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Pergamon Mechanics Research Communications, Vol. 21, No. 2, pp. 131-138, 1994

Copyright © 1994 Elsevier Science Lid Printed in the USA. All rights reseawed

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IMPACT PRESSURE MEASUREMENTS IN A HIGH SPEED RAREFIED FLOW

Channa Raju, A.K. Sreekanth and Job Kurian Department of Aerospace Engineering, Indian Institute of Technology, Madras-600 036, India

(Received 26 February 1993; accepted for print 6 January 1994)

1. In t roduct ion

The pitot probes are primary and often complementary tools in flight and laboratory measurements. In continuum flow the Mach number can be determined from the ratio of impact to static pressure using the well known Rayleigh formula in supersonic flow, and isentropic relation in subsonic flow. At low Reynolds numbers the pressure measured using conventional pitot tubes will have large departures from that calculated using the above mentioned relations due to various rarefaction effects, generally termed as viscous effects at low densities. At a Reynolds number of the order of 10 the measured pressure using a pitot tube at a Mach number of 2.0 can depart by a order of 200 percent, depending on the geometry of the probe, and larger departures at higher Mach numbers.

The performance of pressure probes has been studied by a large number of investigators [1,2,3] and the correction factors to be applied to the measured values of pressure as a function of Reynolds number based on probe diameter and Mach number are available in the form of curves and tables [4]. The process is cumbersome and the viscous correction factors are available only to a limited Mach number range up to 8.0 and many methods are suggested to calculate the same for higher Mach numbers. Therefore even the most careful measurements of pressure will become question- able if not interpreted properly.

Recently, Sankovich [5] based on the static pressure survey in a circular tube introduced a new design of an impact probe whose performance is free of rarefaction effects. Since the concept is new and promising for the low density research, verification of its utility in well known flow situations is desirable. This paper presents an experimental study on the various aspects performance of this probe.

2. Experimental Investigation

2.1 Experimental Facility

The facility consisted of a low density wind tunnel together with its accompanying instrumentation. The continuous flow tunnel has an upstream stagnation chamber, nozzle support unit and downstream plenum chamber and is evacuated by a vane type rotary pump, Roots pump and a pair of vapour diffusion pumps. A schematic representation of the experimental apparatus is shown in Fig. [1]. The instrumentation included pressure sensors of MKS make of 1 torr and 10 tort ranges with the accuracy of 0,08% of the reading and Barocel electronic sensors for measuring upstream, probe and downstream chamber pressures. The probe pressure was measured by two high

131

132 C. RAJU, A.K. SREEKANTH and J. KURIAN

Time Response of Probes

After connecting to the transducer unit, each probe was tested for its time response to a very rapid

rise in the chamber pressure from a fraction of micron to about 100 microns. The pressure was

measured using the instrumentation described. The time required to record 99.9 percent of the

pressure increase varied from few seconds to about 2 minutes with the longest probe.

2.3 Experimental Procedure

The tunnel was made ready for experiments by evacuating to a pressure less than 10 -5 torr and well

outgassed for several hours using an Edwards diffstak pump. At room temperature dry air from

compressed cylinders was admitted to the stagnation chamber through a constant pressure regula-

tor and a throttle valve. The probe along with the transducer was fixed on the vertical flange of a

three axes traversing mechanism, operated remotely. Once the steady flow was set for a given up-

stream pressure, the probe was moved along the axis of the jet and the pressure values recorded at

close intervals. The same was repeated for different upstream pressures.

3. Results and Discussion

The axisymmetric jets issued from circular orifices expanding to very low pressures have been

studied by Sherman and Ashkenas [6] and their empirical relations were used for comparisons.

The measured pitot pressures on the axis were converted to Mach numbers using normal shock

relations. Birds parameter 'p' calculated using upstream conditions and measured Mach numbers,

was used for knowing the onset of departure from continuum flow.

The results of one of the type 1 probes for three upstream conditions are given in Fig. [3]. It shows

that beyond a x /d value of about 3.5 on the axis of the jet large departures of measured pressures

from those given by Sherman-Ashkenas relation occur. At large x/d large departures occur and at

lower upstream pressures the corrections involved are higher. The results of all the type 1 probes for

one of the upstream pressure is presented in Fig. [4] and the results agree quite well after applying

the appropriate correction factors.

The results of all the three type 2 probes are compared with the results of two of type 1 probes in Fig.

[5]. The results of type 1 are uncorrected for viscous effects and it is seen that the correction

required for the probe of 1.6 mm diameter are slightly larger due to lower probe Reynolds number

than that of probe with the diameter 2 mm, which is a well known result. In the case of type 2 probes,

PRESSURE MEASUREMENTS IN RAREFIED FLOW 133

accuracy MKS 170 series temperature controlled transducers of 1 torr and 10 torr. These gauges

could be used inside the vacuum chamber mounted on a three axes traversing mechanism along

with the probe, and had an accuracy of 0.05% of the reading.

The free jet issued from a circular sonic orifice of diameter 6.8mm (made out of a thin aluminum

sheet, I/d = 0.015) was used for studying the performance of the probes.

2.2 Details of Probes

For comparison two kinds of probes were fabricated and used.

The first set of 4 probes, which are conventional pitot tubes similar to those used by Enkenhus [1]

and Ashkenas [4] and the second set consisting of 3 probes of Sankovich [5] type. These two

sets are referred to as type 1 and type 2 respectively for identification. The constructional details

are shown in Fig. [2].

The salient features of the probes are described below:

TYPE 1 PROBE

a. 10 degree external chamfer

b. Ratio of O.D to I.D = 1.25

c. Ratio of length to O.D = 50

The outer diameter of the four probes were: 1.2mm ([1]), 1.6mm, 2mm and 4.76mm.

TYPE 2 PROBE

The probe essentially consists of two concentric tubes, the inner tube having an orifice whose

center coincides with the edge of the outer tube. The outer tube was sealed at the rear end as

shown in Fig. [2]. The three probes had diameters 'D' (O.D of outer tube) of 4mm, 3mm and 3.6mm,

the first two had a length 'L' of 50mm and the length of the third one was 75mm. The diameter of

the inner tube 'd' was 2mm and the orifice width 'h' was O.5mm, and these were kept constant for all

the probes.

Leak Testing

All the probes were leak tested thoroughly before installation using a helium mass spectrometer type

leak detector. The entire pressure measuring system and the jet source assembly was also tested

similarly for possible leaks.


no perceptible difference was noticed between the readings of different sizes of probes. As seen in

Fig. 5, there is no systematic deviation from the results of Ashkenas and Sherman in the case of

newtype of probes, irrespective of their sizes. The well established fact of a smaller conventional pitot

probe having more rarefaction effects is clearly seen in the same figure. In these experiments only

three different sizes of newtype probe were used. Because of difficulties of fabrication the smallest

was of 3 mm outside diameter. A series of experiments with still smaller probes will be meaningful to

throw more light into question of rarefaction effects.

The longer probe of type 2 not only had longer time response but also measured lower pressures at

all x stations, hence the Mach number curve is shifted almost parallel to that of curves of probes of

same family. The shorter probes of type 2 with the same length and different diameters of 3 mm and

4 mm show almost the same performance. The onset of departure from continuum on the axis of

the jet is shown using the results of probe 1 and also using Bird's parameter p = 0.05 [7] which

signifies the transition. The typical pitot pressure plots obtained using 4 mm dia type 2 probe is

presented in Fig. [6]. The position of Mach disc location Xm/d for the upstream pressure value of 10

torr is marked, and agrees well with the value obtained from the empirical relation of ref [6].

The effect of pressure ratio on the measurements for both the types of probes is shown separately in

Figs. [7] and [8]. From Fig. [7] it can be seen that there is a large scatter beyond M = 7.5, due to

uncertainty in applying viscous corrections in that range.

The results of one of the type 2 probes are shown in Fig. [8]. The Mach number values are directly

obtained from the pressure measurements without applying any corrections. Obviously there is a

strong gradient in impact pressure along the axis of the freejet due to change in oncoming Mach

number. Consequently, the shock stand off distance also gets modified at each axial location of the

probe. Because of non inclusion of such gradients in data deduction, the curves in Fig.8 are only

indicative of the usefulness of the newtype of probe for making impact pressure measurements and

not representative of the probe's calibration. It is seen that the experimental data compares reasona-

bly well with the results of Sherman and Ashkenas.

Another important feature of the new probe is its usefulness to calculate the transition point from

continuum to free-molecular flow. The terminal Mach number is found by means of a log-log plot of

Mach number vs distance. The data fell on two separate lines and the intersection point is taken

to be the transition point. Fig. [9] is a typical plot of terminal Mach number and the location of its

occurrence on the axis as a function of Kn -04 (a parameter used by other investigators) obtained

from the measurements of type 2 probe [5]. The K n is calculated using the upstream conditions and


the orifice diameter. Ref. [3] suggests that the transition region can be regarded to a good approxi-

mation as a surface of freezing where the terminal Mach number is calculated. The figure indicates

that at higher values of K n the transition from continuum to free molecular flow occurs close to orifice

exit.

Exper imental Error

A typical experiment was repeated several times using a sample probe of both the types and from the

repeatability data of these experiments it was found that the maximum error in determination of

Mach number was less than 3%.

4. Conclusions

The performance of the new probe is certainly promising. It offers a new and a more direct method

of determination of pitot pressures in a low density flow. The theoretical aspects of such a probe in

eliminating rarefaction effects in impact pressure measurements warrant further investigation. It is felt

that this probe can be a handy tool for low density research.

References

1,

2.

3.

K.R. Enkenhus, "Pressure probes at very low density", UTIA Rep. No.43, 1957.

K. Rogers, J.B. Wainwright and K.J. Touryan, "Impact and static pressure measurements in

high speed flows with transitional Knudson numbers", 4th RGD, 1964.

J.B. Anderson, R.P. Andres, J.B. Fenn and G. Maise, "Studies on low density supersonic jets",

4th RGD, 1964.

H.I. Ashkenas, JPL Space Programs Summary No.37-15.

V.M. Sankovich, "Stagnation pressure porbefor supersonic rarefied gas flows", 15th RGD

1986.

H.I. Ashkenas and F. Sherman, "The structure and utilisation of supersonic free jets in low

density wind tunnels", 4th RGD, 1964.

G.A. Bird, "Break-down of continuum flow in free jets and rocket plumes", 12th RGD, 1980.


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FIG.S RESULTS OF NEW PROBE COMPARED TO CONVENTIONAL PROBES

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CORRECTED RESULTS OF DIFFF_REIV]" CONVENTIONAL PITOT PROBES

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FIG.6 MEASURED PITOT PRESSURES ON THE AXIS


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FIG. 9 TERMINAL MACH NUMBER AND ITS LOCATION