1

A Five - Hole Pressure Probe for Fluid Flow Measurements in Three - Dimensions .

Dr. Khald A. Ismael Dr. Jalal M. Jalil Mr. Sattar J. Habeeb

Mech. Eng. Dept. Mech. Eng. Dept. Mech. Eng. Dept. Technology University Military College of Eng. Technology University

Prof. Assist. Prof. Assist. Teacher

Keywords:- Flow measurement , pressure probes , calibrat ion devise .

ABSTRACT

A pressure probe which facilitates measurement of mean flow quantities in three dimension simultaneously is described. The surface pressure is sampled at five

location : on the axis of the probe and at four equispaced point on a line encircling this point on a line encircling this central point. This work is applied to an existing

calibration and application procedure for five-hole probe, therefor you must find the flow angles by design transverse mechanism in 3D. The polynomial curve-fit method fourth - order was used , a computer program was built for calibration and

calculation velocity vector ( magnitude and direction ) for wide-range of calibration based on experimental data . The sensitivity of the probe to the Reynolds number was

examined for range of Re = 1000 9000 , also the accuracy of the pressure data from the computer software and direct measurement data from the test section was good with range of error of approximately 3% .

five-hole probe

: 0

, ( ) ( )0

Re=1000-9000 , 3% 0

2

NOMENCLATURE

C Correction factor

pitchCP Pitch coefficient

staticCP Static pressure

coefficient

totalCP Total pressure coefficient

yawCP Yaw coefficient

D 2m / N, )P(P1

g Acceleration of gravity

H Head pressure, m

d Probe diameter, m

P Pressure , 2m / N

P Mean pressure, 2m / N

R Velocity

vector, sec / m

Re Reynolds number

= / dU

U Magnitude of free-stream

velocity z y,x, Coordinate

system wv, u, Velocity

component in 3D.

GREEK NOMENCLATURE

Pitch angle, degree

Yaw angle, degree

Probe angle, degree

Kinematics viscosity of air ,

sec / m2 Density

SUBSCRIPTS

s Static pressure

o Total pressure

1,2,3,4,5 Refer to tube number of the

probe

1. Introduction :- Although a variety of pressure probes have been devised for

decomposing the flow velocity vector , the most well known and widely used

is the five-hole pressure probe . The device is a streamlined axisymmetric body that point into the

flow. The pressure distribution on the surface of the probe depends on the

angle of incidence of the mean flow vector relative to the axis of the probe. To determine the magnitude and

orientation of the flow vector , the surface pressure is sampled at five

location : on the axis of the probe and at four equispaced points on a line encircling this central point [1] .

The pressure differentials between selected pairs of these point may be

related to the inflow velocity vector by using an appropriate calibration to deduce pitch and yaw direction.

Hypothetically,theoretical relationships for the potential flow around the body

may also be used [2] . Two commonly used shapes are the cylindrical tube with a hemispherical

nose and a spherical ball at the end of a slender cylinder. Central pressure tap

gives the conventional stagnation pressure when the flow vector is perpendicular to that point on the

surface. Yaw and pitch angles in clinations of

the flow vector with the axis of the probe result in a imbalance of pressures on pairs of holes. In this case

the spherical probe is used, This arrangement is sketched in fig.1.

The theory yields a format for interpreting the differential pressures between pairs of holes as function of

angles of pitch and yaw. For calibration, the probe may be

installed in a water or wind tunnel and aligned with the known flow direction.

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Pressure differentials are then measured for selected angles of yaw

and pitch placed on the probe relative to the flow direction.

The purpose of this paper is to present a simplified calibration and

polynomial curve fitting forth - order method of using five-hole probe for

three dimension flow measurements and built a software computer Program for well range of calibration

of five - hole probe based on experimental data .

2. Probe Geometry :-

In the current work , five-hole probe was constructed by from five

stainless steel tubes of (1.0 mm) outside diameter by (0.6 mm) inside diameter, soldered together into a

(514 mm) of (5 mm) outside diameter stainless steel tube as shown in fig.2 .

The tube number (2) in the center is

filed perpendicular to its axis and the other four tubes surrounding tube number (2) are filed at probe angle

( 45 ). The ends of the tubes are cleaned out with a (0.6 mm) drill to

remove burrs. Each tube was coated with (5 mm) of load solder tube in

order to bend it smoothly by using tube bender [3] . An example , consider in fig. 3

the vector decomposition of the flow velocity (R) which is incident on the

five pressure taps (5,2,4,1,3) of a spherical probe. The center of the

coordinate axes coincides with the center of the probe. The holes (5,2,4) lie on a circle in the

xy-plane, (1,2,3) lie on a circle in the xz-plane. The angles between holes in

their respective planes all (probe angle 45 ). velocity vector (R) has a

component xyR in the xy- plane at an

yaw angle with the x-axis, and a

component xzR in the xz-plane at an

pitch angle with x-axis [4] .

3. Experimental Set-Up :-

Experiments were conducted

In low-speed open test section, with a

height 0.3m * 0.3m width * 0.3m length as shown as fig.4 .

The longitudinal freestream turbulence intensity was no greater than 0.6%

over the speed range of the experiments ( Re = 1000 to 9000).

The five-hole probe was mounted in a variable-angle calibrator in the center of the test section . The probe are

connected to the selection box ( Furness controls LTD.,type FCO9-6),

it has six pairs of channels with two rotary switches allow individual call up of any of the twelve solenoids in the

box. A micro-manometer ( Furness controls

LTD. , type FCO12) , was used to measure the pressure and the pressure differentials. The manometer has 1.%

accuracy , and measure maxP up

to OmmH 19.9 2 . This allows

the measurement of the

differential pressure between any two holes on a five-hole probe , plus the

comparison of any hole with a static source.

3.1 The Traversing Mechanism :-

To traverse the pressure probe , a standard traversing mechanism which

has a three-dimensional movability, was designed , The mechanism was

composed of two sliders, two rulers were fixed to the guides for measuring the distance traveled by the sliders in

both vertical and horizontal directions

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in test models as shown as fig.5. The special instrument designed to

perform the calibration runs , consisting of vertical and horizontal

protractor with sockets that fixed in the traverse mechanism, to enable the probe to yaw ( angular deviation in

the plane ) and pitch ( angular deviations about the axis of the plane).

The two protractors control the yaw and pitch angles as shown in fig.5.

3.2 Pressure Probes:-

3.2.1 Static-Pitot Tube:-

A standard ellipsoidal nosed Static - pitot tube was used to measure the tunnel reference

velocity . It had an external

diameter ( 7.98mmd ),a stem of (458 mm) long , a total pressure

hole of (1.32 mm ) diameter and seven static holes distance equals ( 8.02d ) .

The correcting of the reading of the tube was determined according

to the British standard [5] , as followsin :-

2RCair

0.5static

Ptotal

Pgwater

) (HP

where the above equation called eq.(1), and

CC

C =correction factore.

C =stem - static hole distance term.

= viscosity term.

=distance of the tube from wall term for this work

C =0.9975 , =0.0 , may be

determined from ref.[4].

3.2.2 Five-hole probe:-

This device is a spherical ball

at the end of a slender cylinder as

shown in fig.1. , used to determine and direction of the flow velocity vector R.

This probe was also used for static pressure measurement [6].For the five-

hole probe the calibration coefficients are defined as :-

D )P(P2CP

D )PP(CP

DP4)(P5CP

DP1)(P3CP

total

Sstatic

yaw

pitch

(2)

where

P - P2 D

4 / P4)P3P2(P5P

..(3)

The preceding sets of calibration

coefficients were found to be the most convenient and to have high sensitivities.

Characteristic of the steady term CP with respect to the pitch and yaw

angles must be determined experimentally because they deviate gradually from the theoretical

characteristics when the angle between the velocity vector and the radial line

through the pressure hole becomes large [6].

4. Calibration Procedure :-

The probe was calibrated in a small test section, in the free stream of inlet region the spatial variation of

velocity was 0.5% and the turbulence level 0.6% . A velocity

range ( 2 /secm 16.871.87 ) were used for the calibration, the probe was

held on a joint- tracked guide rod through out the calibration and remained fixed in that rod during use,

the rod was held in a traversing mechanism which allowed translation

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of the probe along, and rotation about its axis.

A protractor permanently attached to the traverse mechanism was used to

determine rotation (yaw angle ). The mechanism was mounted on an arm which could be rotated an axis

normal to the probe axis and the test section axis. The arm rotated about the

probe tip, then the pitch angle could be altered without moving the probe tip.

Point calibration were carred out at all combination of pitch and yaw angles

10 in 20 to 20 increments , at each orientation the four pressure

coefficients totalstaticpitchyaw CP,CP,CP,CP ,

and the air velocity were recorded. The four pressure coefficients were

calculation with the relationships :

),f(CP

),f(CP

),f(CP

),f(CP

total

static

yaw

pitch

(4)

Were then determined at regular intervals in and .

5. Calibration Results :-

The calibration coefficient at an air velocity of ( 15 m/sec ) are

presented in fig.6 and 7. , they are presented in the following forms:-

i. yawpitch CP vs. CP at various and .

ii. yawstatic CP vs. CP at various and .

iii. vs. CPtotal at various .

A computer program based on above algorithm was wrote in visual basic

langouge to meet the requirements of the problem see fig.9. The calibration

process is very sensitive to the probe alignment, probe support, and any

blockage so the procedure is repeated more times that get smoothing curves

where the polynomial curve-fit method fourth-order was used. The accuracy of

the processed data shown in table.1. was good with a range of errors of approximately 3% .

5. Measurement Procedure for flow field:-

Before starting the reading, two tests are made to check the

Instrumentation . The first test is to ensure that the pressure reading in

micro - manometer is zero before running. After running, the second test is to make sure of there is no leaking in

the pressure lines. In this case the five-hole probe is fitted with a cap, which

makes sure that the tubes of the probe connected to each others, and hence register the same pressure.

Then, if there is any significant difference between the two reading for any of the pressure , there is a leak in

one of the pressure lines. The relevant connection between the probe , and the

pressure can then be checked [7,8] .

5.1 Flow Angle Calculation :-

The computer program reads

the data P,PP5,P4,P3,P2,P1, S while

the coefficient of the calibration curves already are stored in the program. The

first step for the computer program is to calculate the drift of the datum pressure readings. It is assumed to drift

linearly with the number of reading taken . The pressures coefficient

totalstaticpitchyaw CP , CP , CP , CP are

calculated for each measuring point. The computer program is then used to

carry out two tests to check that and are within the calibration range. The

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first test to check pitch angle by comparing the values of the pressure

coefficient pitchCP to the maximum

values of the calibration curves in

fig.6. If is in the calibration curve , the second test is carried out ,otherwise the program moves to the next

measurnning point . The second test to check in two

stages, the first stage is to look at the values of P4)(P2P5),(P2 if these

value are both less than zero then is out of the calibration range, then the program moves to the next

measurnning point . In the second stage the values of the

pressure coefficient yawCP are

compared with the maximum and minimum values of the calibration

curves in fig.6. If is out of calibration range, the program again

moves to the next measurning point , if is within the calibration range, the calculation procedure continues .

Then we check from fig.7 by using the same value of and

totalstatic CP,CP

to find , must be the same value of from fig.6 . Further iteration on

the fitting curves in fig.6 and 7. , until and do not vary significantly ( the error in and

is less then 0.5% degrees) with furthe computation.

5.2 Velocity Calculation :-

After obtaining the values of

and , they are used with fitting curves in fig.7 according to the values

of and the values of

totalstatic CP,CP calculated and from

these values we get P,PS . Then from

eq.1. we get velocity vector R after determine the air density

from the atmospheric pressure and

temperature at the time of the experiment .

The value of yaw angle modified

by adding the probe angle ( 45 ) ( measured between the nose of the probe and the perpendicular to the measurement plane , see fig.2 ).

The component of the relative velocity can be determined :-

)cos()cos(Ru

) sin()cos(Rw

)sin(Rv

c

c

c

..(5)

6. Reynolds Number Sensitivity :-

Since a calibration is typically performed at a single velocity, where measurements are often acquired in

flows of spatially varying velocity .The sensitivity of the probe to the Reynolds

number was examined as shown in fig.9.Pitot-static probes and directional

pressure probes typically exhibit a sensitivity at low flow velocity. For Re < 1000-3000 [6].

So the investigation was focused on flows with velocities lower than the

calibration velocity .

7. Conclusions :-

Experiments were conducted in a low-speed test section with a spherical five-hole pressure probe , to

examine the calibration persuader using polynomial curve fitting method

fourth - order. A general computer program was built for calibration five hole probe based on experimental

data. The sensitivity of the probe to the Reynolds number was also studied.

The result was very suitable with measurement data.

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8. References :- (1) I . C. Shepherd , A Four - Hole Pressure Probe of Fluid Flow

Measurements in Three Dimensions

. ; ASME , Journal of Fluids Engineering ,December 1981,vol.103 ,

pp.590-594. (2) Schlichting , Boundary Layer

Theory . ; McGraw-Hill , New York, 2000 .

(3) N. Sitaram , A.L. Treaster , A Simplified Method of using Four-

Hole Probes to Measure Three-

Dimensional Flow Fields . ; Journal

of Fluids Engineering ,March 1985 ,vol.107 , pp.31-35 .

(4) Richard J. Goldstein , Fluid Mechanics Measurements . ; Berlin ,1983 .

(5) Britsh-Standaed 1042 , part :2.1 .

(6) D. Sumner , Calibration Method for a Seven-Hole Pressure Probe . ;

Dep. of Mechanical Engineering , University of Saskatchewen , Canada ,

internet paper , 2000 . (7) R . K. Jain , Mechanical

and Industrial Measurment . ; seventh edition , 1988 .

(8) Robert P. Benedict Fundamentals of Temperature , Pressure , and Flow

Measurement . ; third edition ,1984 .

Pitch Angle

in (deg.)

Yaw Angle in (deg.)

Velocity Vector R

in (m/sec )

Actual Measu

-red

Error

%

Actual Measu-red

Error

%

Actual Measu-red

Error

%

-20 -19.8 1 -20 -20.4 1.9 15.6 15.9 1.8

-20 -19.7 1.5 0 -0.5 1 15.9 16.1 1.2

-20 -19.9 0.5 20 20.5 2.4 15 14.8 1.3

0 0. 0. 20 19.4 3 15.7 16.1 2.4

0 -0.1 1 0 -0.3 1 15.1 14.9 1.3

0 0. 0. -20 -20.6 2.9 15.8 16 1.2

+20 19.7 1.5 -20 -20.4 1.9 15.9 16.3 2.4

+20 19.9 0.5 0 -0.4 1 15 14.7 2

+20 19.6 2 20 19.5 2.5 15.1 15.4 1.9

8

Table(1). Probe Measurement Error.

Fig. 1.b. Five-hole probe geometry.

514

42 5

8

8 1

2 3

4 5

All dimensions in mm Front view

Fig. 1.a. 3D presentation of traversing mechanism.

9

Rxy

R

Rxz

x

z

y

x

z

y R

3

2

4

5 1

Fig. 3. Vector decomposition of hole geometry and flow direction for a 5-hole pitot tube.

P3 P5

P2

P1 P4

Spherical Tip

=45 Reference

Line

Rxy

Rxz R

Yaw Plane

Pitch Plane Flow Direction

x y

z (b)

1 2 3

5

45

15mm

1

2

5 3 5

2

3 4

5mm

42mm

3

4 5 1 ID 0.6mm

OD 1mm

Fig. 2. Five-hole probe construction.

(a)

11

8.8.8.8

2

Interface Cart

Computer

Main 6V

Main 220V

1

3

Off

On

Pressure Static

1 2 3 4 5

Pressure

Pressure

1 2 3 4 5 S

8

S 1

2 3

4 5

4

5

6

Air

7

11

10

12

9

1. Selection box (FC091-Furness) 5. Five-hole probe 9. Thermometer

2. Micro-manometer (FC92-Furness) 6. Traversing mechanism 10. Test section

3. Power supply 7. Fan 11. Inlet flow region

4. Ruler 8. P.V.C. tubes (1mmID, 3mmOD) 12. Exit flow region

Fig. 4. Schematic arrangement of experimental rig.

11

13

Vertical protector

(Pitch angle )

Ball & socket joint

Wind tunnel test section Flow direction

Vertical guide

Vertical slider 5-Hole probe

Ruler

Horizontal guide Horizontal slider

Model test section

b. Standard traversing mechanism

a. Calibration traversing mechanism

Fig. 5. Traversing mechanism for calibration and models tests.

Horizontal protector

(Yaw angle )

14

-3.00 -1.00 1.00-4.00 -2.00 0.00 2.00

Cp pitch

-1

1

3

-2.00

0.00

2.00

4.00

Cp

yaw

Alfa ( Pitch Angle ) = -20,-10,0,10,20

Beta ( Y

aw A

ng

le ) =20,10,0,-10,-20

-10.00 10.00-20.00 0.00 20.00

Alfa ( Pitch Angle )

-0.5

0.5

-1

0

1

Cp

to

tal

Cp

sta

tic

Yaw angle = 20Yaw angle = 10Yaw angle = 0Yaw angle = -10Yaw angle = -20

Fig. 6. Calibration curves for CPyaw respect to CPpitch

Fig. 7. Calibration curves for CPtotal and CPstatic respect to pitch angles

15

2.5E+3 7.5E+30.0E+0 5.0E+3 1.0E+4

Reynolds Number

-1.00

1.00

-2.00

0.00

2.00

Cp

pit

ch

Yaw and Pitch angles = 20Yaw and Pitch angles = 10Yaw and Pitch angles = 0Yaw and Pitch angles = -10Yaw and Pitch angles = -20

2.50E+3 7.50E+30.00E+0 5.00E+3 1.00E+4

Reynolds Number

0.05

0.15

0.00

0.10

0.20

Cp

ya

w

2.50E+3 7.50E+30.00E+0 5.00E+3 1.00E+4

Reynolds Number

0.20

0.60

0.00

0.40

0.80

Cp

sta

tic

2.50E+3 7.50E+30.00E+0 5.00E+3 1.00E+4

Reynolds Number

-0.25

0.25

-0.50

0.00

0.50

Cp

to

tal

(a) (b)

(c) (d)

Fig. 8. Reynolds number effect on calibration curves.

16

Start

Input No. of measuring point = N , I = 1

I = I + 1, (i)old = 0,

(i)old = 0

Read P1, P2, P3, P4, P5, PS, Pt

Read all the coefficients of calibration curves. Fig. 6 and Fig. 7

Calculate , CPyaw(i), CPpitch(i), CPstatic(i), CPtotal(i)

IF CPpitch(i) < CPpitchmax AND

IF CPpitch(i) > CPpitchmin from Fig. 6

IF (P2 - P3) AND (P2 - P1)

A Yes No

IF CPyaw(i) < CPyawmax AND

IF CPyaw(i) > CPyawmin from Fig. 6

A

17

End

(i)old = (i)

(i)old = (i)

IF abs[ (i) - (i)old ]

AND

IF abs[ (i) - (i)old ]

IF (P2 P4) AND (P2 P5)

B Accuracy = < < Accuracy

0<

1 B

A