Wind-tunnel tests have been made to determine the static-pressure error resulting from external interference effects of flow through the static-pressure orifices of an NACA airspeed head at Mach numbers of 2.4, 3.0, and 4.0 for angles of attack of 0 deg, 5 deg, 10 deg, and 15 deg. Within the accuracy of the measurements and for the range of mass flow covered, the static-pressure error increased linearly with increasing mass-flow rate for both the forward and rear sets of orifices at all Mach numbers and angles of attack of the investigation. For a given value of flow coefficient, the static-pressure error varied appreciably with Mach number but only slightly with angle of attack. For example, for a flow coefficient out of the orifices of 0.01 (the approximate value for a vertically climbing airplane for which the airspeed system incorporates an airspeed meter, a Mach meter, and an altimeter), the error increased from about 5 percent to about 12 percent of the static pressure as the Mach number increased from 2.4 to 4.0 with the airspeed head at an angle of attack of 0 deg

Silsby, Norman S.

English

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NASA MEMO 2-13-59L
NASA
MEMORANDUM
EXTERNAL INTERFERENCE EFFECTS OF FLOW
THROUGH STATIC-PRESSURE ORIFICES OF AN AIRSPEED HEAD
AT SEVERAL SUPERSONIC MACH NUMBERS
AND ANGLES OF ATTACK
By Norman S. Silsby
Langley Research Center
Langley Field, Va.
NATIONAL
SPACE
AERONAUTICS AND
ADMINISTRATION
WASHINGTON
March 19 59
https://ntrs.nasa.gov/search.jsp?R=19980231949 2020-06-15T23:14:41+00:00Z

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MEMORANDUM 2-13-59L
EXTERNAL INTERFERENCE EFFECTS OF FLOW
THROUGH STATIC-PRESSURE ORIFICES OF AN AIRSPEED HEAD
AT SEVERAL SUPERSONIC MACH NUMBERS
AND ANGLES OF ATTACK
By Norman S. Silsby
SUMMARY
Wind-tunnel tests have been made to determine the static-pressure
error resulting from external interference effects of flow through the
static-pressure orifices of an NACA airspeed head at Mach numbers of
2.4, 3.0, and 4.0 for angles of attack of 0 °, 5° , lO °, and 15 °.
Within the accuracy of the measurements and for the range of mass
flow covered, the static-pressure error increased linearly with increasing
mass-flow rate for both the forward and rear sets of orifices at all
Mach numbers and angles of attack of the investigation. For a given
value of flow coefficient, the static-pressure error varied appreciably
with Mach number but only slightly with angle of attack. For example,
for a flow coefficient out of the orifices of 0.O1 (the approximate
value for a vertically climbing airplane for which the airspeed system
incorporates an airspeed meter, a Mach meter, and an altimeter), the
error increased from about 5 percent to about 12 percent of the static
pressure as the Mach number increased from 2.4 to 4.0 with the airspeed
head at an angle of attack of 0°.
INTRODUCTION
Airspeed installations on climbing or diving airplanes are subject
to air flowing into or out of the static-pressure orifices because of
the volume of the instruments and the connecting tubing. This air flow
causes a pressure loss, and hence the instruments are subjected to a
pressure that is different from the pressure at the static- or total-
pressure sources. This is the well-known pressure-lag error. (See
refs. 1 and 2.) Another error associated with flow into or out of the
airspeed measuring system is the interference effect of the flow through
the airspeed static-pressure orifices on the external flow when the
external flow is supersonic. If the interference is appreciable, the
static pressure in the region of the orifices may be expected to be
different from that with no flow through the system. For example, at
supersonic speeds flow out of the statlc-pressure orifices may cause
a shock wave and hence an increase in static pressure, whereas flow into
the orifices may cause an expansion wave or a decrease in static pressure.
The results of tests to determine this error at a Mach number of 3
and an angle of attack of 0° are reported in reference 3. Because the
magnitude of this error was appreciable, it was considered of interest
to extend the tests to include other Mach numbers and angles of attack.
Consequently, additional tests were made at _ach numbers of 2.4, 3.0,
and 4.0 for angles of attack of 0°, 5° , lO °, and 15 ° and the results
are presented herein.
Measurements of static pressure in the crifice chamber were made
with flow out of the orifices at mass-flow rates up to about 2.2 x l0 -6,
2.9 × l0 -6, and 5.7 x lO -6 slugs per second for the Mach numbers of 2.4,
3.0, and 4.0, respectively. The maximum Reyrolds numbers (based on the
diameter of the airspeed head) were 0.82 × 1C6, 0.77 × lO 6, and
1.15 × l06 for Mach numbers of 2.4, 3.0, and 4.0 and tunnel stagnation
pressures of 50, 75, and 190 lb/sq in., respectively.
SYMBOLS
A
Cw
M=
P
Pc
Pc,O
total area of static-pressure orifices leading to each chamber
of airspeed head, 1.25 x lO -4 sq ft
mass-flow coefficient,
W
p_v_
length of mass-flow measuring tube, 3.72 ft
free-stream Mach number
static pressure, ib/sq ft
pressure in chamber of airspeed hesd, ib/sq ft
pressure in chamber of airspeed he_d with zero flow through
orifices, ib/sq ft
pressure drop in mass-flow measurirg tube, ib/sq ft
Rr
T
v
V_
w
ct
7
c
gas constant for air, 53.3 ft/deg
internal radius of mass-flow measuring tube, 3.2 x 10-3 ft
temperature, OR
total volume of airplane airspeed installation, cuft
free-stream velocity, ft/sec
_r 4
mass flow, --£_PP2' slugs/sec (positive values for flow out
of airspeed-head orifices)
angle of attack of airspeed head, deg
flight-path angle, deg
nondimensional pressure error,
Pc - Pc,O
POO
absolute viscosity of air in mass-flow measuring tube,
slugs/ft-sec
mass density of air, slugs/cu ft
Subscripts:
OO
i
2
tunnel or free stream
airplane airspeed installation
mass-flow measuring tube
APPARATUS AND TESTS
The NACA airspeed head and the test method used in the present
investigation were the same as those used in the tests of reference 5.
(See fig. i.) The tests were again conducted in the Langley 9- by
9-inch high Mach number jet.
In the tests reported in reference 5, two different stagnation
pressures were used to determine whether there was an effect due to
Reynolds number. Because no effect was found over the range of Reynolds
numbers covered, only one stagnation pressure was used at each Mach
number in the present tests, namely 50, 75, _nd 190 ib/sq in. for the
Machnumbers of 2.4, 3.0, and 4.0, respectiw_ly. The corresponding
Reynolds numbers, based on airspeed-head di_eter_ were 0.82 x 106,
0.77 x i0 O, and 1.15 x 106.
The tests of reference 3 were madefor conditions of flow both into
and out of the orifices to simulate the conditions of an airplane diving
or climbing. Becausethe results of those tests indicated essentially
the samerate of change of static-pressure error with mass flow for
both flow directions, tests were madeonly f(,r the condition of flow out
of the orifices in the present investigation The Reynolds numberof
the flow through the orifices, based on the (iameter of the larger orifice
(0.052 inch) was 350 for the mass-flow rate of 3.7 x 10-6 slugs per
second.
Results of the tests of reference 3 indicated that, although varying
flQw rates for the rear orifices had no effect on the pressure at the
forward orifices (a result which would be e_ected for supersonic flow)_
there was a small effect (about i percent) OILthe pressure at the rear
orifices for the full range of mass-flow rat_ used at the forward orifices.
Because this effect had already been found t(. be small, no attempt was
made to isolate this effect in the present t(_sts.
Measurementswere recorded by meansof _tandard differential-
pressure cells. Differential pressures were measuredbetween: (i) tun-
nel static and chamber static pressures, (2) chamberstatic pressure and
pressure at the end of the mass-flow tube, a_Ld(3) the pressure drop in
the mass-flow tube. (See fig. 2.) Also rec(_rded during the tests were
tunnel stagnation temperatures and pressures and the temperature of air
flowing through the mass-flow measuring tube Photographs were taken
of the airspeed head in the tunnel for the p_trposeof verifying the angle
of attack, which was set in by a coarse indic_ator; in all cases the angle
of attack was verified to within ±1/2° of th_ desired setting. The mass
flow of the tests ranged from 0 to a maximumof about 2.2 x I0-6_
2.9 x 10-6, and 3.7 x i0 -° slugs per second _'or the Machnumbersof 2.4,
_.0, and 4.0, respectively.
RESULTSANDDISCUSSI(_
The static-pressure error was determine(L as the difference between
the static pressure in the airspeed-head chm_ers and the static pressure
at a tunnel-wall orifice about I foot upstre_ of the orifices in the
airspeed head. The static-pressure error du(_to the external interfer-
ence effects of flow through the orifices wa_ obtained by subtracting
the pressure difference for zero mass flow from the corresponding pres-
sure differences with various values of mass flow.
5The static-pressure error due to flow through the orifices, made
nondimensional by dividing by the tunnel static pressure and indicated
by c, is shownplotted against the nondimensional mass-flow coefficient
Cw in figures 3(a), 3(b), and 3(c) for Machnumbers of 2.4, 3.0, and
4.0_ respectively, for angles of attack of 0°, 5° , i0 °3 and 15° . For
someof the test conditions the data exhibit substantial scatter and
hysteresis_ which were mainly the result of pressure lag due to the
small-diameter tubing leading to the airspeed-head chambers.
Although there was somescatter, hysteresis, and, in somecases,
a scarcity of data points in figure 3, it was believed that a straight-
line fairing of the data was the best fit in view of the linearity of
the results of reference 3, wherein there was a substantial number of
data points with little scatter. The data of figure 3 showthat the
static-pressure error e increased with increase of the flow coeffi-
cient Cw for both the forward and rear orifices at all three Math num-
bers and all four angles of attack. The data also show that at a given
value of flow coefficient the static-pressure error varies with both
angle of attack and Machnumber.
In order to showmore clearly the effects of angle of attack and
Machnumberon the static-pressure error, the slopes of the curves d(___)
of figure 3 at each Machnumberare plotted in figure 4 against angle
of attack for both the forward and rear orifices. In general there
appears to be a substantial variation of static-pressure error with
Machnumberbut only a small variation with angle of attack over the
range covered. The reason for the somewhatlarger variation with angle
of attack for the rear orifice at M_ = 4 is not known.
The variation with Machnumber of d___eat an angle of attack of 0°
dCw
is shown in figure 5. Also shown in figure 5 are two test points at
Mach numbers of 0.915 and 1.125 (_ = 0°) as obtained by Mabey (ref. 4)
from tests of a British Mark 9A pitot-static head, a standard probe on
British high-speed aircraft, which has two sets of static slots instead
of multiple round static holes. The two test pointsj expressed in dif-
ferent quantities in reference 4, have been converted to correspond to
the quantities of figure 5, and have been used as an aid in extending
the fairing of the curve to a Mach number of zero. The curve shows a
substantial increase in the static-pressure error with increase in Mach
n_mber. For example, there is an increase in d-!-e from about 5 to about
d%
12 as the Mach number increases from 2.4 to 4.0.
6Because of the method used in determining the interference of the flow
through the orifices with the external flc_, the values of the pressure
errors as determined by these tests include the loss across the orifices
(from the chamber to the outside). Some bench tests made with no exter-
nal flow but with flow through the orifices over the same range of con-
ditions as in the tunnel tests indicated an average orifice discharge
coefficient of about 0.66. On the basis cf this discharge coefficient
the loss across the orifices for an airspeed installation with a non-
dimensional flow coefficient Cw of, for example, 0.01 in flight, was
computed to be 0.18, 0.36, and 0.95 percezt of the free-stream static
pressure at Mach numbers of 2.4, 3.0, and 4.0, respectively. In these
estimates the temperature of the air in tke airspeed system was assumed
to be the stabilized surface temperature in the boundary layer with a
recovery factor of 0.85. These losses in pressure across the orifices
would presumably be accounted for in the usual pressure-lag corrections.
The significance of the results of figures 4 and 5 for a climbing
airplane (flow out of the orifices) may be more readily indicated if
the flow coefficient Cw is converted into a related parameter involving
flight conditions. As has been shown in reference 2, one form of the
mass-flow coefficient in terms of the flight quantities involved is
Cw _ w _ v sin
ARTl
With this expression for flow coefficient, a quicker interpretation of
the results of figures 4 and 5 may be made. For example, for an air-
plane in a vertical climb at high altitude for which the airspeed instal-
lation incorporates an airspeed indicator, a Mach meter, and an altimeter,
the flow coefficient Cw is of the order of 0.01. For this value of
flow coefficient and an angle of attack of 0°, the data of figure 5
indicate static-pressure errors of about _ percent of free-stream static
pressure at M_ = 2.4, about 8 percent at M_ = 3.0, and about 12 percent
at M_ = 4.0. Because the variation of t_e static-pressure error with
flow coefficient is linear, static-pressure errors for other values of
flow coefficient Cw can be obtained directly by multiplying the values
of d-i-e from figures 4 and 5 by such values of Cw. The percentage
dCw
error in Mach number is essentially one-hslf the static-pressure error
for this range of Mach numbers and these relatively small pressure errors.
7CONCLUSIONS
Results of tests to determine the static-pressure error resulting
from external interference effects of flow through the static-pressure
orifices of an NACA airspeed head at Mach numbers of 2.4, 3.0, and 4.0
and at angles of attack of 0°, 5° , i0 °, and 15 ° have indicated that,
within the accuracy of the measurements and for the range of mass flow
covered, the static-pressure error increased linearly with increasing
flow rate at all Mach numbers and angles of attack of the investigation.
For a given value of flow coefficient, the static-pressure error varied
appreciably with Mach number but only slightly with angle of attack.
For example, for a flow coefficient of 0.01 (the approximate value for
a vertically climbing airplane at high altitude for which the airspeed
system incorporates an airspeed meter, a Mach meter, and an altimeter)
the static-pressure error increased from about 5 percent to about 12 per-
cent of free-stream static pressure as the Mach number increased from
2.4 to 4.0 with the airspeed head at an angle of attack of 0°.
Langley Research Center,
National Aeronautics and Space Administration,
Langley Field, Va., November 13, 1958.
REFERENCES
i. Lamb, J. P., Jr.: The Influence of Geometry Parameters Upon Lag Error
in Airborne Pressure Measuring Systems. WADC Tech. Rep. 57-351,
Wright Air Dev. Center, U. S. Air Force, July 1957. (Available as
ASTIA Doc. No. AD 130790.)
2. Huston, Wilbur B.: Accuracy of Airspeed Measurements and Flight Cali-
bration Procedures. NACA Rep. 919, 1948. (Supersedes NACA TN 1605.)
3. Silsby, Norman S.: External Interference Effects of Flow Through
Static-Pressure Orifices of an NACA Airspeed Head at a Mach Number
of 3. NACA TN 4122, 1957.
4. Mabey, D. G.: The Calibration at Transonic Speeds of a Mark 9A Pitot
Static Head With and Without Flow Through the Static Slots. C.P.
No. 384, British A.R.C., 1958.
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.02 -- _
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13
16
12
V
M
4
_ mmmm m mmmm|_
4
Forward orifices
5
2.4
dE
dCw
0
16
I
Reor orifices
L
8 - ,-m.. ,.5
2.4
4
0
0 5 10 15
a, deg
Figure 4.- Variation with angle of attack of rate of change of static-
pressure error with rate of change of mass-flow parameter.
zk
16
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dCw
12
8
4
s
c rifice s
0
0 I 2 3 4
Figure 9.- Variation with Mach number of rate of change ef static-
pressure error with rate of change of ma_,s-flow coefficient, m = 0°.
NASA- L_ln_ley Field, Va. L-167


External Interference Effects of Flow Through Static-Pressure Orifices of an Airspeed Head at Several Supersonic Mach Numbers and Angles of Attack

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