Jet Flow Measured with a Hot-wire
Prepared by Professor J. M. Cimbala, Penn State University
Latest revision: 11 January 2012
Nomenclature
A
B
D
D0
m
cross-sectional area of the jet
an arbitrary function of x
diameter at the exit plane of the jet
diameter of the settling chamber of the jet nozzle
mass flow rate through a cross section of the jet (kg/s)
m0
mass flow rate through the exit plane of the jet (kg/s)
I
P
P0
Patm
r
r0
R
U
U0
UCL
Uj
x
x0
an integral
static pressure
stagnation pressure in the settling chamber of the jet nozzle
atmospheric (ambient) pressure in the room
radial coordinate from the jet centerline
centerline radial location, as read from the micrometer
jet radius (maximum extent of the jet in the radial direction)
mean velocity in the axial (x) direction: U is a function of both x and r in a jet
mean velocity of the air in the settling chamber of the jet nozzle: U0 is very small compared to Uj
mean centerline velocity of the jet (at r = 0): UCL decays with x beyond the potential core region
mean velocity of the air across the jet exit where the velocity profile is nearly a top-hat shape
axial flow direction of the jet, measured from the jet exit plane
axial location at the jet exit plane, as measured by the traverse
coordinate in the circumferential direction around the jet.
density of the fluid (for water,   998 kg/m3 at room temperature)


Educational Objectives
1.
2.
Demonstrate the calibration and use of hot-wire anemometry and a linear variable displacement transducer.
Become acquainted with basic concepts in jet flow, such as the axial extent of the jet's potential core and the variation
of mass flux with axial position.
Equipment
1.
2.
3.
4.
5.
6.
7.
8.
9.
jet nozzle, with settling chamber
hot-wire stand, with vertical traverse and horizontal
micrometer positioning system
personal computer with data acquisition hardware and software
TSI Model 1210-20 hot-wire probe
TSI Model 1054B hot-wire anemometer system
TSI Model 1076 RMS/mean square/DC voltmeter
Frequency Devices Model 901F low-pass filter
BK precision Model 2120 20 MHz dual trace oscilloscope
Validyne electronic pressure transducer with digital display
Background
A.
Hot-wire anemometry
A hot-wire is a very tiny (typically less than 0.01 mm
diameter) tungsten or platinum-coated tungsten wire, soldered
between two small needles, as sketched in Figure 1. Because of its
small size, the hot-wire is extremely fragile. Never touch the hot-wire
or let anything come in contact with it — it will break!
Figure 1. Close-up sketch of the tip of a hotwire probe.
In operation, an electrical current is applied through the wire. This causes the wire to heat up (typically to 200-250C);
hence the name “hot-wire”. If the hot-wire is placed in an air flow, the air tends to cool it down, in the same way that you
cool down your food by blowing at it. The electronic bridge circuitry attached to the hot-wire senses the cooling effect, and
responds by supplying more current so that the wire stays hot. The harder the air blows, the more current is required to
maintain the hot-wire at a constant temperature. The final output of the circuit is a voltage that increases with velocity. Thus,
hot-wire anemometry is a technique useful for measuring the flow velocity of an air stream.
Modern electronics has provided us with hot-wire anemometers that can respond to a rapidly changing flow field.
Thus, a hot-wire can be used to measure not only a steady or mean velocity, but velocity fluctuations (turbulence) as well.
Typical hot-wires can respond easily to fluctuations as high as 5 or 10 kHz (5,000 or 10,000 fluctuations per second).
In this lab experiment, you will use a hot-wire to measure the development of a turbulent jet. Data will be sampled at
10000 Hz for approximately one second per data point.
B.
Digital data acquisition
A computer will assist you in gathering data for this lab experiment. A schematic diagram of the electronics setup is
shown in Figure 2. The voltage output from the hot-wire anemometer is first passed through an electronic low-pass filter,
which filters out very high frequency noise. (For example, the hot-wire itself acts like a small antenna — it can pick up radio
signals and other noise, which can affect your data. These extraneous voltages must be eliminated, i.e. filtered out.) In our
setup, the cut-off frequency is 5,000 Hz. The filtered voltage is then sent to three devices: an oscilloscope, a voltmeter, and
the computerized data acquisition system. The analog-to-digital conversion card in the computer converts the analog
(voltage) hot-wire signal into digital data that is stored and manipulated by the computer. The voltage range of the A/D
converter is -5 to 5 Volts.
Anemometer
Vertical
traverse
Oscilloscope
Low-pass filter
Probe
Output
Input
Output
Gain = 0
Bypass = OUT
Input = A
Cutoff f = 5000 Hz
Hot wire
Voltmeter
In
3.267
A/D screw terminal
Ribbon cable to A/D card in computer
Jet
0
Uj
1
2
3
Jet nozzle
Filter and
screens
Stagnation
pressure tap
Pressure transducer
+
-
Transducer display
In Out
0.60
High pressure air
supply (shop air)
Horizontal
traverse
Figure 2. Schematic of the experimental setup
C.
Introduction to turbulent jets
A well-designed jet nozzle produces a “top hat” or nearly uniform velocity distribution at its exit plane (x = 0). In other
words, the mean jet velocity U is independent of radial distance r over the jet exit area, and drops rapidly to zero at the edges
of the jet. This is illustrated as Profile 1 in Figure 3. Due to viscosity and turbulence, however, the potential core of uniform
velocity slows down at its edges. The potential core gets narrower and narrower with increasing axial distance (x) from the jet
exit plane. Instead of a sudden drop to zero velocity at the edge of the jet, the drop is more gradual in a region called the
shear layer. In Profile 2 of Figure 3, the potential core region is still identifiable, but the flat top portion of the profile is
much narrower than it was in Profile 1. At some axial distance from the jet exit plane, the potential core disappears
altogether, and the shear layer fills up the entire jet, as illustrated in Profile 3 of Figure 3. From here on, the centerline
velocity UCL continuously decreases, while the jet width continues to spread. We say now that the jet is fully developed, and
the velocity profile takes on the shape of a Gaussian curve.
Mixing
Entrained ambient fluid
Uj
UCL
Jet exit
plane
r
x
Profile 1
Profile 2
Potential core
of the jet
x=0
Mixing
layer
Profile 3
Figure 3. Development of a turbulent jet.
An interesting aspect of a turbulent jet is that the jet mass flux increases with axial distance. Let us define mass flux
through a plane perpendicular to the jet as
m    UdA
(1)
A
where A is the cross-sectional area of the jet.
In cylindrical (r, , x) coordinates, and assuming axisymmetric flow (no dependence on angle ), dA = 2rdr, and Eq.
(1) becomes
m  2
r R
 Urdr
(2)
r 0
where R is the maximum radial extent (half-width) of the jet. If the integration of Eq. (2) is performed on the velocity profiles
of Figure 3, the mass flux would be found to increase with x, i.e.,
m3  m2  m1 .
Where does this extra mass come from? The answer is that a
flow pattern is set up which sucks ambient air surrounding the jet into
the shear layer at the edge of the jet. This process is called
entrainment. In other words, ambient air from the surroundings is
entrained into and becomes part of the jet flow. Entrainment is
strongly enhanced by turbulence in the jet.
A good example of this entrainment process can be observed
when someone uses a blow dryer, as sketched in Figure 4. The air
coming from the blow dryer is extremely hot. However, the hot air
quickly mixes with colder ambient air, with the result that the jet
Figure 4. Illustration of mass entrainment in the
striking his head is a lot cooler than that at the jet exit. The farther
turbulent jet from a hair dryer.
away from the hair dryer, the cooler the jet. Because of entrainment,
the original hot air exhausted by the hair dryer represents only a
fraction of the air that actually strikes his head. The person in the sketch should be thankful for entrainment — without it she
would burn her hair to a crisp when she used her blow dryer!
References
1.
Çengel, Y. A. and Cimbala, J. M., Fluid Mechanics – Fundamentals and Applications, McGraw-Hill, NY, 2006.
2.
White, F. M., Fluid Mechanics, Ed. 5, McGraw-Hill, NY, 2003.