The transient dynamic characteristics of a test chamber Mach number was established for a disturbance initiated in the test chamber. An approximate linear expression was given, showing that the change in the Mach number is linearly proportional to the algebraic sum of the static pressure change in the test chamber and the stagnation pressure change. The static pressure change is the dominating factor. The two pressure changes were also calculated for small Mach number variations, and these results were applied to instrumentation requirements

Tcheng, P.

English

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f	 i
TRANSIENT RESPONSE CHARACTERISTICS OF TEST
CHAMBER MACH NUMBER
by
Ping Tchengl
The research reported herein was done under grant NSG 1079 during the
period November 1975 - April 1976.
1. Establishment of linear relationship between the Mach number and pressures.
The test chamber Mach number is computed from the following equation:
[(P ^Zh =1M = 5 pt	 1	 (1)s
where
M = test chamber Mach number
pt = test chamber stagnation, psf
ps = test chamber static pressure, psf
Equation (1) is derived quasi-statically and is applicable only to the
equilibrium states of the wind tunnel. Assuming that the tunnel is initially
in equilibrium state 1, a second equilibrium state will eventually be reached
after a stepped disturbance is initiated in the test chamber. The Mach number
change between the two equilibrium states could be computed by equation (2).
I0
	 D5pt7Mls 	 ptl PS11	 (2)
where
AM = M2 - M1 = Mach number change
l Associate Professor of Engineering, Old nominion University, Norfolk,
Virginia 23508.
L _.
&Pt = Pte - ptl = stagnation pressure change, psf
pps
	 s2
= p - psl = static pressure change, psf
Equation (2) is the linear approximation of equation (1) and is valid for
small changes of pressures only. The validity of equation (2) is established by
a comparison in Table 1 of the Mach number changes computed from equation (1)
with those computed from equation (2). Small variations between these two
changes are seen. Dote that SEL data of pt and p  were used for the calcu-
lation. In other words, for one ambient pressure (latm) and elevated temperature
(120°F) flap-model test, a linear relationship between Mach number change and
pressure changes exists for Mach number change up to '--.070. The block diagram
in Figure 1 illustrates this cause-effect relationship. Note that the gain values
in the three blocks of Figure 1 are different for different equilibrium conditions
of the tunnel.
2. Relative contributions of the two pressure changes on the Mach number change.
The two terms inside the brackets of equation (2) are percentage changes of
stagnation and static pressures. Experimental results of these two percentage
changes are listed in Table 2. The last column shows the ratio of percentage
change of static pressure over the percentage change of stagnation pressure.
The average ratio found is -6.4. If a new variable, a defined as the ratio of
these two percentage changes is introduced, then equation (2) can be rewritten
as:
P	 2i ^P 	 l
where
^f = -5 
t 7Ms	
s (1 - a/
	
(3)
1	 Ps
Ap 1	 1
- 
—
PSI^\Ptl/ - VS ,)`Apt/	
(4)
The negative sign of X inuicates that the two pressure changes are opposite
in signs, i.e., when one increases then the other decreases and vice-versa. The
z:
	
	
magnitude of a shows that the test chamber Mach number change is dominated by
the test chamber static pressure change. Therefore, equation (3) cea be
approximated as
r
fi	 2
t`
^	 I	 I	 I	 i
I
pt7Mps 2/' \ pssAM = - 1
3. Mach number response speed.
A set of experimental data of test chamber pressure changes (from FM
recordings) as shown in Figure 2 illustrated that these changes are almost .
instantaneous at subsonic speeds and are completed within threL seconds at
M = 1.20 . Thus, according to equation (5), fast response speed on
Mach number is implied. Since the approximation given by equation
(5) is only good for X X 1 or 86% of the total Mach number change, it means
that once the test section is disturbed, the test chamber Mach number will be
changed almost instantaneously to within 86% of its total change. The final
14% change of test chamber Mach number then will be dictated by the large time
constant (6 or 8 seconds) of the stagnation pressure change Ap t as given by
equations (2) or (3). The dynamic relationship between the drag change AD in
the test chamber and the resulting Mach change AM can be described by the
block diagram shown in Figure 3.
It should be noted that gain K in the first block of Figure 3 has the unit
of psf/lb and assumes different values for different equilibrium conditions of
the test chamber. Experimental values of K were found at .0168, .0313, .0617,
0.143 for nominal Mach numbers of .80, .95, 1.05, 1.20, respectively.
4. Summaries and recommendations.
The following characteristics of the test chamber Mach number change AM
due to disturbance AD initiated in the test chamber were observed experimentally:
a. AM can be computed from the linearly approximated expression given by
equation (2). This implies that AM is linearly proportional to the algebraic
in the test chamber and the stagnationsum of the static pressure ch g  Aps 
pressure change Opt . The establishment of this linearity should simplify the
on-line computation requirement and procedure of Mach number change significantly.
b. Aps is the dominating factor in determining 4M . Percentage change of
Ap s
 was found approximately 6.4 times the percentage change of Opt . Since Aps
occurs rather rapidly, it means that AM also changes very rapidly initially
when Aps is the dominating factor. The last portion of Al (about 14% of the
total change) is a sluggish process influenced by the large time constant of Op t .
3
(5)
iThe dynamic characteristic of test chamber Mach number change is thus established
and is shown in Figure 3.
The following requirements on instrumentation were also observed based on
experimental evidence:
a. Together with equation (2) and data in Tables 1 and 2, it is possible
to calculate the two pressure changes for smai.l Mach number variations. Table 3
lists these pressure changes for Mach number changes of .002 at different
operating conditions. This implies that the stagnation pressure measurement
device has to be sensitive to the fraction of one psf in order to control the
test chamber Mach number with an accuracy of .002.
b. If. the test chamber Mach number is the desirable Mach number to be
controlled, then either the probe of the pressure measuring device should be
located inside the test chamber or the dynamic enhancement technique developed
at IRD or other prediction techniques should be applied to the pressure measure-
ments made outside the test chamber. A trace of the static pressure made by a
probe in the plenum obtained on the SEL system is shown in Figure 4. A lag in
response is clearly indicated. It is fairly safe to assume that this lag is
due to the combination of the dynamics of the plenum filling or emptying process
and the dynamics of the manometer.
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ISCHOOL OF ENGINEERING
OLD DOMINION UNIVERSITY
NORFOLK., VIRGINIA
Technical Report 76-T9
TRANSIENT RESPONSE CHARACTER ISTICS OF TEST
CHAMBER MACH NUMBER
By
Ping Tcheng
Progress Report
Prepared for the
National Aeronautics and Space Administra-.ion
Langley Research Center
Hampton, Virginia 23665
Under
Grant NSG 1079
November 1975 - April 1976
Dr. J. S. Tripp, Technical Monitor
Instrument Research Division
p	
Submitted by the
Old Dominion University Research Foundation
^`^ "tititi`	 Norfolk, Virginia 23508
May 1976


Transient response characteristics of test chamber Mach number

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