Experimental Fluid Dynamics and Uncertainty Assessment

Methodology

S. Ghosh, M. Muste, F. Stern

Table of

Definition & purpose EFD philosophy EFD Process Types of measurements & instrumentation Measurement systems Uncertainty analysis 57:020 Laboratories

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Experimental Fluid Dynamics Definition:

Experimental Fluid Dynamics: Use of experimental methodology and procedures for solving fluids engineering systems, including full and model scales, large and table top facilities, measurement systems (instrumentation, data acquisition and data reduction), dimensional analysis and similarity and uncertainty analysis.

Purpose: Science & Technology: understand and investigate a phenomenon/process, substantiate and validate a theory (hypothesis) Research & Development: document a process/system, provide benchmark data (standard procedures, validations), calibrate instruments, equipment, and facilities Industry: design optimization and analysis, provide data for direct use, product liability, and acceptance Teaching: Instruction/demonstration

A pretty experiment is in itself often more valuable than twenty formulae extracted from our minds." 

- Albert Einstein 3

EFD Philosophy D E F IN E P U R P O S E O F T E S T A N D

R E S U LT S U N C E R TA IN T Y R E Q U IR E M E N T S

U N C E R TA IN T YA C C E P TA B L E ?

IM P R O V E M E N TP O S S IB L E ?

D E T E R M IN E E R R O R S O U R C E SA F F E C T IN G R E S U LT S

Y E SN O

N O

Y E S Y E S

Y E S

N O

S E LE C T U N C E R TA IN T Y M E T H O D

E S T IM AT E E F F E C T O FT H E E R R O R S O N R E S U LT S

- M O D E L C O N F IG U R AT IO N S (S )- T E S T T E C H N IQ U E (S )- M E A S U R E M E N T S R E Q U IR E D- S P E C IF IC IN S T R U M E N TAT IO N- C O R R E C T IO N S T O B E A P P L IE D

- D E S IR E D PA R A M E T E R S (C , C , ... .)D R

D E S IG N T H E T E S T

- R E F E R E N C E C O N D IT IO N- P R E C IS IO N L IM IT- B IA S L IM IT- T O TA L U N C E R TA IN T Y

D O C U M E N T R E S U LT S

N O T E S T

C O N T IN U E T E S T

IM P L E M E N T T E S T

S O LV E P R O B LE M

R E S U LT SA C C E P TA B L E ?

M E A SU R E-M E N T

S YS TE MP RO BLE M ?

N O

P U R P O S EA C H IE V E D ?

Y E S

N O

S TA R T T E S T

E S T IM AT EA C T U A L D ATAU N C E R TA IN T Y

Decisions on conducting experiments are governed by the ability of the expected test outcome to achieve the experiment objectives within allowable uncertainties.

Integration of UA into all test phases should be a key part of entire experimental program

test design

determination of error sources

estimation of uncertainty

documentation of the results

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EFD Process

EFD labs provide “hands on” experience with modern measurement systems, understanding and implementation of EFD in practical application and focus on “EFD process”:

Test Set-up

Facility & conditions

Install model

Prepare measurement

systems

Data Acquisition

Data Reduction

Uncertainty Analysis

Data Analysis

Initialize data acquisition software

Run tests & acquire data

Store data

Statistical analysis

Estimate bias

limits

Compare results with benchmark data, CFD, and

/or AFD

Evaluate fluid

physics

Calibration

Prepare experimental procedures

Data reduction

equations

Estimate

precision limits

Estimate total

uncertainty

Prepare report

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Types of fluid mechanics measurements and instrumentation

Types of measurement Variable Instrumentation Temperature (T) digital thermometer

Viscosity (m) viscosimeter Fluid

Properties Density (r) hydrometer Surface pressure

(Pstat) pressure taps, surface paints, pressure transducers

Pressure

Stagnation pressure

(Pstag) Pitot tubes

Flow rate (Q) Venturi-meter, orificemeter, flow nozzle

Mean velocity (U, V, W) pitot tube, hotwire, LDV, PIV, etc.

Velocity

Turbulence quantities

( vu ) hotwire, LDV, PIV

Free-surface elevation (z) point gauge, capacitance wire, servo probe

Force and moment (L, D) Hydrometric pendulum, load cell

Wall shear stress

()

Preston tube, Stanton gauge, Thermal methods (mass and

heat transfer probes)

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Instrumentation (sensors, probes) Data acquisition

Serial port devices Analog to Digital (A/D) converters Signal conditioners/filters Plug-in data acquisition boards Desktop PC’s DA software - Labview

Data analysis and data reduction Data reduction equations Curve fitting techniques Statistical techniques Spectral analysis (Fast Fourier Transform) Proper orthogonal decomposition Data visualizations

Measurement systems

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ManometersPrinciple of operation: Manometers are devices in which columns of suitable liquid are used to measure the difference in pressure between two points, or between a certain point and the atmosphere (patmatm)).

Applying fundamental equations of hydrostatics the pressure difference, P, between the two liquid columns can be calculated.

Manometers are frequently used to measure pressure differences sensed by Pitot tubes to determine velocities in various flows.

Types of manometers: simple, differential (U-tube), inclined tube, high precision (Rouse manometer).

U-tube manometer

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Inclined-tube manometer

Inclined tube manometer

Used for accurate measurement of small pressure differences

The density of manometric fluid is not equal to that of the working fluid (e.g. working fluid is gas)

is small to magnify the meniscus movement compared with a vertical tube

Angles less than 5 are not usually recommended.

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Pressure transducers

Transducer read out

Pressure transducer

A pressure transducer converts the pressure sensed by the instrument probe into

mechanical or electrical signals

Elastic elements used to convert pressure within transducers

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Pressure transducers

Schematic of a membrane-based pressure transducer

A a diaphragm separates the high and low incoming pressures. The diaphragm deflects under the pressure difference thus changing the capacitance(C) of the circuit, which eventually changes the voltage output(E). The voltages are converted through calibrations to pressure units. Pressure transducers are used with pressure taps, pitot tubes, pulmonary functions, HVAC, mechanical pressures, etc.

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Pressure taps

Static(Pstat) and stagnation(Pstag) pressures

Pressure caused only by molecular collisions is known as static pressure.

The pressure tap is a small opening in the wall of a a duct (Fig a.)

Pressure tap connected to any pressure measuring device indicates the static pressure. (note: there is no component of velocity along the tap axis).

The stagnation pressure at a point in a fluid flow is the pressure that could result if the fluid was brought to rest isentropically (i.e., the entire kinetic energy of the fluid is utilized to increase its pressure only).

Single and multi pressure taps

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Bernoulli’s Equation

PEz

KEg

V

workflowg

p

heightz

velocityV

pressurep

consantCzg

V

g

p

,2

,

,

,

,

);(2

2

2

For an incompressible flow with no heat or work exchange, the mechanical energy equation can be written as

1

2

Z1

Z2

Reference level

Flow

directi

on

2

2

22

1

2

11

22z

g

V

g

pz

g

V

g

p

Assumptions:• energy is conserved along a streamline• incompressible flow• no work or heat interaction

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Pitot tubePrinciple of pitot tube operation

The tubes sensing static and stagnation pressures are usually combined into one instrument known as pitot static tube.

Pressure taps sensing static pressure (also the reference pressure for this measurement) are placed radially on the probe stem and then combined into one tube leading to the differential manometer (pstat).

The pressure tap located at the probe tip senses the stagnation pressure (p0).

Use of the two measured pressures in the Bernoulli equation allows to determine one component of the flow velocity at the probe location.

Special arrangements of the pressure taps (Three-hole, Five-hole, seven-hole Pitot) in conjunction with special calibrations are used two measure all velocity components.

It is difficult to measure stagnation pressure in real, due to friction. The measured stagnation pressure is always less than the actual one. This is taken care of by an empirical factor C.

/)(2

/)(2

)(,2

1

0

0

20

stat

stat

stat

ppCV

ppV

BernoulliVpp

P0 = stagnation pressurePstat = static pressure

14

Venturi meterPrinciple of venturi meter operation

The venturi meter consists of two conical pipes connected as shown in the figure. The minimum cross section diameter is called throat. The angles of the conical pipes are established to limit the energy losses due to flow separation.

The flow obstruction produced by the venturi meter produces a local loss that is proportional to the flow discharge.

Pressure taps are located upstream and downstream of the venturi meter, immediately outside the variable diameter areas, to measure the losses produced through the meter.

Flow rate measurements are obtained using Bernoulli equation and the continuity equation (see below the derivation). An experimental coefficient is used to account for the losses occurring in the meter (Va and Vb are the upstream and downstream velocities and is the density. (Aa and Ab are the cross sectional areas).

ghppwhere

Bernoullig

V

g

p

g

V

g

p

mba

bbaa

,

)(22

22

)(ContinuityAVAV bbaa Volumetric flow

rate

bbVAQ

98.095.0,

,)1/(222

dtheordactual

m

ba

batheor

CQCQ

hgAA

AAQ

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Hotwire

Single hot-wire probe

• Platinum plated Tungsten

• 5 m diameter, 1.2 mm length

Cross-wire (X) probe

• Two sensors perpendicular to each other

• Measures within 45

Constant temperature anemometer

Used for mean and instantaneous (fluctuating) velocity measurements

Principle of operation: Sensor resistance is changed by the flow over the probe and the cooling taking place is related through calibration to the velocity of the incoming flow.

The tool is very reliable for the measurement of velocity fluctuations due to its high sampling frequency and small size of the probe. 16

Load cellPrinciple

Principle of Load cell operation

Load cells measure forces and moments by sensing the deformation of elastic elements such as springs.

Usually it comprises of two parts

the spring: deforms under the load (usually made of steel)

sensing element: measures the deformation (usually a strain gauge glued to the deforming element).

Load cell measurement accuracy is limited by hysteresis and creep, that can be minimized by using high-grade steel and labor intensive fabrication.

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Particle Image Velocimetry [PIV]

PIV setup Images of the flow field are captured with camera(s).

1 camera is used for 2-dimesional flow field measurement

2 cameras are used for stereoscopic 2-dimesional measurement, whereby a third dimension can be extracted

→ 3-dimensional

3 or more cameras are used for 3-dimensional measurement

Illumination comes from laser(s), LED’s, or other lights sources

Fluid is saturated with small and neutrally buoyant particles

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Particle Image Velocimetry

Principle of PIV operationParticles in flow scatter laser(s) light

Two images, per camera, are taken within a small time of one another Δt.

Both images are divided into identical smaller sections, called interrogation windows

Patterns of particles within an interrogation window are traced

Image pixels are calibrated to a known distance

Number of pixels between a particle and the same particle Δt later == a distance

→process called cross correlation

Velocity = direction × (distance a particle travels/ Δt)

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Particle Image Velocimetry

Advantages of PIV Entire velocity field can be calculated

Capability of measuring flows in 3-D space

Generally, the equipment is nonintrusive to flow

High degree of accuracy

Disadvantages of PIVRequires proper selection of particles

Size of flow structures are limited by resolution of image

Costly

←PIV Image #1 and #2

Cross correlated images provide a velocity field

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Data acquisition outline

General scheme of a data acquisition hardware (one channel):

Current trends: multi-channel (simultaneous sampling), microprocessor- controlled Special considerations:

Correlate sampling type, sampling frequency (Nyquist criterion), and sampling time with the dynamic content of the signal and the flow nature (laminar or turbulent) Correlate the resolution for the A/D converters with the magnitude of the signalIdentify sources of errors for each step of signal conversion 21

Data acquisition components

Signal conditioning

Analog multiplexers

Converters

Clock

Master controller

Digital input/output device

Input/output buffer

Output devices

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DA components

Signal conditioning: Output signal from transducers are conditioned prior to sampling and digital conversion. Analog multiplexer: Is a multiple port switch that permits multiple analog inputs to be connected to a common output. Converters: DAS uses an analog to digital converter to sample and convert the magnitude of the analog signal into binary numbers. Clock: Clock provides master timing for the DAS process by providing a precise stream of pulses to the various system components. Master controller: It provides the start and stop sequences for data acquisition to control actual flow into and out of the system. I/O device: Some transducers and measuring devices output a digital signal directly which, enables bypassing the A/D converter of the DAS. I/O buffer: This is a digital random access memory (RAM) where the data is stored before sending it to some other storage device. Output devices: Permanent storage or display devices (zip disk, hard disk, printer, etc.)

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Signal typesSignal classification

Analog

A signal that is continuous in time

Discrete

Contains information about the signal only at discrete points in time

Assumptions are necessary about the behavior of the variable during times when it is not sampled

Sampling rate should be high so that the signal is assumed constant between the

samples

Digital

Useful when data acquisition and processing are performed using a computer

Digital signal exists at discrete values in time

Magnitude of digital signal is determined by Quantization

Quantization assigns a single number to represent a range of magnitude of a continuous signal.

analog

discrete

digital24

Preprocessing analog signals

Filtering : eliminate aliasing, noise removal (filtering) Low pass filter High pass filter Band pass filter Notch filter

Offset : offset voltage value subtracted from actual signal Offset helps in assessing the intensity of fluctuation of a signal

Amplification : signal level amplified to optimally suit the hardware it is fed into

Gain helps to amplify the signal Generally the values are amplified to take full advantage of the

range of A/D converter.

Preprocessing deals with conditioning signals or optimizing signal levels to obtain desired accuracies.

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AliasingConcept of sampling frequency :

Digitization (conversion of analog to digital signal expressed in the binary system) of analog signals is performed at equally spaced time intervals, t.

Of great importance is to determine the appropriate value of t (sampling data rate).

Accurate sampling of a fluctuating signal needs to be made with at least twice the maximum frequency in the flow (Nyquist criterion). Otherwise, aliasing occurs (confusion between low and high frequency signal components).

To eliminate aliasing, all the information in original data is removed above the Nyquist frequency (fA = 1/(2t)). Removal is achieved by using low-pass filtering that removes frequencies above fA before the data passes through the A/D conversion.

Effect of sampling rate26

Filtering

band pass filter

Low pass filters Permits frequencies below f Eliminates high frequency noise Prevents aliasing associated with sampling process

High pass filters Permits frequencies above f Used for suppressing contribution from certain frequency ranges

Band pass filters Permits frequencies between f1 and f2

To get finer details in the range of interest

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Data acquisition hardware

Adapter cable

8 – channel analog input module

8 port smart switch

RS232 PCI serial card

Computerized automated data acquisition system

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Data Acquisition software

Introduction to Labview

Labview is a programming software used for data acquisition, instrument control, measurement analysis, etc. Graphical programming language that uses icons instead of text. Labview allows to build user interfaces with a set of tools and objects. The user interface is called the front panel and a block diagram controls the front panel. The program is written on the block diagram and the front panel is used to control and run the program.

Labview literature

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Labview - Opening a new program

Labview demo

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Running a Labview program

Front panel

Block diagram

31

Labview controls

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Labview program for pipe flow

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Uncertainty Analysis

Uncertainty analysis (UA): rigorous methodology for uncertainty assessment using statistical and engineering concepts

ASME and AIAA standards (e.g., ASME, 1998; AIAA, 1995) are the most recent updates of UA methodologies, which are internationally recognized

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Uncertainty Analysis

Definitions

Accuracy: closeness of agreement between measured and true value

Error: difference between measured and true value

Uncertainties (U): estimate of errors in measurements of individual variables Xi (Uxi) or results (Ur) obtained by combining Uxi

Estimates of U made at 95% confidence level

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Uncertainty Analysis

Block diagram showing elemental error sources, individual measurement systems measurement of individual variables, data

reduction equations, and experimental results

r = r (X , X ,......, X ) 1 2 J

1 2 J

M EASUREM ENTOF INDIVIDUALVARIABLES

INDIVIDUALM EASUREM ENTSYSTEMS

ELEM ENTALERROR SOUR CES

DATA REDUCTIONEQUATION

EXPERIM EN TALRESULT

XB , P

1

1 1

XB , P

2

2 2

XB , P

J

J J

rB , P

r r

36

Comparison of EFD with CFD

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Lab Schedule and Report Instructions

Lab Schedule: See the class website:

http://css.engineering.uiowa.edu/~fluids/fluids.htm

Lab report instructions See the class website:

http://css.engineering.uiowa.edu/~fluids/documents/instructions_for_lab_report.pdf

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57:020 Lab 1

39

57:020 Lab 2

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57:020 Lab 3

ToS caniva lve

Chord-w iseP ressure

TapsTygonTubing

Load Cell

Load CellL

D

41

Facilities location: general map

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