flowdirection

S d dditi l t f St ti tSummary and additional notes for Static pressure measurements:

Determination of static pressure a) Wall tapping b) static tube

Error in pressure is function of:

Error in pressure is function of:Error in pressure is function of:

And it is also function of laminar or tubulent condition of the wall-bounded flow.Here,

(e.g. In a pipe flow, D is ( g p p ,the diameter of pipe)

Total pressure measurement summary:

Flow Direction Measurements

Flow Direction Measurements

To describe a flow-field, both the flowdirection and velocity magnitude areneeded.needed.

The flow direction measurements also allowa better alignment of the probe to the flowdirection as required for accurate staticdirection as required for accurate staticpressure measurements.

Variations of the velocity component in theplane perpendicular to the probe stem aremeasured by the yaw angle. Variations ofthe velocity direction in the planeperpendicular to it are measured by thepitch angle.

Yaw Angle Measurements

The simplest geometry of a directional probe is a slanted tube. It consists of a total head probe with its nose cut at an angle A.


Rotating the probe around the stem axisallows the flow angle to be defined byseeking the maximum pressure readingseeking the maximum pressure reading.

The response of the slanted tube to inletflow angle allows the determination of theyaw angle within ±5° only.

O t i th fOne pressure measurement is thereforenot sufficient to provide accuratedirectional information.


The large pressure gradientsobserved at negative yaw (α) anglescan be used for an accuratecan be used for an accuratedefinition of the flow direction bymeasuring the pressure differencebetween two symmetric slantedbetween two symmetric slantedtubes (ex: A=30° and A=-30°)

Different probe geometries based on e e t p obe geo et es based othis principle:

Conrad’s “Cobra” probe is the most widely used.y


Typical examples of probes which combine total, static-pressure anddirection measurements are shown on Fig. 3.5


There are two ways in which a pressuresensitive direction probe can be used.

The simpler and more direct one is themethod in which the probe is rotated tobalance the pressure difference betweenthe two orifices. The flow angle is thenjust the rotation angle of the probe.

NACA short prism probe


In the alternative approach, theprobe is in a fixed positionprobe is in a fixed positionfacing the flow and the flowdirection is defined from themeasured pressure differenceby means of a calibrationcurve.


A typical calibration curve of a NACA shortprism probe is shown on Fig. 3.6

The pressure difference PL-PR, varies linearlywith the yaw angle.


The variation of measuredstatic pressure and totalpressure with yaw angle:

Yaw angle


A typical dependence onyp ppitch angle of zero yawangle, static and totalpressure:

Pitch anglePitch angle


Other directional probes are: cylinder probes, aerofoils and bent tube (finger probes)( g )


A typical calibration curve of a cylindrical probe:

Three dimensional flow direction probes

Adding a pair of symmetrically slanted tubes in the plane perpendicularto the yaw plane, allows the simultaneous definition of pitch and yawangle.


The calibration is morecomplex as it requires asymmetric variation of thesymmetric variation of theyaw angle at different pitchangles.

The calibration curves allowthe calculation of pitch andyaw angle, static and totalyaw angle, static and totalpressure, as a function of

Pop , PL, PR, PU, PDop , L, R, U, D


Other probe geometries:

•Conrad’s four holes probe has four holes for directional measurements and total•Conrad s four holes probe has four holes for directional measurements and total and static pressure holes for velocity measurements. •The collar downstream of the static pressure holes is adjusted in such away to maintain the measured static pressure close to the true value over a wide rangemaintain the measured static pressure close to the true value over a wide range of Mach numbers.


Adjusting the probe during theAdjusting the probe during themeasurements to zero yaw angleallows a simpler calibration in functionof the pitch only

Pitch angle

of the pitch only.

7 hole Probe

Measurestotal pressuretotal pressurestatic pressure3 velocity components

Seven-Hole Pressure Probe Coordinate System is yDefined By Pitch and Yaw Angles

u V cos cosr

θu V cos cosv V sin

= ⋅ ⋅

= ⋅r

θ ψ

θ

w V cos sin= ⋅ ⋅r

θ ψ

θ V∞

Probe

Pitch

ψ Yawθ

ψ

Computer Controlled

PitchDial

Computer ControlledRotary Table

Stepper Motor

Velocity Invariant, Non-Dimensional Seven-Hole Probe Pressure Coefficients

0.035"

0 109"3

4 5

CB PP CCCC

−Flow Angle Coefficients:

0.109"

1 2 6

7

( )

CB

A

PPPP

CC1C

2CC

+

+=α Pitch

CP PP PP

4 1A

=−

( )CB PPP CC

3C +=

β Yaw

CP P

CP PP P

P7

P3 6

A

B

−

=−

CP P

CP P7 Total Static− −

Total and Static Pressure Coefficients:

P P

CP PP P

7

P2 5

7

B

C

−

=−−

CP P

CP PP

7 Total

7P

Static

7Total Static

=−

=−

P P

P16

P

7

1

6

==∑ ii

( )( )V2

P P 1 C C7 P PStatic Total=

⎛⎝⎜

⎞⎠⎟ − + −

r

ρ1=i

Seven-Hole Probe Angular Sensitivity Must be Calibrated in a Uniform Flow FieldCalibrated in a Uniform Flow Field

V

Probe4

5

θ = -28°ψ = 30°

θ V∞

1

2

3 θ = 28°ψ = 30°

(Cp β

)

ψ

-1

0

1

e C

oeffi

cien

t

Δψ = 5°

PitchDi l

-3

-2

aw P

ress

ure

Δθ = 4°Dial

-5

-4

θ = -28°ψ = -30°

Constant Pitch (θ)

Ya Δθ 4

Computer ControlledRotary Table -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

-7

-6 θ = 28°ψ = -30°

Constant Pitch (θ)

Constant Yaw (ψ)

Pit h P C ffi i t (C )Stepper Motor Pitch Pressure Coefficient (Cpα )

θSeven-Hole Pressure Probe Calibration Data

(θ) 10

20

30

ent (

CpT

)

0

1

θ CpTotal

Pitc

h An

gle

30

-20

-10

0

al P

ress

ure

Coef

ficie

-4

-3

-2

-1

Pitch Pressure Coefficient (C P essure Coefficient (Cpβ)

-8-6

-4-2

02

4 -8 -6 -4 -2 0 2 4 6

-30

Angle (θ)

Yaw Angle (ψ)

Tota

-100

1020

20-10

010

20

-5

4

30 30

Ct (Cpα ) Yaw Pressure 8

20

30

)

Pitch Angle ((ψ) -2010-20

(Cp S

)

0.5

1

CpStatic

-20

-10

0

10

Yaw

Ang

le (ψ

)

ress

ure

Coef

ficie

nt (

-1

-0.5

0

0.5

ψ

-2 0 2 4

6-4

-20

24

6-30

Yaw Pressure Coeffi ficient (Cpα) Yaw ASt

atic

P

010

200

1020

-2

-1.5

30

30

-8 -6 -4 2-8

-6efficient (Cp

β ) Pitch Pressure Coefficient (Cpα

Pitch Angle (θ)w Angle (ψ)

-30-20

-100

-30-20

-10

Computation of Flow Direction, Flow Velocity, total pressure, static pressure from Seven-Hole Pressure Probe

Interpolate on probe calibrationdata to find total and static

pressure coefficients:C ƒ(θ )

Measure ProbePressures

(P1, P2, P3, P4,P P P ) CPtotal = ƒ(θ , ψ)

CPstatic = ƒ(θ , ψ)

P5, P6, P7)

Compute total and static pressure:( )( )

P P P P C

P P P P C

Total 7 7 Ptotal= − −

=

Compute:CPα = ƒ(Pi)i=1,7

CPβ = ƒ(Pi)i=1 7

Compute magnitude of flow velocity:

( )P P P P CStatic 7 Pstatic= − −CPβ ƒ(Pi)i=1,7

( )P = mean Pi i 1,7=

( )( )rV

2P P 1 C C7 PStatic PTotal

=⎛⎝⎜

⎞⎠⎟ − + −

ρ

Interpolate on probeCompute velocity components:

( ) ( )( )

u V cos cosv V sin

=

=

r

rΘ Ψ

Θ

Interpolate on probecalibration data tofind flow angles:θ = ƒ(CPα , CPβ) ( )

( ) ( )w V cos sin=r

Θ Ψψ = ƒ(CPα , CPβ)

Measuring the tip vortex behind a NACA 2412 wing section in the low-speedExample Experiment

Measuring the tip vortex behind a NACA 2412 wing section in the low speed wind tunnel

Mach Number Influence

A properly designed and constructed directional probe should not beaffected by changes in Reynolds or Mach number, as long as the flow is

t i l b t th b isymmetrical about the probe axis.

The accuracy of a directional probe will not be impaired, even not ins personic flo s if the probe is parallel ith the flo beca se this illsupersonic flows, if the probe is parallel with the flow, because this willgive a symmetric shock pattern.

However a fixed probe at non zero incidence may be seriously in errorHowever, a fixed probe at non-zero incidence may be seriously in error,because the shock on one side may be very different from its counterpart,which will affect the measurement.

The static pressure measurement however is very sensitive to Machnumber and yaw angle.

Mach Number Influence

Mach number and geometry of the probe head have an influence on angular sensitivity: S=PL-PR/(P0-Ps)

Velocity and pressure gradientsThe finite distance between the slanted tube orifices prevents an accurate measurement of the flow direction in flows with a velocity gradient.

Th fl l di t ib ti h Fi 3 14 i d i th k b hi dThe flow angle distribution shown on Fig. 3.14 is measured in the wake behind a compressor blade, by means of a NACA short prism directional probe.

Th d i id l i ti f th fl l i th k i i l d tThe measured sinusoidal variation of the flow angle in the wake is uniquely due to the probe size.

Velocity and pressure gradients

Large velocity gradients occurring in transonic flows where expansion waves, shocks and wakes are interfering require special probes to assure accurate measurements.

Velocity and pressure gradientsThe requirement of measuring total pressure, static pressure and the differential pressure for

flow angle, simultaneously in one point, is not feasible and has to be replaced by:

A Measurement of all values along a line perpendicular to a two dimensional flow-field byA. Measurement of all values along a line perpendicular to a two dimensional flow field by means of separate sensing elements (neptune and needle probe)

B. Use of very compact probes, having all sensing elements, or at least the total and static h l l h ( d d d b )pressure holes, close together (wedge and truncated cone probe)

Velocity and pressure gradientswedge and truncated cone probe

Velocity and pressure gradients

•NACA short prism probes have to be excluded fortransonic flow measurements because of the longtransonic flow measurements because of the longdistance between the total and static pressure orifices.

•AVA wedge probe and VKI needle probe isused to measure the transonic flowdownstream of turbine cascades.

•A paper on calibration of 5 hole probes:A paper on calibration of 5 hole probes:Reichert BA and Wendt BJ (1994) A New Algorithm for Five-Hole Probe Calibration, Data Reduction, and Uncertainty Analysis. NASA Technical Memorandum 106458

htt // t / hi / / i t /19950005965 1995105965 dfhttp://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19950005965_1995105965.pdf

•You can find an example code in the following website for the calibration of 5 hole Probe:Probe:

http://www.nongnu.org/fivehole/download.html

Diagram showing local pressures and velocities in vicinity of fuselage like bodyg g p y g y

flowdirection

Engineering

yaw angle measurementsin

yaw angle measurementsrotating

yaw angle measurementsthere

flow angle coefficients

inletflow angle

rotation angle

thepitch angle

static pressure measurements