of a molecule possessing a vibrational energy hν is

Question 1 (a) A pulse N:YAG laser is to be employe in a Rayleigh scattering experiment to etermine gas temperature. The laser can be use at 532 nm (secon harmonic), 355 nm (thir harmonic), or 266 nm (fourth harmonic). If the laser linewiths are the same for the three wavelengths, an the corresponing laser energies are 1 J/pulse, 550 mj/pulse, an 280 mj/pulse respectively, etermine which wavelength shoul be chosen to maximise the Rayleigh scattering signal per laser pulse, given that the Rayleigh scattering cross-section σ 1 ( )Rayleigh. [6 marks] 4 Ω λ (b) A Raman scattering experiment conucte in an acetylene-oxygen flame prouce a measure Stokes signal of 10 000 photons, an an anti-stokes signal of 1400 photons, obtaine from water molecules prouce in the flame. Given that the vibrational frequency of water is 3657 cm -1, an the probability hν hν of a molecule possessing a vibrational energy hν is kt kt P( hν ) e 1 e, estimate the temperature of the water vapour prouce in the flame. Boltzmann s constant k 1.38 x 10-23 J/K, h 6.63 x 10-34 J.s, c 2.998 x 10 10 cm/s. (c) A Pitot tube is connecte to a water base manometer. The Pitot tube is place in a win tunnel operating with a static temperature an static pressure of 300 K an 100 kpa respectively. The measurement of stagnation pressure relative to static pressure prouces a height ifference of 9.5 cm. Determine the local air velocity in the win tunnel. ρ water 1000 kg/m 3, g 9.81m/s 2, R 287 J/kg.K () Explain, with the ai of rawings, an equation which relates the voltage applie to a hot wire probe to flui flow velocity in three imensions. Inclue in your explanation the origin of the various terms. Page 1 of 5

Question 2 The two-level steay-state estimate for the average number of fluorescence photons incient on a gate etector after being excite by a laser pulse of uration t, making a soli angle Ω sin θ θ φ at right angles to the measurement zone can be expresse as N 2 A θ φ N t 4π B21 A + Q u( ν ) n0 ( x, y, z) N u( ν ) 1+ u sat A P( J ) A x y z θ φ t 4π where A + Q u sat B + B, P(J) is the probability of occupancy of the J th rotational 21 state employe for excitation, n 0 (x, y, z) is the local molar NO concentration, an N A is Avogaro s number (6.0225 x 10 23 /mole). (a) Explain the physical meaning of the terms u(ν), A, B 21, an Q appearing in the above equation. (b) A pulse laser sheet with uniform profile operating at 10 mj energy per pulse, of 10 ns uration, 4 mm height, 3 mm with, 226.0 nm wavelength, 5.9 GHz line-with excites the Q 1 (20.5) line on the 0 0 ban of the A 2 Σ X 2 Π transition of the NO molecules in the untreate exhaust of a gas turbine combustor operating with an exhaust temperature an pressure of 1800 K an 10 bar respectively. A 5 x 5 pixel ICCD camera is employe to image an measure the NO fluorescence intensity. The ICCD camera obtains a full fiel image corresponing to a 5. cm x 5. cm region in the gas turbine exhaust, using a 25 mm iameter aperture, 100 mm focal length uv lens with an object istance of 50 cm ( Ω sinθ. θ. φ 0.0025). The total number of image fluorescence photons reaching the CCD array on the camera is 2.62 x 10 6 photons. Estimate the mean NO mole fraction (using units of parts per million) in the exhaust. [20 marks] 5 1 1 18 3 2 Note: A ~ 4 10 s, Q ~ 4 10 s, B B ~ 1.74 10 m Js, 21 21 21 / c 2.998 x 10 8 m/s, P(20.5) 0.030, R u 8.3143 J/mole.K. Page 2 of 5

Question 3 Simultaneous Raman/Rayleigh scattering measurements were obtaine from the exhaust of an experimental hyrogen-oxygen rocket engine. The plot of signal intensity versus wavelength is shown in Figure Q1 below. Rayleigh scattering measurements in the surrouning ambient air at 300 K an 100 kpa prouce a signal of 50 000 photons, while corresponing measurements in the exhaust gas prouce a signal of 3500 photons. Assuming the local pressure in the exhaust is also 100kPa, etermine: (a) the mole fractions of water, hyrogen an oxygen in the exhaust, [10 marks] (b) the temperature of the exhaust gas. [15 marks] 41 800 Signal Intensity (photons) 6 900 560 532 580.05 660.55 683.30 laser O 2 H 2 O H 2 Wavelength (nm) Figure Q1 Table Q1: Rayleigh an Raman Scattering Cross-Sections at 532.1 nm for Various Gases σ σ )Rayleigh ( )Raman Vibrational frequency (cm -1 ) Gas ( Ω Ω (x 10-28 cm 2 /ster at 532 nm) (x 10-31 cm 2 /ster at 532 nm) H 2 1.1 4.89 4161 N 2 5.1 3.04 2331 O 2 4.4 3.96 1556 Air 5.0 H 2 O 3.8 7.79 3657 Page 3 of 5

Question 4 (a) What are the two main criteria for selecting the size of the tracers (or sees) in a LDV technique an explain briefly how the maximum size of the tracers can be etermine to ensure that they o follow the flow? Also explain briefly why larger tracers (compare to fringe spacing) results in egraation of the signal quality. (b) Use the general lens formula to show that, for a ual-beam LDV system shown below, the waist beam iameter at the measuring volume is: e 4 f 1 π f 2 f 3 λ o where o is the original laser beam iameter at laser output, f 1, f 2, f 3 are the focal lengths of the lenses L 1, L 2, L 3, respectively, λ is the light beam wave length an α is the angle between the two light beams. Also from geometrical configuration of crossing volume of the two beams show that the iameter an length of the control volume are m e cos( α / 2) an l m e sin( α / 2) (c) For the LDV system shown below, an Argon-Ion laser operates in green moe with a wavelength of 514.8 nm an an output beam iameter of 1.1 mm. If the lenses 2 an 3 have the same focal length of 300 mm, the lens 1 has a focal length of 100 mm an the parallel beams separation S is 56 mm, calculate: (i) the intersection angle between the two beams, [2 marks] (ii) the iameter an length of thecontrol volume, an [4 marks] (iii) the number of fringes in the control volume. 4 fλ e 2 π De [2 marks] λ Use equation f to calculate the fringe spacing 2sin( α / 2) Lens, L1, f1 Laser S α Diffraction grating Collimating lens L2, f2 Figure Q4 Focusing lens, L3, Page 4 of 5 f3

Question 5 (a) Use a simple fringe moel, with a schematic iagram, to show how the phase between two fluctuating signals are relate to scatterer size. [ marks] (b) Explain uner which conition the linearity between phase shift an size exists. [4 marks] (c) The measure phase shift, Φ, is proportional to the geometrical factor which epens on geometrical optical angles of θ, the angle between the two incient beams, the scattering angle φ an the angle ψ between the two etectors. Explain how these three angles affect the slope of size/phase relationship in terms of the range of measure size, the system sensitivity or resolution, an their limitation. [9 marks] Questions 6 (a) Make comments on the avantages an isavantages of using Thermochromic liqui crystals (TLC) for wall surface temperature measurement. Comparisons can be mae with the uses of thermocouples an IR cameras. [10 marks] (b) Sketch a complete optical setup of a Schlieren system. Name each optical component use in the system an escribe their purposes. [15 marks] Examiners: Dr J. M. Nouri Dr R. D. Lockett Dr Y. Yan External Examiners: Professor M. Imregun Professor D. I.A. Poll Page 5 of 5