probe and a pressure probe positioned in a flow duct carrying mean flow and progres- sive acoustic ... Acoustic pressure field amplitude spectra, propagation directions ...... Notes. Tony L. Parrott: Langley Research Center, Hampton, Virginia.
NASA
NAsA-Tp-2581 198G0017571
Technical Paper
2581 June 1986
Pressure Probe and Hot-Film Probe Responses to Acoustic Excitation in Mean Flow Tony L. Parrott and
-
Michael' G. Jones
jij;,i
a 'i!_35
L RNGLILY R_:.oLAr A and T < i). The negative sign for this term indicates that the fluctuating temperature contribution is out of phase with the mass flux term. This result is physically realistic because an increase in fluid temperature causes less heat transfer from the hot film. Contributions to fluctuating Reynolds number from fluctuating Knudsen number and temperature ratio due to acoustic wave interaction with the hot film were estimated from measurements of acoustic pressure at a flush-mounted pressure sensor in the same plane as the hot film. This necessitated that Kn and _ be expressed in terms of fluctuating pressure, P. The Reynolds number of the flow about the hot film based on the film diameter, d, is given by equation (3), which can be linearized to give
Re : i + _ _ _ Re u p
(14a)
Alternatively, by defining fluctuating Mach number as
c
equation 14(a) can be written as
Re
M
P
From reference ii, the relation between Knudsen number, Mach number, and Reynolds number is given as
Kn = _2_
R-_ M
(15)
Linearizing produces
ii
By substitution from equation (14b), equation (16) becomes
Kn = Kn
_-
(17)
This equation, together with the acoustic field equations which follow, is used to express fluctuating Knudsen number in terms of fluctuating pressure. From reference 12, fluctuating velocity, density, and temperature are related to fluctuating pressure in a progressive wave as follows:
Qc
(18a)
c2
(18b)
According to Schlichting (ref. 13, p. 329), a power law that closely approximates Sutherland's formula for the viscosity dependence on temperature is given by
