Manual Laser Doppler Anemometry Manual remote experiment Project e-Xperimenteren+ J. Snellenburg, J.M.Mulder

19-01-2006

Colofon Manual Laser Doppler Anemometry Manual remote experiment Project e-Xperimenteren+ Stichting Digitale Universiteit Oudenoord 340, 3513 EX Utrecht Postbus 182, 3500 AD Utrecht Phone 030 - 238 8671 Fax 030 - 238 8673 E-mail buro@du.nl Author(s) J. Snellenburg, J.M.Mulder Copyright Stichting Digitale Universiteit

De Creative Commons Naamsvermelding-GeenAfgeleideWerken-NietCommercieel-licentie is van toepassing op dit werk. Ga naar http://creativecommons.org/licenses/by-nd-nc/2.0/nl/ om deze licentie te bekijken.

Date 19-01-2006

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Table of contents 1 Introduction 4 2 Theory 4

2.1 Introduction 4 2.2 Classical derivation of the Doppler frequency in relation to the velocity 4 2.3 Relation between Doppler frequency and velocity 5 2.4 Navier-Stokes: liquid flow through a pipe 6

3 Setup 7 3.1 Schematic setup 7 3.2 Pictures 8

4 Remote interface 11 4.1 Settings 11 4.2 Measure 13 4.3 Analyses 15 4.4 Journal 17

5 Constants and parameters 18 6 Appendix A: system requirements 18

6.1 Hardware 18 6.2 Software 18

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1 Introduction This manual describes a web-experiment based on the technique of Laser Doppler Anemometry to measure the velocity profile of water flowing through a tube. The experimental setup is located at the Vrije Universiteit Amsterdam and is maintained by the Physics student laboratory. The web-experiment can be accessed from practically any location in the world, provided the user’s system meets the minimum system requirements as listed in Appendix A. Before starting the experiment it is recommended to formulate a research plan to work as productively as possible. To this end, besides reading this manual, it may help to study the background theory available on the website to find out what the possibilities and limitations are of online experimenting.

2 Theory

2.1 Introduction

Laser Doppler Anemometry (LDA) is a technology used to measure velocities of flows, or more specifically the velocity of small particles in flows. The technique is based on the measurement of laser light scattered by particles that pass through a series of interference fringes (a pattern of light and dark surfaces) resulting from the interference of two coherent laser beams. The intensity of the scattered laser light oscillates with a frequency that is related to the velocity of the particles. Using simple geometrical optics one can determine the radial position in the tube. Calculating the velocity at different positions one can construct a radial velocity profile of the flow within the tube.

2.2 Classical derivation of the Doppler frequency in relation to the velocity

From a classical point of view the two beams will interfere at the point of intersection (also called the measurement volume). This results in a series of light and dark surfaces or fringes, parallel to the optical axis of the system as shown in Figure 2.1.

Figure 2.1: interference fringes at the intersection of two laser beams

A particle passing through these fringes will scatter light with a specific frequency related to the velocity of the particle and the distance between two fringes (also known as the spatial period). The spatial period, the distance d in Figure 2.1, is given by formula 1

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2sin

d λθ

= (1)

Where the angle 2θ is the angle between the two intersecting laser beams and λ is the wavelength of the laser light. Assuming the flow is perpendicular to the fringes a particle passing through these fringes with a constant velocity v will scatter light with a frequency fd equal to the illumination frequency, i.e.:

2sinxd x

vf vd

θλ

= = (2)

The reason for denoting the frequency by fd is that the same expression for fd can also be derived from a relativistic approach. In this case fd is referred to as the Doppler frequency.

2.3 Relation between Doppler frequency and velocity

The determination of the relation between the measured Doppler frequency and the velocity of particles in the flow within the tube is the first step in making a velocity profile. Next it’s important to consider the geometry of the LDA setup. The intersection of the two laser beams inside the flow tube which determines the position of the measurement volume has to be corrected for the refraction of the beams in the air to water transition. In fig. 2.2 the situation is sketched for a horizontally positioned flow pipe with incoming laser beams in the plane of the sketch.

Figure 2.2: A sketch of the path of two laser beams through a flow pipe. The actual geometry of the measurement volume is based on angle γ, which on its turn is related to the angle Φ through Snell's law.

With Snell's law one can rewrite eq. 2 as:

Φ

2sin 2sinfluid d air d

x

f fvλ λ

γ φ= =

(3)

Furthermore one may extend the trajectory of the beams at either side of the flow pipe as if there were no flow pipe. The two intersections then form the virtual measurement volumes for an observer at the position of lenses L1 and L2 respectively. These two positions are fixed with respect to the lenses, irrespective of the location of the flow pipe. This will turn out to come in handy in the design of the system.

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2.4 Navier-Stokes: liquid flow through a pipe

The characteristics of flows are studied in the field of fluid dynamics. The most general description of a flow is known as the Navier-Stokes equation1, from which a general description of the flow inside a tube can be derived. Assuming the flow is laminar inside a horizontal cylindrical pipe one can show2 that the velocity distribution is given by equation 4:

2

2( ) (0) 1x xrv r vR

⎛ ⎞= −⎜ ⎟

⎝ ⎠ (4)

The flow pattern is also known as Poiseuille flow and shows that the velocity distribution is parabolic. The volumetric throughput then is found through integration over the cross section of the flow pipe (Hagen-Poiseuille law):

2

(0)2V xRv π

Φ = (5)

The former derivation is applicable as long as the laminar model can be assumed. For higher velocities however a new regime is entered, known as turbulence. In this regime the Navier-Stokes equation can no longer be solved analytically. To describe the different regimes of the flow one uses the Reynolds number Re defined as the dimensionless ratio of the inertia forces and the viscous forces (which is temperature dependant);

Re( )vlT

ρμ

= (6)

where l is some length characteristic for the dimensions of the flow, which in this case is the diameter of the flow pipe. Roughly speaking, for a straight cylindrical flow pipe, the flow is laminar for Re < 2000. If 2000 < Re < 2500 the flow may change to be turbulent. A range is given because other phenomena bisides the viscous and inertia forces may be of influence. One may think for instance of oscillations introduced by the pump since influences like these promote the instability of the laminar flow.

1 See also: http://mathworld.wolfram.com/Navier-StokesEquations.html 2 See the website for more background information

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3 Setup

3.1 Schematic setup

The experimental setup consists of a laser which is split into two beams by means of a beam splitter. These two coherent laser bundles pass through a lens and are focuses inside a flow tube. Here the two beams interfere and a finite measurement volume is created. The beams are blocked out from reaching the detector and only scattered light is able to pass through to a detector. The flow and temperature of the water inside the tube is controlled by an external flow controller and a so called lauda-bath.

Figure 3.1: schematic overview of experimental setup

Flow tubeOptics

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3.2 Pictures

Below some pictures of the experimental setup are shown. Legend: A He-Ne Laser B Mirror C Beam splitter D Lens E flow tube F Diaphragm G Detector K Web cam L Lauda-bath

Top view experimental setup.

F

E

D

BCA

K

K

G

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Close-up lauda-bath.

A side view of the flow tube and the detector.

L

D

G

E

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A

E

D

A side view of the flow tube and the detector.

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4 Remote interface Below is a description of the software interface of the experiment. The panel is organized into several tabs: 1. Settings 2. Measure 3. Analyses 4. Journal Each tab is described below:

4.1 Settings

On this tab one can adjust various experimental parameters: the pump speed, the position of the flow tube ( i.e. the position of the measuring volume) and the temperature of the water. In addition to this there are indicators for the temperature of the water and the flow, as well as two web cam views of the experimental setup.

Figure 4.1: screenshot of the “SETTINGS” tab in the remote panel overview.

– Position flow tube: A new position of the measuring volume (the red dot) can be set within the flow tube. An actual change has to be confirmed by the button below the “position flow tube” control.

– Pump speed: Five pump speeds can be selected. The actual pump speed is shown in the flow indicator.

– Flow [m^3/sec]: the actually measured flow through the flow tube.

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– Water temperature: the red indicator and the red part in the thermometer show the measured temperature. The temperature is set by changing the value below the thermometer or by dragging the black bar in the thermometer up or downwards. A change in temperature will take some time to settle.

– Refresh rate: sets the update rate of the web cam images.

– Large image: when selected the color will change to blue and a large web cam image is displayed.

– Small image: when selected the color will change to blue and a small web cam image is displayed.

– Camera top view: shows the top view of the experimental setup.

– Camera flow tube: shows a close-up of the two laser beams and the measurement volume in the flow tube.

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4.2 Measure

On this tab the signal from the detector is shown in the upper left window. With the time range slider the length of the time axis can be changed. From this signal a frequency spectrum is calculated by means of a Fourier transform and is shown in the lower left window. This spectrum can be averaged when the corresponding switch is turned on. In addition trigger conditions can be set so that the program will only average the spectrum that conforms to the set conditions.

Figure 4.2: screenshot of the “MEASURE” tab in the remote panel overview.

– Time range [s]: here the time range of the measurement is set. A longer time range results in a higher frequency resolution.

– Frequency range [Hz]: sets the maximum range of the x-axis in the frequency spectra on tabs “single spectrum” and “averaged spectrum”.

– Offset [Hz]: sets the minimum value of the x-axis in the frequency spectra on tabs “single spectrum” and “averaged spectrum”. A minimum value of 500 Hz is advised due to disturbances in the signal.

– Averaging: Here averaging can be activated. The conditions are set by the controls below the switch.

– Averaging mode: continuous or fixed. Fixed: stops averaging after the preset number of averages is completed. Continuous: averaging continues. The displayed averaged frequency spectrum is the average of the last ‘number of averages’ measured.

– Number of averages: here the number of averages is set.

– Number of averages completed: shows the number of measurements done.

– Single average done: lights green if the number of measurements is done.

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– (re)start averaging: starts or restarts the averaging measurement.

– Advanced trigger conditions: sets the advanced trigger conditions on or off. Default set to off. If set to on a number of additional trigger conditions are shown.

– Trigger level peak detection: peak amplitudes above this value triggers the measurement.

– Frequency range: between the min. [Hz] and max. [Hz] –values peak detection is performed.

– Normalize spectrum: if set to yes all spectra are first normalized before they are added to the average.

– Maximum number of peaks allowed: the maximum number of peaks allowed in the peak detection algorithm.

– # peaks found: the number of peaks found in the last triggered measurement.

– Y scale: if marked the y-axis in the frequency spectra is in decibel.

– X scale: if marked the x-axis in the frequency spectra is scaled automatically.

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4.3 Analyses

On this tab the averaged spectrum from the previous tab is displayed. It is possible to fit a Gaussian to the peak to determine the mean frequency of a peak. To get the best result it’s possible to change the fit parameters after which the program will calculate the optimum value based on the technique of minimizing the mean square error. The residual will be shown in the upper graph window.

Figure 4.3: screenshot of the “ANALYSES” tab in the remote panel overview.

Fit parameters

Initial guess – Amplitude: starting value of the amplitude of the peak.

– Position: starting value of the position of the peak.

– FWHM: starting value of the Full Width at Half Maximum of the peak.

– Offset: starting value of the baseline of the fit.

Fit results – Amplitude: fitted value of the amplitude.

– Position: fitted value of the position.

– FWHM: fitted value of the Full Width at Half Maximum.

– Offset: fitted value of the baseline.

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– Number of iterations: the number of iterations performed in the fit.

– Mse: the Mean squared estimation of the fit.

– Do FIT: starts the fit calculation with the initial guess parameters.

– Remove fit trace: remove the fit trace from the graph.

– Save averaged spectrum: saves the averaged measured spectrum.

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4.4 Journal

In this tab you can enter items to your lab journal. This is done by selecting a “Journal Item” and “Journal Status” from the lists at the top of this tab and entering a text in the field “Journal Text”. Optionally you can add a reference to an earlier journal entry or log entry. This is done by clicking the entry in the list box at the bottom of the tab or entering its number in the “Reference” field. By clicking the button “Submit”, the journal entry is added to the log. Note that some actions are automatically logged.

Figure 4.5: screenshot of the “JOURNAL” tab in the remote panel overview. – Journal Item: here it is possible to choose a category for your journal entry.

– Journal Status: here you can choose a qualification of your journal entry.

– Journal Text: here the actual text of the journal entry can be typed.

– Reference: You can refer to an earlier journal entry or experiment log entry by clicking in

the table of entries or choosing a number in the Reference field.

– Submit: by clicking the button Submit the journal entry is added to the experiment log.

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5 Constants and parameters Name Description Value / range, error, unit Laser light (in air) Wavelength 632.816 nm Inside diameter flow tube (at max. width)

Diameter

29.0 ± 0.1 mm

Inside diameter flow tube (at min. width)

Diameter

15.2 ± 0.1 mm

Angle between the laser beams

Angle

0.168 Radians

6 Appendix A: system requirements

6.1 Hardware

Processor PIII - 1Ghz or equivalent Screen resolution 1024 x 768 pixels Internet connection 56k but broadband (>512k) recommended Free disk space 100MB

6.2 Software

For e-Xperimenteren+ you need the following software (free). Required programs are marked by an asterix. * LabVIEW runtime engine 7.1 ftp://ftp.ni.com/support/labview/runtime/ * Java Runtime Environment 5.0 (or higher) http://www.java.com/en/download/manual.jsp Adobe Reader (free pdf reader) www.adobe.com/products/acrobat/readstep2.html Foxit Reader (free pdf reader windows only) http://www.foxitsoftware.com/pdf/rd_intro.php

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Manual Laser Doppler Anemometry