Laser velocimetry of a plane mixing layer with a specific initial condition for study of turbulence characteristics of enhanced growth rate

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1 Journal of Mechanical Science and Technology 26 (4) (2012) 1049~ DOI /s Laser velocimetry of a plane mixing layer with a specific initial condition for study of turbulence characteristics of enhanced growth rate Mojtaba Mehrjooei, Nader Montazerin * and Abraham Damangir Mechanical Engineering Department, Amirkabir University of Technology, 424 Hafez Ave, Tehran, Iran (Manuscript Received July 10, 2011; Revised December 5, 2011; Accepted January 2, 2012) Abstract Mixing layers are sensitive to the mixing angle and turbulence in the primary streams. Although there is extensive available research on this rather basic flow, there are still no suggestions for a clearly best configuration. For example, the combination of a laminar initial boundary layer and a large mixing angle has received little attention. In this work we test a new experimental configuration with large mixing angle and laminar/turbulent initial boundary layer that was not examined experimentally by LDA and PIV. This setup is expected to be a representation of the initial conditions that must result in better mixing. A plane mixing layer with a velocity ratio of 0.6 is produced by rebuilding an open circuit wind tunnel. Extensive calibration tests on velocity profiles and Reynolds stresses established the position of the self similar region. Velocity field measurements with laser Doppler anemometer (LDA) and particle image velocimeter (PIV) showed enhanced mixing layer growth. PIV plots showed the presence of stream-wise and cross stream vortices in the self-similar region without any considerable change in turbulence characteristics to that of reported in the literature. The article presents a combination of different experimental results that give a deeper understanding of this very configuration. Keywords: Laser Doppler anemometry; Mixing angle; Particle image velocimetry; Plane mixing layer Introduction Shear flow in the mixing layer has been the subject of many investigations because it has several industrial applications such as in aerodynamics, chemical lasers, ejectors and combustion systems. Apart from the technological importance of this flow, such continuous efforts are due to discrepancies in available results for this relatively simple and predictable flow [1, 2]. In mixing of streams with different velocities, it is a prime advantage and an indication of its strength that more mass entrains from the smaller velocity fluid into the larger velocity side. Kuethe 1935 (as cited in Ref. [1]) was first to investigate two-dimensional shear layer and calculate the velocity profile and growth rate using Prandtl s mixing length to model the Reynolds shear stress term in the boundary layer equation. Since then others have extensively investigated the effect of various initial flow parameters and Reynolds numbers on the development of shear layers. For a mixing angle of one degree, the effect of initial boundary layers is studied [1, 3], and it is confirmed that when they are laminar, the growth rate is larger. The reason is the existence of stream-wise vortices inside the * Corresponding author. Tel.: , Fax.: address: mntzrn@aut.ac.ir Recommended by Associate Editor Simon Song KSME & Springer 2012 mixing layer that leads to more fluid entrainment and larger growth rate. Such vortices are absent when the initial boundary layer is turbulent [1, 2, 4]. Another research has studied the effect of the mixing angle (α) on the structure of the mixing layer for turbulent initial boundary layer. Zero and 18 mixing angles with different velocity ratios were examined. The growth rate was larger for 18 than that of zero degree and declined for larger velocity ratios [5]. Such evidence demonstrates the importance of, and the need to study, large mixing angle and initial laminar boundary layer. It was therefore decided to study the fluid mechanics and turbulence structure as the result of the combination. This is an experimental study of turbulent quantities where existing structures are studied with LDA and PIV. An existing wind tunnel is modified to produce the required shear layer. The velocity profiles and Reynolds stresses were investigated extensively to ensure the self-similarity development at the test section. Finally, a study of the growth rate compares the turbulence characteristics with results from other setups. 2. Flow configuration and experimental apparatus A slice view of the experimental apparatus is shown in Fig. 1. It is known that shear flow is sensitive to the test geometry and initial boundary conditions. The target in this study was to

2 1050 M. Mehrjooei et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1049~1057 Table 1. Free stream turbulence intensities before mixing. u'/u(%) w'/u(%) Upper stream Lower stream Fig. 1. Flow Slice view of wind tunnel. select a special flow setup with large mixing angle and laminar boundary layer on one side and study its flow characteristics in detail. Therefore, this open circuit suction type wind tunnel has a maximum air velocity of 40 m/s. At the tunnel entrance the flow was kept uniform by a honeycomb and a lace. A plate with a trailing edge angle of 12 divided the wind tunnel into two parts. There was a pressure gradient along the wind tunnel entrance nozzle through to the splitter edge that damped the perturbations and ensured laminar boundary layer at the top of the splitter plate [6]. There was an extra honeycomb in the lower part that reduced air velocity but also produced disturbances. Instant velocities were measured on both sides of the splitter plate at 5 mm upstream of the edge in order to calculate turbulence intensity of the free streams before mixing. These LDA measurements showed turbulence intensities as indicated in Table 1. The upper stream with 27 m/s and the lower one with 16.5 m/s mix together after the splitter plate. This produces a Reynolds number of Re δ = at the location where the PIV images were captured. The test section was cm crossstream and 2 m stream-wise. It was made from Plexiglas to allow velocity measurement by laser velocimeter. Exit air was conducted outside the lab in order to avoid any interference with inlet flow. The fan was not directly connected to the tunnel and was placed 5 cm away. This prevented a transfer of fan vibration to the test section and also adjusted test section velocity. More information about the details of experimental setup is in Ref. [7]. The similarity of results in the future sections of this article shows that this tunnel is able to reproduce the data from previous experiments. 3. Instrumentation Laser velocimeters (LDA and PIV) are non-intrusive measuring devices that produce instantaneous velocity data without interfering with flow patterns. LDA measures velocities at a single point (measuring volume) with a time resolution on the order of micro seconds, while PIV produces velocity maps of a complete field of view at larger time intervals (tenth of a second). The two-dimensional laser Doppler anemometer consisted of a 5 watt Argon-Ion laser that provided the nm (green) and the nm (blue) beam pairs. A Bragg cell frequency shifted one beam from each pair by 40 MHz to remove directional ambiguity. Burst spectrum analyzers and the dedicated commercial software (Dantec Dynamics) collected and analyzed the data. A fiber optic system with beam spacing of 75 mm and focal length of 310 mm focused the beams on the desired measuring point and also collected the data in back scatter mode. Measuring volume dimensions were mm 3 for green beams (u-component) and mm 3 for blue beams (w-component). Different sources of error could change both LDA and PIV results. As for LDA, the error in positioning the measuring volume was less than 0.3% of the traverse length. Seeding was applied through SAFEX F2010pluse fog generator that produced fog with 1 μm diameter. To decrease slip between seeding particles and air, the value of stokes number (τ) as calculated from Eq. (1) should be less than 0.05 where the ρ p and d p denote density and diameter of the seed particle, respectively, and ΔU is the velocity difference. μ and δ are absolute viscosity and vorticity thickness, respectively. The value is about 10-6 in this article, which shows negligible slip between particles and air [8]. Present seeding follows flow behavior up to 232 MHz and the mixing layer frequency is expected to be no more than 75 KHz [9]. 2 p ρ pd ΔU τ = (1) 18μδ w The continuous wave mode of measurement for LDA experiments obtained more data from slower-moving particles and in this way reduced the bias error to less than 2% [10]. The PIV system included a Quantel Brilliant double-cavity 150 mj Nd-Yag laser, a Dantec light sheet delivery system, two double frame CCD cameras with pixels and AF Micro Nikkor lenses in angular configuration. A System Hub synchronized lasers and cameras with the acquisition system. About 2400 pictures at a frequency of 10 Hz were taken and subsequently analyzed with the commercial software. Pictures of the existing flow structures were taken in two groups at different directions. The first group was perpendicular to the flow (Fig. 2(a)) and captured the cross section of stream-wise vortices where the second group was in line with the flow (Fig. 2(b)) for span-wise vortices. The position of PIV tests corresponded with LDA measurements and was aligned with the beginning of the self-similar region. The size of the measurement area L L = mm was decided y z

3 M. Mehrjooei et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1049~ for both configurations. The time between pulses for the first setup was finally 30 μs and for the second was 20 μs. Nintd pitch 1 Δ t < (3) 4 Mu max (a) where N int denotes the number of pixels in the interrogation area and d pitch is the camera pixel pitch. Post processing included adaptive cross-correlation from the initial interrogation area of pixels to a final interrogation area of pixels for the first PIV setup and to the final interrogation area of pixels for the second PIV configuration. An error analysis, based on uncertainty of ensemble averaged velocity, δ < u > / < u > was Fig. 2. Schematic of PIV setup. (b) ( ) 0.5 δ < u > / < u > = 1/ N δu/ u (4) where N is the number of acquired data. For LDA experiments with 10 5 acquired data in the center of mixing layer, this resulted in δ < u > / δ < u > 0.03% and for PIV experiments with 2400 acquired data, δ < u > / δ < u > 0.16%. An error analysis, based on the uncertainty of turbulent parameters, such as Reynolds stresses, was estimated from Eq. (5). from a compromise between the resolution required to avoid phase lock and the overall field of view size that covered the largest vortices. In the first setup (a), where the measurement area is perpendicular to the flow and the final interrogation area is pixels, the interrogation spot size is 4.74 mm. In the second setup (b), where the measurement area is in line with the flow and the final interrogation area is pixels, the interrogation spot size is 2.37 mm. This spatial resolution is adequate for detecting large scale vortices that are in the order of mixing layer thickness. The PIV setup could change the error in measured velocity and turbulence characteristics. In the first setup, cameras were angled 60 to the laser sheet in order to make the error in the velocity components inside the laser sheet less than that of the perpendicular velocity component [11]. To prevent the parallax error for the perpendicular component of velocity, the time interval between laser pulses (Δt) was selected from Eq. (2) [12]: 1 ΔzL Δ t < (2) 4 M u z where Δz L denotes the laser sheet thickness and M is the aggrandized coefficient and U Z is the mean velocity in z-direction. The time between pulses was calculated for the velocity components inside the laser sheet from Eq. (3) [13, 14]. This produced acceptable (less than a quarter lengths) movement of particle in each interrogation area. Finally, the actual time between pulses was the minimum of those values and was then slightly adjusted during tests. Similar steps were followed δ < u > / < u >= 2 δ < u > / < u > u / < u > (5) where u' is the velocity fluctuations. For the u-component of normal stress in LDA experiments, this resulted in 2 2 δ < u > / < u > 1.5% and for PIV experiments, it was 4.6%. 4. Self-similarity Three groups of experiments were conducted in the test section. The first set of experiments was by means of a Pitotstatic tube for rig commissioning and estimating the position where self similarity starts. Following criteria are known for self similarity of mixing shear layers [5]: (1) The shape of the non-dimensional mean velocity profile is constant with downstream distance, scaled by vorticity thickness. (2) Growth of vorticity thickness is linear with downstream distance. (3) The shapes of all non-dimensional turbulent quantity profiles do not change with downstream distance scaled by vorticity thickness. Fig. 3 shows the velocity profiles from the Pitot-static tube experiments in downstream locations 0, 55 and 70 cm from the edge of the splitter plate. Seventeen points were measured at each location in the y-direction. A comparison of different profiles suggests that a self-similar shear layer is established at 70 cm from the splitter plate. Wall boundary layers at the top and bottom show that there was no interference between the shear layer and tunnel walls. Once the self-similar region was estimated, LDA velocity

4 1052 M. Mehrjooei et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1049~1057 Fig. 3. Velocity profiles by Pitot-static tube tests at three stream-wise positions. Fig. 5. Stream-wise evolution of the vorticity thickness. Fig. 6. Reynolds stress profiles normalized with U 2 m at several streamwise positions in self-similar region. Fig. 4. Mean velocity profiles obtained at several stream-wise positions. traverses measured velocities and the turbulent components at specified locations. LDA tests were at four different locations along the x-direction, namely 70, 75, 80 and 90 cm from the edge of the splitter plate in the estimated self similarity region. In each location 14 points were measured in the y-direction and for every point about 10 5 velocity data were sampled. At the last location (x = 90 cm), two other LDA traverses at 2 cm from the tunnel axis were carried out. Results showed that differences between turbulent quantities of these three traverses are less than 4.5%, which was a demonstration of the level of flow two-dimensionality. Fig. 4 shows mean velocity profiles from LDA experiments at different downstream locations. Mean velocity was calculated from time averaging of instantaneous velocities. This confirms the Pitot-static tube experiments that self-similar shear layer was formed at 70 cm from the splitter edge. Fig. 5 from LDA experiments shows vorticity thickness at different distances from the splitter plate. Only three points are used to draw the straight line since different methods have already demonstrated self-similarity. The growth of the vorticity thickness is linear after 75 cm from the splitter plate where the second condition for self-similarity is satisfied. This was also examined by the expansion factor of the shear layer: S = (U m /ΔU)(Δδ/Δx) where U m is the convective velocity, (U m =(U 1 +U 2 )/2). This is expected to be in the range 0.06 < S < 0.11 for the self-similar region [15] and was 0.1 in the present study. Reynolds stress profiles in different downstream distances are in Fig. 6. This figure also shows that the layer is self similar from 75 cm forward, and therefore the three conditions for self-similarity are satisfied after 75 cm from the edge of the splitter plate. 5. PIV measurements and results Instantaneous PIV measurements started 75 cm after the splitter plate and 270 cm from the tunnel entrance where selfsimilar flow was established. It is already known that when initial boundary layers are laminar, stream-wise vortices are present in the self-similar region but they gradually decay downstream [4]. We selected this region for PIV measurements to ensure both self-similarity and the presence of these vortices. For each PIV test, 2400 double images were captured, which was far less than 10 5 data that LDA had measured at each point. The wind tunnel was open loop and seeding was added to the flow before the tunnel inlet. Not all pictures produced acceptable velocity data to calculate Reynolds stresses. A standard filtering procedure deleted unacceptably higher or lower velocities in the flow field [7, 12]. The midpoint of the mixing layer is a sample for Reynolds stress convergence since it is expected to be a critical point in the measurement domain. The horizontal axis in Fig. 7(a)-(c) shows the number of PIV data used for averaging and the vertical axis is the value of the Reynolds stress. All turbulent quantities converge after averaging with 700 data.

5 M. Mehrjooei et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1049~ (a) (a) (b) (b) (c) Fig. 7. Convergence of Reynolds stresses, a: <u'u'>, b: <v'v'>, c: <w'w'>. (c) Fig. 8. Mean velocity profiles obtained with LDA, PIV and Error function in self-similar region. (d) Fig. 9. Reynolds stresses profiles from LDA and PIV measurements. Once adequate confidence in the experimental data was established, mean velocities and Reynolds stresses were calculated from time averaging of instantaneous velocities. Mean velocity profiles are shown in Fig. 8 from both LDA and PIV data. The error function of Townsend [16] (Eqs. (6), (7)) is also shown in this figure. ( ) * U = 1 + erf η /2 (6) η = Y / δ. (7) Fig. 9(a)-(d) shows the normalized Reynolds stresses from LDA and PIV measurements at x = 75 cm and z = 0. The

6 1054 M. Mehrjooei et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1049~1057 Fig. 10. Stream-wise vortices obtained with PIV measurements. Fig. 12. Span-wise vorticity obtained with PIV measurements. Fig. 11. Span-wise vortices and braid region between them obtained with PIV measurements. Fig. 13. Mean stream-wise vortices at y = 0 in self-similar region. LDA data are two-dimensional and the v-component is only available from PIV data. Reynolds stresses are maximum in the middle of the mixing layer and are minimum next to free streams. Normal stresses have positive values, but primary shear stress was negative. Figs. 8 and 9 show the agreement between LDA and PIV data and add to experimental confidence. Sample instantaneous velocity fields for two different PIV setups (Fig. 2(a) and (b)) are in Figs. 10, 11 and 12. Velocity scale is in the lower left corner of these velocity fields; its magnitude in Fig. 10 is 4 m/s and in Figs. 11 and 12 is 10 m/s. Fig. 10 has captured the cross section of four stream-wise vortices (setup a) with clockwise and anti-clockwise rotation. Velocity vectors are positive stream-wise, and therefore no vortices are visible in their respective raw data. To detect the span-wise vortices from such initial PIV velocity fields, an average velocity is calculated and then it is subtracted from instantaneous vectors [17]. There are two kinds of pictures for the second PIV setup. First, two half span-wise vortices with no interaction and one braid (Fig. 11) and second, two braids and one span-wise vortex that is slightly inclined to the right in Fig. 12. Stream-wise vortices form in braid regions between span-wise vortices, are smaller and are grouped in two rows. Fig. 13 shows mean stream-wise vorticity at y = 0, x = 75 cm from the edge of the splitter plate, and is a confirmation of vortex capture in Fig. 10. Mean stream-wise vorticity is calculated by time averaging on instantaneous stream-wise vortices at self-similarity region. This data is calculated from the first PIV setup. Mean stream-wise vorticity varies between -60 to 60 per second. Oscillations in the figure indicate that there are vortices with opposite rotating direction beside each other as seen in Fig Discussion The configuration in this study produces a very particular flow since a high speed laminar stream mixes with a slower turbulent stream and therefore mixing is combined with laminar-turbulent transition. Table 2 compares maximum Reynolds stresses from Fig. 9 with available similar experimental research. In this table L and T denote laminar and turbulent initial boundary layers, respectively. Each study has different initial boundary conditions as shown in the table. The general statement is that Reynolds stresses are in close agreement with other previous research. They reveal that although some trends repeat but different initial conditions have little effect on normalized Reynolds stresses in self-similar region. Normal stresses for u- and v- components here are within the range of other previous investigations, and the differences are no larger than the experimental error. In the present study peak normal stress for u-component is more than peak normal stress for v- and w-components. This characteristic is also evident in other

7 M. Mehrjooei et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1049~ Table 2. Comparison of peak turbulence quantities. Present study α λ <u'u'>/ U² <v'v'>/ U²<w'w'>/ U² <u'v'>/ U² q 2 State L/T [18] * T [8] * * T [3] L [3] T * Not available Table 3. Comparison of growth rates. Case State r α dδ/dx 1 Present study L/T λ 2 [3] L λ 3 [3] T λ 4 [5] T λ 5 [5] T λ 6 [18] T 0.44 * 0.141λ 7 [19] * 0.47 * 0.16λ * Not available research. The peak of w-component of normal stress is slightly higher than other investigations. This difference can be a consequence of experimental apparatus and different boundary conditions such as mixing angle and Reynolds number. Another quantity for comparison in Table 2 is twice the turbulent kinetic energy (q), which in this research is larger than that of previous experiments. It is expected to be a consequence of stronger stream-wise vortices that are present in the flow because of laminar initial boundary layer and larger mixing angle. The growth rate of mixing layer in the current work is compared with results of similar investigations in Table 3.The results from Ref. [3] show that the mixing growth rate of initially laminar flow is larger than that of the turbulent one, and therefore, laminar inflow condition causes enhanced mixing. Also, the results of Ref. [5] indicate that an angled mixing layer grows faster than the parallel one. In the present study, we combine laminar initial condition and large mixing angle where, as expected, the growth rate increases to a value more than that of these two references. The growth rate in the present study is larger than that of Refs. [18] and [19], but their experimental setups are not fully introduced in these references, and therefore no firm comparison may be made. Table 4 shows another aspect of this larger growth rate of the mixing layer. In this table the peak mean stream-wise vorticity as calculated from PIV measurements (Fig. 13) is compared with another similar research with a different mixing angle, same velocity ratio and laminar initial boundary layer. A larger mixing angle has caused stream-wise vorticity to be Table 4. Comparison of peak mean stream-wise vorticity. x State α λ Vorticity Ω/ U (cm - ¹) dδ/dx Present study 75 cm L/T λ [2] 78 cm L λ Table 5. Comparison of current anisotropy factors. Present study <u'u'>/<v'v'> <u'u'>/<w'w'> <u'u'>/<u'v'> λ State dδ/dx L/T 0.21λ [3] L 0.09λ [20] 1.75 * L 0.09λ [20] 1.6 * L 0.092λ [21] L * [22] T * [18] T 0.14λ [3] T 0.07λ * Not available stronger, which in turn increases the amount of flow entrainment into the mixing layer with a consequent increase in the growth rate of mixing layer. Both results are in similar locations (x), which makes them more comparable. Anisotropy factors in the self-similarity region are compared in Table 5 for different experimental results with similar modified velocity ratio, (λ=(1-r)/(1+r)). Although initial boundary layers are different, anisotropy factors fall in the same range and no clear trend is evident. The normal to shear stress ratio (column 4) is slightly higher for the present study than other investigations, but this is within the range of experimental error. The anisotropy of turbulence can also be characterized by the Lumley-Newman triangle [23]. This method is based on the second (II) and third (III) invariants of the anisotropy tensor (a ij ). The anisotropy tensor is defined by dividing each component of the deviator tensor (b ij ) by the turbulent kinetic energy (k): bij u' i u' j 2 aij = = δij. (8) k k 3 The invariants of the anisotropy tensor of the present experiments and other experimental results with various initial boundary conditions are in Fig. 14. They show that the gap between anisotropy in all experiments and 3D isotropy remains almost the same in the self-similar region. 7. Conclusion A new configuration of plane mixing layer was examined in detail. This included a 12 mixing angle and a laminar initial condition on the faster moving side. Evaluation of initial LDA

8 1056 M. Mehrjooei et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1049~1057 Fig. 14. Lumley-Newman triangle. measurements confirmed the shear layer build up and formation of the self-similar region from 75 cm downstream of the edge of the splitter plate. Experiments consisted of LDA and PIV measurements in two perpendicular planes. Average velocity, normal and shear stresses, vorticity and anisotropy were calculated in order to study turbulence properties. Turbulence properties were within the same range as that of available literature, but streamwise vortices were stronger. The combination of the present test results and other cited references suggest that non-parallel laminar-turbulent mixing layers produce stronger growth rates that are coupled with stronger stream-wise vortices. Such enhanced growth rates are useful in industrial applications such as aerodynamics, chemical lasers, ejectors and combustion systems in reducing the mixing length and therefore the overall dimensions of the application. Acknowledgment This study has been performed at the laboratory of velocity measurement (laser) at Amirkabir University of Technology. Financial support from the Department of Mechanical Engineering is gratefully acknowledged. Nomenclature dp : Seed particle diameter dpitch : Camera pixel pitch K : Turbulent kinetic energy L : Laminar flow Lx, Ly, L : Dimensions of measurement area by PIV M : Aggrandized coefficient Nint : Number of pixels in interrogation area q : Twice the turbulent kinetic energy r : Mixing layer velocity ratio (=U 1 /U 2 ) Rδ : Reynolds Number (=U m δ/ν) S : Expansion factor of the shear layer T : Turbulent flow U1 : Lower mean stream-wise velocity, m/s U2 : Higher mean stream-wise velocity, m/s U * : Normalized mean stream-wise velocity (=(U-U 1 )/ (U 2 -U 1 )) Um : Convective velocity (=(U 1 +U 2 )/2) m/s Umax : Maximum mean velocity, m/s ΔU : Velocity difference (=U 2 -U 1 ) m/s Uz : Mean velocity in z-direction, m/s u,v,w : Velocity fluctuations in the X,Y,Z directions, respectively, m/s u 2, v 2, w 2 : Normal stress components in the X,Y,Z directions, respectively, m 2 /s 2 u v : Reynolds primary shear stress, m 2 /s 2 x : Distance from the edge of the splitter plate Y0 : Center line of mixing layer (from error function fit) α : Mixing angle, the angle between the two streams on the edge of the splitter plate δ : Vorticity thickness ΔZL : Laser sheet thickness δ u : Uncertainty of ensemble averaged velocity η : Similarity parameter (=(Y-Y 0 )/ δ) λ : Modified velocity ratio (=(1-r)/(1+r)) μ : Absolute viscosity ρp : Seed particle density τ : Stokes number References [1] E. Balaras, U. Piomelli and J. M.Wallace, Self-similar states in turbulent mixing layers, J. Fluid Mechanics, 446 (2001) [2] J. H. Bell and R. D. Mehta, Measurements of the streamwise vertical structures in a plane mixing layer, J. FuidMechanics, 239 (1992) [3] J. H. Bell and R. D.Mehta, Development of a two-stream mixing layer from tripped and untripped boundary layers, AIAA journal, 28 (12) (1990) [4] K. C. Wiecek and R. D. Mehta, Effects of velocity ratio on mixing layer three-dimensionality, Experimental thermal and fluid science, 16 (1998) [5] M. AbdulAzim and A. K. M. Sadrul Islam, Plane mixing layer from parallel and non-parallel merging of two streams, Experiments in Fluids, 34 (2003) [6] H. Shlichting, Boundary-layer theory. Chapter XVII, McGraw-Hill Book Company (1968). [7] M. Mehrjooei, Investigation of plane mixing layer by using PIV. M.Sc. thesis, Amirkabir University of Technology, Tehran, Iran (2009). [8] M. G. Olsen and J. C. Dutton, Stochastic estimation of large structure in an incompressible mixing layer, AIAA journal, 40 (12) (2002) [9] G. Akbari, N. Montazerin and M. Akbarizadeh, Stereoscopic particle image velocimetry of the flow field in the rotor exit region of a forward-blade centrifugal turbo machine, Proceedings of the Institution of Mechanical Engineers, Part A, Journal of Power and Energy, 226 (2) (2012)

9 M. Mehrjooei et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1049~ [10] D. A. Johnson, D. Modarress and F. K. Owen, An experimental verification of laser-velocimetersampling bias and its correction. Trans. ASME, J. FluidsEng, 106 (1984) [11] A. K. Prasad and R. J. Adrian, Stereoscopic particle image velocimetry applied to liquid flows, Exp. Fluids, 15 (1993) [12] Flow manager software and introduction to PIV instrumentation. Tonbakken DK-2740 Skovlunde Denmark, dantec Dynamics A/S (2002). [13] R. D. Keane and R. J. Adrian, Optimization of particle image velocimeters. Part 1: Double pulsed systems, Meas. Sci. Technology, (1990) 1: [14] Yi-ChihChow, PIV measurements of flow structure and turbulent in rotor wake within a multi-stage turbo machine, PhD thesis, John Hopkins University (2005). [15] S. B. Pope, Turbulent flows, Cambridge University Press (2000). [16] A. A. Townsend, Structure of turbulent shear flow, Cambridge Univ. Press, Cambridge, England (1976) [17] R. J. Adrian, K. T. Christensen and Z. C. Liu, Analysis and interpretation of instantaneous turbulent velocity fields, Experiments in fluids, 29 (2000) [18] P. Druault, J. Delville and J. Bonnet, Experimental 3D analysis of the large scale behavior of a plane turbulent mixing layer, Flow Turbulence and Combustion, 74 (2005) [19] AGARD-AR-345 Report: A selection of test cases for the validation of large eddy simulations of turbulent flows, (1998). [20] R. D. Mehta, Effect of velocity ratio on plane mixing layer development : Influence of the splitter plate wake, Exp. Fluids, 10 (1991) [21] D. Oster and L. Wygnanski, The forced mixing layer between parallel streams, J. Fluid mech. 123 (1982) [22] L. Perret, J. Delville, R. Manceau and J. Bonnet, Generation of turbulent inflow condition for large eddy simulation from stereoscopic PIV measurements, Int. J. of Heat and Fluid Flow, 27 (2006) [23] R. Escudie and L. Alian, Analysis of turbulence anisotropy in a mixing tank, Chemical Engineering Science, 61 (2006) MojtabaMehrjooei received his Bachelor s degree from the University of Tabriz and MSc degree from Amirkabir University of Technology. His research interests include experimental fluid mechanics and development of gas refineries. He works with gas refinery companies. Nader Montazerin is professor of Mechanical Engineering at Amirkabir University of Technology. He received his Bachelor s degree fromsharif University of Technology, Tehran, Iran. This was followed by MSc and Ph.D degrees in Mechanical Engineering from Cranfield University, Bedford, England. His research interests include turbomachines, experimental fluid mechanics, natural gas distribution systems and applied energy systems. He has done various consultancy works with natural gas and power industries. Abraham Damangir is Emeritus assistant professor in Mechanical Engineering at Amirkabir University of Technology. He received his BSc. and Ph.D from the same university but earned his MSc from the Imperial College of Science and Technology, England.