measuring circuit
draws some current so
that the charge, Q, leaks away. To minimize this leakage, the
input impedance of the
circuit must be made very large. Early approaches to this
problem involved the use of
valve voltmeters. The input impedance of such valves are very
high so that negligible
current is drawn less than 10-12 Amp. Used in a simple voltage
amplification circuit, Fig.
2.14, the output signal is function of cable capacitance CC, and
any stray capacitance CS between the input and ground as well as on
the range- setting capacitor C1
-
35
Figure 2.14 Voltage amplifier
Thus, CS CCCC
mQV+++
=
10
This strong dependence on cable and stray capacitance is
circumvented by using a
charge-amplifier. This is an operational amplifier, in which the
high input impedance is
retained but strong negative capacitive feedback is employed as
shown in Fig. 2.15.
For such an arrangement, the output voltage V is given by
( ) ( ) inF CmmCQV
111 ++
=
If the open loop gain m, of the amplifier is very large (m >
50000), the output becomes
FC
QV =
Thus a voltage proportional to charge Q is produced.
Figure 2.15 Charge amplifier
2.4 Data Acquisition System :
Data acquisition systems are used to measure, indicate and/or
record signals originating
from transducers and signal conditioning process. Such systems
can be categorized into
-
36
two major classes : analog system and digital system. The type
of data acquisition
system, whether analog or digital, depends largely on the
intended use of the recorded
input data. In general, analog systems are used when wide
bandwidth is required or when
lower accuracy can be tolerated. Digital systems are used when
the physical process
being monitored is slowly varying (narrow bandwidth) and when
high accuracy and low
pre-channel cost is required. Digital data acquisition systems
are in general more
complex than analog systems both in terms of instrumentation
involved and the volume
and complexity of input data they can handle.
2.4.1 Analog System
An analog system may be defined as continuous function such as a
plot of voltage versus
load (Fig. 2.16) or displacement versus pressure. Examples of
the analog systems are the
analog panel meter, CRO, strip-chart recorder, X-y plotter
etc.
Figure 2.16 Analog system
A complete analog instrumentation system used in wind tunnel
testing may consist of
some or all of the following elements :
a) Transducers: for translating physical parameters into
electric signal.
b) Signal Conditioners: for amplifying, modifying etc. of these
signals.
-
37
c) Visual Display Devices: for continuous monitoring of the
input signals. These
devices may include single or multi-channel CRO, storage CRO,
panel meter,
numerical display and so on.
d) Graphic Recordings Instruments: for obtaining permanent
records. These
instruments include strip chart recorder to provide continuous
records on paper
charts, X-y plotter, ultraviolet recorders etc.
e) Magnetic Tape Instruments: for acquiring data, preserving
their original
electrical form and reproducing them at a later data for more
detailed analysis.
2.4.2 Digital System :
Digital systems handle information in digital form. A digital
quantity may consist of a
number of discrete and discontinuous pulses (Fig. 2.17) which
contains information about
the magnitude or nature of quantity. Digital system may consist
of digital panel meter,
data-logger, computer etc. It is worth noting that if a digital
system is employed, an
analog-to-digital (A/D) converter must be used before since the
output signal from the
signal conditioner is in analog form.
Figure 2.17 Digital system
A complete digital instrumentation system may include some or
all of the following
elements (Fig. 2.18).
a) Transducers: for translating physical parameters into
electrical signals.
b) Signals Conditioners: for amplifying, modifying, etc. of
these signal.
-
38
c) Scanner or Multiplexer: for sequentially connecting multiple
analog signals to
one measuring/recording system.
d) Signal Converter: translates the analog signal to a form
acceptable by analog-to-
digital converter. An example of signal converter is an
amplifier for amplifying
log-level voltages generating by strain gauges.
e) Analog to Digital (A/D) converter: converts the analog
voltage to its equivalent
digital form.
f) Digital Recorder: records digital information on punched
cards, perforated
paper tape, magnetic tape, or a combination of these
systems.
g) Auxiliary Equipment: this section contains instruments for
system
programming functions and digital data processing. These
functions may be
performed by individual instruments or by a digital
computer.
Figure 2.18 Complete digital instrumentation system
Transd-ucer
Signal Condit-ioner
Scanner/Multiple-xer
Signal Conver-ter
A/D Conver-ter
Digital Record-er
Auxiliary Equipment and
System Programming
-
39
Chapter 3
TUNNEL CHARACTERISTICS
3.1 Introduction : Once a wind tunnel is designed and
constructed, the primary task is to calibrate and
evaluate the tunnel characteristics in terms of uniformity in
wind speed and direction, and
also level of turbulence. A wind tunnel can be considered to
have good characteristics if
the flow in the test section has uniform speed, no angular
variation in direction and low
level of turbulence. Four tests are generally necessary for
calibrating and evaluating a
tunnel. These are:
1. Air speed calibration.
2. Determination of velocity variation in the test section.
3. Determination of angular flow variation in the test
section.
4. Determination of turbulence level.
3.2 Air Speed Calibration : In any experiment, the wind tunnel
flow speed (or dynamic pressure) must be known for
calculation of flow quantities. However, it is not desirable top
insert a pitot-static tube in
the tunnel in the presence of a model. This is because of two
reasons; firstly, the tube will
interfere with the model and secondly the tube will not read
true owing to the effect of
model on it. It is therefore necessary to determine the airflow
speed during an experiment
without using the pitot-static tube. This is possible by a prior
calibration of a wind tunnel
manometer with respect to air speed.
The pitot-static tube (Fig.3.1) at station J is considered. If
P0 be the total pressure, pj be
the static pressure and UJ be the oncoming flow speed at the
test section, then from
Bernoullis equation
-
40
20 21
JJ UpP +=
or, ( ) JJ PPU = 02 (3.1)
Figure 3.1 Calibration of wind tunnel manometer
The pitot-static tube is connected to manometer M1 which shows a
difference in water-
level of hJ , then
ghPP JwaterJ = 0
The manometer M1 is inclined at an angle of 600,
gSinhPP JWaterJ =0
0 60 (3.2)
From equation (3.1) and (3.2)
-
41
gSinhU JWaterJ =0602 (3.3)
The air flow speed at test section can now be calculated from
equation (3.3)
The calibration of flow speed UJ or dynamic pressure
= 2
21
JJ Uq can now be
calibrated with the help of another manometer M2 . Applying
Bernoullis equation at L
and S stations gives
2221
21
SSLL UpUp +=+
or, SSLL qpqp +=+ where q is the dynamic pressure.
If the pressure drop between S and L stations due to friction is
considered, total head at L
will be slightly smaller by an amount (say qSK1 where K1is he
loss coefficient), then
1kqqpqp SSSLL +=+
or, ( ) LSSL qkqpp = 11
Applying equations of continuity between stations L and S
LLSS UAUA = ; ( ) SLSL UAAU =
Therefore, ( )[ ]211 LSSSL AAkqpp = (3.4) Applying equation of
continuity between S and J
JJSS UAUA = ; ( ) JSJS UAAU =
or, ( ) JSJS qAAq 2=
Putting in equation (3.4)
( ) ( )[ ]212 1 LSJSJSL AAkqAApp = jqk2=
or, ( ) 2kppq SLJ = where k2 is a constant.
Now, if another manometer M2 is connected to stations L and S,
then
ghpp LSwaterSL =
or, ( ) 2kghq LSwaterJ =
LSkh= (3.5)
where k is a constant.
-
42
Equation (3.5) shows that the free stream dynamic pressure is
linearly proportional to the
pressure difference in terms of manometer water level difference
hLS. Free stream speed
(U) at station J Is also therefore directly related to pressure
difference (in terms of hLS )
between two points L and S.
The lows peed wind tunnel (LSWT) in the department can be run at
11 different speed
setting. For 11 different speeds a table can be made concerning
free stream speed C at
station J and hLS, as shown in Table 3.1.
Table 3.1. : Calibration of tunnel speed
No. of runs hJ (cm) qJ (N/m2) U at J (m/s) hLS(cm)
1.
2.
3.
-
-
11.
Calibration graphs (Fig. 3.2) can now be made in terms of q vs
hLS and U vs hLS. Using
these graphs velocity or dynamic pressure in any subsequent
experiment can be obtained
simply from hLS (without using pitot-static tube).
-
43
q U (N/m2) (m/s)
hLS (cm) hLS (cm)
Figure 3.2 calibration graphs
3.3 Determination of Velocity variation in test section :
Velocity in the test section, even in the absence of model, is not
uniform either in
horizontal or vertical direction. Owing to the effects of
viscosity, the velocity near the
tunnel wall will be slower than the velocity on the centerline
and velocity at downstream
will be greater than at upstream. To achieve uniformity of speed
various means like using
guide vanes, breathers or screens are used.
To check uniformity of speed in vertical direction velocity at
different vertical positions
(for example, points 1, 2, 3, 4, 5, in Fig. 3.3) can be measured
by pitot-static tube.
Velocity at these points for a particular tunnel speed setting
can be obtained from
ghU water =060sin2 (3.6)
Tunnel Roof
0 5 Test Section
Exit 0 4 Entrance
0 0 0 3 0 0
5 4 3 2 1
0 2
0 1
Tunnel Floor
Figure 3.3 Velocity measurement at five vertical and five
horizontal positions
-
44
Velocity in the wind tunnel varies in longitudinal directions
(i.e. along the axis of the test
section) because of viscous effects. As the flow progresses
towards the exit, the boundary
layer is thickened resulting in an effective reduction of area,
increase in velocity and
decrease in static pressure. Because of the decrease of static
pressure there is tendency of
the model to be drawn downstream. This creates a drag force
acting on the body, termed
horizontal buoyancy (chapter 10, 11), which is to be calculated
and subtracted in any drag
measurement experiment.
Velocities (dynamic pressure) at different points along the
tunnel center line (1, 2, 3, 4,
5 in Fig. 3.3) can be measured using the pitot-static tube as
before. Subtraction of
dynamic pressure from total pressure (atmospheric pressure) will
give static pressure at
these points.
A table can now made for calculation of velocity variation in
vertical and horizontal
directions as shown below.
Table 3.2: Calculation of velocity at 9 points
Stations y cm h cm U m/s Stations x cm h cm U m/s p (N/m2)
1. 1.
2. 2.
3. 3.
4. 4.
5. 5.
-
45
U U (m/s)
(m/s) p (N/m2)
Height from floor, Distance along tunnel
y (cm) Centerline, x (cm)
Figure 3.4 Velocity variation in vertical and horizontal
direction
Velocity variation with tunnel height (y) and velocity and
static pressure variation with
distance along tunnel center line (x) can now be plotted (Fig.
3.4). Static pressure
gradient (p/x) should be calculated and noted.
3.4 Determination of Angular Flow Variation in the Test Section
:
Due to defectiveness in design and construction, the flow in the
test section may not be
horizontal. It is therefore necessary to know whether such
angularity in flow exists and if
it exists then to measure it so as to allow compensations due to
this angularity of flow.
The angular variation in the flow can be checked by using a
spherical yawhead as shown
in Fig. 3.5. The yawhead has two smooth orifices usually 900
apart on the forward face of
a sphere. Obviously, if they are exactly placed, they will read
equal pressure when the
flow is directed along the axis of the yawhead. If the pressure
at the two points a and b
are not equal then it will indicate that the flow is inclined at
an angle. This angle of yaw
may then be determined by simply rotating the yawhead till the
pressures at these points
become equal. The angle of rotation of yawhead is then the angle
of yaw of the flow. A
similar procedure can be adopted for measuring yaw in the
horizontal plane by measuring
pressure at two other points a and b in the horizontal plane
again 900 apart.
-
46
Figure 3.5 Spherical yawhead
An alternative way of measuring yaw angle is to fix yawhead in
tunnel and to determine
the flow angularity by reading the pressure difference between
two orifices and
comparing with a previous calibration of the yawhead.
It is believed that accurate testing can not be done if the
variation in angle is greater than
5.0 degree. The larger angles of yaw distorts the span load
excessively.
Unfortunately, the variation of flow angle across the jet may
change with the tunnel
speed. If such a change is noted, a testing speed must be
selected and the guide and anti-
twist vanes should be adjusted to give smooth flow at that
speed.
3.5 Turbulence Level : The flow conditions inside the wind
tunnel are not exactly same as those in free air. The
flow inside the tunnel is more turbulent than the free air
because of the effects of the
propeller, the guide vanes and the vibrations of tunnel walls.
This discrepancy in the
turbulence level results in disagreement of tests made in the
wind-tunnel and in the free
air at the same Reynolds number. By the same reasoning, tests
made in different tunnels
at the same Reynolds number may not agree. A correction factor
is therefore necessary
for compensating the turbulence created in the tunnel.
It is found that the flow pattern in the tunnel at a given
Reynolds number corresponds
closely to the flow pattern in the free air at a higher Reynolds
number. The increase ratio
is called the turbulence factor and the effective Reynolds
number RNe of the tunnel can
be obtained from the calculated Reynolds number using the
turbulence factor of the
tunnel from
RNTFRNe = (3.7)
-
47
The turbulence may be found with a sphere in two ways :
a) Drag sphere
b) Pressure sphere
3.5.1 Drag Sphere :
The drag coefficient of sphere is affected greatly by change in
velocity. Contrary to the
laymans guess, CD for a sphere decrease with increasing airspeed
since the result of
earlier transition to turbulent flow is that the air sticks
longer to the surface of the sphere.
This action decreases form or pressure drag, yielding a lower
total drag coefficient.
Obviously, the Reynolds number at which the transition occurs at
a given point on the
sphere is a function of the turbulence already present in the
air and hence the drag
coefficient of a sphere can be used to measure turbulence . The
method is to measure the
drag, D, for a small sphere 15 or 20 cm in diameter, at many
tunnel speeds. After
subtracting the horizontal buoyancy drag DB the drag coefficient
may be computed
from
( ) 22 4
21
=
Ud
DDC BD
(3.8)
Figure 3.6 Variation of CD with Reynolds Number
-
48
The sphere drag coefficient is then plotted against the
calculated Reynolds number, RN
(Fig.3.6). The Reynolds number at which the drag coefficient
equals 0.30 is noted and
termed the critical Reynolds number, RNC. The above particular
value of the drag
coefficient occurs in free air at RN = 385000, so it follows
that the turbulence factor may
be given by
TF = 385000/RNC (3.9)
Once the turbulence factor (TF) is obtained from equation (3.9),
the effective Reynolds
number, RNe, can now be calculated from equation (3.7).
3.5.2 Pressure Sphere :
An alternative method (which will be used) of measuring
turbulence makes use of
pressure sphere. No force tests are necessary and the difficulty
of finding the support
drag is eliminated. The pressure sphere has an orifice at the
front stagnation point and
four more interconnected and equally spaced orifices at 0
2122 from the theoretical rear
stagnation point (Fig.3.7).
Figure 3.7 Pressure Sphere
A lead from the front orifices is connected across a manometer
to the lead from the four
rear orifices. After the pressure difference due to the static
longitudinal pressure gradient
is subtracted, the resultant pressure difference, p for each
Reynolds number is divided
-
49
by the dynamic pressure for the appropriate Reynolds number, and
the quotient is plotted
against Reynolds number (Fig. 3.8). It has been found that the
pressure difference p/q
is 1.22 when the sphere drag coefficient is 0.30 and hence this
value of p/q determines
the critical Reynolds number RNC. Once the turbulence factor is
determined, the
turbulence factor may then be determined, as before, from
equation (3.9).
Figure 3.8 Variation of p/q with Reynolds number
This experiment is carried out on a sphere of diameter 20 cm.
The following table may be
made for plotting p/q vs Reynolds number.
-
50
Table 3.3 : Experimental measurement of turbulence factor
No.of
Runs
hLS (cm)
U from Fig.
1.2 b (m/sec)
q from
Fig.1.2 a
(N/m2)
hj
(cm)
p
= hjwg.sin600
(N/m2)
p/q RN
= UD/
1.
2.
3.
-
11.
Turbulence factor usually varies from 1.0 to 3.0. Values above
1.4 indicate that the tunnel
has too much turbulence for reliable testing. Low turbulence
factor is necessary for the
test data to be reliable.
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51
Chapter 4
FLOW VISUALISATION
4.1 Introduction : Flow visualization techniques are a means of
obtaining the qualitative pattern of the flow
about a body. Flows encountered in engineering application are
often complex in nature.
Such techniques of flow visualization helps in obtaining a
better understanding of the
flow characteristics. Many a times suitable mathematical methods
have been developed
for a particular flow problem based on such qualitative
studies.
Flow visualisation techniques can be classified as follows :
Flow visualisation techniques
Incompressible flow Compressible flow
Entire flow field Only on model Flow pattern Shock
visualisation
1. Smoke 1. Tuft 1. Oil flow 1. Shadowgraph
2. Tuft on wire mesh 2. Oil flow 2. Interferometer
3. Evaporation 3. Schlieren
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52
4.2 Incompressible Flow Visualisation Techniques : 4.2.1 Smoke
Method :
Flow visualisation with smoke is achieved in a smoke tunnel with
a facility to emit
cleaned smoke in streamer form (Fig. 4.1). Smoke is generated by
burning kerosene or
paraffin. Particular care is needed in introducing the smoke in
the tunnel by a blower
without disturbing the flow in the tunnel. This smoke follows
the air flow and makes the
flow pattern visible. Smoke tunnels are usually low-velocity
tunnels and most of them
have two dimensional test sections. Such tunnels are usually
open circuit type to prevent
accumulation of smoke in the tunnel. The walls of test section
are made of glass so that
the flow can observed (Fig. 4.2) and/or photographed.
Figure 4.1 Smoke Tunnel
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53
Figure 4.2 Flow separation at high angle of incidence
4.2.2 Tuft Method :
Tufts are simplest and most often used. A large number of silk
tuft are pasted at one end
on the surface of the wing. The length of each tuft is taken
about 2 cm. The most rapid
method of installing the tufts is to attach them about every one
inch to the tape and
pasting the tape on the model (Fig. 4.3). To obtain clear
photography the model is usually
painted black while the tufts used are white. Since the open
ended tufts align with the
flow the general direction of he tufts indicate the direction of
the flow on the surface of
the body. Motion of tufts usually means that the flow in the
boundary layer has become
turbulent. Violent motion or tendency a tendency to lift from
the surface and point
upstream indicates separation.
If the tufts are to be used to examine the entire flow field
they may be supported on wires
on a mesh installed inside the tunnel. Complete grids of wires
normal to the flow can be
fixed in the tunnel behind a wing model. Tufts attached on one
end on the mesh junctions
will align with the flow direction and show up trailing
vortices.
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54
Figure 4.3 Visualisation of flow over a straked wing by tuft
method
4.2.3 Oil Flow Method :
In this method the model is pasted with a semi-liquid mixture of
mobil oil and grease
and a dye. The dye taken for this purpose is a chemical known as
Rhodamin B. When the
model is installed in the tunnel, the air flow spreads the
mixture along the streamlines so
that after the tunnel has been stopped the flow pattern remains.
The process requires
about 30 minutes of continuous air flow in the tunnel. The model
is thereafter removed
from the tunnel and the flow pattern (Fig. 4.4) can be examined
afterwards under
ultraviolet light.
An alternative approach is to mix mobil oil and titanium dioxide
(dye) and paste on the
model. In this case the mixture gets dried up in a few minutes
and the flow pattern can be
observed without using ultraviolet light. Care must be taken so
that the oil does not
follow machining marks on the surface.
Figure 4.4 Visualisation of flow over a straked wing by oil flow
method
-
55
4.2.4 Evaporation Method :
Napthalin may be dissolved in acetone and pasted on a model.
When the tunnel runs
napthalin evaporated quickly from the turbulent portion making
that portion white. If the
model is painted black, transition from laminar to turbulent
flow can be observed easily.
Among the incompressible flow visualization techniques it may to
be noted that tuft, oil
flow and evaporation method gives pattern of flow on the surface
of the model only while
the smoke method (and tuft on mesh screen) gives the picture of
the entire flow field.
Among the compressible flow visualization techniques, only the
oil flow method,
described in section 4.2.3, can be used. Other methods are not
suitable because of the
high speed involved.
4.3 Compressible Flow Visualisation Techniques :
4.3.1 Shadowgraph Method :
A parallel beam of light is produced by a point source. It is
passed through a converging
lens and then through the working section. Since the flow in the
working section is
compressible, refraction of light rays through the compressible
medium will be different.
The screen will be illuminated where rays have converged. Shock
waves then appear on
the screen as two adjacent bands, one dark and one light,
corresponding to the sudden
increase in density gradient at the front of the shock and the
sudden decrease in gradient
at the rear.
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56
Figure 4.5 Shadowgraph picture of flow about a sphere
4.3.2 Schlieren Method :
Schlieren method is most widely used. It is sensitive to density
changes whereas
shadowgraph method is sensitive to change in density gradient.
The light rays passing
through the varying density area (test section) will be
deflected. The screen will be
illuminated or darkened depending on the deflection of the light
beam. This method is
described in details in chapter 20.
4.3.3 Interferometer Method :
A direct response to density changes is given by the
interferometer which depends on the
interference fringes formed on the recombination of two light
rays from the same source
which have taken different times to make the journey.
If he two path lengths are same, interference fringes may be
produced. The light paths are
adjusted with no airflow disturbance to produce a uniform and
parallel set of interference
fringes on screen giving uniform illumination. When the tunnel
is run with model
installed, fringe spacing will change by an amount proportional
to the phase change by
the disturbance at any point which is in turn proportional to
the change of fluid density
integrated along the light path. If the interferometer is
pre-calibrated, it will give absolute
values of density.
-
57
Figure 4.6 Schematic diagram of the interferometer system
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58
Chapter 5
PRESSURE MEASUREMENT BY MECHANICAL DEVICE
5.1 Introduction : Pressure, at different points on the surface
of model, can be obtained by drilling holes on
the surface and connecting tubes from these points to a
mechanical device like a multi-
tube liquid level manometer (Fig. 5.1). liquid levels, which are
initially in the same level,
undergo changes in height proportional to the pressure applied
and pressure at different
points in the surface can be calculated from the heights of the
columns.
Figure 5.1 Liquid level manometer
Multi-tube, indicated schematically in Fig. 5.1 may be used in
vertical position. For
increased sensitivity the manometer may be inclined at various
angles in which readings
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59
are multiplied by appropriate factors. Also, in stead of water,
liquid of specific gravity
less than 1.0 may be used.
The reservoir for manometer liquid is usually mounted on a
vertical rod at a height which
is adjustable. It is recommended that the reservoir be normally
left open to atmospheric
pressures. Pressures p1, p2, p3,.are then gauge pressures i.e.,
pressures relative to
atmospheric datum. Pressure relative to some other chosen datum
may be obtained by
connecting the reservoir and one manometer tube to the required
datum.
Manometers are generally graduated so that height of liquid
level may be read in cm and
the pressure is calculated from the height of the liquid column
in the relevant tube. Some
manometers are graduated directly in N/m2 or in millibar (1mb =
100 N/m2 ).
5.2 Measurement of Cp : Pressure is usually expressed in
non-dimensional form as pressure coefficient Cp . by
definition Cp is given by
2
21
=U
ppC p
(5.1)
Using a liquid-level manometer as shown in Fig. 5.1, pressure
coefficient Cp can be
obtained in two ways depending on whether the tunnel is
precalibrated or not.
5.2.1 Without Pre-Calibration of the Tunnel :
If the tunnel is not pre-calibrated to give U, two holes are to
be drilled on the walls of
the settling chamber and the test section and directly connected
to the manometer in
addition to connecting pressure port of the configuration.
Now, by Bernoullis theorem,
SPUpP =+= 2
0 21
where PS is the settling chamber pressure.
Or, = ppU S2
21
If the manometer is graduated in N/m2 ,(p - p) and (PS - p) can
be obtained directly in
units of N/m2 and Cp can be obtained as the ratio of the two
given by
-
60
=pPppC
Sp (5.2)
Non-dimensional pressure coefficient is thus obtained simply as
a ratio of pressure
differences and value of U is not needed. If U is needed (e.g.,
to calculate Reynolds
number) U can be obtained in a simple manner by assuming no
frictional loss between
settling chamber and test section.
Under this assumption, U can be obtained as
( ) = pPU S2 (5.3)
If the manometer is graduated to give height of liquid column,
Cp can be obtained as ratio
of column heights as shown below.
( ) ghhpp liquid =
and ( ) == hhppU SliquidS 221
Where,
hS = height of column in the tube connected to settling
chamber.
h = height of the water column in the tube connected to the
pressure port on the
configuration where pressure is being measured.
h = height of the column in the tube connected to test
section
This gives ,
=pPppC
Sp
( )( )
=
hhghhg
Sliquid
liquid
=hhhh
S
(5.4)
Cp is then obtained as ratio of height difference of liquid
columns.
By assuming zero frictional loss between settling chamber and
test section U can be
obtained as
( ) = pPU S2
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61
( ) ghhSliquid = 2 (5.5)
5.2.2 With Pre-Calibration of the Tunnel :
If the tunnel is pre-calibrated to give U, pressure coefficient
can be derived in terms of
U.
( )
22
21
21
=
=U
ghh
U
ppC liquidp
If the manometer is inclined at 600, then
( )
2
0
21
60sin
=U
ghhC liquidp
If the liquid is water, height is graduated in cm and density of
air is taken as 1.225 kg/m3,
then
( )
2225.121
866.081.91000
=
U
hhC p
( ) 270.138 = Uhh (5.6) Experimental measurement of pressure
distribution on a few simple models are described
in the following sections. In all models several holes are
drilled on the surface and
connected to the multi-tube manometer. Pressure distribution can
then be obtained from
equation (5.4) or (5.6) depending on whether the tunnel is
pre-calibrated or not. These
models include :
a) Circular cylinder model
b) Elliptical cylinder model
c) Spherical model
5.3 Pressure Distribution on Circular Cylinder Model : Exact
analytical solutions are available for limited cases of direct
potential flow
problems. The problem of two dimensional flow about a
cylindrical body is one of such
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62
problems. For steady, inviscid, incompressible irrotational
flow, for which the governing
equation is Laplaces equation, the non lifting two dimensional
flow about a cylindrical
body can be simulated by placing a doublet in uniform flow. The
total velocity at any
point P (Fig. 5.2) is obtained as
sin2 = Uqt (5.7)
Figure 5.2 Circular cylinder in uniform flow
The pressure distribution can be obtained from Bernoullis
equation,
22
2sin411
21
=
=
=
Uq
U
ppC tP (5.7)
It may be noted that the expression for total velocity or
pressure is independent of the
diameter of the cylinder.
The ideal pressure distribution, given by equation (5.8), over
the surface of the cylinder
will be symmetrical about the axis in the direction of the flow
and about the plane normal
to it. Consequently, the net forces, lift and drag, are
zero.
An experimental study can be undertaken to check how far the
real solution deviates
from the ideal solution. For the case of uniform flow of real
fluid, both the effects due
to compressibility and viscosity are to be taken into account.
For the low speed test case
(0.1 Mach number) the effect due to compressibility may be
justifiably ignored.
However, effect of viscosity alone will change the flow pattern
considerably.
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63
Primarily, the flow will be asymmetric about the axis normal to
the uniform stream and
hence pressure distribution will also be asymmetric resulting in
a net force (drag) acting
on the cylinder along the flow direction. However, the flow is
still symmetrical about the
axis in the direction of the flow and hence no lift force acts
on the cylinder.
Secondly, while the ideal flow is always attached to the body
surface, in real fluid, the
flow may separate under adverse pressure gradient. In the
forward face of the cylinder (
between 00 to 900), the flow speed increases and pressure
decreases, hence the flow is not
likely to separate in this region. In the backward face, (
between 900 to 1800), the speed
decreases and pressure increases. Under the action of this
increasing pressure (i.e.
adverse pressure gradient), the flow is likely to separate.
This separation is the so-called boundary layer separation.
Since the flow velocity is
less in the boundary layer than in the free stream outside the
boundary layer, the flow
separates in the boundary layer. The exact process of separation
is yet little understood.
Generally speaking, at low speed the flow in the boundary layer
is laminar and will be
attached to the body. Since the flow speed is less, kinetic
energy associated with the flow
is also less, and the laminar flow is more susceptible to
separation. As the flow speed is
increased, the boundary layer becomes turbulent. Transition for
laminar to turbulent flow
is governed primarily by the Reynolds number of the flow.
The model chosen for experimental work is a circular cylinder of
diameter 10.8 cm and
span 60.8 cm which extends from wall to wall (so that the flow
is two dimensional).
Sixteen pressure holes are equally spaced at 0
2122 apart (Fig. 5.3) on the surface of the
cylinder and are connected to a multi-tube manometer.
Advantage, however, can be taken for this circular cylinder
model. Only one hole can be
drilled and pressure at different points on the circular section
can be obtained by simply
rotating the model (chapter 12).
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64
Figure 5.3 Pressure holes on cylinder surface
Both the theoretical and experimental Cp distribution can now be
obtained from equation
(5.8) and equation (5.4) or (5.6) and plotted against . The
difference is due to viscous
effects.
The following table may be made for plotting Cp vs. (Fig.
5.4).
Table 5.1 : Pressure distribution on circular surface
Tap
points
hLS U h h Cp
(Theoretical) eq. (5.7)
Cp
(Experimental) eq. (5.6)
1. 0
2. 22.50
3. 450
-
16. 337.50
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65
Cp
-Ve
0 90 180 270 300 330 360
+Ve
Figure 5.4 Pressure distribution on cylinder surface
5.4 Pressure Measurement on Elliptical Cylinder Model :
Exact analytical solution exists also for the case of potential
flow about elliptical;