[net.physics] Hot Wire Anemometers

drabik@sdccs7.UUCP (08/01/84)

Hot wire anemometers are being used to measure mass flow rate of intake
air in many modern automobile engines.  The operation of these devices
depends on the properties of heat transfer by forced convection past a
body (e.g. a circular cylinder).  Can anyone tell me what the functional
dependence is of heat flow with respect to temperature of the cylinder,
temperature of the ambient air, velocity of the air, and density of the
air (at low Reynolds numbers), that is, in

	dQ/dt = f (v, rho, Ta, Tw),

what is the form of f?  It seems that, by being clever, one can use only
one (or maybe two) wires and measure mass flow directly.  This I would
like to know.


					Thanks in advance,

					Tim Drabik
					...sdccs7!drabik
					UCSD EECS

drabik@sdccs7.UUCP (drabik) (08/02/84)

Sorry, false alarm.

Scheuer.Wbst@XEROX.ARPA (08/07/84)

The following description of the how wire anemometer is taken from
Holman, J.P., Experimental Methods for Engineers (2nd Ed.), McGraw-Hill
Book Co., 1966, pp. 206-209.

"The hot-wire anemometer is a device that is most often used in research
applications to study varying flow conditions.  A fine wire is heated
electrically and placed in the flow stream.  the heat transfer rate from
the wire has been shown to be (ref. King, L.V.,"On the Convection of
Heat from Small Cylinders in a Stream of Fluid, with Applications to
Hot-wire Anemometry", Phil. Trans. Roy. Soc. London, vol. 214, no. 14,
p373, 1914.)

	q=(a + b(rho*u)^.5)*[T(w)-T(oo)] Btu/(hr)(ft^2)

where T(w) = wire temperature
	T(oo) = fluid temperature
	rho = fluid density
	u = fluid velocity
	a,b = constants that are obtained by a calibration of the device
(and those letters at the end are some archaic units, or something like
that.)

The heat transfer rate must also be given by

	q = i^2 * R(w) = i^2 * R(0)[1 + alpha*(T(w)-T(0))]

where i = electric current
	R(0) = resistance of wire at reference temperature T(0)
	alpha = temperature coefficient of resistance

For measurement purposes the hot wire is connected to a bridge circuit
shown in the book (too complicated to reproduce here).  The current is
determined by measuring the voltage drop across a standard resistor and
the wire resistance is determined from the bridge circuit....Time
constants of the order of 1 msec may be obtained with 0.0001 in. diam.
platinum or tungsten wires operating in air.  A modification of the
hot-wire method consists of a small cylinder that is coated with a thin
metallic film a few microns thick.  This film then serves as the
variable resistance and is extremely sensitive to fluctuations in the
fluid velocity.  Such hot-film probes have been used for measurements
involving frequencies as high as 50,000 hz.

The calibration of hot-wire probes is quite complicated, and the
interested reader is referred to the discussion by Kovasznay for more
information.

[ref. Kovasznay, L.S.G., "Hot-wire Method", in Physical Measurements in
Gas Dynamics and Combustion," p. 219, Princeton University Press,
Princeton, N.J., 1954.]"

Mark