Instytut Fizyki Doświadczalnej Wydział Matematyki, Fizyki i Informatyki UNIWERSYTET GDAŃSKI

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1 Instytut Fizyki Doświadzalnej Wydział Matematyki, Fizyki i Informatyki UNIWERSYTET GDAŃSKI

2 I. Bakground theory. 1. Laser doppler anemometry LDA (Doppler model): a) LDA priniples; b) single and multi-hannel LDA systems; ) appliations of LDA, advantages and disadvantages. 2. Eletromagneti waves. 3. Phenomena assoiated with the wave nature of light: a) diffration; b) interferene; ) beats; d) moiré patterns; e) Doppler effet. 4. Sattering of light by partiles (Mie sattering). 5. Fluid mehanis: a) laminar and turbulent flow; b) Reynolds number. 6. Signal proessing and analysis: a) spetral analysis of signals: Fourier transform; disrete Fourier transform; spetral power density; fast Fourier transform (FFT). b) digital-analogue proessing: sampling; Nyquist Shannon sampling theorem; aliasing (masking); high and low-pass filters; signal onditioning. 7. Beam path through a system of lenses and mirrors. 8. Constrution and operation of He-Ne lasers. Instytut Fizyki Doświadzalnej 1.

3 II. Experimental tasks. 1. Refer to the experimental set-up in Piture 1. Piture 1. Experimental set-up for the analysis of laser Doppler anemometry: 1 - base plate; 2 - He-Ne laser; 3 - laser power supply with ontroller; 4 - photodetetor amplifier; 5 - Cobra 3 interfae; 6 - plane mirror; 7 - beam splitter; 8 - lenses; 9 - mounted uvette; 10 - photodetetor; 11 - iris diaphragm; 12 - bottle (1000 ml). 2. Turn on the laser and the Cobra 3 interfae ( 3 and 5 in Piture 1 ). 3. Start the Measure program and selet Miernik-Cobra 3 Analiza zęstotliwośi from the menu. 4. Assemble the measuring system as desribed in part I of Appendix A. 5. Fous the interferene pattern. 6. Take measurements of the distanes desribed in Figure 2 in part I of Appendix A. 7. Prepare a solution of miro-partiles as desribed in part III of Appendix A. 8. Set up the experiment as desribed in part II of Appendix A. 9. Following the instrutions in Appendix B, reord an interferene signal as a funtion of time and perform a Fourier analysis. 10. Based on the results obtained in part I of Appendix A and Formula (9) of Appendix C, alulate the half-angle φ (the angle between the beams, Figure 2 in Appendix A). 11. Calulate the veloity of the miro-partiles using Formula (8) in Appendix C. 12. Inrease the flow-rate and repeat steps Instytut Fizyki Doświadzalnej 2.

4 III. Apparatus. 1. Base plate. 2. He-Ne laser, λ=632.8 nm, 5 mw. 3. Laser power supply and ontroller. 4. Photodetetor amplifier. 5. Cobra 3 interfae. 6. Two plane mirrors :50 Beam splitter. 8. Lenses with foal lengths : 20 mm, 50 mm, 100 mm. 9. Mounted uvette. 10. Photodetetor. 11. Iris diaphragm, irular aperture of 30µm. 12. Two 1000 ml bottles. 13. Sreen. IV. Literature. 1. L.E. Drain The Laser Doppler Tehnique, John Wiley and Sons, F. Durst, M. Zare Laser Doppler Measurements in Two-Phase Flows, LDA-Symposium, Copenhagen, 1975, p Y. Yeh, H.Z. Cummings Loalized Fluid Flow Measurements with an He-Ne Laser Spetrometer, Appl. Phys. Lett. 4, 176, J. F. Douglas Fluid Mehanis, Harlow, Longman, F. Durst, A. Melling, J. Whitelaw Priniples and Praties of Laser Doppler Anemometry, Aademi Press, P.W. Milonni, J.H. Eberly Lasers, John Wiley and Sons, G.F. Lothion Optis and its Uses, VNR, M. Tadeusiewiz Signals and Systems, Tehnial University of Łódź, A. Reimann Physis, Part 1 & 2, Barnes and Noble, Sears and Zemansky s University Physis with Modern Physis, Pearson Addison - Wesley,2008. Instytut Fizyki Doświadzalnej 3.

5 Appendix A Preliminaries I. Obtaining an interferene signal. a) Using Piture 2 and the diagram in Figure 3, set up the system omponents on the base plate, remembering that the oordinates are a guide for ourse adjustments only (aided by the grid on the base plate). Coordinates for the various iruit elements are given in square-brakets. Mirror M1 = [1,8] Beam splitter BS = [1,2.5] Mirror M2 = [1,1.5] Lens L1 with foal length f=+100 mm =[2,2] Sreen S = [11,2]. The distane between the beam splitter BS and mirror M2 should not exeed 3 m. The beam splitter BS should be plaed on the silvered side of the mirror M1. The reommended height of the beam above the base plate is 13 m. The parallel beams from the beam splitter BS and mirror M2 should be aimed symmetrially about the entre of lens L1. Two red spots will appear on the sreen S. Plae the 30 µm iris diaphragm PK at position [4,2], at the point of intersetion of the beams (10 m from lens L1). Adjust the positions of mirror M2, iris diaphragm PK, and optionally the beam splitter BS and lens L1 to reate an interferene pattern with the two beams. After refletion by mirror M2, the beam s spot on the sreen S should appear to the left, while the spot from the beam through the beam splitter BS should appear on the right (Piture 2b). Instytut Fizyki Doświadzalnej 4.

6 (a) (b) Piture 2. a) Ciruit geometry resulting in interferene of light beams; b) view of the image on the sreen showing an interferene pattern. Adjustment of the height and diretion of the two beams oming from mirror M2 and beam splitter BS will help to obtain an interferene image. To do this, set the lens L2 with foal length f=+20 mm at position [4.5,2], rotate the sreen 45 0 (as shown in Fig.1) and hek that the two beams are at the same height by adjusting the srews in the mirror M2. Then remove lens L2 from the optial path and get an interferene pattern (the aperture PK remains at position [4,2], but may be temporarily removed during adjustments). Figure 1. Diagram of set-up to ensure orret high and diretion of beams (Phywe): L1, L2 - lenses with foal lengths f = +100 mm and f = +20 mm; S - sreen. Instytut Fizyki Doświadzalnej 5.

7 b) After obtaining a lear interferene pattern, remove the aperture PK and measure the distanes l and D (Figure 2). Figure 2. Shemati setup to determine the angle ϕ: l - distane from lens L1 to the plane of observation; D distane between the two spots of light on the plane of observation (Phywe). II. Setting up the apparatus to determine miro-partile veloities. Remove the sreen S from the base plate. Replae the aperture PK by the uvette T = [4,2], ensuring that the light beams interset at its entre. The uvette is very fragile, handle it with are. With the help of Figure 3 and Piture 3, orretly position the following elements, whose oordinates are given enlosed in square brakets: Iris diaphragm PI = [5,2] (to restrit the area of observation to the Moiré rings); Lens L2 with foal length f = +50 mm = [7,2]; Photodetetor PD = [8,2]. Instytut Fizyki Doświadzalnej 6.

8 Figure 3. Shemati setup for determining the veloity of miropartiles (Phywe). Piture 3. System geometry allowing the determination of instantaneous flow rate. Instytut Fizyki Doświadzalnej 7.

9 III. Preparing the solution. Add one drop of a suspension of miro-partiles to be studied (silveroat hollow glass spheres - meandiameter 10 µm in water) to 10 ml distilled water and mix 1-2 ml of the solution with 500 ml distilled water. It is neessary to add a few drops of formaldehyde to the prepared solution to inhibit the growth of bateria. Mount a bottle of the prepared solution on a tripod. Mount a seond empty bottle below the bottle with solution (Piture 1). Adjust the lamps on the rubber hoses very slowly to establish a flow of liquid. Instytut Fizyki Doświadzalnej 8.

10 Appendix B Reording a signal Choose Rejestraja pomiaru from the menu. Establish the voltage and frequeny measurement. Start with small values (e.g.: U = 0.3 V; f = 10 khz). Selet the options Bez Wyzwalaza and Pomiar iągły. Clik the button Pomiar. After obtaining a good signal, lik Zahowaj. Figure 4. View of the program to measure flow veloity. Figure 5. Interferene signal as a funtion of time. Instytut Fizyki Doświadzalnej 9.

11 Make a Fourier analysis of the spetrum and alulate the peak frequeny. The tool Pokaż ekstrema allows an aurate reading of the frequeny. Figure 6. Fourier transform of the measured interferene signal. After 30 minutes, stir the solution to avoid sedimentation. Do not lean on the table during measurements. In the ase of a weak signal, Fourier analysis an only be performed on the interesting part of the speturm. To do this, selet Zmierz, selet the desired range, and then hoose Analiza Fouriera. Instytut Fizyki Doświadzalnej 10.

12 a b Figure 7. a) Example of analysis of a weak signal; b) Peak frequenies obtained by the Fourier transform of the signal. In order to improve the signal, the positions of lens L2 with foal length f = +50 mm and the photodetetor PD an be gently adjusted. At low flow rates, it is possible to shift the maximum frequeny of the measured signal too lose to zero. In this ase, you may have a problem determining the value of the measured frequeny in the frequeny domain (you should make measurements for different outputs on the photodetetor ontroller - Piture 1, element 4). Instytut Fizyki Doświadzalnej 11.

13 Appendix C Laser anemometry fundamentals Laser anemometry allows for measuring the speed of moving partiles (elements) by sattered light [1]. Anemometry is based on two physial phenomena. These are, the Doppler effet (A) and interferene (B). (A) The Doppler effet is the hange in frequeny due to relative movement between the wave soure and the observer. Two ases of the Doppler effet have been used o disuss the priniples of LDA (Figure 8). Figure 8. Two ases of the Doppler effet. a) In the first ase, the soure is stationary and the observer is moving, with a veloity of U. The frequeny observed by the reeiver f R is given by: f R = f S 1 U l (1) where: - speed of light in air,f s frequeny of light emitted by the soure. Instytut Fizyki Doświadzalnej 12.

14 b) In the seond ase, the soure is moving and the reeiver is stationary. The observed frequeny is given by: f R = f S 1 U k (2) In LDA, a stationary light soure shines light whih is then sattered by moving miro-partiles and then reorded by the photodiode. Combining the two equations above (1-2), gives the frequeny of the sattered light deteted by the stationary reeiver (see Figure 9). 1 U l f R = f S 1 U k (3) Figure 9.Light sattered by a moving partile. Dual-beam anemometer As a onsequene of the Doppler effet, there is a small shift in frequeny of the sattered light due to the movement of the miro-partiles (as follows from Equation (3)) and diret measurement of the frequeny (e.g. using a Fabry-Pérot interferometer) annot be made with suffiient auray. There are various methods to avoid diret measurement of optial frequenies. Due to the square shape of the photodetetor lines, it is possible to mix the two frequenies and reord the beats in the resulting signal. For example, the method of self-beats where a shifted signal is mixed with itself (where the frequeny measured is twie the frequeny differene). Instytut Fizyki Doświadzalnej 13.

15 In Experiment 11, a double-beam onfiguration is used two interseting light beams from the same soure. A laser beam is split into two partial beams of the same intensity. Later, they are reombined and interset at a ertain point (mv) (uvette), where a flow of miro-partiles in suspension ross the area where the beams interset. The Doppler shift of the sattered light is different for the two partial beams (different vetors l, but the same vetors k ). This differene leads to the beat frequeny. The frequenies of the sattered light for eah of the partial beams are given by: f R1 = f S 1 U l 1 1 U k 1 f R2 = f S 1 U l 2 1 U k 2 (4) (5) The frequeny differene (referred to as the Doppler frequeny) is given as: f D = f R1 f R2 = f S U l 2 l 1 (6) The frequeny differene is signifiantly lower and has a narrower bandwidth than the frequeny of the soure, thereby allowing aurate measurement. Using the relations in Figure 10 and the relationship = f S λ ( λ wavelength of the laser beam), the Doppler frequeny an be expressed as follows: f D = f R1 f R2 = f S U l 2 l 1 = U 2 sin φ λ (7) where: U partile s veloity omponent perpendiular to the bisetor of the angle between the beams. Figure 10. The differene in unit vetors (Phywe). Instytut Fizyki Doświadzalnej 14.

16 Knowing the Doppler frequeny, we an alulate the partile veloity. Equation (7) shows that the veloity of a partile an be determined by measuring the Doppler frequeny, if the partile passes through the uvette (mv). U = f D λ 2 sin φ (8) During the experiment, you an also determine the half-angle ϕ by measuring the distane from lens L1 to the plane of observation (l ) and the distane between the two dots of light on the plane of observation (D) (Figure 2 in Appendix A). The angle ϕ is obtained as follows: tgφ = D 2l φ = artan D 2l (9) where: l = l f( f foal length of lens L1). (B) The priniples behind LDA an also be explained by the use of Moiré fringes (or a fringe model) (Figure 11a, b). In this model, two laser beams interset and form parallel interferene fringes at the uvette (mv). Small moving partiles satter the alternating onstrutive and destrutive interferene fringes. As a result, you an observe pulses with a frequeny proportional to the veloity (omponent perpendiular to the grid), and inversely proportional to the distane between the fringes. (a) (b) Figure 11. a) LDA fringe model (Phywe); b) Distane between interferene fringes. The frequeny of intensity hanges is given by: f D = U Δx (10) Instytut Fizyki Doświadzalnej 15.

17 The distane x between fringes is given by: Δx = λ 2 sin φ (11) Finally, Equations (10) and (11) leads to Equation (7), whih is used to alulate flow veloities. To onlude veloity measurements are redued to measuring the radiation intensity hanges over time. In the ase of (A) we measure the beat frequeny, in (B) we measure the frequeny of the partiles passing through the interferene maxima formed by the interseting beams [1]. The frequeny an be found from the experimental results using the fast Fourier transform proedure (FFT) (referene [1] in the literature). Instytut Fizyki Doświadzalnej 16.