Performance analysis was made of oscillating hot-wire anemometer electrical output in gas stream. Advantages include no calibration and measurement of fluid direction as well as fluid speed

Conley, J. M.

English

NASA Technical Reports Server

Electrical 
Output 
December 1972
	
B72-10609 
NASA TECH BRIEF 
NASA Pasadena Office 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
Commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Oscifiating Hot-Wire Anemometer 
Anemometers which have a stationary hot wire 
operate on the principle that heat transfer from the 
wire to the fluid in which it is immersed is a func-
tion of the motion of the fluid past the wire. Unfortu-
nately, anemometers of this type are severely re-
stricted in their usefulness not only because they 
Oscillating 
Device
A 
Sine Wave
	 - 
Anemometer 
Output 
must be calibrated empirically, but also because all 
nonspeed parameters must be continuously monitored 
to insure accurate indication of speed, in as much as 
the rate of heat loss from the wire is a function of the 
ambient gas viscosity, thermal conductivity, density, 
and temperature as well as the motion of the fluid. 
Anemometers which have a vibrating hot wire have 
been used to minimize the effect of local convection 
currents and the thermal boundary layer surrounding
the wire at low fluid speeds, but the calibration prob-
lems are still present. 
The results of a detailed analysis of the electrical 
output of an anemometer which has a hot wire oscil-
lating in a gas stream suggest that this type of ane-
mometer does not require calibration; moreover, the 
direction as well as the speed of the fluid can also be 
determined if the tip of the oscillating probe moves 
in a circle or if two probes are used, each oscillating 
perpendicular to the other. The diagram portrays the 
simplicity of construction of an oscillating hot-wire 
anemometer. On the other hand, the electrical output 
of the probe is quite complex; as indicated in the 
diagram, the fluctuating electrical component does not 
resemble the pure sine wave motion of the probe, for 
it is composed of at least a fundamental and higher 
harmonics. The deviation of the electrical output 
from a pure sine wave is greater at A than at B; the 
distortion has been exaggerated in the diagram for 
sake of clarity. 
The relationship between fluid speed and the elec-
trical output of a hot-wire anemometer (King's law) is 
normally written in the dimensionless form N = A 
+ B(Re)" where N u is the Nusselt number, A and B are 
dimensionless functions of the fluid properties, Re is 
the Reynolds number with respect to the wire diam-
eter, and n is a constant which is very nearly 0.5. For 
operation at constant temperature, the expression is 
best written in the dimensional form, P = A' + B'V, 
where P is the wire heating power, V is the fluid speed 
normal to the wire, and A' and (B'V') are the dimen-
sional (watts) analogs of A and B. In practice, the 
voltage output of the wire is proportional to the 
fourth root of the fluid velocity. 
(continued overleaf) 
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	 information contained in this document, or warrants that such use 
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https://ntrs.nasa.gov/search.jsp?R=19720000608 2020-03-17T03:36:39+00:00Z
When the wire is harmonically oscillated in the fluid 
stream at amplitude a and frequency , the apparent 
fluid speed relative to the wire is V = u + o a cos üt 
where u is the component of fluid velocity normal to 
the wire. Hence, the dimensional form of King's law 
becomes 
P = A' + B'a1 '2
 [1+(wa/u) cos wt] 1/2. 
The trigonometric term is expanded by the binomial 
theorem to yield: 
P = A' + B'u112 [1—(wa/4u)2
 + (a/2u)cos ot 
—(ua/4u) 2 cos 2t + . . . 1 
Now, if the signal components at the fundamental 
frequency and the second harmonic are filtered, their 
ratio is
P2-/P., = 
and, for constant resistance, the wire voltage second 
harmonic distortion is 
E2.,/E = (wa/8u)1/2. 
As can be seen from the above equation, the cal-
ibration constants A' and B' have been eliminated; 
the harmonic distortion is a function only of the oscil-
lation frequency and amplitude as well as the speed 
of the fluid normal to the wire.
The probe frequency and amplitude can be mea-
sured or controlled precisely and made to remain con-
stant indefinitely. Thus, the anemometer can record 
fluid speed without being degraded by variations in 
other parameters or by surface contaminants on the 
hot wire. 
Note: 
Requests for further information may be directed 
to:
Technology Utilization Officer 
NASA Pasadena Office 
48000 ak Grove Drive 
Pasadena, California 91103 
Reference: TSP 72-10609 
Patent status: 
NASA has decided not to apply for a patent. 
Source: Joseph M. Conley of

Caltech/JPL
under contract to

NASA Pasadena Office
(NPO-11634)
I 
I 
B72-10609	 Category 02


Oscillating hot-wire anemometer

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